User:Anthony.Sebastian > SebastianSandbox

By today’s standards, Hippocrates was a profoundly abnormal physician. Medicine’s founding father routinely tasted his patients’ urine, sampled their pus and earwax, and smelled and scrutinized their stool. He assessed the stickiness of their sweat and examined their blood, their phlegm, their tears, and their vomit. He became closely ac¬quainted with their general disposition, family, and home, and he studied their facial expressions….In deciding upon a final diagnosis and treatment, Hippocrates recorded and considered dietary habits, the season, the local prevailing winds, the water supply at the patient’s residence, and the direction the home faced. He absorbed everything, examining exhaustively and documenting meticulously. ^[6]</ref>

xx

The worth of a book, as of a man, must be judged by results, and, so judged, the "Fabrica" is one of the great books of the world, and would come in any century of volumes which embraced the richest harvest of the human mind. In medicine, it represents the full flower of the Renaissance. As a book it is a sumptuous tome—a worthy setting of his jewel—paper, type and illustration to match....the 'chef d'œuvre of any medical library.^[19]

The worth of a book, as of a man, must be judged by results, and, so judged, the "Fabrica" is one of the great books of the world, and would come in any century of volumes which embraced the richest harvest of the human mind. In medicine, it represents the full flower of the Renaissance. As a book it is a sumptuous tome—a worthy setting of his jewel—paper, type and illustration to match....the 'chef d'œuvre of any medical library.^[19]

In the first chapter of his 1998 book on evolutionary biology, Douglas Futuyma claims evolutionary biology as the "most sweeping and comprehensive" of all of the biological sciences. ^[17] By way of justification, he illustrates the kinds of questions asked by evolutionary biologists. Many echo questions asked some thirty years earlier by Theodosius Dobzhansky.^[16]

• Why so many different kinds of organisms living today?
• Why do they share some common characteristics but differ in others?
• Why do the countless different species of organisms have the particular features they have?
• Why do almost all species of organisms have the same genetic code for specifying protein structures?
• Why the difference in life spans among species?
• Why do they differ in what they can learn?
• Why chromosomal crossing over?
• What brought about the immense variety of enzymes in cells?
• Why do men have nipples?
• Why does swallowing risk choking in humans?
• Why the particular geographic distribution of species on Earth?
• How did human cognition arise?
• How did humans become bipedal?
• Why did humans become nearly hairless?

One might add many other questions asked by evolutionary biologists not specifically addressed by Professor Futuyma in Chapter One:

• Why do humans develop chronic degenerative diseases?
• Why do we have an obesity epidemic?
• Why sexual reproduction?
• Why a limited rather than indefinite life span?
• Why autoimmune diseases?
• Why breast cancer?
• Why mental illnesses?
• Why do we have the particular instincts we have?
• Why murder, war?
• Why do living things exist at all?
• How does novelty arise in living things?

All of the above questions give some sense of the sweep and importance of evolutionary biology.

1. ↑ Calabrese EJ. (2008) [pii;10.1080/10408440802026315 Addiction and dose response: the psychomotor stimulant theory of addiction reveals that hormetic dose responses are dominant.] Crit Rev Toxicol 38:599-617.
2. ↑ Hayes DP. (2008) [pii Adverse effects of nutritional inadequacy and excess: a hormetic model.] Am J Clin Nutr 88:578S-81S.
3. ↑ Dudekula N, Arora V, Callaerts-Vegh Z, Bond RA. (2005) The temporal hormesis of drug therapies. Dose Response 3:414-24.
4. ↑ Tuomisto J, Pekkanen J, Kiviranta H et al. (2006) Dioxin Cancer Risk - Example of Hormesis? Dose Response 3:332-41.
5. ↑ Tara Parker. (2008) What Would Hippocrates Do? See complete review.
6. ↑ ^6.0 6.1 Newman DH M.D. (2008) Hippocrates' Shadow: Secrets from the House of Medicine. Scribner. 256 pages. ISBN 978-1-4165-5153-9.
   • Publisher’s Description: Everyone knows of the Hippocratic Oath, the famous invocation sworn by all neophyte physicians. But most don't realize that the father of modern medicine was an avid listener and a constant bedside presence. Hippocrates believed in the doctor-patient connection and gained worldwide renown for championing science over mysticism while respecting and advocating the potency of human healing. Today, argues Dr. David H. Newman, medicine focuses narrowly on the rewards of technology and science, exaggerating their benefits and ignoring or minimizing their perils. Dr. Newman sees a disconnect between doctor and patient, a disregard for the healing power of the bond, and, ultimately, a disconnect between doctors and their Oath….The root of this divergence, writes Dr. Newman, lies in the patterns of secrecy and habit that characterize the "House of Medicine," modern medicine's entrenched and carefully protected subculture. In reflexive, often unconscious defense of this subculture, doctors and patients guard medical authority, cling to tradition, and yield to demands that they do something or prescribe something. The result is a biomedical culture that routinely engages in unnecessary and inefficient practices, and leaves both patient and doctor dissatisfied. While demonstrating an abiding respect for, and a deep understanding of, the import of modern science, Dr. Newman reviews research that refutes common and accepted medical wisdom. He cites studies that show how mammograms may cause more harm than good; why antibiotics for sore throats are virtually always unnecessary and therefore dangerous; how cough syrup is rarely more effective than a sugar pill; the power and paradox of the placebo effect; how statistics and studies themselves are frequently deceptive; and why CPR is violent, invasive -- and almost always futile….Through an engaging, deeply researched, and eloquent narrative laced with rich and riveting case studies, Newman cuts to the heart of what really works -- and doesn't -- in medicine and rebuilds the bridge between physicians and their patients.
   • Publisher’s Excerpt: See: http://www.simonsays.com/content/book.cfm?tab=1&pid=625462&agid=2
7. ↑ Note: This article represents a permissible (Creative Commons Attribution License) adaption and modification of an article by Science Writer John Whitfield, living in London, United Kingdom (e-mail:ja_whitfield@hotmail.com) published in the open-access journal, PLoS Biology, PLoS Biol 6(7): e186 in 2008, under the full title: Across the Curious Parallel of Language and Species Evolution.
   • Original article citation: Whitfield J (2008) Across the Curious Parallel of Language and Species Evolution. PLoS Biol 6(7): e186.
   • Copyright: Copyright: © 2008 John Whitfield. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
   • John Whitfield is a science writer living in London, UK (email ja_whitfield@hotmail.com).
   • Article reformatted to correspond to Citizendium style, initially by Citizendium Biology Editor Anthony.Sebastian("A.S"), with subheaders added, with Editors explanatory interpolations in square brackets, annotations of references, and editorial notes in References section.
   • Citizendium makes no claim that the originator of the open-access article, John Whitfield, endorses Citizendium's modification of the article, the unmodified original of which, cited above, the reader can find at Across the Curious Parallel of Language and Species Evolution.
8. ↑ Note: Citations with author names bolded represent those added by Citizendium.
9. ↑ Mark Pagel HomePage - Reading Evolutionary Biology Group
10. ↑ Profile of Mark Pagel, Sante Fe Institute
    • From his biographical sketch: Mark Pagel is an evolutionary theorist with interests in mathematical and statistical modeling of evolutionary processes. His current interests include language and cultural evolution, networks, regulation, emergence of complex systems, robustness and evolvability, punctuational versus gradual evolutionary change, and evolutionary genomics.
11. ↑ Garrutti G, Cotecchia S, Giampetruzzi, Giorgino F, Giorgino R. (2008) Neuroendocrine Deregulation of Food Intake, Adipose Tissue and the Gastrointestinal System in Obesity and Metabolic Syndrome. (Free Full-Text) J Gastrointestin Liver Dis 17:193-198. PMID 18568142
12. ↑ Note: Other pioneering 17th century microscopists: the Dutch (Delft) 1676 discoverer of microbes, Antonie van Leeuwenhoek (1632-1723); the ‘renaissance’ British scientist and 1665 describer of the first cells, Robert Hooke (1635-1703); the Dutch (Amsterdam) 1658 discoverer of red blood cells, Jan Swammerdam (1637-1680).
13. ↑ Marcello Malpighi (Free Full-Text Article, Britannica Online).

    • xxxx

14. ↑ Pearce JMS. (2007) Malpighi and the Discovery of Capillaries. European Neurology 58:253-255.
15. ↑ Lengeler JW, Drews G, Schlegel HG. (1999) Biology of the Prokaryotes. New York: Blackwell Science.
16. ↑ ^16.0 16.1 Dobzhansky TG. (1973) Nothing in biology makes sense except in the light of evolution. The American Biology Teacher 35:125-129
17. ↑ ^17.0 17.1 Futuyma DJ. (1998) Evolutionary Biology. Sinauer Associates, Inc. Sunderland. ISBN 0-87893-189-9
18. ↑ Shepherd LD, Lambert DM. (2005) Mutational bias in penguin microsatellite DNA. J. Hered. 96:566-571. PMID 15994417
19. ↑ ^19.0 19.1 Osler W. (1921) The Evolution of Modern Medicine: A Series of Lectures Delivered at Yale university on the Silliman Foundation, in April, 1913. New Haven: Yale University Press.

Evolutionary medicine

Introduction

The term 'evolutionary medicine' refers to the study of, teaching of, and application of the concepts, principles and perspectives of evolution and evolutionary biology to the prevention and management of human disease, both mental and physical, and to the improvement of human well-being. Advocates of evolutionary medicine target those projects as stemming from an understanding of human biology as an evolved living system in an environment of diverse evolved living systems. They implicitly or explicitly subscribe to the declaration of the 20th century's pioneer evolutionary biologist, the Russian-American, Theodosius Dobzhansky, to wit: "Nothing in biology makes sense except in the light of evolution." Often those advocates of evolution-informed medicine see the light shining from the theories of Charles Darwin, in particular that of adaptation due to natural selection, hence the term 'Darwinian medicine' in alternative use. As we approach the bicentennial of Darwin's birth (February 12, 2009), we now know that evolutionary forces comprise a wide range of natural processes in addition to selection. ^[20]

Does medicine without evolution make sense?

That question echoes the title of a recent (April, 2007) editorial in the open-access journal, PLoS Biology,^[21] by senior editor Catriona J. MacCallum (see: http://www.plos.org/about/people/biology.html). MacCallum laments the fact that evolution does not figure prominently in the medical community and in the curriculum of medical schools. He notes one of the reasons:

As explained at a meeting on evolution and medicine I recently attended in York, United Kingdom (the Society for the Study of Human Biology and the Biosocial Society’s 2006 symposium, “Medicine and Evolution”), medicine is primarily focused on problem-solving and proximate causation, and ultimate explanations can seem irrelevant to clinical practice. Crudely put, does a mechanic need to understand the origins, history, and technological advances that have gone into the modern motor vehicle in order to fix it?

Biology Workgroup Editorial Comment: As if the most complex living system on Earth could find correspondence of organizational constitution in the modern motor vehicle, or any other human artifact for that matter.

MacCallum continues to highlight the York meeting mentioned in the previous quote:

Participants at the York meeting discussed:

• not only how vulnerability to cancer is an inevitable but unfortunate consequence of imperfect human engineering and natural selection (Mel Greaves, Institute of Cancer Research, UK),
• but how life history theory can potentially explain patterns of pregnancy loss (Virginia Vitzthum, Indiana University),
• how a comparative approach applied to different human cultures and different primates can improve rates of breastfeeding (Helen Ball, University of Durham),
• whether clinical depression has an adaptive origin (Lewis Wolpert, University College London), and
• if suicide attempts are really just evolutionary bargaining chips in intense social disputes (Ed Hagen, Humboldt University).

The time has clearly come for medicine to explicitly integrate evolutionary biology into its theoretical and practical underpinnings. The medical students of Charles Darwin’s day did not have the advantage of such a powerful framework to inform their thinking; we shouldn’t deprive today’s budding medical talent of the potential insights to be gained at the intersection of these two great disciplines.

Medicine needs evolution

"Medicine Needs Evolution"^[22] introduces another recent (February, 2006) editorial arguing for the need of a discipline of evolutionary medicine, published in the journal Science, by Randolph M. Nesse, professor of Psychiatry and Psychology at the University of Michigan, working in the field of evolution and medicine; Stephen C. Stearns, Edward P. Bass Professor of Ecology and Evolutionary Biology at Yale University, working in the field of evolutionary biology; and, Gilbert S. Omenn, president of AAAS and professor of Medicine and Genetics at the University of Michigan, working in cancer proteomics, computational biology, and science policy. Those researchers argue the value of evolutionary explanations for:

• the narrowness of the birth canal
• the persistence of genes involved in bipolar disease
• the persistence of genes involved in senescence
• the nature of the arms race among bacteria that account for bacterial resistance to natural plant and artifactual antibiotics
• vector-related increases in pathogen virulence
• the biological role of cough, fever, and diarrhea and when to counter them
• why the commonality of low-back problems
• why the body synthesizes bilirubin
• how the modern diet causes diseases by thwarting evolutionary dietary norms
• why the modern high incidence of breast cancer

Neese, Stearns and Omenn end editorial with the argument that "…both the human body and its pathogens are not perfectly designed machines but evolving biological systems shaped by selection under the constraints of tradeoffs that produce specific compromises and vulnerabilities. Powerful insights from evolutionary biology generate new questions whose answers will help improve human health."

1. ↑ Calabrese EJ. (2008) [pii;10.1080/10408440802026315 Addiction and dose response: the psychomotor stimulant theory of addiction reveals that hormetic dose responses are dominant.] Crit Rev Toxicol 38:599-617.
2. ↑ Hayes DP. (2008) [pii Adverse effects of nutritional inadequacy and excess: a hormetic model.] Am J Clin Nutr 88:578S-81S.
3. ↑ Dudekula N, Arora V, Callaerts-Vegh Z, Bond RA. (2005) The temporal hormesis of drug therapies. Dose Response 3:414-24.
4. ↑ Tuomisto J, Pekkanen J, Kiviranta H et al. (2006) Dioxin Cancer Risk - Example of Hormesis? Dose Response 3:332-41.
5. ↑ Tara Parker. (2008) What Would Hippocrates Do? See complete review.
6. ↑ ^6.0 6.1 Newman DH M.D. (2008) Hippocrates' Shadow: Secrets from the House of Medicine. Scribner. 256 pages. ISBN 978-1-4165-5153-9.
   • Publisher’s Description: Everyone knows of the Hippocratic Oath, the famous invocation sworn by all neophyte physicians. But most don't realize that the father of modern medicine was an avid listener and a constant bedside presence. Hippocrates believed in the doctor-patient connection and gained worldwide renown for championing science over mysticism while respecting and advocating the potency of human healing. Today, argues Dr. David H. Newman, medicine focuses narrowly on the rewards of technology and science, exaggerating their benefits and ignoring or minimizing their perils. Dr. Newman sees a disconnect between doctor and patient, a disregard for the healing power of the bond, and, ultimately, a disconnect between doctors and their Oath….The root of this divergence, writes Dr. Newman, lies in the patterns of secrecy and habit that characterize the "House of Medicine," modern medicine's entrenched and carefully protected subculture. In reflexive, often unconscious defense of this subculture, doctors and patients guard medical authority, cling to tradition, and yield to demands that they do something or prescribe something. The result is a biomedical culture that routinely engages in unnecessary and inefficient practices, and leaves both patient and doctor dissatisfied. While demonstrating an abiding respect for, and a deep understanding of, the import of modern science, Dr. Newman reviews research that refutes common and accepted medical wisdom. He cites studies that show how mammograms may cause more harm than good; why antibiotics for sore throats are virtually always unnecessary and therefore dangerous; how cough syrup is rarely more effective than a sugar pill; the power and paradox of the placebo effect; how statistics and studies themselves are frequently deceptive; and why CPR is violent, invasive -- and almost always futile….Through an engaging, deeply researched, and eloquent narrative laced with rich and riveting case studies, Newman cuts to the heart of what really works -- and doesn't -- in medicine and rebuilds the bridge between physicians and their patients.
   • Publisher’s Excerpt: See: http://www.simonsays.com/content/book.cfm?tab=1&pid=625462&agid=2
7. ↑ Note: This article represents a permissible (Creative Commons Attribution License) adaption and modification of an article by Science Writer John Whitfield, living in London, United Kingdom (e-mail:ja_whitfield@hotmail.com) published in the open-access journal, PLoS Biology, PLoS Biol 6(7): e186 in 2008, under the full title: Across the Curious Parallel of Language and Species Evolution.
   • Original article citation: Whitfield J (2008) Across the Curious Parallel of Language and Species Evolution. PLoS Biol 6(7): e186.
   • Copyright: Copyright: © 2008 John Whitfield. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
   • John Whitfield is a science writer living in London, UK (email ja_whitfield@hotmail.com).
   • Article reformatted to correspond to Citizendium style, initially by Citizendium Biology Editor Anthony.Sebastian("A.S"), with subheaders added, with Editors explanatory interpolations in square brackets, annotations of references, and editorial notes in References section.
   • Citizendium makes no claim that the originator of the open-access article, John Whitfield, endorses Citizendium's modification of the article, the unmodified original of which, cited above, the reader can find at Across the Curious Parallel of Language and Species Evolution.
8. ↑ Note: Citations with author names bolded represent those added by Citizendium.
9. ↑ Mark Pagel HomePage - Reading Evolutionary Biology Group
10. ↑ Profile of Mark Pagel, Sante Fe Institute
    • From his biographical sketch: Mark Pagel is an evolutionary theorist with interests in mathematical and statistical modeling of evolutionary processes. His current interests include language and cultural evolution, networks, regulation, emergence of complex systems, robustness and evolvability, punctuational versus gradual evolutionary change, and evolutionary genomics.
11. ↑ Garrutti G, Cotecchia S, Giampetruzzi, Giorgino F, Giorgino R. (2008) Neuroendocrine Deregulation of Food Intake, Adipose Tissue and the Gastrointestinal System in Obesity and Metabolic Syndrome. (Free Full-Text) J Gastrointestin Liver Dis 17:193-198. PMID 18568142
12. ↑ Note: Other pioneering 17th century microscopists: the Dutch (Delft) 1676 discoverer of microbes, Antonie van Leeuwenhoek (1632-1723); the ‘renaissance’ British scientist and 1665 describer of the first cells, Robert Hooke (1635-1703); the Dutch (Amsterdam) 1658 discoverer of red blood cells, Jan Swammerdam (1637-1680).
13. ↑ Marcello Malpighi (Free Full-Text Article, Britannica Online).

    • xxxx

14. ↑ Pearce JMS. (2007) Malpighi and the Discovery of Capillaries. European Neurology 58:253-255.
15. ↑ Lengeler JW, Drews G, Schlegel HG. (1999) Biology of the Prokaryotes. New York: Blackwell Science.
16. ↑ ^16.0 16.1 Dobzhansky TG. (1973) Nothing in biology makes sense except in the light of evolution. The American Biology Teacher 35:125-129
17. ↑ ^17.0 17.1 Futuyma DJ. (1998) Evolutionary Biology. Sinauer Associates, Inc. Sunderland. ISBN 0-87893-189-9
18. ↑ Shepherd LD, Lambert DM. (2005) Mutational bias in penguin microsatellite DNA. J. Hered. 96:566-571. PMID 15994417
19. ↑ ^19.0 19.1 Osler W. (1921) The Evolution of Modern Medicine: A Series of Lectures Delivered at Yale university on the Silliman Foundation, in April, 1913. New Haven: Yale University Press.
20. ↑ Jablonka E, Lamb MJ (2005) Evolution in Four Dimension: Genetic, Epigenetic, Behavioral, and Symbolic Variation in the History of Life. Cambridge: MIT Press. ISBN 978-0-262-10107-3 MIT Press summary Table of Contents and Downloadable Sample Chapters
21. ↑ MacCallum CJ. (2007) 10.1371/journal.pbio.0050112 Does Medicine without Evolution Make Sense? PLoS Biol 5(4): e112
22. ↑ Nesse RM, Stearns SC, Omenn GS. (2006) Medicine needs evolution Science 311:1071 PMID 16497889

Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

Joel E. Cohen

Citation: Cohen JE (2004) Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better. PLoS Biol 2(12): e439 doi:10.1371/journal.pbio.0020439

Published: December 14, 2004

Copyright: © 2004 Joel E. Cohen. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Joel E. Cohen is at the Laboratory of Populations, Rockefeller and Columbia Universities, New York, New York, United States of America. E-mail: cohen@rockefeller.edu

Although mathematics has long been intertwined with the biological sciences, an explosive synergy between biology and mathematics seems poised to enrich and extend both fields greatly in the coming decades (Levin 1992; Murray 1993; Jungck 1997; Hastings et al. 2003; Palmer et al. 2003; Hastings and Palmer 2003). Biology will increasingly stimulate the creation of qualitatively new realms of mathematics. Why? In biology, ensemble properties emerge at each level of organization from the interactions of heterogeneous biological units at that level and at lower and higher levels of organization (larger and smaller physical scales, faster and slower temporal scales). New mathematics will be required to cope with these ensemble properties and with the heterogeneity of the biological units that compose ensembles at each level.

The discovery of the microscope in the late 17th century caused a revolution in biology by revealing otherwise invisible and previously unsuspected worlds. Western cosmology from classical times through the end of the Renaissance envisioned a system with three types of spheres: the sphere of man, exemplified by his imperfectly round head; the sphere of the world, exemplified by the imperfectly spherical earth; and the eight perfect spheres of the universe, in which the seven (then known) planets moved and the outer stars were fixed (Nicolson 1960). The discovery of a microbial world too small to be seen by the naked eye challenged the completeness of this cosmology and unequivocally demonstrated the existence of living creatures unknown to the Scriptures of Old World religions.

Mathematics broadly interpreted is a more general microscope. It can reveal otherwise invisible worlds in all kinds of data, not only optical. For example, computed tomography can reveal a cross-section of a human head from the density of X-ray beams without ever opening the head, by using the Radon transform to infer the densities of materials at each location within the head (Hsieh 2003). Charles Darwin was right when he wrote that people with an understanding “of the great leading principles of mathematics… seem to have an extra sense� (F. Darwin 1905). Today's biologists increasingly recognize that appropriate mathematics can help interpret any kind of data. In this sense, mathematics is biology's next microscope, only better.

Conversely, mathematics will benefit increasingly from its involvement with biology, just as mathematics has already benefited and will continue to benefit from its historic involvement with physical problems. In classical times, physics, as first an applied then a basic science, stimulated enormous advances in mathematics. For example, geometry reveals by its very etymology (geometry) its origin in the needs to survey the lands and waters of Earth. Geometry was used to lay out fields in Egypt after the flooding of the Nile, to aid navigation, to aid city planning. The inventions of the calculus by Isaac Newton and Gottfried Leibniz in the later 17th century were stimulated by physical problems such as planetary orbits and optical calculations.

In the coming century, biology will stimulate the creation of entirely new realms of mathematics. In this sense, biology is mathematics' next physics, only better. Biology will stimulate fundamentally new mathematics because living nature is qualitatively more heterogeneous than non-living nature. For example, it is estimated that there are 2,000–5,000 species of rocks and minerals in the earth's crust, generated from the hundred or so naturally occurring elements (Shipman et al. 2003; chapter 21 estimates 2,000 minerals in Earth's crust). By contrast, there are probably between 3 million and 100 million biological species on Earth, generated from a small fraction of the naturally occurring elements. If species of rocks and minerals may validly be compared with species of living organisms, the living world has at least a thousand times the diversity of the non-living. This comparison omits the enormous evolutionary importance of individual variability within species. Coping with the hyper-diversity of life at every scale of spatial and temporal organization will require fundamental conceptual advances in mathematics.

The Past

The interactions between mathematics and biology at present follow from their interactions over the last half millennium. The discovery of the New World by Europeans approximately 500 years ago—and of its many biological species not described in religious Scriptures—gave impetus to major conceptual progress in biology.

The outstanding milestone in the early history of biological quantitation was the work of William Harvey, Exercitatio Anatomica De Motu Cordis et Sanguinis In Animalibus (An Anatomical Disquisition on the Motion of the Heart and Blood in Animals) (Harvey 1847), first published in 1628. Harvey's demonstration that the blood circulates was the pivotal founding event of the modern interaction between mathematics and biology. His elegant reasoning is worth understanding.

From the time of the ancient Greek physician Galen (131–201 C.E.) until William Harvey studied medicine in Padua (1600–1602, while Galileo was active there), it was believed that there were two kinds of blood, arterial blood and venous blood. Both kinds of blood were believed to ebb and flow under the motive power of the liver, just as the tides of the earth ebbed and flowed under the motive power of the moon. Harvey became physician to the king of England. He used his position of privilege to dissect deer from the king's deer park as well as executed criminals. Harvey observed that the veins in the human arm have one-way valves that permit blood to flow from the periphery toward the heart but not in the reverse direction. Hence the theory that the blood ebbs and flows in both veins and arteries could not be correct.

Harvey also observed that the heart was a contractile muscle with one-way valves between the chambers on each side. He measured the volume of the left ventricle of dead human hearts and found that it held about two ounces (about 60 ml), varying from 1.5 to three ounces in different individuals. He estimated that at least one-eighth and perhaps as much as one-quarter of the blood in the left ventricle was expelled with each stroke of the heart. He measured that the heart beat 60–100 times per minute. Therefore, the volume of blood expelled from the left ventricle per hour was about 60 ml × 1/8 × 60 beats/minute × 60 minutes/hour, or 27 liters/hour. However, the average human has only 5.5 liters of blood (a quantity that could be estimated by draining a cadaver). Therefore, the blood must be like a stage army that marches off one side of the stage, returns behind the scenes, and reenters from the other side of the stage, again and again. The large volume of blood pumped per hour could not possibly be accounted for by the then-prevalent theory that the blood originated from the consumption of food. Harvey inferred that there must be some small vessels that conveyed the blood from the outgoing arteries to the returning veins, but he was not able to see those small vessels. His theoretical prediction, based on his meticulous anatomical observations and his mathematical calculations, was spectacularly confirmed more than half a century later when Marcello Malpighi (1628–1694) saw the capillaries under a microscope. Harvey's discovery illustrates the enormous power of simple, off-the-shelf mathematics combined with careful observation and clear reasoning. It set a high standard for all later uses of mathematics in biology.

Mathematics was crucial in the discovery of genes by Mendel (Orel 1984) and in the theory of evolution. Mathematics was and continues to be the principal means of integrating evolution and genetics since the classic work of R. A. Fisher, J. B. S. Haldane, and S. Wright in the first half of the 20th century (Provine 2001).

Over the last 500 years, mathematics has made amazing progress in each of its three major fields: geometry and topology, algebra, and analysis. This progress has enriched all the biological sciences.

In 1637, René Descartes linked the featureless plane of Greek geometry to the symbols and formulas of Arabic algebra by imposing a coordinate system (conventionally, a horizontal x-axis and a vertical y-axis) on the geometric plane and using numbers to measure distances between points. If every biologist who plotted data on x–y coordinates acknowledged the contribution of Descartes to biological understanding, the key role of mathematics in biology would be uncontested.

Another highlight of the last five centuries of geometry was the invention of non-Euclidean geometries (1823–1830). Shocking at first, these geometries unshackled the possibilities of mathematical reasoning from the intuitive perception of space. These non-Euclidean geometries have made significant contributions to biology in facilitating, for example, mapping the brain onto a flat surface (Hurdal et al. 1999; Bowers and Hurdal 2003).

In algebra, efforts to find the roots of equations led to the discovery of the symmetries of roots of equations and thence to the invention of group theory, which finds routine application in the study of crystallographic groups by structural biologists today. Generalizations of single linear equations to families of simultaneous multi-variable linear equations stimulated the development of linear algebra and the European re-invention and naming of matrices in the mid-19th century. The use of a matrix of numbers to solve simultaneous systems of linear equations can be traced back in Chinese mathematics to the period from 300 B.C.E. to 200 C.E. (in a work by Chiu Chang Suan Shu called Nine Chapters of the Mathematical Art; Smoller 2001). In the 19th century, matrices were considered the epitome of useless mathematical abstraction. Then, in the 20th century, it was discovered, for example, that the numerical processes required for the cohort-component method of population projection can be conveniently summarized and executed using matrices (Keyfitz 1968). Today the use of matrices is routine in agencies responsible for making official population projections as well as in population-biological research on human and nonhuman populations (Caswell 2001).

Finally, analysis, including the calculus of Newton and Leibniz and probability theory, is the line between ancient thought and modern thought. Without an understanding of the concepts of analysis, especially the concept of a limit, it is not possible to grasp much of modern science, technology, or economic theory. Those who understand the calculus, ordinary and partial differential equations, and probability theory have a way of seeing and understanding the world, including the biological world, that is unavailable to those who do not.

Conceptual and scientific challenges from biology have enriched mathematics by leading to innovative thought about new kinds of mathematics. Table 1 lists examples of new and useful mathematics arising from problems in the life sciences broadly construed, including biology and some social sciences. Many of these developments blend smoothly into their antecedents and later elaborations. For example, game theory has a history before the work of John von Neumann (von Neumann 1959; von Neumann and Morgenstern 1953), and Karl Pearson's development of the correlation coefficient (Pearson and Lee 1903) rested on earlier work by Francis Galton (1889).

[[Image:]]

Table 1. Mathematics Arising from Biological Problems

The Present

To see how the interactions of biology and mathematics may proceed in the future, it is helpful to map the present landscapes of biology and applied mathematics.

The biological landscape may be mapped as a rectangular table with different rows for different questions and different columns for different biological domains. Biology asks six kinds of questions. How is it built? How does it work? What goes wrong? How is it fixed? How did it begin? What is it for? These are questions, respectively, about structures, mechanisms, pathologies, repairs, origins, and functions or purposes. The former teleological interpretation of purpose has been replaced by an evolutionary perspective. Biological domains, or levels of organization, include molecules, cells, tissues, organs, individuals, populations, communities, ecosystems or landscapes, and the biosphere. Many biological research problems can be classified as the combination of one or more questions directed to one or more domains.

In addition, biological research questions have important dimensions of time and space. Timescales of importance to biology range from the extremely fast processes of photosynthesis to the billions of years of living evolution on Earth. Relevant spatial scales range from the molecular to the cosmic (cosmic rays may have played a role in evolution on Earth). The questions and the domains of biology behave differently on different temporal and spatial scales. The opportunities and the challenges that biology offers mathematics arise because the units at any given level of biological organization are heterogeneous, and the outcomes of their interactions (sometimes called “emergent phenomena� or “ensemble properties�) on any selected temporal and spatial scale may be substantially affected by the heterogeneity and interactions of biological components at lower and higher levels of biological organization and at smaller and larger temporal and spatial scales (Anderson 1972, 1995).

The landscape of applied mathematics is better visualized as a tetrahedron (a pyramid with a triangular base) than as a matrix with temporal and spatial dimensions. (Mathematical imagery, such as a tetrahedron for applied mathematics and a matrix for biology, is useful even in trying to visualize the landscapes of biology and mathematics.) The four main points of the applied mathematical landscape are data structures, algorithms, theories and models (including all pure mathematics), and computers and software. Data structures are ways to organize data, such as the matrix used above to describe the biological landscape. Algorithms are procedures for manipulating symbols. Some algorithms are used to analyze data, others to analyze models. Theories and models, including the theories of pure mathematics, are used to analyze both data and ideas. Mathematics and mathematical theories provide a testing ground for ideas in which the strength of competing theories can be measured. Computers and software are an important, and frequently the most visible, vertex of the applied mathematical landscape. However, cheap, easy computing increases the importance of theoretical understanding of the results of computation. Theoretical understanding is required as a check on the great risk of error in software, and to bridge the enormous gap between computational results and insight or understanding.

The landscape of research in mathematics and biology contains all combinations of one or more biological questions, domains, time scales, and spatial scales with one or more data structures, algorithms, theories or models, and means of computation (typically software and hardware). The following example from cancer biology illustrates such a combination: the question, “how does it work?� is approached in the domain of cells (specifically, human cancer cells) with algorithms for correlation and hierarchical clustering.

Gene expression and drug activity in human cancer.

Suppose a person has a cancer. Could information about the activities of the genes in the cells of the person's cancer guide the use of cancer-treatment drugs so that more effective drugs are used and less effective drugs are avoided? To suggest answers to this question, Scherf et al. (2000) ingeniously applied off-the-shelf mathematics, specifically, correlation—invented nearly a century earlier by Karl Pearson (Pearson and Lee 1903) in a study of human inheritance—and clustering algorithms, which apparently had multiple sources of invention, including psychometrics (Johnson 1967). They applied these simple tools to extract useful information from, and to combine for the first time, enormous databases on molecular pharmacology and gene expression (http://discover.nci.nih.gov/arraytools/). They used two kinds of information from the drug discovery program of the National Cancer Institute. The first kind of information described gene expression in 1,375 genes of each of 60 human cancer cell lines. A target matrix T had, as the numerical entry in row g and column c, the relative abundance of the mRNA transcript of gene g in cell line c. The drug activity matrix A summarized the pharmacology of 1,400 drugs acting on each of the same 60 human cancer cell lines, including 118 drugs with “known mechanism of action.� The number in row d and column c of the drug activity matrix A was the activity of drug d in suppressing the growth of cell line c, or, equivalently, the sensitivity of cell line c to drug d. The target matrix T for gene expression contained 82,500 numbers, while the drug activity matrix A had 84,000 numbers.

These two matrices have the same set of column headings but have different row labels. Given the two matrices, precisely five sets of possible correlations could be calculated, and Scherf et al. calculated all five. (1) The correlation between two different columns of the activity matrix A led to a clustering of cell lines according to their similarity of response to different drugs. (2) The correlation between two different columns of the target matrix T led to a clustering of the cell lines according to their similarity of gene expression. This clustering differed very substantially from the clustering of cell lines by drug sensitivity. (3) The correlation between different rows of the activity matrix A led to a clustering of drugs according to their activity patterns across all cell lines. (4) The correlation between different rows of the target matrix T led to a clustering of genes according to the pattern of mRNA expressed across the 60 cell lines. (5) Finally, the correlation between a row of the activity matrix A and a row of the target matrix T described the positive or negative covariation of drug activity with gene expression. A positive correlation meant that the higher the level of gene expression across the 60 cancer cell lines, the higher the effectiveness of the drug in suppressing the growth of those cell lines. The result of analyzing several hundred thousand experiments is summarized in a single picture called a clustered image map (Figure 1). This clustered image map plots gene expression–drug activity correlations as a function of clustered genes (horizontal axis) and clustered drugs (showing only the 118 drugs with “known function�) on the vertical axis (Weinstein et al. 1997).

[[Image:]]

Figure 1. Clustered Image Map of Gene Expression–Drug Activity Correlations

Plotted as a function of 1,376 clustered genes (x-axis) and 118 clustered drugs (y-axis). From http://discover.nci.nih.gov/external/CIM_example3/cgi_user_matrix.html. (updated 27 April 2000; accessed 7 October 2004). This image is more recent than the published image (Scherf et al. 2000). Used by permission of John N. Weinstein.

What use is this? If a person's cancer cells have high expression for a particular gene, and the correlation of that gene with drug activity is highly positive, then that gene may serve as a marker for tumor cells likely to be inhibited effectively by that drug. If the correlation with drug activity is negative, then the marker gene may indicate when use of that drug is contraindicated.

While important scientific questions about this approach remain open, its usefulness in generating hypotheses to be tested by further experiments is obvious. It is a very insightful way of organizing and extracting meaning from many individual observations. Without the microscope of mathematical methods and computational power, the insight given by the clustered image map could not be achieved.

The Future

To realize the possibilities of effective synergy between biology and mathematics will require both avoiding potential problems and seizing potential opportunities.

Potential problems.

The productive interaction of biology and mathematics will face problems that concern education, intellectual property, and national security.

Educating the next generation of scientists will require early emphasis on quantitative skills in primary and secondary schools and more opportunities for training in both biology and mathematics at undergraduate, graduate, and postdoctoral levels (CUBE 2003).

Intellectual property rights may both stimulate and obstruct the potential synergy of biology and mathematics. Science is a potlatch culture. The bigger one's gift to the common pool of knowledge and techniques, the higher one's status, just as in the potlatch culture of the Native Americans of the northwest coast of North America. In the case of research in mathematics and biology, intellectual property rights to algorithms and databases need to balance the concerns of inventors, developers, and future researchers (Rai and Eisenberg 2003).

A third area of potential problems as well as opportunities is national security. Scientists and national defenders can collaborate by supporting and doing open research on the optimal design of monitoring networks and mitigation strategies for all kinds of biological attacks (Wein et al. 2003). But openness of scientific methods or biological reagents in microbiology may pose security risks in the hands of terrorists. Problems of conserving privacy may arise when disparate databases are connected, such as physician payment databases with disease diagnosis databases, or health databases with law enforcement databases.

Opportunities.

Mathematical models can circumvent ethical dilemmas. For example, in a study of the household transmission of Chagas disease in northwest Argentina, Cohen and Gürtler (2001) wanted to know—since dogs are a reservoir of infection—what would happen if dogs were removed from bedroom areas, without spraying households with insecticides against the insect that transmits infection. Because neither the householders nor the state public health apparatus can afford to spray the households in some areas, the realistic experiment would be to ask householders to remove the dogs without spraying. But a researcher who goes to a household and observes an insect infestation is morally obliged to spray and eliminate the infestation. In a detailed mathematical model, it was easy to set a variable representing the number of dogs in the bedroom areas to zero. All components of the model were based on measurements made in real villages. The calculation showed that banishing dogs from bedroom areas would substantially reduce the intensity of infection in the absence of spraying, though spraying would contribute to additional reductions in the intensity of infection. The model was used to do an experiment conceptually that could not be done ethically in a real village. The conceptual experiment suggested the value of educating villagers about the important health benefits of removing dogs from the bedroom areas.

The future of a scientific field is probably less predictable than the future in general. Doubtless, though, there will be exciting opportunities for the collaboration of mathematics and biology. Mathematics can help biologists grasp problems that are otherwise too big (the biosphere) or too small (molecular structure); too slow (macroevolution) or too fast (photosynthesis); too remote in time (early extinctions) or too remote in space (life at extremes on the earth and in space); too complex (the human brain) or too dangerous or unethical (epidemiology of infectious agents). Box 1 summarizes five biological and five mathematical challenges where interactions between biology and mathematics may prove particularly fruitful.

Acknowledgments

This paper is based on a talk given on February 12, 2003, as the keynote address at the National Science Foundation (NSF)–National Institutes of Health (NIH) Joint Symposium on Accelerating Mathematical–Biological Linkages, Bethesda, Maryland; on June 12, 2003, as the first presentation in the 21st Century Biology Lecture Series, National Science Foundation, Arlington, Virginia; and on July 10, 2003, at a Congressional Lunch Briefing, co-sponsored by the American Mathematical Society and Congressman Vernon J. Ehlers, Washington, D.C. I thank Margaret Palmer, Sam Scheiner, Michael Steuerwalt, James Cassatt, Mike Marron, John Whitmarsh, and directors of NSF and NIH for organizing the NSF–NIH meeting, Mary Clutter and Joann P. Roskoski for organizing my presentation at the NSF, Samuel M. Rankin III for organizing the American Mathematical Society Congressional Lunch Briefing, and Congressman Bob Filner for attending and participating. I am grateful for constructive editing by Philip Bernstein, helpful suggestions on earlier versions from Mary Clutter, Charles Delwiche, Bruce A. Fuchs, Yonatan Grad, Alan Hastings, Kevin Lauderdale, Zaida Luthey-Schulten, Daniel C. Reuman, Noah Rosenberg, Michael Pearson, and Samuel Scheiner, support from U.S. NSF grant DEB 9981552, the help of Kathe Rogerson, and the hospitality of Mr. and Mrs. William T. Golden during this work. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the NSF.

Box 1. Challenges

Here are five biological challenges that could stimulate, and benefit from, major innovations in mathematics.

1. Understand cells, their diversity within and between organisms, and their interactions with the biotic and abiotic environments. The complex networks of gene interactions, proteins, and signaling between the cell and other cells and the abiotic environment is probably incomprehensible without some mathematical structure perhaps yet to be invented.
2. Understand the brain, behavior, and emotion. This, too, is a system problem. A practical test of the depth of our understanding is this simple question: Can we understand why people choose to have children or choose not to have children (assuming they are physiologically able to do so)?
3. Replace the tree of life with a network or tapestry to represent lateral transfers of heritable features such as genes, genomes, and prions (Delwiche and Palmer 1996; Delwiche 1999, 2000a, 2000b; Li and Lindquist 2000; Margulis and Sagan 2002; Liu et al. 2002; http://www.life.umd.edu/labs/Delwiche/pubs/endosymbiosis.gif).
4. Couple atmospheric, terrestrial, and aquatic biospheres with global physicochemical processes.
5. Monitor living systems to detect large deviations such as natural or induced epidemics or physiological or ecological pathologies.

Here are five mathematical challenges that would contribute to the progress of biology.

1. Understand computation. Find more effective ways to gain insight and prove theorems from numerical or symbolic computations and agent-based models. We recall Hamming: “The purpose of computing is insight, not numbers� (Hamming 1971, p. 31).
2. Find better ways to model multi-level systems, for example, cells within organs within people in human communities in physical, chemical, and biotic ecologies.
3. Understand probability, risk, and uncertainty. Despite three centuries of great progress, we are still at the very beginning of a true understanding. Can we understand uncertainty and risk better by integrating frequentist, Bayesian, subjective, fuzzy, and other theories of probability, or is an entirely new approach required?
4. Understand data mining, simultaneous inference, and statistical de-identification (Miller 1981). Are practical users of simultaneous statistical inference doomed to numerical simulations in each case, or can general theory be improved? What are the complementary limits of data mining and statistical de-identification in large linked databases with personal information?
5. Set standards for clarity, performance, publication and permanence of software and computational results.

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MathBiol77

Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

Joel E. Cohen

Citation: Cohen JE (2004) Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better. PLoS Biol 2(12): e439 doi:10.1371/journal.pbio.0020439

Published: December 14, 2004

Copyright: © 2004 Joel E. Cohen. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Joel E. Cohen is at the Laboratory of Populations, Rockefeller and Columbia Universities, New York, New York, United States of America. E-mail: cohen@rockefeller.edu

Although mathematics has long been intertwined with the biological sciences, an explosive synergy between biology and mathematics seems poised to enrich and extend both fields greatly in the coming decades (Levin 1992; Murray 1993; Jungck 1997; Hastings et al. 2003; Palmer et al. 2003; Hastings and Palmer 2003). Biology will increasingly stimulate the creation of qualitatively new realms of mathematics. Why? In biology, ensemble properties emerge at each level of organization from the interactions of heterogeneous biological units at that level and at lower and higher levels of organization (larger and smaller physical scales, faster and slower temporal scales). New mathematics will be required to cope with these ensemble properties and with the heterogeneity of the biological units that compose ensembles at each level.

The discovery of the microscope in the late 17th century caused a revolution in biology by revealing otherwise invisible and previously unsuspected worlds. Western cosmology from classical times through the end of the Renaissance envisioned a system with three types of spheres: the sphere of man, exemplified by his imperfectly round head; the sphere of the world, exemplified by the imperfectly spherical earth; and the eight perfect spheres of the universe, in which the seven (then known) planets moved and the outer stars were fixed (Nicolson 1960). The discovery of a microbial world too small to be seen by the naked eye challenged the completeness of this cosmology and unequivocally demonstrated the existence of living creatures unknown to the Scriptures of Old World religions.

Mathematics broadly interpreted is a more general microscope. It can reveal otherwise invisible worlds in all kinds of data, not only optical. For example, computed tomography can reveal a cross-section of a human head from the density of X-ray beams without ever opening the head, by using the Radon transform to infer the densities of materials at each location within the head (Hsieh 2003). Charles Darwin was right when he wrote that people with an understanding “of the great leading principles of mathematics… seem to have an extra sense” (F. Darwin 1905). Today's biologists increasingly recognize that appropriate mathematics can help interpret any kind of data. In this sense, mathematics is biology's next microscope, only better.

Conversely, mathematics will benefit increasingly from its involvement with biology, just as mathematics has already benefited and will continue to benefit from its historic involvement with physical problems. In classical times, physics, as first an applied then a basic science, stimulated enormous advances in mathematics. For example, geometry reveals by its very etymology (geometry) its origin in the needs to survey the lands and waters of Earth. Geometry was used to lay out fields in Egypt after the flooding of the Nile, to aid navigation, to aid city planning. The inventions of the calculus by Isaac Newton and Gottfried Leibniz in the later 17th century were stimulated by physical problems such as planetary orbits and optical calculations.

In the coming century, biology will stimulate the creation of entirely new realms of mathematics. In this sense, biology is mathematics' next physics, only better. Biology will stimulate fundamentally new mathematics because living nature is qualitatively more heterogeneous than non-living nature. For example, it is estimated that there are 2,000–5,000 species of rocks and minerals in the earth's crust, generated from the hundred or so naturally occurring elements (Shipman et al. 2003; chapter 21 estimates 2,000 minerals in Earth's crust). By contrast, there are probably between 3 million and 100 million biological species on Earth, generated from a small fraction of the naturally occurring elements. If species of rocks and minerals may validly be compared with species of living organisms, the living world has at least a thousand times the diversity of the non-living. This comparison omits the enormous evolutionary importance of individual variability within species. Coping with the hyper-diversity of life at every scale of spatial and temporal organization will require fundamental conceptual advances in mathematics.

The Past

The interactions between mathematics and biology at present follow from their interactions over the last half millennium. The discovery of the New World by Europeans approximately 500 years ago—and of its many biological species not described in religious Scriptures—gave impetus to major conceptual progress in biology.

The outstanding milestone in the early history of biological quantitation was the work of William Harvey, Exercitatio Anatomica De Motu Cordis et Sanguinis In Animalibus (An Anatomical Disquisition on the Motion of the Heart and Blood in Animals) (Harvey 1847), first published in 1628. Harvey's demonstration that the blood circulates was the pivotal founding event of the modern interaction between mathematics and biology. His elegant reasoning is worth understanding.

From the time of the ancient Greek physician Galen (131–201 C.E.) until William Harvey studied medicine in Padua (1600–1602, while Galileo was active there), it was believed that there were two kinds of blood, arterial blood and venous blood. Both kinds of blood were believed to ebb and flow under the motive power of the liver, just as the tides of the earth ebbed and flowed under the motive power of the moon. Harvey became physician to the king of England. He used his position of privilege to dissect deer from the king's deer park as well as executed criminals. Harvey observed that the veins in the human arm have one-way valves that permit blood to flow from the periphery toward the heart but not in the reverse direction. Hence the theory that the blood ebbs and flows in both veins and arteries could not be correct.

Harvey also observed that the heart was a contractile muscle with one-way valves between the chambers on each side. He measured the volume of the left ventricle of dead human hearts and found that it held about two ounces (about 60 ml), varying from 1.5 to three ounces in different individuals. He estimated that at least one-eighth and perhaps as much as one-quarter of the blood in the left ventricle was expelled with each stroke of the heart. He measured that the heart beat 60–100 times per minute. Therefore, the volume of blood expelled from the left ventricle per hour was about 60 ml × 1/8 × 60 beats/minute × 60 minutes/hour, or 27 liters/hour. However, the average human has only 5.5 liters of blood (a quantity that could be estimated by draining a cadaver). Therefore, the blood must be like a stage army that marches off one side of the stage, returns behind the scenes, and reenters from the other side of the stage, again and again. The large volume of blood pumped per hour could not possibly be accounted for by the then-prevalent theory that the blood originated from the consumption of food. Harvey inferred that there must be some small vessels that conveyed the blood from the outgoing arteries to the returning veins, but he was not able to see those small vessels. His theoretical prediction, based on his meticulous anatomical observations and his mathematical calculations, was spectacularly confirmed more than half a century later when Marcello Malpighi (1628–1694) saw the capillaries under a microscope. Harvey's discovery illustrates the enormous power of simple, off-the-shelf mathematics combined with careful observation and clear reasoning. It set a high standard for all later uses of mathematics in biology.

Mathematics was crucial in the discovery of genes by Mendel (Orel 1984) and in the theory of evolution. Mathematics was and continues to be the principal means of integrating evolution and genetics since the classic work of R. A. Fisher, J. B. S. Haldane, and S. Wright in the first half of the 20th century (Provine 2001).

Over the last 500 years, mathematics has made amazing progress in each of its three major fields: geometry and topology, algebra, and analysis. This progress has enriched all the biological sciences.

In 1637, René Descartes linked the featureless plane of Greek geometry to the symbols and formulas of Arabic algebra by imposing a coordinate system (conventionally, a horizontal x-axis and a vertical y-axis) on the geometric plane and using numbers to measure distances between points. If every biologist who plotted data on x–y coordinates acknowledged the contribution of Descartes to biological understanding, the key role of mathematics in biology would be uncontested.

Another highlight of the last five centuries of geometry was the invention of non-Euclidean geometries (1823–1830). Shocking at first, these geometries unshackled the possibilities of mathematical reasoning from the intuitive perception of space. These non-Euclidean geometries have made significant contributions to biology in facilitating, for example, mapping the brain onto a flat surface (Hurdal et al. 1999; Bowers and Hurdal 2003).

In algebra, efforts to find the roots of equations led to the discovery of the symmetries of roots of equations and thence to the invention of group theory, which finds routine application in the study of crystallographic groups by structural biologists today. Generalizations of single linear equations to families of simultaneous multi-variable linear equations stimulated the development of linear algebra and the European re-invention and naming of matrices in the mid-19th century. The use of a matrix of numbers to solve simultaneous systems of linear equations can be traced back in Chinese mathematics to the period from 300 B.C.E. to 200 C.E. (in a work by Chiu Chang Suan Shu called Nine Chapters of the Mathematical Art; Smoller 2001). In the 19th century, matrices were considered the epitome of useless mathematical abstraction. Then, in the 20th century, it was discovered, for example, that the numerical processes required for the cohort-component method of population projection can be conveniently summarized and executed using matrices (Keyfitz 1968). Today the use of matrices is routine in agencies responsible for making official population projections as well as in population-biological research on human and nonhuman populations (Caswell 2001).

Finally, analysis, including the calculus of Newton and Leibniz and probability theory, is the line between ancient thought and modern thought. Without an understanding of the concepts of analysis, especially the concept of a limit, it is not possible to grasp much of modern science, technology, or economic theory. Those who understand the calculus, ordinary and partial differential equations, and probability theory have a way of seeing and understanding the world, including the biological world, that is unavailable to those who do not.

Conceptual and scientific challenges from biology have enriched mathematics by leading to innovative thought about new kinds of mathematics. Table 1 lists examples of new and useful mathematics arising from problems in the life sciences broadly construed, including biology and some social sciences. Many of these developments blend smoothly into their antecedents and later elaborations. For example, game theory has a history before the work of John von Neumann (von Neumann 1959; von Neumann and Morgenstern 1953), and Karl Pearson's development of the correlation coefficient (Pearson and Lee 1903) rested on earlier work by Francis Galton (1889).

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Table 1. Mathematics Arising from Biological Problems

The Present

To see how the interactions of biology and mathematics may proceed in the future, it is helpful to map the present landscapes of biology and applied mathematics.

The biological landscape may be mapped as a rectangular table with different rows for different questions and different columns for different biological domains. Biology asks six kinds of questions. How is it built? How does it work? What goes wrong? How is it fixed? How did it begin? What is it for? These are questions, respectively, about structures, mechanisms, pathologies, repairs, origins, and functions or purposes. The former teleological interpretation of purpose has been replaced by an evolutionary perspective. Biological domains, or levels of organization, include molecules, cells, tissues, organs, individuals, populations, communities, ecosystems or landscapes, and the biosphere. Many biological research problems can be classified as the combination of one or more questions directed to one or more domains.

In addition, biological research questions have important dimensions of time and space. Timescales of importance to biology range from the extremely fast processes of photosynthesis to the billions of years of living evolution on Earth. Relevant spatial scales range from the molecular to the cosmic (cosmic rays may have played a role in evolution on Earth). The questions and the domains of biology behave differently on different temporal and spatial scales. The opportunities and the challenges that biology offers mathematics arise because the units at any given level of biological organization are heterogeneous, and the outcomes of their interactions (sometimes called “emergent phenomena” or “ensemble properties”) on any selected temporal and spatial scale may be substantially affected by the heterogeneity and interactions of biological components at lower and higher levels of biological organization and at smaller and larger temporal and spatial scales (Anderson 1972, 1995).

The landscape of applied mathematics is better visualized as a tetrahedron (a pyramid with a triangular base) than as a matrix with temporal and spatial dimensions. (Mathematical imagery, such as a tetrahedron for applied mathematics and a matrix for biology, is useful even in trying to visualize the landscapes of biology and mathematics.) The four main points of the applied mathematical landscape are data structures, algorithms, theories and models (including all pure mathematics), and computers and software. Data structures are ways to organize data, such as the matrix used above to describe the biological landscape. Algorithms are procedures for manipulating symbols. Some algorithms are used to analyze data, others to analyze models. Theories and models, including the theories of pure mathematics, are used to analyze both data and ideas. Mathematics and mathematical theories provide a testing ground for ideas in which the strength of competing theories can be measured. Computers and software are an important, and frequently the most visible, vertex of the applied mathematical landscape. However, cheap, easy computing increases the importance of theoretical understanding of the results of computation. Theoretical understanding is required as a check on the great risk of error in software, and to bridge the enormous gap between computational results and insight or understanding.

The landscape of research in mathematics and biology contains all combinations of one or more biological questions, domains, time scales, and spatial scales with one or more data structures, algorithms, theories or models, and means of computation (typically software and hardware). The following example from cancer biology illustrates such a combination: the question, “how does it work?” is approached in the domain of cells (specifically, human cancer cells) with algorithms for correlation and hierarchical clustering.

Gene expression and drug activity in human cancer.

Suppose a person has a cancer. Could information about the activities of the genes in the cells of the person's cancer guide the use of cancer-treatment drugs so that more effective drugs are used and less effective drugs are avoided? To suggest answers to this question, Scherf et al. (2000) ingeniously applied off-the-shelf mathematics, specifically, correlation—invented nearly a century earlier by Karl Pearson (Pearson and Lee 1903) in a study of human inheritance—and clustering algorithms, which apparently had multiple sources of invention, including psychometrics (Johnson 1967). They applied these simple tools to extract useful information from, and to combine for the first time, enormous databases on molecular pharmacology and gene expression (http://discover.nci.nih.gov/arraytools/). They used two kinds of information from the drug discovery program of the National Cancer Institute. The first kind of information described gene expression in 1,375 genes of each of 60 human cancer cell lines. A target matrix T had, as the numerical entry in row g and column c, the relative abundance of the mRNA transcript of gene g in cell line c. The drug activity matrix A summarized the pharmacology of 1,400 drugs acting on each of the same 60 human cancer cell lines, including 118 drugs with “known mechanism of action.” The number in row d and column c of the drug activity matrix A was the activity of drug d in suppressing the growth of cell line c, or, equivalently, the sensitivity of cell line c to drug d. The target matrix T for gene expression contained 82,500 numbers, while the drug activity matrix A had 84,000 numbers.

These two matrices have the same set of column headings but have different row labels. Given the two matrices, precisely five sets of possible correlations could be calculated, and Scherf et al. calculated all five. (1) The correlation between two different columns of the activity matrix A led to a clustering of cell lines according to their similarity of response to different drugs. (2) The correlation between two different columns of the target matrix T led to a clustering of the cell lines according to their similarity of gene expression. This clustering differed very substantially from the clustering of cell lines by drug sensitivity. (3) The correlation between different rows of the activity matrix A led to a clustering of drugs according to their activity patterns across all cell lines. (4) The correlation between different rows of the target matrix T led to a clustering of genes according to the pattern of mRNA expressed across the 60 cell lines. (5) Finally, the correlation between a row of the activity matrix A and a row of the target matrix T described the positive or negative covariation of drug activity with gene expression. A positive correlation meant that the higher the level of gene expression across the 60 cancer cell lines, the higher the effectiveness of the drug in suppressing the growth of those cell lines. The result of analyzing several hundred thousand experiments is summarized in a single picture called a clustered image map (Figure 1). This clustered image map plots gene expression–drug activity correlations as a function of clustered genes (horizontal axis) and clustered drugs (showing only the 118 drugs with “known function”) on the vertical axis (Weinstein et al. 1997).

[[Image:]]

Figure 1. Clustered Image Map of Gene Expression–Drug Activity Correlations

Plotted as a function of 1,376 clustered genes (x-axis) and 118 clustered drugs (y-axis). From http://discover.nci.nih.gov/external/CIM_example3/cgi_user_matrix.html. (updated 27 April 2000; accessed 7 October 2004). This image is more recent than the published image (Scherf et al. 2000). Used by permission of John N. Weinstein.

What use is this? If a person's cancer cells have high expression for a particular gene, and the correlation of that gene with drug activity is highly positive, then that gene may serve as a marker for tumor cells likely to be inhibited effectively by that drug. If the correlation with drug activity is negative, then the marker gene may indicate when use of that drug is contraindicated.

While important scientific questions about this approach remain open, its usefulness in generating hypotheses to be tested by further experiments is obvious. It is a very insightful way of organizing and extracting meaning from many individual observations. Without the microscope of mathematical methods and computational power, the insight given by the clustered image map could not be achieved.

The Future

To realize the possibilities of effective synergy between biology and mathematics will require both avoiding potential problems and seizing potential opportunities.

Potential problems.

The productive interaction of biology and mathematics will face problems that concern education, intellectual property, and national security.

Educating the next generation of scientists will require early emphasis on quantitative skills in primary and secondary schools and more opportunities for training in both biology and mathematics at undergraduate, graduate, and postdoctoral levels (CUBE 2003).

Intellectual property rights may both stimulate and obstruct the potential synergy of biology and mathematics. Science is a potlatch culture. The bigger one's gift to the common pool of knowledge and techniques, the higher one's status, just as in the potlatch culture of the Native Americans of the northwest coast of North America. In the case of research in mathematics and biology, intellectual property rights to algorithms and databases need to balance the concerns of inventors, developers, and future researchers (Rai and Eisenberg 2003).

A third area of potential problems as well as opportunities is national security. Scientists and national defenders can collaborate by supporting and doing open research on the optimal design of monitoring networks and mitigation strategies for all kinds of biological attacks (Wein et al. 2003). But openness of scientific methods or biological reagents in microbiology may pose security risks in the hands of terrorists. Problems of conserving privacy may arise when disparate databases are connected, such as physician payment databases with disease diagnosis databases, or health databases with law enforcement databases.

Opportunities.

Mathematical models can circumvent ethical dilemmas. For example, in a study of the household transmission of Chagas disease in northwest Argentina, Cohen and Gürtler (2001) wanted to know—since dogs are a reservoir of infection—what would happen if dogs were removed from bedroom areas, without spraying households with insecticides against the insect that transmits infection. Because neither the householders nor the state public health apparatus can afford to spray the households in some areas, the realistic experiment would be to ask householders to remove the dogs without spraying. But a researcher who goes to a household and observes an insect infestation is morally obliged to spray and eliminate the infestation. In a detailed mathematical model, it was easy to set a variable representing the number of dogs in the bedroom areas to zero. All components of the model were based on measurements made in real villages. The calculation showed that banishing dogs from bedroom areas would substantially reduce the intensity of infection in the absence of spraying, though spraying would contribute to additional reductions in the intensity of infection. The model was used to do an experiment conceptually that could not be done ethically in a real village. The conceptual experiment suggested the value of educating villagers about the important health benefits of removing dogs from the bedroom areas.

The future of a scientific field is probably less predictable than the future in general. Doubtless, though, there will be exciting opportunities for the collaboration of mathematics and biology. Mathematics can help biologists grasp problems that are otherwise too big (the biosphere) or too small (molecular structure); too slow (macroevolution) or too fast (photosynthesis); too remote in time (early extinctions) or too remote in space (life at extremes on the earth and in space); too complex (the human brain) or too dangerous or unethical (epidemiology of infectious agents). Box 1 summarizes five biological and five mathematical challenges where interactions between biology and mathematics may prove particularly fruitful.

Acknowledgments

This paper is based on a talk given on February 12, 2003, as the keynote address at the National Science Foundation (NSF)–National Institutes of Health (NIH) Joint Symposium on Accelerating Mathematical–Biological Linkages, Bethesda, Maryland; on June 12, 2003, as the first presentation in the 21st Century Biology Lecture Series, National Science Foundation, Arlington, Virginia; and on July 10, 2003, at a Congressional Lunch Briefing, co-sponsored by the American Mathematical Society and Congressman Vernon J. Ehlers, Washington, D.C. I thank Margaret Palmer, Sam Scheiner, Michael Steuerwalt, James Cassatt, Mike Marron, John Whitmarsh, and directors of NSF and NIH for organizing the NSF–NIH meeting, Mary Clutter and Joann P. Roskoski for organizing my presentation at the NSF, Samuel M. Rankin III for organizing the American Mathematical Society Congressional Lunch Briefing, and Congressman Bob Filner for attending and participating. I am grateful for constructive editing by Philip Bernstein, helpful suggestions on earlier versions from Mary Clutter, Charles Delwiche, Bruce A. Fuchs, Yonatan Grad, Alan Hastings, Kevin Lauderdale, Zaida Luthey-Schulten, Daniel C. Reuman, Noah Rosenberg, Michael Pearson, and Samuel Scheiner, support from U.S. NSF grant DEB 9981552, the help of Kathe Rogerson, and the hospitality of Mr. and Mrs. William T. Golden during this work. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the NSF.

Box 1. Challenges

Here are five biological challenges that could stimulate, and benefit from, major innovations in mathematics.

1. Understand cells, their diversity within and between organisms, and their interactions with the biotic and abiotic environments. The complex networks of gene interactions, proteins, and signaling between the cell and other cells and the abiotic environment is probably incomprehensible without some mathematical structure perhaps yet to be invented.
2. Understand the brain, behavior, and emotion. This, too, is a system problem. A practical test of the depth of our understanding is this simple question: Can we understand why people choose to have children or choose not to have children (assuming they are physiologically able to do so)?
3. Replace the tree of life with a network or tapestry to represent lateral transfers of heritable features such as genes, genomes, and prions (Delwiche and Palmer 1996; Delwiche 1999, 2000a, 2000b; Li and Lindquist 2000; Margulis and Sagan 2002; Liu et al. 2002; http://www.life.umd.edu/labs/Delwiche/pubs/endosymbiosis.gif).
4. Couple atmospheric, terrestrial, and aquatic biospheres with global physicochemical processes.
5. Monitor living systems to detect large deviations such as natural or induced epidemics or physiological or ecological pathologies.

Here are five mathematical challenges that would contribute to the progress of biology.

1. Understand computation. Find more effective ways to gain insight and prove theorems from numerical or symbolic computations and agent-based models. We recall Hamming: “The purpose of computing is insight, not numbers” (Hamming 1971, p. 31).
2. Find better ways to model multi-level systems, for example, cells within organs within people in human communities in physical, chemical, and biotic ecologies.
3. Understand probability, risk, and uncertainty. Despite three centuries of great progress, we are still at the very beginning of a true understanding. Can we understand uncertainty and risk better by integrating frequentist, Bayesian, subjective, fuzzy, and other theories of probability, or is an entirely new approach required?
4. Understand data mining, simultaneous inference, and statistical de-identification (Miller 1981). Are practical users of simultaneous statistical inference doomed to numerical simulations in each case, or can general theory be improved? What are the complementary limits of data mining and statistical de-identification in large linked databases with personal information?
5. Set standards for clarity, performance, publication and permanence of software and computational results.

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Self-Organization in High-Density Bacterial Colonies: Efficient Crowd Control

HoJung Cho1[[Image:]], Henrik Jönsson2[[Image:]], Kyle Campbell3, Pontus Melke2, Joshua W. Williams4, Bruno Jedynak5, Ann M. Stevens4, Alex Groisman3*, Andre Levchenko1*

1 Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, Maryland, United States of America, 2 Department of Theoretical Physics, Lund University, Lund, Sweden, 3 Department of Physics, University of California San Diego, La Jolla, California, United States of America, 4 Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States of America, 5 Center for Imaging Science, The Johns Hopkins University, Baltimore, Maryland, United States of America

Colonies of bacterial cells can display complex collective dynamics, frequently culminating in the formation of biofilms and other ordered super-structures. Recent studies suggest that to cope with local environmental challenges, bacterial cells can actively seek out small chambers or cavities and assemble there, engaging in quorum sensing behavior. By using a novel microfluidic device, we showed that within chambers of distinct shapes and sizes allowing continuous cell escape, bacterial colonies can gradually self-organize. The directions of orientation of cells, their growth, and collective motion are mutually correlated and dictated by the chamber walls and locations of chamber exits. The ultimate highly organized steady state is conducive to a more-organized escape of cells from the chambers and increased access of nutrients into and evacuation of waste out of the colonies. Using a computational model, we suggest that the lengths of the cells might be optimized to maximize self-organization while minimizing the potential for stampede-like exit blockage. The self-organization described here may be crucial for the early stage of the organization of high-density bacterial colonies populating small, physically confined growth niches. It suggests that this phenomenon can play a critical role in bacterial biofilm initiation and development of other complex multicellular bacterial super-structures, including those implicated in infectious diseases.

Funding. This study was funded by the National Institutes of Health grant GM66786, National Science Foundation IGERT grant DGE-0504196, and NSF NIRT grant 0608863. HJ was in part funded by the Swedish Research Council.

Competing interests. The authors have declared that no competing interests exist.

Academic Editor: James McGrath, University of Rochester, United States of America

Citation: Cho H, Jönsson H, Campbell K, Melke P, Williams JW, et al. (2007) Self-Organization in High-Density Bacterial Colonies: Efficient Crowd Control. PLoS Biol 5(11): e302 doi:10.1371/journal.pbio.0050302

Received: May 8, 2007; Accepted: September 21, 2007; Published: October 30, 2007

Copyright: © 2007 Cho et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abbreviations: 2-D, two dimensional; GFP, green fluorescent protein; RIR, rhombus in rhombus

* To whom correspondence should be addressed. E-mail: alev@jhu.edu (AL), agroisman@ucsd.edu (AG)

[[Image:]]These authors contributed equally to this work.

Author Summary

Bacterial cells form colonies with complex organization (aka biofilms), particularly in response to hostile environmental conditions. Recent studies have shown that biofilm development occurs when bacterial cells seek out small cavities and populate them at high densities. However, bacteria in cavities may suffer from poor nutrient supply or waste removal, or disorganized expansion leading to blockage of cell escape. In this study, we observed Escherichia coli in a microfluidic device that allows direct observation of the growth and development of cell colonies in microchambers of different shapes and sizes through multiple generations. Combining this experimentation with computational analysis of colony growth and expansion, we characterize a process of colony self-organization that results in a high degree of correlation between the directions of cell orientation and growth of collective cell movement. We also find that this self-organization can significantly facilitate efficient escape of cells from the confines of cavities where they reside, while improving the access of nutrients into the colony interior. Finally, we suggest that the aspect ratio of the shape of E. coli and other similar bacteria might be generally subject to a constraint related to colony self-organization.

Introduction

The past few decades witnessed an emergence of the realization that bacterial cells in their natural environments are not asocial, but can exist as colonies with complex organization and exhibit sophisticated and highly regulated collective behaviors [1–5]. Consequently, significant efforts have been made to investigate the collective behavior of bacteria in various settings, with a particular emphasis on the formation of highly organized, multicellular super-structures. Instances of such colony formation include tightly packed bacterial “pods� in epithelial cells, colonies of luminescent bacteria in light organs of marine animals, or biofilms forming on plastic or glass surfaces in various high-humidity environments [6–10]. One important aspect of these naturally occurring tightly packed bacterial colonies (henceforth referred generically to as biofilms) is that they frequently arise despite, and possibly in response to, unfavorable environmental conditions including various types of chemical stress, variable temperature, fluid flow, the host immune system, and limited supply of nutrients [5]. In the initial stages of the biofilm development, it is crucial for bacterial cells to overcome the above-mentioned adverse environmental conditions, while laying foundations for highly ordered, mature biofilm structures. Recent studies have revealed that one of the important initial steps in this process might be for bacterial cells to actively seek out small cavities and populate them, reaching very high densities [11–13]. In addition to providing partial shelter, physical confinement might facilitate the onset of quorum sensing that is thought to be important for the successful progression of biofilm development. However, there are also severe potential disadvantages to forming packed colonies that are partially isolated from the surrounding environment, including increasingly poor nutrient supply and waste removal, as well as the possibility of disorganized expansion leading to cell damage and even blockage of cell escape from the growth niches. How cells cope with these constraints to successfully initiate biofilm development is currently unclear.

A clue to understanding cell behavior in these early stages of biofilm development might come from the high degree of multicellular organization found in stalk formation of yeast cells emerging from microscopic pits in agar gels [14,15]. Initial confinement of cells to small cavities and mechanical interaction between cells and the cavity walls appeared to be essential not only for the formation of complex tall structures uncharacteristic of lab yeast strains, but also for the high degree of functional order and differentiation within these structures. Colony organizations in various organisms such as Bacillus subtilis and Escherichia coli, that were visualized using scanning and transmission electron microscopy [2], also show strikingly well-ordered multicellular arrays within the colonies. Recently, with the aid of advanced microscopy systems, biofilm structures were also found to comprise millions of bacterial cells in regular arrangements that facilitate the physiological interactions within the community [9]. It is of interest therefore to investigate whether this functional organization in biofilms, as in yeast stalks, might emerge from the initial ordering of bacterial colonies growing in small cavities—ordering that might facilitate nutrient exchange and relieve the mechanical stress stemming from cell proliferation.

Although these dynamical reorganizations of the biofilm-like bacterial colonies are likely to be controlled by cell–cell interactions, lack of convenient experimental platforms allowing a dynamic analysis of large, tightly packed colonies on the single cell level has hampered research progress in this area. Recently, we developed a microfluidic device with chemostatic microchambers, which allows bacterial cells to grow over multiple generations in controlled microenvironments [16]. However, these chambers were relatively deep (∼6 μm), making it difficult to reach single-cell resolution at high cell densities. In addition, the device was designed to prevent the escape of cells from the chambers, and the packed colonies could only be monitored over a very limited number of cell generations. In this study, we sought to overcome these limitations and create a device for monitoring tightly packed colonies of actively dividing cells in chambers with different geometries over at least 24 h with single-cell resolution. Using a combination of modeling and experiments in these new devices, we found that developing E. coli colonies achieve progressively higher levels of spatial organization, enabling them to increase the nutrient supply and the efficiency of escape from the chamber. The results of the study suggest added importance of the asymmetrical shape of some bacterial species and have direct implications for biofilm organization. The device we describe can also have wider applications for robust long-term culture of bacterial cells under controlled conditions with real-time microscopy at single-cell resolution.

Results

The Design of the Microfludic Device

Similar to the previously described microfluidic chemostat [16], the main functional area of the microfludic device (Figure 1) is an array of flow-through channels and chambers between the channels. The symmetric binary branching of the flow-through channels from a single channel on both the inlet and outlet sides leads to highly balanced pressures at opposite sides of the chambers. Because the depth of the chambers is much smaller than the depth of the flow-through channels (∼1.5 μm versus 15 μm; Figure 1A), the chambers are much more resistant to flow than the channels. Therefore, there is practically no active flow through the chambers (flow at 0.1–0.2 μm/s for a typical channel flow rate of ∼100 μm/s), and the exchange of chemicals between them and the flow-through channels occurs by diffusion only.

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Figure 1. Microfluidic Device

(A) A drawing of the microchannels; microchannels with depths of 15 and 1.5 μm are shown in blue and black.

(B) A micrograph of a fragment of the array of channels and chambers. White arrows indicate the direction of flow. Scale bar, 100 μm. See a magnified view of the central part of the device in Figure P1 of Protocol S1.

There are three important differences between the device in Figure 1 and that described in [16]. First, the depth of the chambers of our device is close to the diameter of E. coli cells (∼1 μm) and substantially smaller than the cell length (∼3 μm). Therefore, all cells in the chambers are oriented in the plane of the device and create a monolayer, making it possible to detect cellular responses at a single-cell resolution. Second, there are no capillaries impermeable for cells between the flow-through channels and the chambers. Therefore, there are no physical barriers for cells to enter and exit the chambers. Third, although the distance between all flow-through channels is the same (140 μm), the chambers greatly vary in shapes (Figure 1B). The shapes of the outer boundaries of the chambers include circles, squares, diamonds, triangles, and strips. Furthermore, many chambers have one or several posts inside, adding inner boundaries to the geometries (Figure 1B). The posts have different sizes and are shaped as circles, squares, diamonds, triangles, parallel rectangles, and crosses.

The Development of a Microcolony in a Confining Space

As in the cells in a microfluidic chemostat [16], the E. coli cells loaded into the chambers were found to readily form microcolonies. The microcolonies started from as few as 1–2 cells and eventually filled the chambers completely, with cells being in a densely packed state. However, since cells could freely exit the chambers into the adjacent flow-through channels, cell proliferation was not limited in time and continued for as long as the flow of fresh medium in the flow-through channels was maintained. The combination of cell proliferation and escape led to a continuous collective motion of cells of the densely packed colonies toward the microchamber exits. The rate of flux of cells through the exits is proportional to the rate of colony expansion and, given constant volume of the chamber and constant number of cells in the colony in a steady state, the rate of flux is also proportional to the mean cell growth rate in the colony. We did not observe any noticeable decrease in the growth rates of high-density colonies during prolonged continuous incubation, as judged by the characteristic rate of motion of cells toward chamber exits (see, e.g., Figure S3A).

For effective visualization of the organization of microcolonies, we used a strain of E. coli, transformed with a low-copy plasmid carrying green fluorescent protein (GFP) controlled by the truncated version of the Vibrio fischeri lux operon responsive to exogenously added V. fischeri–specific autoinducer [17], N-3-oxo-hexanoyl homoserine lactone (HSL), but deficient in endogenous AI production (Figure S1). In the presence of exogenously added autoinducer supplied with the medium ([AI] = 10 nM), the GFP mediated fluorescence allowed us to visually identify individual cells and perform analysis of their shape, size, and orientation.

We analyzed images of the colonies in different chambers (see Videos S1–S8 for typical examples) and were surprised to observe that, at high densities, the orientations of cells were often anisotropic and highly correlated over distances much larger than the cell length. Typical evolution of a colony in one of the chambers is shown in Figure 2A. Both inner and outer boundaries of the chamber are shaped as rhombi (“rhombus in a rhombus� or RIR chamber). The cell growth initiated in region I, and the orientations of cells appeared random in the beginning. The microcolony then filled the entire chamber to dense cell packing in 8–9 h of growth. (Dense packing in a subcolony was defined as a state in which there was no cell-free region with the area equal to or greater than the area of a daughter cell following a cell division.) As the colony reached dense packing, most cells gradually became oriented along the direction of the collective cell flow toward the chamber exits, which frequently coincided with the directions of the internal and external walls of the chamber.

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Figure 2. Self-Organization of an E. coli Colony in an RIR Chamber

(A) Representative time-lapse epi-fluorescence images of an E. coli colony expressing GFP under the LuxR-lux box control. The fluorescence intensity was adjusted for visualizing the colony at single-cell resolution. The first sub-panel is a large-scale view of the RIR chamber, and the other sub-panels show the left “elbow� region of the chamber at different time points (0,2,4,12,24h). Scale bars: 30 μm, the 1st sub-panel; 10μm, all other sub-panels. See also Video S1–S3

(B) Comparison between the gradient and major axis analyses of cell orientation. Histograms of cell orientations in region I in (A) resulting from each analysis are shown for indicated time points. The range of the x-axis is in degrees in all histograms in this and other Figures.

(C) The steady-state orientation histograms for cells in regions I–IV. The frequency within each bin is averaged over five time points between 19 and 24 h. Values are expressed as means ± standard deviation.

(D) Time-dependence of the fraction, β, of cell population oriented within 45° of the preferred cell orientation in selected regions. The preferred cell orientations were estimated based on the steady state orientation distributions: I- 45°; II- 135°; III- 135°; IV- 45° with respect to the x-axis. The arrows indicate when the colony becomes densely packed (black: I–III; red: IV).

To quantify the orientation of cells, we processed fluorescence images of the chambers using two different methods that we termed the “gradient analysis� and the “major-axis analysis� (Protocol S1 and Figure S2). In the major-axis analysis, the images were segmented to outline individual cells. Following this, the orientations of the major axes of the cells were determined. In the gradient analysis, cell orientation was estimated by determining the direction of the fluorescence gradients from the pixel intensity matrices, without explicit identification of individual cells. Sharp changes of fluorescence occur at cell boundaries, and the directions of fluorescence gradients are perpendicular to the orientation of cells. We applied both methods to sequences of images taken with an interval of 1 h in selected regions of the chambers and found that the two methods consistently yielded similar results (Figure S2).

In region I of the RIR chamber (Figure 2A), at the early time points 0 h and 2 h, the orientation histograms had nearly uniform distributions, indicating that cells were oriented randomly (Figure 2B). As the cell density in the colony increased, the distribution of cell orientations evolved to a shape with a peak at 45°, the direction of the chamber walls and of the collective cell flow in this region. Histograms of the orientation of cells in densely packed states in the other selected regions of the chamber (Figure 2A) were similar to the distribution in region I (Figure 2C). In particular, all histograms had peaks at angles corresponding to directions of the chamber walls—135°, 135°, and 45° for regions II, III, and IV, respectively. The shapes of the orientation histograms of densely packed colonies at distinct time points differed relatively little (Figure 2C), and there were no detectable tendencies in the variation of their shapes with time (Figure 2B). This invariance of histograms indicated that the microcolony reached a steady state in terms of cell orientation.

To assess the evolution of cell orientation, we introduced an order parameter, β, calculated as the fraction of cells oriented within ±45° of the angle at the peak of the eventual steady state histogram (e.g., at 0°−90° for region I). We plotted the time evolution of β for the four regions of the chamber (Figure 2D). The value of β is 0.5 for randomly oriented cells and it is 1 when all cells are aligned in the preferred direction, which is parallel to the chamber walls. Values of β ∼ 0.5 with large variations in time, suggesting basically random orientation of cells with large fluctuations, were typical at the early stages of colony development when cell densities were low. As time progressed and cell densities increased, variations of β became minimal, as expected for a microcolony at a steady state. In this steady-state regime, the values of β were 0.85 on average, indicating a major bias in the orientation of cells toward the directions of the nearby chamber walls. (Calculation of the order parameter using a reduced range of angles around the preferred orientation resulted in smaller values of β at the steady state but did not change the shapes of the curves.) The large value of the order parameter was attained in spite of the fact that the distance between the walls (∼30 μm) was much larger than the cell diameter. The cells in the region I reached a highly ordered state earlier, and in the region II reached it later, than cells in other regions, in accordance with the relative timing of expansion of the colony into these regions.

In addition to the RIR chamber, we used the same methods to analyze the cell orientation in chambers with other shapes. Two typical examples are described here. One chamber was shaped as a rhombus with no internal boundary (Figure 3A), and the other was shaped as a circle with a square internal boundary (Figure 3B). In both chambers, the walls were substantially further apart from each other than in the RIR chamber, which could be expected to lead to less order in the orientation of cells. Surprisingly, the analysis of images of densely packed colonies in both chambers showed that, in most regions, the orientation of cells was highly correlated over large distances. In a chosen region of interest (e.g., regions I, III, IV, and V in Figure 3A and 3B), the preferred orientation of cells usually coincided with the orientation of a nearby wall and always coincided with the direction of flow of cells toward chamber exits. In the central region of the rhombus-shaped chamber (region I and inset I in Figure 3A), close to 95% of cells were oriented within ±45° from the vertical axis, which was the direction of flow toward the chamber exits (Figure 3C and 3D). The orientations of cells in region I were highly correlated over a distance ∼20 times the cell length, in spite of the absence of chamber walls nearby. The orientation order was similarly high in most other regions of the chamber. Exceptions were the side corners (region II and inset II in Figure 3A), where cells appeared to be oriented nearly randomly, as indicated by a close-to-uniform distribution of angles (Figure 3C) and the order parameter β ≈ 0.5 in the steady-state regime. In the “square within a circle� chamber, the distributions of cell orientations in regions IV and V reached the steady states rapidly, and the order parameter attained high values β > 0.9 (Figure 3C and 3D). In region III, the steady state was reached considerably later than in regions IV and V, and the cell orientation was less anisotropic, as indicated by a lower value of the order parameter, β ≈ 0.8 (Figure 3C and 3D). In contrast to regions III and V, in region IV, the direction of flow of cells toward the exit (the flow direction defined the preferred orientation of cells) was orthogonal to the orientation of a nearby chamber wall. As a result, the flow pattern in region IV was rather complicated, with two fluxes of cells (from the left and from the right in Figure 3B) merging into one and with an analogue of a separation line in the middle.

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Figure 3. Colony Self-Organization in Chambers of Different Geometries

Colony self-organization in various regions in the chambers of two geometries: rhombus (A) and square in circle (B). The images of the chambers were obtained in the same experiment as in Figure 1 (Videos S4–S8).

(C) The histograms of the steady state cell orientations in the selected regions based on major axis analysis as in Figure 1.

(D) Time-dependence of the fraction, β, of cell population oriented within 45° of the preferred cell orientation in selected regions: I- 90°; II- 90°; III- 45°; IV- 90; V- 90° with respect to x-axis. The arrows indicate when the colony becomes densely packed. Scale bars: 50 μm.

Simulations of the Microcolony Development

The observation that a high degree of correlation in cell orientation occurred only at high cell densities, in the absence of active cell movement, suggested that the correlation originated from purely mechanical forces. Locally, these forces result from contact interactions of cells with each other and from the constraint of 2-D motion in the plane of the chamber. Globally, the cells are mechanically influenced by their collective motion toward chamber exits. The pattern of this motion depends on the position and orientation of the chamber walls and exits. To investigate if cell self-organization could be solely due to these contact interactions, we simulated the development of a colony in a 2-D region corresponding to the footprint of a chamber, with cells modeled by 2-D objects with shapes, lengths, and widths typical for E. coli cells. The model simulations were based on our previously reported analysis of yeast colony growth [11] with appropriate modifications accounting for differences in cell shape, for symmetric cell division, for the presence of boundaries, etc. (see Methods for more details). Cells were assumed to grow steadily along their major axes, to divide at even time intervals, and to have spring-like deformation potentials. Forces experienced by cells were due to cell–cell and cell–wall interactions. We found that this simple mechanical model reproduced all the major features of colony expansion in different geometries, including the gradual onset of anisotropic orientation of cells with long-range spatial correlations at high cell densities. Both the time evolution and the steady-state distributions of the cell orientation angles in the RIR chamber strongly resembled the corresponding experimental results (Figures 2 and 4A). Similar evolution and steady-state patterns were obtained in the other modeled geometries (Videos S9–S11 and unpublished data). The agreement between the model and experiments corroborated the suggestion that the self-organization of cells within the colonies originated from purely mechanical effects.

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Figure 4. Computational Modeling of Colony Self-Organization

(A) The organization of a colony and the corresponding distributions of cell orientation based on the major axis analysis of the simulated data at four different stages of the colony development within the region I of the RIR geometry (see Videos S9 and S10 for the RIR and S11 for a rhombus microchamber).

(B) Comparison of the cell orientations from simulations with different cell lengths in quadrants I and II of the RIR geometry (0.5L, L, 2L, and 4L; see text and Videos S12–S15 for all the quadrants). To aid the visual comparison, histograms are shown in the ranges where the majority (90%) of cells are found. Each bar represents the average value calculated from 200 simulation time points, all in a densely packed state; the error bars indicate standard deviation.

(C) Simulated spatial distributions of the force metric for different cell lengths. Simulations following dense packing were used to calculate average spatial distributions of mechanical stress experienced by cells (see Protocol S1 for definition of the force metric; zero stress corresponds to virtually no force experienced by the cell; see Videos S12–S15 for the distributions at single-cell resolution).

(D) A snapshot of a simulated colony of the 4L cells at high density. The mechanical stress experienced by individual cells is color-coded. See also Videos S16.

Since a preferred direction of orientation can only exist for nonspherical, elongated objects, the self-organization of E. coli cells in the colony and the anisotropy in their orientation are closely related to the elongated shape of E. coli cells. We used the model to examine how the orientation anisotropy and β in the high-density steady states depend on the ratio between the length and width of cells and simulated colonies composed of cells with maximum lengths shorter (0.5L) and longer (2L, 4L) than “normal� (the normal length, L, corresponded to the average aspect ratio 3.75:1 calculated given that the cell lengths vary from half-maximal to maximal in the course of cell growth). We found that cells with the reduced aspect ratio had smaller orientation order and lower β than the “normal� cells (0.81 vs. 0.99 for region I). On the other hand, we found no significant difference in the anisotropy of orientation between the “normal� cells and the cells with the increased aspect ratios, with the β values of 1.00 and 0.97 for 2L and 4L cells versus 0.99 for the normal cells. The results of the simulation suggest that the actual aspect ratio of E. coli (3:1–4:1) might be close to the minimal aspect ratio sufficient to ensure a high level of coordination of cell orientation within a colony.

We further interrogated the model to evaluate the forces experienced by cells of different lengths at different stages of colony development (see Methods, Videos S12–S15). For cells of 0.5L length simulated within a RIR chamber, the stress at the steady state increased with the distance from the chamber exits and was maximal along the horizontal axis of symmetry of the chamber (Figure 4C). The distribution of stress in the simulated colony was similar to the distribution of pressure in a model of a Newtonian fluid with spatially uniform source term, corresponding to a uniform and steady growth of cells in a chamber of the same geometry (Figure S3B).

By contrast, for the longer cells(2L and 4L) than “normal� cells, the simulations indicated the existence of areas of high stress near the chamber exits. Near the exits, the directions of flow of cells in two merging streams change abruptly by 45°, the total width of the cell stream decreases, and the flow lines merge, causing many cells to become misaligned. The misalignment can lead to high stresses due to both growth of cells in the direction perpendicular to the flow and possible “stampede�-like exit blockage exacerbated by the convergence of flow lines (Videos S13 and S14).

Additionally, we observed that if the cells were oriented perpendicularly to a nearby chamber wall and their growth was not directed toward one of the exits, the cells experienced high localized forces (Figure 4D, left and right corners of the chamber). This observation suggested that self-organization of colony expansion in parallel to the chamber walls may decrease the mechanical stress induced by cell growth.

Facilitation of Nutrient Transport in Organized Colonies

A high degree of anisotropy achieved in the steady-state colonies might affect the efficiency of diffusive transport of nutrients into and metabolites out of the bulk of the colony through the chamber exits. Indeed, a recent theoretical study suggested that increased anisotropy of a porous tissue can lead to a dramatic reduction of its tortuosity and enhancement of diffusion in a preferred direction [18]. The study also analyzed diffusion in a 2-D medium with an array of excluded regions having shapes of identical extended rectangles, oriented parallel to each other, which is a good approximation of the high-density steady-state colonies in the microchambers. The effective diffusion coefficient in the direction along the rectangles was found to be [[Image:]], where D is the diffusion coefficient of the medium without excluded regions, L₁ is the longer, and L₂ is the shorter axes of the rectangles. For E. coli cells with the aspect ratios 3:1–4:1, in a highly ordered steady state with β ≈ 1, one might thus expect an effective diffusion coefficient of 0.75D to 0.8D along the directions from the chamber's exit into the bulk of the colony. For randomly oriented cells, D_eff would drop to 0.5D or even less, due to possible “dead-end poresâ€�, i.e., blockages of openings between pairs of parallel cells by perpendicularly oriented cells. Thus, increasing the anisotropy of cell orientation within a colony is expected to enhance the supply of nutrients to internal regions of the colony and the evacuation of metabolites from the internal regions.

To test this prediction, we took advantage of the sensitivity of the lux operon to glucose levels. Transcription in this operon is positively regulated by the cAMP-receptor protein (CRP) [19], which is progressively activated at decreasing glucose levels due to elevated intracellular cAMP concentrations. As a result, the level of GFP expression substantially increased at reduced glucose levels that were expected to be found in densely populated microfluidic chambers with impaired diffusive transport (Figure P3 of the Protocol S1). We found that, for all chamber shapes, fluorescence of individual cells increased as the colony became denser and filled the chamber, which was consistent with the expected reduction of glucose concentration. Moreover, in the high-density steady-state colonies, well-formed gradients of fluorescence were often observed, with cells becoming progressively less fluorescent toward the chamber exits (Figures 2 and 3 and Figure S5). Because the exits were a source of the exogenously added autoinducer, this type of distribution of fluorescence in the colony was inconsistent with the possibility that autoinducer did not reach cells in the internal regions. The variation of the glucose level appeared to be the only plausible explanation of this fluorescence distribution, and we concluded that the level of cell fluorescence could be used as an indicator of the local concentration of glucose. This conclusion was further corroborated by a high degree of correlation between the expression of GFP driven by the lux operon promoter and the expression of HcRed protein under exclusive control of cAMP-CRP complex (both expressed in the same strain of E. coli) in different cells growing in the same chamber [20] (Figure P4 of Protocol S1).

We then investigated the evolution of GFP fluorescence in different regions of the previously analyzed chambers (Figure 5). In the case corresponding to region I in Figure 3A (rhombus-shaped chamber), we found that, following a maximum level reached around 13 h, the fluorescence intensity gradually dropped by approximately 30% (Figure 5A). Additionally, the fluorescence intensity gradient along a line connecting region I with a chamber exit gradually became shallower, indicating better penetration of the nutrients into internal regions of the colony (Figure 5A-ii). These observations could be explained by noting that the alignment of cells in the rhombus chamber reached its highest level at least 4 h after the colony became densely packed. Therefore, initially, nutrient transport through the colony would be hampered by decreasing intercellular spaces and increasing nutrient consumption leading to increased fluorescence intensity. However, over time, the transport efficiency can be improved by increased anisotropy within the colony, leading to a progressive decrease in the GFP signal at the colony interior. Consistent with this hypothesis, the drops in the GFP fluorescence intensity from the maximal levels were much more limited in the other two chambers analyzed, where by the time the colonies became densely packed, cells were already arranged in a highly anisotropic fashion (Figure 5B and 5C). Taken together, the results suggest that fluctuations in the nutrient supply available to the colony can depend on whether the colony self-organization accompanies or follows achieving the densely packed state. A significant increase in the colony growth rate, as judged by the rate of cell movement out of a chamber, which was observed in the rhombus but not RIR chamber at a later stage of experiment provided independent further support for this suggestion (Figure 5A-i and Figure S3A).

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Figure 5. Glucose-Dependent lux Operon-GFP Response in Microchambers with Different Shapes: Rhombus (A), RIR (B), and Square in a Circle (C)

The average fluorescence intensities in the selected regions were normalized to their value at the end of the experiment, which was taken as 1. (A-i) the flow of cells from the RIR chamber toward an exit during two time intervals corresponding to the red and orange bars in (A). An average of distances traveled by 10 tracked cells from their initial positions is shown as a function of time. The tracking was done in the region indicated by the green trapezium in the inset. The error bars are standard deviation. Each plot was fitted to a quadratic curve. (A-ii) the fluorescence intensity within the rhombus chamber was measured at indicated times along a line from the center (0 μm) to an exit (65 μm). Note the correspondence of the variation in the absolute intensity at distance 0 μm with the temporal variation shown in (A). Each data point represents the mean fluorescence value ± standard deviation from square regions containing approximately 30 cells each.

Discussion

This study has demonstrated that long-term growth of E. coli colonies within small enclosed spaces can be accompanied by self-organization of the colonies into states characterized by highly correlated cell orientation. A simple agent-based model incorporating the details of asymmetric cell shape, mechanical interactions arising from cell growth and division, and the confinement of colonies within specific boundaries has reproduced the salient features of this organization process. The success of the model strongly suggests that self-organization is due to localized mechanical cell–cell and cell–chamber wall interactions, and most importantly, elongated cell shape.

When viewed on a coarse scale—that of hundreds of cells—the dynamics of steady-state colonies bear a marked similarity to the patterns of flow of Newtonian fluid continuously generated within confined spaces of various shapes. This similarity is exemplified by the coincidence of the streamlines of Newtonian fluid with the directions of the collective cell motion (Figure S3B). In addition, the areas corresponding to high fluid pressure overlap with those of increased stress experienced by cells with low aspect ratio (Figure S3B). These simple patterns are further refined on the scales comparable to the size of a single cell, where the effects of elongated shape of the cells become especially pronounced. In particular, it becomes evident that not only the direction of movement but also the orientations of individual cells become aligned with the predicted streamlines and also become mutually correlated. The directional correlation increases with increasing cell aspect ratio. This self-organization behavior, involving hundreds to thousands cells, contrasts with the previously reported transient local alignment of relatively small cell clusters ([21], Figure S4), and is strongly dependent on the geometry of the confining boundaries and chamber exits and on the direction of the collective cell flow (Figure 3D and Figure S5). Based on the results described here, we propose that colony self-organization can endow the constituent cells with at least two important advantages.

First, orientation of cell growth toward the exits connecting microchambers to external space can lead to the relaxation of the stress experienced by the cells due to constriction by the chamber boundaries. In a cell population lacking such an orientational order, cell growth toward chamber walls can create local foci of high stress (see e.g., Figure 4D). Interestingly, increasing the cell aspect ratios beyond the values comparable to those of the wild-type E. coli does not seem to affect the degree of self-organization, but can increase the cellular stresses at the chamber exits due to rapid changes in cell orientation. In this regard, it is interesting to contrast the collective behavior of bacterial cells to the self-driven movement of a large crowd in a confined space. The model in [22] suggests that a combination of a relatively narrow bottleneck coupled with self-propelled, panic-like movement of people within a confined space can easily result in a blockage of the exits, leading to potentially widespread injuries. Arguably, bacterial cells in tightly packed colonies populating small cavities or other confining environments might face similar stampede-like blockage challenges. Our results suggest, however, that the potential for “bacterial stampedes� arises only for relatively long cells, which have feature sizes comparable to the dimension of the cavity exit openings. Therefore, from the standpoint of stress relief, one can speak of an optimal cell length, such that cells are long enough to undergo robust self-organization, and yet short enough to avoid increased stress at the exits from a confined space, and potential blockage of cell escape. It can be proposed that these constraints on cell shape, in addition to the potential importance of elongated cell shape for cell motility and other functional responses [23], might have contributed to the evolutionary pressure defining the aspect ratios of cells in many extant bacterial species, in particular those that have morphology similar to E. coli and form biofilms.

The second advantage of anisotropic colony organization is the reduction of the tortuosity of the intercellular spaces progressively enhancing the diffusion of nutrients into the colony. Efficient diffusive transport of nutrients and metabolites is an important determinant of the well-being of bacterial cells within the bulk of the colony, ensuring sufficient energy supply for cell division and other functions. A corollary of this finding is that signal molecules might also diffuse more easily along the flow lines formed by the cells, thus introducing anisotropy into cell-cell communication, e.g., through quorum sensing.

Our findings provide a fresh perspective on possible mechanisms of emergence of the structurally complex biofilms and other types of multicellular super-structures. Although the order inherent in biofilms is clearly shaped by a complex interplay of multiple processes, including intercellular signaling [24] and regulated migration of cell sub-populations within the developing and differentiating colonies [25], this order and the chances of survival of bacterial biofilms might critically depend on the initial self-organization of cells during their anchorage and expansion within small cavities and other niches in complex growth substrata. The complex mechanical interactions between cells themselves and between cells and physical boundaries confining them, determined in large part by cell morphologies, can help create patterns of extensive organization and enhanced chemical transport, which can lay the foundation of complex functional multicellular ensembles. The understanding of these processes might help control biofilm growth, and ultimately facilitate treatment of the related diseases.

Finally, we note that the microchamber device presented here provides a convenient and effective way to observe bacterial cells over multiple generations and track the evolution of a colony at single-cell resolution. It enabled us to observe the individual cellular response in both fluorescence and phase-contrast microscopic settings. We envision that the flexibility of design and convenience of use will make this type of devices a platform of choice for many scientific and biotechnological applications.

Methods

Details on strain construction and growth conditions are presented in the Protocol S1. Epi-fluorescence imaging of GFP expression is described in the Protocol S1. Design and fabrication of the microfluidic device are included in the Protocol S1.

Image analysis.

In our study, we defined the “orientation� of a cell as the angle that the cell forms with respect to the x-axis of the Cartesian coordinates of each image (inset in Figure 2B). Its range is [0°, 180°]. The custom software package to determine the cell orientations was developed and implemented in Matlab 7.0.0., including the image-processing toolbox. Time-lapse fluorescence images in the 16-bit TIFF format indexed by location and time stamps were used as the input. In the package, two different routines were applied to find the orientation of individual cells. (Gradient analysis and Major axis analysis; see Protocol S1 for a detailed description).

Modeling.

Individual cells are explicitly modeled as separate agents and are assumed to have an area enclosed by two semi-circles attached to opposite sides of a rectangle of constant width but variable length. Positions and lengths of the cells are defined by two generalized coordinates designating the centers of the semi-circles attached to the rectangle. The dynamics of the colonies is considered to be dominated by viscous friction, with velocity rather than acceleration being proportional to the force. See Protocol S1 and Videos S17 and S18 for details of the model set-up and simulations.

Supporting Information

Figure S1. A Representative Map of the Plasmid pJWP01S Used for Visualization of lux Operon Expression pPROBE-gfp(tagless) with luxR-luxbox-P_luxI Inserted into the EcoRI-KpnI Sites of Multiple Cloning Site.

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Figure S2. Two Different Approaches for Analyzing the Cell Directions in the Colony

(A) The major axis analysis consists of several steps: (Left) start with the raw image; (Middle) find the local maxima (blue) and short axes (green lines); (Right) connect the short axes to the long axes and filter out the wrong axes to generate the final major axis (yellow lines).

(B) The gradient analysis. (Left) Compute the gradient of the image; (Middle) threshold the norm of the gradient; (Right) calculate the angle of the gradient with respect to the y-axis to determine the principal orientations of cells.

(C) Histograms of cell orientations based on two analyses show similar distributions.

(2.8 MB TIFF)

Figure S3. Quantification of Cell Outflow from the RIR Chamber

(A) Quantification of the flow of cells from the RIR chamber toward an exit in a densely packed colony. Three consecutive time intervals were selected, all at the stage of the steady-state colony growth. For each time interval, 10 individual cells were chosen from the inner side of one of the green-shaded regions in the chamber shown in the inset (closer to the center of the chamber), and their positions on consecutive fluorescence images were manually tracked every 5 min. After 1 h, most of the cells were found at the outer side of the region (closer to the exit of the chamber). A typical trajectory of the cells is indicated by the arrow in the inset. The mean distance traveled by cells from their initial positions is shown as a function of time. The error bars indicate standard deviation. Each plot was fitted to a quadratic curve. The pair-wise difference among the three fits was not significant (p-values of <0.05 were considered significant; F-test). The mean velocity of the escaping cells is a measure of the rate of colony growth in the corresponding time interval.

(B) The simulated flow stream lines (arrows) and pressure distribution (color-coded) inside the RIR chamber and rhombus chamber filled with a Newtonian fluid with spatially uniform source term, corresponding to a uniform and steady cell proliferation.

(4.7 MB TIFF)

Figure S4. Colony Expansion with No Confining Boundaries

(A) Comparison of simulation and experimental results of colony growth with no boundaries. Scale bar is 12μm.

(B) Distributions of cell orientations from the final stage of the simulation and the experiment.

(3.3 MB TIFF)

Figure S5. The Effect of Internal Boundaries in Microchambers on Colony Organization

The external boundaries of all chambers are identical and have a shape of a square, whereas the internal boundaries have different shapes. Representative examples and enlarged views of selected regions, a and b, are shown. The internal geometries are (1) rhombus; (2) circle; (3) square; (4) “equality sign�; and (5) no internal boundary.

(A) An enlarged view of cell escape points (the exit of chambers). The cells facing the bottom exits (boxes 'a' in panels 1–4), which are situated in the separation areas between fluxes from the right and left of the exits, are found to be less fluorescent than cell in the surrounding regions. This is likely because cells in the separation area do not arrive from internal regions of the chamber, but rather grow and divide in relative proximity of the exit. In contrast, the fluorescence in the “flux� areas reflects the history of exposure of cells to lower glucose concentrations in more internal regions of the chambers. This effect becomes increasingly pronounced from panel 1 to panel 4, as the variations in the shape of the internal boundary facing the exit (from a pointed apex of a rhombus, to a circle, to a square, to a horizontal line on top of two exits) create increasingly wide separation areas.

(B) The orientation of the internal boundaries strongly influences the direction of orientation of cells in the colony. Notice that in the case of the “equality sign� (panel 4), the horizontal orientation of the internal boundaries imposes horizontal orientation on cells in the middle of the chamber, whereas when no internal boundaries are present (panel 5), the cell orientation is vertical. Scale bars: 50 μm, upper panels; 20 μm, panels (a) and (b). For examples of cell orientations in chambers of other geometries, please consult the Levchenko lab website: http://rd.plos.org/pbio.0050302.

Acknowledgments

We thank Alexander van Oudenaarden (MIT) for his donation of a plasmid used in the study.

Author contributions. HC, HJ, AG, and AL designed research. HC, HJ, PM, and AL performed the experiments and simulations. KC, AL and AG designed and fabricated the microfluidic devices. JWW, BJ, and AMS contributed new reagents/analysis tools. HC, HJ, PM, and AL analyzed data. HC, HJ, PM, AG, and AL wrote the paper.

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All

Water

In some bacterial communities, individuals can send chemical messages to other members to encourage them to kill themselves, speculatively so that a fraction of the population under stress sacrifices itself to provide nutrients for the survival of group; to protect against spread of bacterial viruses infecting the group; or, to preserve the group's genetic integrity.^[23]

In common usage 'water' refers to the liquid substance that makes up the bulk of the oceans, lakes and rivers, the liquid that we and other animals, and plants, must take into our bodies to keep them living, and the liquid we use to wash our bodies and our clothes and put out fires. We learn early in life that we can transform liquid water into a solid water — ice — by 'freezing' it, and into a gas — steam, water vapor — by boiling it or allowing it to evaporate, and we come to realize that such transformations occur in naturally, accounting for glaciers, icy roads, and humid weather.

To scientists, 'water' refers to a particular molecule, and to collections of that molecule, each molecule consisting of the binding together in a particular way the atoms of two of the ninety-two naturally occurring chemical elements, oxygen and hydrogen — two hydrogen atoms binding to one oxygen atom per water molecule. A scientist specializing in a particular discipline (e.g., physics, chemistry, geology, biology) study, describe and/or apply characteristics of water particular her discipline.

This article approaches those particulars in a multi-disciplinary, cross-disciplinary and interdisciplinary way.

The earth sciences perspective

Among the many subjects dealt with by the earth sciences, water presents itself as a major focus and challenge. In its broadest focus it deals with the distribution and masses of water on Earth. 'Oceanography' deals with water in the oceans; 'hydrology', with water on land and underground; 'meterology', with the characteristics of water in the Earth's atmosphere; 'glaciology', with water as glaciers and polar ice; 'climatology', with the role of water in Earth's climate. Earth scientists also study and teach about the history of water in Earth's history as a planet, and unavoidably, about the possibility of water elsewhere in the Universe.

Water is one of the Earth's basic naturally occurring substances. It covers about 70% of the world's surface…

The biology perspective

Other views

The word "water" itself is practically synonymous with the word "liquid", as we refer to different liquids as water-like: "watered down", or "watery". We know that water moves and flows and is a force; to come across another liquid which visibly resembled water with an unknown chemical makeup, we might infer that it is water but would not know until more evidence was discovered.

Uses

The availability of water on the Earth affords humanity an incredible number of uses, aside from consumption as an integral part of survival. Water can be used to cool machinery and facilities such as nuclear power plants and industrial milling tools. Sometimes isotopes of hydrogen are used for that purpose: Deuterium, which is also known as "heavy water". For obvious reasons not the radioactive Tritium, the third isotope of Hydrogen. Water can also be heated to generate power--the focus of the steam engine which was born out of the industrial revolution, and hydroelectric dams which use water flow and gravity to turn turbines and rotors to generate electricity. Water can also be pressurized, creating a narrow stream that can cut through concrete and steel.

MyWord

3D model of a water molecule showing the relative sizes and positions of the constituent atoms.

Word

Balancing Robustness and Evolvability

Richard E. Lenski, Jeffrey E. Barrick, Charles Ofria

Funding. Our research in this area is supported by DARPA grant 344-4065. Competing interests. The authors have declared that no competing interests exist. Citation: Lenski RE, Barrick JE, Ofria C (2006) Balancing Robustness and Evolvability. PLoS Biol 4(12): e428 doi:10.1371/journal.pbio.0040428 Published: December 12, 2006 Copyright: © 2006 Lenski et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Richard E. Lenski is Professor in the Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, Michigan, United States. Jeffrey E. Barrick is Postdoctoral Fellow in the same department. Charles Ofria is Assistant Professor, Department of Computer Science and Engineering, Michigan State University, East Lansing, Michigan, United States.

* To whom correspondence should be addressed. E-mail: lenski@msu.edu

Series Editor: Simon Levin, Princeton University, United States of America

One of the most important features of biology is the ability of organisms to persist in the face of changing conditions. Consider the remarkable fact that every organism alive today is the product of billions of generations in which its progenitors, without fail, managed to produce progeny that survived to reproduce. To achieve this consistency, organisms must have a balance between robustness and evolvability, that is, between resisting and allowing change in their own internal states #journal-pbio-0040428-b001 1–3. Moreover, they must achieve this balance on multiple time scales, including physiological responses to changes over an individual life and evolutionary responses, in which a population of genomes continually updates its encoded information about past environments and how future generations should respond given that record.

Examples of robust biological systems are found at many scales, from biochemical to ecological. At each scale, robustness may reflect the properties of individual elements or, alternatively, the dynamic feedbacks between interacting elements. The expression of some metabolic function, for example, may be robust in the face of temperature change, because an enzyme maintains its shape and specificity across a range of temperatures or because an interconnected network of reactions sustains the supply of product, even when some enzyme fails. A genome may be robust because it encodes proofreading and repair systems that reduce replication errors or because it is organized such that many mutations have little effect on its phenotype. An ecosystem might be robust if it resists the extinction of some keystone species or, if extinction does occur, because surviving species can compensate over physiological, demographic, or evolutionary time scales.

One important question is whether there exists a single unifying mathematical framework that can encompass such diverse examples of biological robustness. Might new insights come from such a conceptual unification, or will future understanding require detailed analyses of specific cases? Across the different scales, recurring mechanisms for achieving robustness—including redundancy of component parts and negative feedbacks—might serve as organizing principles. Yet, similarities in mechanism could mask important differences in the evolutionary origins of those mechanisms. At the level of genes in genomes or of cells in multicellular organisms, it is reasonable to suggest that redundancy evolved by natural selection to maintain some functional capacity in the face of perturbation #journal-pbio-0040428-b004 4. But whereas species redundancy could also be critical for robustness of ecosystem functions, differences in redundancy might be an emergent property rather than an ecosystem-level adaptation, because selection generally acts at lower levels (but see #journal-pbio-0040428-b005 5 for another view).

And if robustness has evolved to maintain performance, what prevents systems from becoming ever more robust? We will focus on genomic robustness to mutations, because it provides a concrete example, although many ideas are speculative and much work is needed to formalize and test them. Two mechanisms that could make a genome more robust are genetic redundancy, so that many otherwise deleterious mutations are masked, and proofreading during replication, so that fewer mutations occur. Redundancy imposes a cost of replicating the additional gene copies #journal-pbio-0040428-b006 6, whereas proofreading entails costs of encoding and expressing that function #journal-pbio-0040428-b007 7.

Mutational robustness can also arise in more subtle ways. Populations evolving at high mutation rates may settle in regions of genotypic space where mutations are less deleterious, on average, than those regions that attract populations that experience low mutation rates. The idea is that evolution at low mutation rates favors populations that achieve high fitness peaks, even if they are surrounded by steep cliffs, because mutations that push progeny off those cliffs are rare. By contrast, at high mutation rates, most offspring carry mutations, and selection favors populations that find lower fitness peaks surrounded by less precipitous mutational chasms. Experiments with digital organisms (self-replicating computer programs) provide direct support for “survival of the flattest” at high mutation rates #journal-pbio-0040428-b008 8. RNA viruses also have very high mutation rates, and a recent experiment implicated the importance of mutational robustness for them, in this case, by showing the loss of robustness in viruses that evolved at high multiplicities of infection, where co-infecting particles guaranteed redundancy and allowed their native robustness to decay #journal-pbio-0040428-b009 9.

But generalizing to other organisms presents some difficulties. The strength of selection for robustness should be weaker in larger genomes if the advantage to a mutation that increases robustness locally is correspondingly smaller. According to one alternate hypothesis, mutational robustness is not so much a directly evolved property as it is a correlated benefit of selection for robustness in the face of variable environments #journal-pbio-0040428-b010 10. The essential ideas here are that environmental change is a pervasive feature of nature, and those physiological mechanisms that allow organisms to adjust to changing environments, such as by regulating gene expression, will also compensate for the effects of many mutations #journal-pbio-0040428-b003 3. Robustness might also evolve to minimize internal noise in biochemical systems. The genetic code itself, once viewed as a frozen accident from the early history of life, has been shown to be remarkably well designed for minimizing the production of proteins that, owing to translational errors, have the amino acids most likely to disrupt protein function #journal-pbio-0040428-b011 11. Individual proteins, too, have been strongly selected for robustness to translational errors #journal-pbio-0040428-b012 12.

Two recent studies with evolving computational systems have shown, unexpectedly, that sexual reproduction promotes the evolution of mutational robustness [[#journal-pbio-0040428-b013 13],[#journal-pbio-0040428-b014 14]]. The evolutionary value of sex is a fascinating old problem. According to one hypothesis, the advantage of sex depends on negative interactions between deleterious mutations, such that two mutations combined tend to be worse, on average, than expected from their individual effects #journal-pbio-0040428-b015 15. In that case, sex helps to purge them and provides a kind of robustness to multiple mutations. But these new studies found that sexual populations became more robust, on average, to the effects of single mutations, even though they evolved at the same mutation rate as asexual controls. Sex bombards genomes with mutant alleles that arose in other genetic backgrounds, which evidently promotes a kind of “survival of the flattest” similar to that seen at high mutation rates.

Another important issue revolves around the tension between robustness and evolvability. Are genomes that are more robust to mutations less evolvable in the face of changing environments? In other words, does canalizing the phenotype to minimize perturbations—including biochemical and environmental as well as mutational—lead to an evolutionary conservatism that inhibits the discovery of new adaptive solutions? Some mechanisms of robustness, such as proofreading and repair, must inhibit evolvability because they reduce the production of new beneficial mutations. But are robustness and evolvability inversely correlated more generally? In the case of redundancy, the presence of multiple gene copies might mask the beneficial effects of some new mutations, thus suppressing evolvability. But redundancy can also promote adaptation by allowing duplicated genes to evolve distinct functions [[#journal-pbio-0040428-b016 16],[#journal-pbio-0040428-b017 17]].

Evolving populations can also become robust by finding regions of genotypic space that are flat because they contain a high proportion of neutral mutations #journal-pbio-0040428-b018 18. As shown schematically for RNA secondary structures in [#journal-pbio-0040428-g001 Figure 1], the resulting neutral network might provide evolutionary paths to new adaptations by random drift, in effect allowing populations to search wider regions of genotypic space for rare beneficial mutations #journal-pbio-0040428-b019 19. If so, robustness and evolvability might again be positively, rather than negatively, correlated. However, deleterious mutations can also serve as stepping stones to adaptations #journal-pbio-0040428-b020 20. Although deleterious mutations tend to be removed by selection and have shorter half-lives than neutral mutations, they are not instantly eliminated. Moreover, deleterious mutations may lead to genetic neighborhoods that are more promising, from the perspective of adaptation, than neutral mutations. In other words, neutral mutations are neutral precisely because they are isolated from important phenotypes, whereas deleterious ones must be connected to phenotypes that matter for fitness. It is unclear, therefore, whether neutral or deleterious mutations are more important for evolvability, and whether robustness associated with increased neutrality will promote or impede evolvability.

Theoretical population genetics has historically emphasized models with one or two loci, whereas quantitative genetics has relied on a sort of statistical mechanics that ignores underlying detail. Richer mathematical representations of genotypic spaces and fitness landscapes may be required to understand the balance between robustness and evolvability. Meanwhile, empiricists must push ahead to obtain data about evolvability and robustness. Experimental evolution, in which populations are monitored while they evolve under defined conditions, offers the potential to observe changes in these properties as a function of environmental and genetic manipulations #journal-pbio-0040428-b021 21. For example, one could ask how robustness and evolvability change depending on whether evolution occurs in constant or variable environments #journal-pbio-0040428-b022 22. Or one might instead manipulate an organism's regulatory networks to investigate how that affects these properties. As new insights are achieved into the tension between genomic robustness and evolvability, perhaps the findings can inform investigations into robustness at other levels, from cells to ecosystems, as biologists seek to understand the constancy of change.

Acknowledgments

This essay has benefited from discussions with many colleagues including Chris Adami, Michael Deem, Santiago Elena, Simon Levin, Dule Misevic, Paul Sniegowski, Claus Wilke, David Sloan Wilson, Ned Wingreen, and Bob Woods.

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Self-organization

In living systems, self-organization 'emerges' spontaneously as a manifestation of the interactions among the systems' components. In cells, self-organization emerges in part from so-called supramolecular (non-covalent) interactions of proteins with proteins and other molecules.^[24] [25] The proteins make their appearance through a genetic transcription-translation machinery, which itself represents a self-organized molecular machine that emerges in part from the non-covalent interactions of proteins and and nucleic acids and other molecules.

Molecules interact by forming and breaking strong or weak covalent bonds, and also through weaker, quasi-stable non-covalent electromagnetic intermolecular interactions, like hydrogen bonding and van der Waals' forces. Those supramolecular interactions, and the flexibility of bond formation and breaking by weak covalent bonds, self-assemble aggregates of molecules (e.g., organelles, networks), giving them the physical properties that enable many biological processes.^{[25] [26] [27] [28]}

The qualifier that self-organization emerges in part from supramolecular (non-covalent) interactions of proteins with proteins and other molecules reflects the need to invoke not only supramolecular self-assembly but also evolutionary mechanisms of producing and selecting genes that yield proteins whose properties enable interactions that tend to optimize functional self-organization — in other words, adaption. One must also invoke local real-time selective processes that confer stability and appropriate functionality to self-assembly, called homeostasis or adaptability. Self-organization and adaptability conjoin to yield function.^[29]

Professor of Microbiology, Franklin M. Harold, offers the following definition of self-organization:

For the purposes of cell biology, let me define self-organization as the emergence of supramolecular order from the interactions among numerous molecules that obey only local rules, without reference to an external template or global plan...The definition explicitly excludes order imposed by an external template, whether physical (as in a photocopier) or genetic (as in the specification of an amino acid sequence by a sequence of nucleotides)...The structure of the self-assembled complex is wholly specified by the structures of its parts and is therefore implicit in the genes that specify those parts: natural selection crafted those genes to specify parts that assemble into a functional complex.^[30]

Information resides in proteins and other molecules in virtue of their structure, and through them information flows through cells, just as energy does, and determines their organizational nature.^[31]

One way to understand self-organization in a living system is to view the system as a 'computing device'. The inherited and acquired information base of the system specifies the components of the system, which interact to arrange themselves into functional networks spontaneously in accord with their physico-chemical properties — i.e., they 'compute' the system in a complex chemical reaction . Yet that description alone under-characterizes the functional complexity of the system as a 'computing device'. In a multicellular organism, each cell (or each cell type at least) retrieves only its own particular pieces of information from the total information base, and the selection varies with time. Each cell system must perform specific computations to effect that dynamic activity. The behavior of the system's functional networks, again acting only as physico-chemical processes, constitute those specific dynamic computations. The apparent circularity begat by adding that further characterization of the system as a 'computing device' exemplifies two-way nature of the 'computations' self-organizing the living system. With the tinkering and discovering comprising local trial-and-error and evolution’s handiwork, that 'circularity' carries out ('computes') integrative functions not explicitly encoded in the inherited and acquired information base of the system.^[32]

The molecular biologist Sidney Brenner^[33] expressed the 'computing device' metaphor this way:

...biological systems can be viewed as special computing devices. This view emerges from considerations of how information is stored in and retrieved from the genes. Genes can only specify the properties of the proteins they code for, and any integrative properties of the system must be 'computed' by their interactions. This provides a framework for analysis by simulation and sets practical bounds on what can be achieved by reductionist models.^[34]

The patterns of structure and behavior in self-organized systems need no behind-the-scene 'master controller', and no prepared recipes, blueprints or templates that specify the structure and dynamics of the system. Instead, they emerge from interactions among the naturally generated and naturally selected components of a system, dictated by their physico-chemical properties, and dynamically modified by the emergent organization, which is itself modified by the environment. Thus the single-celled zygote self-organizes into a multicellular living system as genetically encoded proteins interact, responding to changing influences from the changing environment generated by growing multicellularity — becoming a network of many cell-types working cooperatively.

That biological systems self-organize has led one prominent biologist to say they are products of a "blind watchmaker".^[35]

Self-organization tends to breed greater complexity of self-organization. One important aspect of self-organization in cells rests on the tendency for lipid molecules with polar (water-loving) and non-polar (water-shunning) ends to line up side-by-side to form bilayers in an aqueous solution, each unit of the bilayer with two lipid non-polar ends mutually attracted in the center and the polar ends surrounded by water. Membranes thereby form. Protein molecules can span the bilayer membrane, or selectively straddle only one or the other side of the membrane and its aqueous surrounding, according to their specific amino-acid sequence and side-groups. Those lipid-protein membranes allow cells to communicate with other cells, either in free-living cellular communities or in multicellular organisms, and those communication activities self-organize by virtue of the properties of the cells, generated by natural experiments and selected for fitness by evolutionary mechanisms, and subject to downward effects by the systems' organization and environmental influences on the systems.

Self-organization occurs on all levels of living systems. For example, the dynamics of communities, such as the feeding relationships within communities of large mammalian species, also reflect self-organization. The animals and components of the ecosystem embedding them self-organize, resulting in "...unitary structures with coherent properties...[that] can operate in an integrated way, which allows for the acceptance of their changes on large time-scales as evolutionary."^[36]

Further elaborating the descriptions of living systems beyond the thermodynamic and evolutionary perspectives, we might say that:

Specializations

Thoughts on what is life (Sebastian)

The perennial question, 'what is life?, has aged well and remains vigorous in the early 21st century.^[37]  Yet what exactly the questioner seeks to know in asking that question she often does not make clear. In trying give an answer to the question, one soon discovers the remarkable linguistic adaptability that the word ‘life’ enjoys. We use it to express myriad distinct meanings, called ‘senses’ of the word. Indeed, the Oxford English Dictionary lists fifteen senses of ‘life’,^[38] many of which include multiple sub-senses, or nuances, yielding more than two dozen ways to use the word. What then do we gain by inquiring what life is unless we specify in what sense we use the word?

anthronet test

• Anthropology on the World Wide Web

• From the website: “The Anthro.Net database contains thousands of reviewed web sites and bibliographic references. On the World Wide Web there are an estimated 250,000 sites that have content relating to the subject matter of anthropology. Unfortunately an estimated four-fifths contain little useful information…Anthro.Net cuts through all of this by using advanced search technology to hunt down sites that contain useful content and information relating to anthropology…Anthro.Net queries a database of over 40,000 pages from reviewed web sites with anthropological content built by users' interests. The system collects the search terms submitted by its users and uses proprietary software to hunt down internet based journal articles, well developed topical sites and bibliographic references for anthropology, archaeology and the other social sciences. Anthro.Net uses a spider or robot program to check for outdated and dead links. The site contains dynamically generated news and anthropology features updated around the clock. Anthro.Net is dedicated to the study of anthropology and archaeology.”

test

xxx^{[39]  [40]}

Epigraph 7

At first glance, life and the laws of thermodynamics seem to be at loggerheads. Most glaringly, the second law states that over time, any system will tend to the maximum level of entropy, meaning the minimum level of order and useful energy. Open a bottle of perfume in a closed room, and eventually the pool of scent [in the bottle] will become a smelly cloud [in the room]. Organisms do their damnedest to avoid the smelly cloud of equilibrium, otherwise known as death, and a common argument of anti-evolutionists is that the universe's tendency toward disorder means that natural selection cannot make living things more complex. The usual counter to this argument is that organisms maintain internal order and build complexity by exporting entropy—importing energy in one form, and radiating it out in another, higher-entropy form. One of the first physicists to ponder these questions, Erwin Schrödinger, described food as negative entropy: “The essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive.” ^[43] [44]

• Darwinian selection….isn't the only thing that can create order.

But recently, some physicists have gone beyond this and argued that living things belong to a whole class of complex and orderly systems that exist not despite the second law of thermodynamics, but because of it. They argue that our view of evolution, and of life itself, should likewise be based in thermodynamics and what these physical laws say about flows of energy and matter. Darwinian selection, these researchers point out, isn't the only thing that can create order. Throughout the universe, the interaction of energy and matter brings regular structures—be they stars, crystals, eddies in fluids, or weather systems in atmospheres—into being. Living things are the most complex and orderly systems known; could they be part of the same phenomenon? And could the process that brings them about—natural selection, driven by competition between organisms—be ultimately explicable in thermodynamic terms?

Eric Smith, a theoretical physicist at the Santa Fe Institute in New Mexico, certainly thinks so. “Darwinian competition and selection are not unique processes,” he says. “They're a complicated version of more fundamental chemical competitive exclusion.” In a paper published last year ^[45], Smith and his colleagues argued that natural selection is a highly sophisticated version of a physical process called self-organization, the still poorly understood means by which energy plus matter can equal order.

Survival of the Likeliest? — Using the laws of thermodynamics to explain natural selection — and life itself — 2007 Essay from PLoS Biology, by John Whitfield

About this article:^[46]

At first glance, life and the laws of thermodynamics seem to be at loggerheads. Most glaringly, the second law states that over time, any system will tend to the maximum level of entropy, meaning the minimum level of order and useful energy. Open a bottle of perfume in a closed room, and eventually the pool of scent [in the bottle] will become a smelly cloud [in the room]. Organisms do their damnedest to avoid the smelly cloud of equilibrium, otherwise known as death, and a common argument of anti-evolutionists is that the universe's tendency toward disorder means that natural selection cannot make living things more complex. The usual counter to this argument is that organisms maintain internal order and build complexity by exporting entropy—importing energy in one form, and radiating it out in another, higher-entropy form. One of the first physicists to ponder these questions, Erwin Schrödinger, described food as negative entropy: “The essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive.” ^[43] [47]

• Darwinian selection….isn't the only thing that can create order.

But recently, some physicists have gone beyond this and argued that living things belong to a whole class of complex and orderly systems that exist not despite the second law of thermodynamics, but because of it. They argue that our view of evolution, and of life itself, should likewise be based in thermodynamics and what these physical laws say about flows of energy and matter. Darwinian selection, these researchers point out, isn't the only thing that can create order. Throughout the universe, the interaction of energy and matter brings regular structures—be they stars, crystals, eddies in fluids, or weather systems in atmospheres—into being. Living things are the most complex and orderly systems known; could they be part of the same phenomenon? And could the process that brings them about—natural selection, driven by competition between organisms—be ultimately explicable in thermodynamic terms?

Eric Smith, a theoretical physicist at the Santa Fe Institute in New Mexico, certainly thinks so. “Darwinian competition and selection are not unique processes,” he says. “They're a complicated version of more fundamental chemical competitive exclusion.” In a paper published last year ^[45], Smith and his colleagues argued that natural selection is a highly sophisticated version of a physical process called self-organization, the still poorly understood means by which energy plus matter can equal order.

Such orderly, self-organized systems are like engines designed to level out energy gradients—while they persist, they produce more entropy, more quickly, than a disordered mishmash of molecules. Weather systems, for example, transport heat from the tropics toward the poles far more quickly than a homogeneous, static atmosphere would. Life does the same thing, Smith points out. Indeed, he believes that this might have been the reason for its origin—that, under the conditions on early Earth, life was the best way to release the build-up of geothermal energy and an inevitable consequence of that energy^[41]. Once biochemistry had got going, subsequent chemical and Darwinian selection would each favor the systems best at dissipating Earth's pent-up energy, whether geothermal or, following the invention of photosynthesis, solar.

It has long been suggested that self-organized systems do not just level out energy gradients more quickly than disordered ones do, they do it as quickly as possible. Models that assume maximum entropy production (MEP) make good predictions about the climates of Earth^[48] and Saturn's moon Titan^[49] and about the growth of crystals in solutions^[50]. But until recently, MEP was just an assumption—there was no mechanism or theory to explain why such systems should tend to this state. Classical thermodynamics is no help— it explains entropy only in closed systems, with no energy going in or coming out. It says nothing about how much entropy open, nonequilibrium systems, such as organisms, ought to produce.

• In physics, to speak of natural selection is to ask, among all possible states, which is the one that nature selects.

Roderick Dewar, a theoretical physicist and ecosystem modeler working at the French agricultural research agency's centre in Bordeaux, believes he has crossed this hurdle. Using information theory, a branch of mathematics that can reformulate the laws of thermodynamics (see the text box: Entropy), Dewar has shown that MEP is the most probable behavior of an open, nonequilibrium system made up of many interacting elements, provided that system is free to “choose” its state and not subject to any strong external forces^[51]. The large-scale state of MEP represents the largest proportion of the countless possible arrangements of the system's microscopic parts, regardless of what those parts are up to.

Natural selection in biology could work the same way, Dewar thinks: “In physics, to speak of natural selection is to ask, among all possible states, which is the one that nature selects.” This, he points out, is a question of probability. “The state that nature selects is the one that can be realized in more ways than any other. Biologists don't think like that, but I want to entertain the hypothesis that natural selection in biology works the same way, and see where that gets us.”^[52]

Adding life to physical systems certainly increases [net] entropy production. A pond full of plankton or a patch of grass absorbs more of the Sun's energy, and so produces more entropy, than a sterile pool or bare rock. Earth turns sunlight into microwave radiation, closer to equilibrium with the background glow of the Universe, more efficiently than either Mars or Venus. Ecological processes such as succession, where a grassland becomes a forest, also increase entropy production (Figure 1). And over evolutionary time, organisms tend to get better at grabbing energy—witness our own species, which now uses about 40% of the energy in sunlight, and is busy releasing the energy trapped in fossil fuels and converting it into entropy. But can such processes be explained as part of a tendency towards maximum entropy production, rather than a Darwinian competition to leave descendents?

• The key question is whether living things are really free to arrive at a state of MEP, or whether natural selection is precisely the sort of force that can override such a process?

Figure 1. Entropy and biodiversity are mathematically equivalent, making tropical forests the most entropic [entropy exporting] environments on Earth. Photograph: John Whitfield. From: Whitfield J (2007) Survival of the Likeliest? PLoS Biol 5(5):e142. Published: May 15, 2007.

It seems odd that natural selection could be not survival of the fittest, but arrival at the likeliest, but Dewar thinks just that. Recently, for example, he and his colleagues showed that the structure and workings of the ATP synthase enzyme are predictable using MEP theory^[53] — that being an efficient generator of cellular fuel and an efficient leveler of energy gradients are one and the same. In general, Dewar wants to show that biological processes that maximize the rate at which energy is captured, or chemicals transported from one spot to another can be explained from the viewpoint of statistical mechanics—the area of physics that explains how predictable behavior emerges from large groups of unpredictable elements. “Statistical theory would say that the molecules choose the state of maximum flux because that is the most probable way for the molecules in the system to arrange themselves,” says Dewar. “Perhaps they're selecting that state simply because it's the most probable one.” And unlike the conventional view of evolution, this approach allows one to make quantitative predictions of how living things should work. “Darwinian selection is a hypothesis that's quite difficult to quantify,” says Dewar. “It doesn't really come up with numbers.”

A few biologists are beginning to use MEP. “Dewar's proof is brilliant and potentially of enormous consequence for many areas of science,” says ecologist John Harte of the University of California, Berkeley. One such area could be ecology, he adds: “Very preliminary initial explorations of its implications for understanding food webs, material and energy allocation within organisms, and climate-ecosystem interactions are encouraging.”

Another physicist trying to use thermodynamics to predict the details of biological structures is Adrian Bejan, an engineer at Duke University in Durham, North Carolina. Rather than thinking about a system's microscopic elements, Bejan has devised what he calls the “constructal law” ^[54] — a description of how energy and matter flow in physical networks such as river basins and biological networks such as blood vessels. Bejan's constructal law states that for a flow system to persist (i.e., live), it must over time provide easier access to the currents that flow through it—it must come to do more with less, in other words. In the process, it minimizes the amount of fuel used and maximizes the amount of entropy produced for each unit of fuel burnt.

Evolution, Bejan believes, has been a process whereby structures have remodeled themselves so that energy and matter flow through them as quickly and efficiently as possible10^[55]. Better flow structures—be they animals or river networks—have replaced poorer. This, says Bejan, is a second arrow of time to set alongside the second law's drive towards disorder. The patterns of animal locomotion, he has argued, in particular how animals' stride or flapping frequency changes with body size, is such that animals flow over the surface of Earth as easily as possible^[56]. “Given the freedom to morph, a flow system will renew itself to construct easier flow structures,” says Bejan. “The way that animal mass flows over the earth follows the same principle as the way the water of the Amazon flows across the landscape.”

Figure 2. If processes underlying life are explained as a tendency towards maximum entropy production, systems such as galaxies and hurricanes might be described as alive. (A) Three dimensional cloud-top image of Hurricane Diana as it was strengthening from a Category III storm to a Category IV storm. Publication of the National Oceanic and Atmospheric Administration (NOAA), NOAA Central Library (Image ID: spac0289, NOAA in Space Collection). (B). The colorful demise of a sun-like star. [Photo credit: NASA, ESA, and K. Noll (STScI); acknowledgment: The Hubble Heritage Team (STScI/AURA)]. From: Whitfield J (2007) Survival of the Likeliest? PLoS Biol 5(5):e142. Published: May 15, 2007.

Dewar is not so sure, arguing that the constructal law deals with phenomena, rather than causes. “Rather than explaining why systems should adopt optimal behaviors, Bejan proposes that they do, and then shows that this is realistic,” he says. “It's not very clear what is being maximized—it seems to be anything he can think of.” For his part, Bejan thinks that Dewar's focus on a system's smallest elements is unnecessary: “One doesn't need to go into the microscopic to account for the macroscopic.”

• The patterns of animal locomotion… is such that animals flow over the surface of the earth as easily as possible.

Besides these differences among physicists, many biologists, not surprisingly, resist attempts to colonize their discipline. The late Ernst Mayr argued that processes such as reproduction, natural selection, and inheritance have no equivalence in, and are not reducible to, physics, and that biology should be seen as an autonomous science, separate and equal^[57]. (Although not everyone in the pantheon of biology thought this way: Francis Crick wrote that the “ultimate aim” of biology should be to explain itself in terms of chemistry and physics^[58].)

Lloyd Demetrius, a mathematical biologist at Harvard University, is certainly no physics-phobe. Taking the statistical mechanics–based approach of treating organisms as if they were molecules in a gas, he has formulated a quantity that he calls “evolutionary entropy”.^[59] This is mathematically equivalent to thermodynamic entropy, but instead of physical disorder, it describes the age range over which an organism reproduces. Over long periods of evolution, Demetrius expects natural selection to increase this, because organisms that can reproduce over a longer period are better at dealing with limited resources and unpredictable environments.

But evolutionary entropy is not maximized in Demetrius' models, nor does it inevitably increase through time. There are, he says, fundamental differences between thermodynamic processes and natural selection, and biological and physical selection become one only at the molecular level. Any more complicated living system is subject to forces that do not operate in purely physical systems. “In an evolutionary process you have analogues to physical laws, but the mechanisms are quite different,” says Demetrius. “As you go from molecules to cells and higher organisms, selection involves replication, and there's no replication in physics. It's what distinguishes the living from the dead.”

• Perhaps in another hundred years, no one will think that we need one set of theories for biology and another for physics.

For the physicists struck by the parallels between self-organized and living systems, however, even this distinction is not as clear-cut as it might seem. “There's a continuum between life and non-life, and the black and white distinction between the two has to be minimized,” says Charles Lineweaver, an astronomer and astrobiologist at the Australian National University in Canberra.

Lineweaver has proposed a category of objects that he calls “far from equilibrium dissipative systems,” which includes all systems that dissipate energy in the process of maintaining themselves in an ordered, non-equilibrium state—including galaxies and hurricanes, as well as plants and animals (Figure 2). It's possible, he believes, that all such systems might be usefully described as alive, and that life should be defined in thermodynamic terms. “As a physicist I'm looking for physics-based definitions of life,” says Lineweaver. ”Biologists are unduly myopic when it comes to this.”

Lineweaver also thinks the replication question is a red herring. To think that life has to store the instructions for its reproduction internally is, he says, arbitrary. The formation of stars, he points out, depends on the preceding generation of stars releasing elements and modifying the gravity of their environment. Everything depends on its environment for energy and materials; where the information is stored doesn't matter. “Shifting the definition of life to a thermodynamic, one removes the mystique from life, in the same way that Darwin said: ‘Hey, we're another type of animal’,” Lineweaver says.

One hundred years ago, one of the hottest debates in biology concerned vitalism—whether living things were made from the same chemicals as inanimate matter, and whether they were animated by a “vital force” unique to biological systems, or obeyed the same laws of physics as dead matter. A century on, we know that living things and dead things are made from the same stuff, and subject to the same forces. Perhaps in another hundred years, no one will think that we need one set of theories for biology and another for physics.

“We should definitely look for common principles,” says Dewar. “If such principles exist, we ought to be able to fuse natural selection in biology with natural selection in physics. Animals competing and dying are ultimately molecular processes that take place under the constraints of energy and resources.”

References

Citations and Notes

References

Citations and Notes

Epigraph5

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^[60]

Denis Nobel.^[61]

^[62]

What is life?...'Where is the program of life?'...there is no such program and...there is no privileged level of causality in biological systems. &nbsp-- Denis Nobel D. (2006) The Music of Life: Biology Beyond the Genome. Oxford University Press. ISBN 978-0-19-929573-9 Brief Biography Multiple Chapter Excerpts Online

References

Citations and Notes

Epigraph4

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The other side of the coin: RNA activation

As this article emphasizes, the finding that various small molecules of RNA can inhibit the final expression of genes to generate the proteins they encode introduced a new paradigm in the biology of gene expression regulation. The possibility that the new paradigm will expand to include activation of gene expression by small RNAs now appears on the biological horizon. In November, 2006, Long-Cheng Li and collaborators^[63] reported on several synthetic small, double-stranded RNAs, similar to small interfering RNAs, that activated the expression of human genes (specifically, E-cadherin, p21, and VEGF) — 2 to 10 fold increases in induction, with detection of protein levels — through sequence-specific effects on noncoding regulatory regions in the genes’ promoters. The authors could not identify the exact mechanism of gene expression activation, except to note the involvement of some of the same auxiliary proteins involved in RNA interference.

A subsequent study by another research group also found evidence of gene expression activation by small double-stranded RNA molecules.^[64]

If unequivocally established and mechanistically defined, RNA activation (RNAa) might prove as therapeutically applicable as RNA interference. Detailed expositions of the research results of the above-mentioned scientists, current work in the field, and the implications of RNAa require a separate treatment (see RNA activation)

Epigraph3

Organisms do not maintain their complexity, and become more complex, in a vacuum. Their high organization and low entropy is made up for by pollution, heat, and entropic export to their surroundings.  Eric D. Schneider and Dorion Sagan

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Epigraph2

Share your knowledge. With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from orbit. With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from. With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from. With knowledge, one can do much. ---Dali Lama

Organisms do not maintain their complexity, and become more complex, in a vacuum. Their high organization and low entropy is made up for by pollution, heat, and entropic export to their surroundings.  Eric D. Schneider and Dorion Sagan

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Epigraph

With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from orbit. With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from. With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from. With knowledge, one can do much. I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from.

What Is Life—and How Do We Search for It in Other Worlds?, essay by Chris P. McKay, NASA Ames Research Center

I need a “tricorder”—the convenient, hand-held device featured on Star Trek that can detect life forms even from orbit.^[65] Unfortunately, we don't have a clue how a tricorder might work, since life forms don't seem to have any observable property that distinguishes them from inanimate matter. Furthermore, we lack a definition of life that can guide a search for life outside Earth. How can we find what we can't define? An answer may lie in the observation that life uses a small, discrete set of organic molecules as basic building blocks. On the surface of Europa and in the subsurface of Mars, we can search for alien but analogous patterns in the organics.

Life As We Know It

The obvious diversity of life on Earth overlies a fundamental biochemical and genetic similarity. The three main polymers of biology—the nucleic acids, the proteins, and the polysaccarides—are built from 20 amino acids, five nucleotide bases, and a few sugars, respectively. Together with lipids and fatty acids, these are the main constituents of biomass: the hardware of life (Lehninger 1975, p 21). The DNA and RNA software of life is also common, indicating shared descent (Woese 1987). But with only one example of life—life on Earth—it is not all that surprising that we do not have a fundamental understanding of what life is. We don't know which features of Earth life are essential and which are just accidents of history.

Our lack of data is reflected in our attempts to define life. Koshland (2002) lists seven features of life: (1) program (DNA), (2) improvisation (response to environment), (3) compartmentalization, (4) energy, (5) regeneration, (6) adaptability, and (7) seclusion (chemical control and selectivity). A simpler definition is that life is a material system that undergoes reproduction, mutation, and natural selection (McKay 1991). Cleland and Chyba (2002) have suggested that life might be like water, hard to define phenomenologically, but easy to define at the fundamental level. But life is like fire, not water—it is a process, not a pure substance. Such definitions are grist for philosophical discussion, but they neither inform biological research nor provide a basis for the search for life on other worlds. The simplest, but not the only, proof of life is to find something that is alive. There are only two properties that can determine if an object is alive: metabolism and motion. (Metabolism is used here to include an organism's life functions, biomass increase, and reproduction.) All living things require some level of metabolism to remain viable against entropy. Movement (either microscopic or macroscopic) in response to stimuli or in the presence of food can be a convincing indicator of a living thing. But both metabolism (fire) and motion (wind) occur in nature in the absence of biology.

The practical approach to the search for life is to determine what life needs. The simplest list is probably: energy, carbon, liquid water, and a few other elements such as nitrogen, sulfur, and phosphorus (McKay 1991). Life requires energy to maintain itself against entropy, as does any self-organizing open system. In the memorable words of Erwin Schrödinger (1945), “It feeds on negative entropy.” On Earth, the vast majority of life forms ultimately derive their energy from sunlight. The only other source of primary productivity known is chemical energy, and there are only two ecosystems known, both methanogen-based (Stevens and McKinley 1995; Chapelle et al. 2002), that rely exclusively on chemical energy (that is, they do not use sunlight or its product, oxygen). Photosynthetic organisms can use sunlight at levels below the level of sunlight at the orbit of Pluto (Ravens et al. 2000); therefore, energy is not the limitation for life. Carbon, nitrogen, sulfur, and phosphorus are the elements of life, and they are abundant in the Solar System. Indeed, the Sun and the outer Solar System have more than 10,000 times the carbon content of the bulk of Earth (McKay 1991). When we scan the other worlds of our Solar System, the missing ecological ingredient for life is liquid water. It makes sense, then, that the search for liquid water is currently the first step in the search for life on other worlds. The presence of liquid water is a powerful indication that the ecological prerequisites for life are satisfied.

Orbital images, such as the canyon in Figure 1, show clear evidence of the stable and repeated, if not persistent, flow of a low-viscosity fluid on Mars at certain times in its past history. The fluid was probably water, but the images could also suggest wind, ice, lava, even carbon dioxide or sulfur dioxide. Recently, results from the Mars Exploration Rover missions have shown that this liquid carried salts and precipitated hematite in concretions. The case for water, we could say, is tight.

On Jupiter's moon Europa, the cracks and icebergs on the surface of the ice indicate water beneath the ice, but not necessarily at the present time. Present water on Europa is indicated by the magnetic disturbance Europa makes as it moves through Jupiter's magnetic field, not unlike the way coins in the pocket of a passenger will set off an airport metal detector. Europa has a large conductor, and this is most likely a global, salty layer of water.

Viking on Mars: Been There, Tried That

The Viking missions to Mars in the late 1970s were the first (and as yet, the only) search for life outside Earth. Each Viking conducted three incubation experiments to detect the presence of metabolism in the Martian soil. Each lander also carried a sophisticated Gas Chromatograph Mass Spectrometer for characterizing organic molecules. The results were unexpected (Klein 1978, 1999). There was a detectable reaction in two of the incubation experiments. In the “Gas Exchange” experiment, a burst of oxygen was released when the soil was exposed to water. The “Labeled Release” experiment showed that organic material was consumed, and that carbon dioxide was released concomitantly. In the Labeled Release experiment, this reaction ceased if the soil was first heated to sterilizing temperatures, but the reaction of the Gas Exchange Experiment persisted. If considered alone, the Labeled Release results would be a plausible indication for life on Mars. However, the Gas Chromatograph Mass Spectrometer did not detect the presence of any organic molecules in the soil at level of one part per billion (Biemann 1979). It is difficult to imagine life without associated organic material, and this is the main argument against a biological interpretation of the Viking results (Klein 1999; but cf. Levin and Straat 1981). It is also unlikely that the oxygen release in the Gas Exchange experiment had a biological explanation, because the reaction was so rapid and persisted after heating. It is generally thought that the reactivity observed by the Viking biology experiments was caused by one or more inorganic oxidants present in the soil, and was ultimately produced by ultraviolet light in the atmosphere. Consistent with the apparently negative results of the Viking biology experiments, the surface of Mars also appears to be too dry for life. Indeed, conditions are such that liquid water is rare and transient, if it occurs at all (e.g., Hecht 2002).

It's Life, Jim, but Not As We Know It

Table 1 shows a categorization of life as we have observed it. Using this diagram, we can speculate about how life might be different on Mars or Europa. At the bottom of the table, life is composed of matter—a reasonable assumption for now. Carbon and liquid water are the next level; this makes Mars and Europa likely candidates, because they have carbon and have, or have had, liquid water. Other worlds may have a different chemical baseline for life. The usual speculation in this area is that the presence of ammonia and silicon, rather than water and carbon, might be preconditions for life on other planets. Such speculation has yet to lead to any specific suggestions for experiments, or to new ways to search for such life, but this may just reflect a failure of human imagination rather than a fundamental limitation on the nature of life.

Table 1. A Categorization of Structures That Comprise Terrestrial Life

Life on Mars is also likely to be the same at the top of the table: at the ecological level. Primary production in a Martian ecosystem is likely to be phototrophic, using carbon dioxide and water. Heterotrophs are likely to be present to consume the phototrophs and in turn to be consumed by predators. Darwinian evolution would result in many of the same patterns we see in ecosystems on Earth. While it may be similar at the top (ecological) and bottom (chemical) levels, life on Mars could be quite alien in the middle, in the realm of biochemistry. Pace (2001) has argued that alien biochemistry will turn out to be the same as biochemistry on Earth, because there is one best way to do things and that natural selection will ensure that life everywhere discovers that way. Only observation will tell if there is one possible biochemistry, or many. Future missions to Mars might find microfossils in sedimentary rocks such as those at Meridiani Planum. Microbes don't readily form convincing fossils; the one exception may be the strings of magnetite formed by magnetotactic bacteria (Friedmann et al. 2001). As interesting as fossils might be, we could not be sure that a fossil found on Mars was not merely another example of Earth life. We know that rocks have come to Earth from Mars, and it is possible that such rocks could have carried life between the planets (Mileikowsky et al. 2000; Weiss et al. 2000). Finding fossil evidence for life on Mars does not demonstrate a second genesis in our Solar System. Finding a Way to Search for Alien Life If we were to find organic material in the subsurface of Mars or on the ice of Europa, how could we determine whether it was the product of a system of biology or merely abiotic, organic material from meteorites or photochemistry? If this life were in fact related to Earth life, this should be easy to determine. We now have very sensitive methods, such as PCR and fluorescent antibody markers, for detecting life like us. This case would be the simplest to determine, but it would also be the least interesting. If the life turned out to be truly alien, then the probes specific to our biology would be unlikely to work. What, then, could we do to determine a biological origin? The question is open and possibly urgent. On space missions already being planned, we may have the opportunity to analyze the remains of alien organics on the surface of Europa or frozen below ground on Mars. The instruments that will make this analysis must be designed in the next couple of years. One approach appears promising. I call it the “Lego Principle.” It is based on the patterns of the molecules of life. Biological processes, in contrast to abiotic mechanisms, do not make use of the range of possible organic molecules. Instead, biology is built from a selected set. Thus, organic molecules that are chemically very similar to each other may have widely different concentrations in a sample of biological organics. An example of this on Earth is the 20 amino acids used in proteins and the use of the left-handed version of these amino acids. The selectivity of biological processes is shown schematically in Figure 2 by the distribution of spikes in contrast to a smooth, nonbiological distribution. General arguments of thermodynamic efficiency and specificity of enzymatic reactions suggest that this selectivity is required for biological function and is a general result of natural selection. Different life forms are likely to have different patterns, and at the very least we might find the mirror symmetry of life on Earth, with D- instead of L-amino acids.

Figure 2. Comparison of Biogenic with Nonbiogenic Distributions of Organic Material Nonbiological processes produce smooth distributions of organic material, illustrated here by the curve. Biology, in contrast selects and uses only a few distinct molecules, shown here as spikes (e.g., the 20 l-amino acids on Earth). Analysis of a sample of organic material from Mars or Europa may indicate a biological origin if it shows such selectivity. This approach has immediate practical benefit in the search for biochemistry in the Solar System. Samples of organic material collected from Mars and Europa can be easily tested for the prevalence of one chirality of amino acid over the other. More generally, a complete analysis of the relative concentration of different types of organic molecules might reveal a pattern that is biological even if that pattern does not involve any of the familiar biomolecules. Interestingly, if a sample of organics from Mars or Europa shows a preponderance of D-amino acids, this would be evidence of life, and at the same time would show that this life was distinct from Earth life. This same conclusion would apply to any clearly biological pattern that was distinct from that of Earth life. Organic material of biological origin will eventually lose its distinctive pattern when exposed to heat and other types of radiation, (examples of this include the thermal racemization of amino acids), but at the low temperatures in the Martian permafrost, calculations suggest that there has been no thermal alteration (Kanavarioti and Mancinelli 1990). An interesting question, as yet unanswered, is how long organic material frozen into the surface ice of Europa would retain a biological signature in the strong radiation environment. On Europa, the organic material for our tests might be collected right from the dark regions on the surface. On Mars, there is ice-rich ground in the cratered southern polar regions (Feldmann et al. 2002), which presumably overlies deeper, older ice. The surprise discovery of strong magnetic fields in the southern hemisphere of Mars (Acuña et al. 1999; Connerney et al. 1999) indicates that the area may be the oldest undisturbed permafrost on that planet. Like the mammoths extracted from the ice in Siberia, any Martian microbes found in this ice would be dead, but their biochemistry would be preserved. From these biological remains, it would then be possible to determine the biochemical composition of, and the phylogenetic relationship between, Earth life and Martian life. We may then have, for the first time, a second example of life. 1. Acuña MH, Connerney JEP, Ness NF, Lin RP, Mitchell D, et al. (1999) Global distribution of crustal magnetism discovered by the Mars Global Surveyor MAG/ER experiment. Science 284:790–793. FIND THIS ARTICLE ONLINE 2. Biemann K (1979) The implications and limitations of the findings of the Viking Organic Analysis Experiment. J Mol Evol 14:65–70. FIND THIS ARTICLE ONLINE 3. Chapelle FH, O'Neil K, Bradley PM, Methé BA, Ciufo SA, et al. (2002) A hydrogen-based subsurface microbial community dominated by methanogens. Nature 415:312–315. FIND THIS ARTICLE ONLINE 4. Cleland CE, Chyba CF (2002) Defining life. Orig Life Evol Biosph 32:387–393. FIND THIS ARTICLE ONLINE 5. Connerney JEP, Acuna MH, Wasilewski P, Ness NF, Reme H, et al. (1999) Magnetic lineations in the ancient crust of Mars. Science 284:794–798. FIND THIS ARTICLE ONLINE 6. Feldman WC, Boynton WV, Tokar RL, Prettyman TH, Gasnault O, et al. (2002) Global distribution of neutrons from Mars: Results from Mars Odyssey. Science 297:75–78. FIND THIS ARTICLE ONLINE 7. Friedmann EI, Wierzchos J, Ascaso C, Winklhofer M (2001) Chains of magnetite crystals in the meteorite ALH84001: Evidence of biological origin. Proc Natl Acad Sci U S A 98:2176–2181. 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McKay CP (1997) The search for life on Mars. Orig Life Evol Biosph 27:263–289. FIND THIS ARTICLE ONLINE 17. Mileikowsky C, Cucinotta FA, Wilson JW, Gladman B, Horneck G, et al. (2000) Natural transfer of viable microbes in space. Icarus 145:391–427. FIND THIS ARTICLE ONLINE 18. Pace N (2001) The universal nature of biochemistry. Proc Natl Acad Sci U S A 98:805–808. FIND THIS ARTICLE ONLINE 19. Raven JA, Kübler JE, Beardall J (2000) Put out the light, and then put out the light. J Mar Biol Ass (UK) 80:1–25. FIND THIS ARTICLE ONLINE 20. Schrödinger E (1945) What is life? Cambridge: Cambridge University Press. 91 p. 21. Stevens TO, McKinley JP (1995) Lithoautotrophic microbial ecosystems in deep basalt aquifers. Science 270:450–454. FIND THIS ARTICLE ONLINE 22. Ultee A, Souvatzi N, Maniadi K, König H (2004) Identification of the culturable and nonculturable bacterial population in ground water of a municipal water supply in Germany. J Appl Microbiol 96:560–568. 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See related articles: Aristotle and Life

References

Citations and Notes

On the Importance of Being Ernst Mayr: PLoS Biology Obituary, by Alex Meyer

Ernst Mayr, “Darwin's apostle” died at the age of 100^{[66] [67] [68]}

Born on July 5, 1904, in Kempten in southern Germany, Ernst Mayr passed away peacefully at the Methuselah-like age of 100 on February 3, 2005, in Bedford near Cambridge, Massachusetts. Mayr was, by the accounts of his Harvard colleagues the late Stephen Jay Gould and Edward O. Wilson, not only the greatest evolutionary biologist of the 20th century, but even its greatest biologist overall.

• Thomas Henry Huxley was dubbed “Darwin's bulldog” for fighting for the acceptance of Darwinian ideas soon after their inception in the last decades of the 19th century.
• Similarly, Ernst Mayr has been called “Darwin's apostle” or the “Darwin of the 20th century” for promoting and dispersing Darwin's hypotheses throughout the past century.

Mayr lived for a century and accomplished more than several lifetime's worth of science in different biological disciplines. Brought up by parents who loved nature and who took the young Ernst on long hikes, he was exposed to natural history early on, but although birds were his passion all his life, he was, like Darwin, first compelled to study medicine. He began his studies at Greifswald — a prime birding spot — and through the chance observation of a rare species of duck that had not been seen in Germany for many years, he came in contact with the Berlin ornithologist Erwin Stresemann, who proposed that he switch to biology. Mayr abandoned medicine for biology and published his first scientific paper (of a total of almost 700) at the age of 19 in 1923, receiving his Ph.D. from Humboldt University in Berlin after only 16 months of graduate work and dissertation research; he was just 22. Ernst Mayr's last book (of a total of 25) was published in August 2004, a month after he turned 100.^[69]

In 1931, thinking that he would not be offered a permanent post in Germany, he moved from Berlin to the American Museum of Natural History in Manhattan. In New York he called himself an ornithologist, and believed then, like many of his contemporaries, in Lamarkian inheritance. Sent by his advisor Erwin Stresemann from Berlin and financed by Lord Rothschild, he had just returned from over two years of perilous fieldwork in New Guinea and the Solomon Islands. The parallels to the lives of Darwin and Wallace may not be coincidental. During these expeditions, forlorn, at times given up for dead, exposed to tropical diseases and the danger of headhunters, he collected the skins of thousands of specimens, eating the flesh of many. Mayr was not only the ornithologist who probably tasted the largest number of different species of birds, but he also named 26 new species and over 400 new subspecies, more than any other taxonomist. In over 300 publications throughout his life, he discussed and described the geographic variation and distribution of birds and he also edited the last eight volumes of the Checklist of the Birds of the World. His main occupation during his 20 years at the American Museum was to curate and research the 280 000 specimens of the Rothschild collection.

In the 1930s, Mayr's friendship and interactions with the Russian-born Columbia University population geneticist Theodosius Dobzhansky, author of the landmark text Genetics and the Origin of Species published in 1937,^[70] started to influence his thinking. Mayr's interests subsequently began to diversify beyond taxonomy into evolutionary biology, and this expansion of his interests culminated in his first, and possibly still most important book, Systematics and the Origin of Species, published in 1942.^[71]

This was his main contribution to the so-called Modern Synthesis of the 1930s and 1940s, a scientific sea change that came about largely through the contributions of Mayr and Dobzhansky and other scientists such as Ronald A. Fisher and George G. Simpson. Mayr's first book combined insights and methods from paleontology, population genetics, systematics, and natural history, thus providing a unified modern evolutionary theory. Patterns and processes in natural populations would now be seen as consistent with Darwinian natural selection and Mendelian mechanisms of inheritance, and the behavior of genes in populations came to be understood through laboratory population genetic experiments and theoretical mathematical predictions. Mayr was the last survivor, and historical eyewitness, among the architects of the Modern Synthesis.

Ernst Mayr had many fundamental insights into evolutionary biology, and almost every topic of importance in evolution was advanced by his ideas. Perhaps his most widely known contribution is to the current notion of what constitutes a species. Darwin did not think that species were real in the philosophical sense, but rather that they were the result of the human predilection to perceive discontinuity among continuously varying individuals. Most biologists nowadays disagree with Darwin's view of species, largely because of Mayr's “biological species concept”. Together with Dobzhansky, Mayr developed this definition of species “as groups of interbreeding populations in nature, unable to exchange genes with other such groups living in the same area”.^[70]&nbsbp;^[71] Barriers to gene flow between species — termed reproductive isolating mechanisms — keep biological species distinct through processes such as species-specific mate choice and hybrid sterility.

Although there are theoretical and operational problems with the biological species concept (e.g., it does not apply to asexually reproducing organisms such as bacteria), it is still, by far, the most widely used species concept among the 20 or so competing definitions that have been proposed in the past several decades. Students of biology all over the world have memorized Mayr's definition of species for more than half a century.

The biological species concept made it possible to study how species arise, since the criterion of reproductive isolation provided a scientifically rigorous litmus test. The origin of species is a topic to which Darwin himself, in spite of the promising title of his famous book, did not say all that much. Mayr's understanding of the biogeographic distributions of bird species, overlaid with extensive knowledge about variation in morphology, led him to develop concepts about the geographic mechanisms of speciation — cornerstones for those studying speciation today. The geographic separation of populations, such as by rivers or valleys, he argued, prohibits homogenizing gene flow between them. If such isolated (termed allopatric) populations accumulate mutations over time, this might lead to the divergence of such populations from each other, and reproductive isolation might arise as a simple byproduct of these separate evolutionary histories. Mayr staunchly defended this idea during sometimes heated debates and further developed it and other hypotheses regarding geographic mechanisms of speciation over many decades (outlined in depth in the 797 pages of Animal Species and Evolution).^[72]

One mechanism of speciation in particular is still contested (see ^{[73]  [74]}). Mayr called it “peripatric speciation” or “founder-effect speciation.” And it is an idea that Ernst Mayr was particularly fond of. He believed it to be his most important contribution to evolutionary biology.

This model was again inspired by Mayr's own natural history observations. He noted that on some New Guinea islands, populations of birds differed markedly from individuals of the mainland population. He reasoned that this differentiation and speciation could result from a small number of individuals founding the island population. By bringing only a subset of all the genes of the main population (causing a genetic bottleneck), genetic drift (random fixation) and natural selection (due to a different set of selection pressures on these islands) would not only promote the formation of new species but would do so rapidly. This mechanism might also account for the paleontological pattern called “punctuated equilibrium,” which was proposed by Nils Eldredge and Gould in 1972.^[75] They noted that long periods of morphological stasis were sometimes interrupted (punctuated) by short periods of drastic phenotypic change in the fossil record. Somewhat ironically, Mayr, who considered himself a “gradualist” all his life, seems to have also provided a mechanism for variability in rates of evolution along evolutionary lineages.

After establishing the Society for the Study of Evolution and serving as the first editor of its journal, Evolution, Mayr moved to Harvard University in 1953 as the Alexander Agassiz Professor of Zoology and curator of birds at the Museum of Comparative Zoology. By this time, one surely would have labeled him primarily an evolutionary biologist rather than an ornithologist. His interests expanded even further into the theory of systematics—another field to which he made many contributions (see Principles of Systematic Zoology^[76]). A lifelong and, it seems fair to say, futile fight with the then emerging idea of cladistics in systematic biology began. Ernst Mayr also served as director of the Museum of Comparative Zoology before his retirement in 1975 and oversaw the building of a new addition to the museum, whose library was renamed after him ten years ago.

What of his retirement? Mayr published 14 of his 25 books in the 30 years that followed after his official retirement. During the last two decades of his life, Mayr began to think and write more about the history and philosophy of biology. His most important work of this period was The Growth of Biological Thought,^[77] a monumental 974 pages. Here, and in later books and publications (he also founded the Journal of the History of Biology), he laid out why he thought that the philosophy of biology is an autonomous science that differs fundamentally from the philosophy of science, which, Mayr implied, was largely derived from physics. He argued that biology is a science that is based on historical contingency as well as on many unpredictable and coincidental factors that make it impossible to discover laws. Rules, not laws, are all that one will be able to find in biology.

Clearly, Ernst Mayr felt very strongly that he had something of importance to say to the world. And the world, not only in its scientific realms, seemed to think likewise. He received almost 20 honorary degrees from major universities, was a member of more academies than any other scientist before him, and received most of the prizes that could possibly be awarded to a biologist, including the Japan Prize, the Balzan Prize, and the Crafoord Prize, the “Nobel Prize for ecologists and evolutionary biologists.”

How could one person possibly fit so much into one lifetime, even such an astonishingly long one? For a start, he was a man of stringent self-discipline, who would get up with (or before) the birds, like a good ornithologist should. Writing (longhand or dictation) was done mostly in the mornings, and long walks were part of every day, as were extended periods of reading and corresponding with his colleagues. Just like Darwin, Mayr wrote thousands of letters minding the business of others, telling his fellow scientists what he thought of their work, praising them but also advising them on missed literature and new directions for further study. He did not like to be bothered with those other menial things that also belong to living on this planet, and, luckily for him, Gretel, his wife of 55 years, mostly took care of that part. So after her death ten years ago, when he was in his early 90s, he had to learn how to cook a hamburger for himself.

Ernst was gifted with an astonishing clarity of thought. Something that always impressed and humbled me was that the transcripts of his dictated manuscripts required very little further editing. Even Mayr's native-English-speaking competitors praised him, obviously a nonnative, for his lucid and clear writing style. Ernst also had the ability to store an astonishing amount of information drawn from many different sources—his memory was spectacular. His ability to synthesize ideas, combined with an amazing recall of natural history, an exact visual memory, and an overall wide scientific horizon, was awe-inspiring and, more than in anyone else I've ever met, produced a plethora of novel ideas. His vitality was also legendary. He would still climb trees in his mid-80s to inspect birds' nests, and he bought his last new car after having passed the age of 90, much to the astonishment of the car salesman, as he once told me.

Pulitzer Prize winner Natalie Angier from the New York Times once described Ernst Mayr in an interview as “opinionated and elitist, courtly and generous.” Ernst Mayr was all that. He was strong-willed, had little patience for people who had not done their homework or talked without having their natural history straight or their line of reasoning well thought out, and he could be damning in his judgment of the ideas of others. Yet he generously shared not only his thoughts, but also charitably donated a good portion of his salary and most of his significant prize money to causes such as the Nature Conservancy and to endow prizes for young evolutionary biologists.

Although Ernst Mayr lived only about a tenth of the 969 years that Methuselah is purported to have lived, he still accomplished much more than one might expect to get done, even in a 100 years. More important than his scientific output is the overarching influence he has had on the thinking of three or four generations of biologists that he was a contemporary of and interacted with. The scientific world lost a giant and an inspirational thinker. His doctoral advisor Stresemann once called Mayr a rising star. Nobody since Darwin shed the light of insight as bright over the firmament of evolutionary biology as Ernst Mayr did. His star has not stopped shining, and his ideas will continue to live on for generations of young evolutionary biologists to come. On the occasion of his 100th birthday Mayr published an article in Science^[78] looking back over eight decades of research in evolution that he closed with the following words: “The new research has one most encouraging message for the active evolutionist: it is that evolutionary biology is an endless frontier and there is still plenty to be discovered. I only regret that I won't be present to enjoy these future developments.”

Author: Axel Meyer is Professor of Zoology and Evolutionary Biology at the University of Konstanz in Germany. E-mail: axel.meyer@uni-konstanz.de

Fundamental Questions in Biology: A 2006 PLoS Biology Editorial by Simon A. Levin

Fundamental Questions in Biology^[79]

Not so long ago, virtually every major university had a department of biology, or perhaps bookend departments of zoology and botany, which complemented physics, chemistry, mathematics, and possibly geology to form its science foundation. Biology was, at least compared to the field today, an integrated discipline, from the molecular and cellular to the ecosystem, firmly resting on Darwinian principles. Weekly colloquia drew biologists from across the spectrum, whether the topic was the genetic code, the nature of the synapse, or the Cambrian Radiation.

But biology has seen its own radiation and is just starting to catch up with this explosion. The amazing pace of advance in our understanding of biology has, perhaps unavoidably, engendered increasing specialization. Much of that advancement has involved the development of new tools, both in the laboratory and in computer models, and this has been dependent on the migration into biology departments of tools and people from physics, mathematics, chemistry, and elsewhere. These new collaborators have catalyzed rapid progress on specific problems, but they often have little interest in the broader scope of biology. Even traditional biologists with broader interests may not have the time to indulge outside of their own research areas because of the speed of scientific progress in those areas and the competitive nature of contemporary science. Departments of biology or botany/zoology have split and split again, producing departments of cell and molecular biology, ecology and evolutionary biology, neurobiology and behavior, genetics and development, physiology, and so on, reflecting the particular cultures of the specific institutions. Where departments of biology have remained intact, intradepartmental asymmetries in quality or funding potential have created tensions and siege mentalities and have encouraged university administrators to follow the money and to accept the fallacious argument that areas that require or attract less funding are hence outdated and dispensable.

But the situation may be changing. The rapid accumulation of information from genomics has reached a point where attention must be turned, if it has not already, to what the now vast library of genetic information means for how organisms function in their natural environments, and indeed for how ecological communities operate. Metagenomic methods are being applied to the collection of storehouses of genetic information about whole ecosystems, especially the oceans; but such information is of limited value unless one understands how that information is organized, how it is distributed over the biota, and why specific genes are associated with particular regions of the ecosystem.

• Are there particular conditions that select for novelty and for high mutation or recombination rates? What about for cooperative behavior?
• What is the relationship between the distribution of specific viral genes and the genes of other organisms, and can we begin to infer from this distributional information the possible role of viruses in mediating oceanic diversity?

At the core of this potential future shift in biological sciences is the recognition that all biological systems are what have come to be known as complex adaptive systems, in which macroscopic patterns reflect the collective dynamics of individual units at lower levels of organization and feed back to affect those more microscopic dynamics. Evolutionary changes operate on multiple levels and multiple scales: from cells, to organisms, to populations, to communities and the biosphere. As my Princeton colleague, Philip Anderson, wrote years ago, “more is different.” Although the details at lower levels govern the behavior at higher levels, understanding those details is not sufficient for understanding how macroscopic patterns emerge or how natural selection operates at lower levels to lead to those patterns. Where those patterns refer to properties of the organism, natural selection operates to modify the details, such as the rules that govern organismal development due to feedbacks from fitness differences among organisms. On the other hand, where those properties refer to those of the biosphere, there is no comparable process of natural selection choosing among competing biospheres. What properties arise are hence largely emergent, reflecting selective events at much lower levels of organization. This is the principal reason that our biosphere is in trouble. It also emphasizes the importance of understanding at what levels selection operates most strongly.

The questions that biologists from diverse subdisciplines are asking have commonalities that make clear the continued existence of fundamental challenges that unify biology and that should form the core of much research in the decades to come. Some of these questions are as follows:

• What features convey robustness to systems?
• How different should we expect the robustness of different systems to be, depending on whether selection is operating primarily on the whole system or on its parts?
• How does robustness trade off against adaptability? How does natural selection deal with environmental noise and the consequent uncertainty at diverse scales?
• When does synchrony emerge, and what are its implications for robustness? When and how does cooperative behavior emerge, and can we derive lessons from evolutionary history to foster cooperation in a global commons?

These are among what we identify as fundamental questions in biology, cutting across subdisciplines and with the potential to reunify the subject. To encourage recognition of these challenges, PLoS Biology is publishing a series of brief discussion papers raising core issues and designed to be provocative. Contributions to the Challenges Series are encouraged; ideas should be sent to biology_editors@plos.org.

See also:
Biology
Systems biology

History of Biology

See related Biology

An unrecorded history of biology began when human foragers first systematically started to accumulate information about the behavior of plants and animals in their environment, which they did for its importance in helping them acquire food for subsistence. Biological studies started therefore probably from the beginning of human existence.

Our species, Homo sapiens, emerged nearly 200,000 years ago, exhibiting unprecedented cognitive abilities in the biological world — cognitive abilities enabling them to operate as observational scientists of the type later known as ‘natural philosopher’ or ‘naturalist’. They could discern cause and effect widely in nature, they could speak and thus share knowledge and cooperatively accumulate it and pass it down the generations, and they could make tools — all prerequisites for a successful naturalist focusing on the study of food sources. Living as hunter-gatherers, so succesfully that their descendants populate the world today, they learned the behavior of animals and plants in the detail needed to subsist and thrive in the wild. How they organized and taught their ethology and taxonomy we can only speculate. Reports of direct observations of 19th and 20th century hunter-gatherer societies give some appreciation of the likely scientific biological expertise important for survival required of our hunter-gatherer ancestors. ^[80]

Our prehistoric ancestors studied human behavior as well as the behavior of their biological food sources, extending their biological studies from ethology and taxonomy into psychology. Their ability to speak to each other, make correlations between events, and discern cause-effect, gave them a ‘theory of mind’ that facilitated tibal cohesiveness.

Eventually, their expertise in biology played a major role in developing agriculture, and encouraging experimental work to further develop crop yields, something present day biologists still pursue vigorously. After 190,000 years of hunter-gatherer free-roaming living, agriculture spawned fixed settlements, which ultimately led to modern civilization. With civilization came writing and recorded history, so this article can proceed next with a summary of the recorded history of biology, including the observations, experimental findings, and theory-building of individual biologists.

The biology of Aristotle, the founding father of biology

Aristotle (384-322 BCE) receives first credit as an individual for major contributions to the development of biology as a science. Nevertheless, he arrived on the biology scene after some 10,000 years of experiments in animal and plant domestication and breeding by unnamed individuals. He also followed and learned from earlier Greek thinkers who postulated biological explanations from observations of the everyday world,^[81] including:

• Thales of Miletus (640-550 BCE), who posited water as the source of all things, including life;

• Anaximander (610-540 BCE), who posited “…that man could not from the beginning have been what he was now, for if man, on his first appearance, had been so helpless at birth, and had required so long an adolescence, as in these later days, he could not possibly have survived”, and who seemed to have a clear idea of biological evolution ;^[81]

• Anaxagoras (500-428 BCE), who discovered respiration in animals and plants and attributed human intelligence to the development of bipedalism;

• Heraclitus (530-470 BCE), whose theory of all things changing favored the idea of evolution;

• Empedocles (ca. 445 BCE), who advanced a theory of evolution, attributing it to the combination of natural experiments and natural selection. Aristotle both acknowledges Empedocles’ ‘survival-of-the-fittest’ argument and rejects it on the basis that nature operates for a purpose and does not offer random variations;^[82][83]

• Leucippus (ca. 445 BCE) and Democritus (460-360 BCE), who rejected design in nature and described nature as a machine.

But Aristotle justifiably earned his title as the founding father of biology through his lifelong wide-ranging observations of biological phenomena, his sometime experimentation, his organization of information, and his philosophy that understanding reality required deductions and inductions from sense experience and not abstract postulations before the fact. He noted that despite the enormous variety of living things, they showed very small gradations from less to more complex forms, and, as Will Durant^[81] summarizes it, citing the primary sources:

…that life has grown steadily in complexity and in power; that intelligence has progressed in correlation with complexity of structure and mobility of form; that there has been an increasing specialization of function, and a continuous centralization of physiological control.

One can do little to improve on the detailed description given by Durant of Aristotle’s myriad observations of animal structure and behavior, relationships among animals, embryological phenomena, and even genetics. Nor could one much improve on Durant’s description of Aristotle’s myriad mistakes and misconceptions. Yet no one before had accumulated and organized so much biological knowledge, and raised so many specific questions, setting the foundation for the evolution of our understanding of the living world.

Aristotle also gave some thought to the question, "what is life?". He thought that a living thing existed in 'potentiality' in the seed or semen, that environment factors initiated the realization of that potential, and that that potential included the "nutritive power" to grow into the living thing.^[84] Corresponding to that triad of suppositions, though it takes more than semen to generate a mammal like a human, for example, it might not have surprised Aristotle to learn that the potentiality of the human exists as molecules in the semen and ovum, that the fluid composition in the oviduct, where the living starts, enables the fusion or fertilization process that starts the life form, and that the zygote (the first cell of the human) has within itself the wherewithal to utilize its own organization to develop itself into a multi-cellular individual human.

Aristotle developed a coherent vision of the nature of living thing. Hisfour components of the causes of complex natural things,^{[85] [86]} anticipates the somewhat more refined modern systems biology approach to the question of life. A living thing comprises:

• A collection of organic and inorganic parts (molecules and ions; cells, organelles, organs and organisms) — Aristotle’s 'material' cause, the parts that make up the living thing; Aristotle only recognized some of the organs;
• Parts relating to each other to form structures (e.g., networks), how they interact with each other (e.g., network dynamics), and how the structures interact with each other in a coordinated dynamic and hierarchical manner — Aristotle’s 'formal' (form-like) cause, the form the living thing takes on from the parts; Aristotle thought in terms of sculpture;
• Parts and structures dynamically coordinated (e.g., gene expression; self-organization) — Aristotle’s 'efficient' (effect-producing) cause, how the living thing gets produced into its form; Aristotle thought about something putting it together;
• How the living system as-a-whole functions and behaves, and the properties that characterize it (e.g., reproduction; locomotion; cognition) — Aristotle’s 'final' cause, its function; Aristotle thought in terms of the thing's 'purpose' or 'goal';

Modern biologists go down the road started as a path by Aristotle, who would have been delighted to know he asked the right questions traveling down the path, even if he didn't know how to get the right answers. Unfortunately, the larger fraction of his writings have disappeared, so we cannot know the full breadth of Aristotle's curiosity and adumbrations. What he did leave had a major effect on Western thought for centuries.

Lucretius and evolution

Titus Lucretius Carus (ca. 94 to ca 55 BCE), a Roman poet, author of De Rerum Natura (On the Nature of Things), familiar with the materialist Greek Philosophers, in particular Democritus (ca 460 to ca 370 BCE), who developed the theory of atoms originated by his teacher Leucippus, and Epicurus (341-270 BCE), who extolled the virtues of intellectual pleasure and admonished against the fear of death and the gods, had a clear notion of the evolution of livings through a selective process, as revealed in the following excerpt from De Rerum Natura: ^[87]

And in the ages after monsters died,

Perforce there perished many a stock, unable

By propagation to forge a progeny.

For whatsoever creatures thou beholdest

Breathing the breath of life, the same have been

Even from their earliest age preserved alive

By cunning, or by valour, or at least

By speed of foot or wing.

  Links

http://www.ifcbiol.org/Dotcweb/index.html Discovery of the cell  http://www.ucmp.berkeley.edu/help/topic/history.html Scientist Biographies at the University of California Museum of Paleontology

http://www.bioexplorer.net/History_of_Biology/

http://www.bioexplorer.net/Biologists_of_Today/

http://www.bioexplorer.net/Biological_Societies/

http://www.bioexplorer.net/Divisions_of_Biology/

http://www.bioexplorer.net/Databases/

http://www.bioexplorer.net/Educational_Resources/

http://www.bioexplorer.net/Journals/

http://www.bioexplorer.net/Institutes/

http://www.bioexplorer.net/Search_Engines/

http://www.bioexplorer.net/Research_Centers/

http://www.bioexplorer.net/Software/

Living systems as self-constructing autonomous homeostatic cognitive machines

In this section we consider living systems, as distinct from non-living systems, in part from the perspective of the concept of ‘autopoiesis’ introduced by Humberto Maturana and Francesco Varela,^[88] and its later developments.

Any entity we recognize as living we recognize also as a ‘system’, an assemblage of components, interrelated structurally, interacting in a coordinated, dynamic, hierarchical way such as to self-construct an autonomously working organization characterizable as a ‘whole’ or ‘operational unit’ in virtue of a boundary selectively separating it from its environment — a universe unto itself. We can hold that view of living systems regardless of the nature of the components that self-construct it, but on Earth we recognize those components as matter in the form of atoms and molecules storing, releasing and actuated by free energy.

The precise description of the organization of living things differs widely among species. Think of an ant and an anteater. We can, however, specify characteristics of the ‘kind’ of organization that all species share here on Earth. For one thing, we can say a living system’s complexity exceeds current human cognitive ability to comprehend it, even with the aid of a powerful computer exo-cortexes. Arguably, in the future that characteristic of the organization in living things may prove non-constitutive.

We can say also that the organizational state of living systems resembles that of a man-made machine, like a super-jet airplane or a super-computer, though not made by man and not obviously made for a purpose. We can think of a living system as a different ‘kind’ of machine than man-made machines. We can see that living machines exhibit a natural, or non-contrived ability to keep many of its internal variables constant, or within narrow bounds — it qualifies as a homeostasis machine.

A living system’s homeostatic ability plays a critical role in defining its uniqueness, as it enables it to homeostatically regulate the most important variable required for its continued living: an organization, whatever its description, that perpetuates its existence as a living system. Through the activity of its organization, the living system produces those components that provide the structural basis for the self-construction of its state as an autonomously working organization. If a living system cannot maintain its organization, it cannot produce the structure whose self-constructed coordinated interactions enable it to remain a living machine.

We can view a living system then as:

• a self-constructed machine organized as a network of interactions that produce, cyclically, the components whose self-organized interactions self-construct the system’s self-perpetuating network of interactions.
• a self-constructed machine organized as a network of interactions that can respond to perturbations either by self-correction of its disturbed organization, or by reorganizing itself into different self-perpetuating network of interactions.

We can encapsulate that view of living systems preliminarily as ‘self-constructed self-perpetuating homeostatic machines’. Maturana and Varela^[88] introduced the term ‘autopoiesis’ and ‘autopoietic organization’ to encapsulate that view of living machines as self-constructed self-perpetuating homeostatic machines as we have characterized them.</ref>  Bitbol and Luisi expressed the definition of autopoiesis as follows:^[89]

The theory of autopoiesis...captures the essence of cellular life by recognizing that life is a cyclic process that produces the components that in turn self-organize in the process itself, and all within a boundary of its own making.

That view of a living system reveals a special property of homeostasis in living machines: adaptability. A human, to take an example mammal, self-perpetuates a life-sustaining organization despite enormous perturbations of its organization during embryonic and fetal ‘development’. It does it by self-reorganizing — the homeostatic property of adaptability. If we think a fetus or a child an immature adult, we must think adults aged fetuses or children. As one individual or identity, fetus and adult represent a single self-constructing self-perpetuating homeostatically adaptable machine.

Ontogeny highlights the living system’s unique property of homeostasis as targeting with highest priority the maintenance of an organization that produces components that self-organize a network of interactions that perpetuates that organization, including its networks of interactions that retain its homeostatic property of adaptability. Homeostatic reorganization goes on continuously. The living machine maintains networks of interactions that define it as a self-constructing self-sustaining machine.

The self-constructed self-perpetuating homeostatic machine also produces its own boundary, as without that it could not maintain its organization against all the chaos outside.

A man-made, non-living machine yields products other than itself, products for human use. A living machine yields itself as its product, a product in continuous production, no matter how much it must modify itself in the process.

Therein defines the living machine’s autonomy —- it works in its own behalf to construct and sustain itself. So central to a living machines uniqueness its homeostatic organizational ability to produce components whose interactions self-organize a self-perpetuating organization that, before accumulated perturbations of its organization overwhelms its homeostatic ability, the machine self-reproduces.

By this view, neither growth nor reproduction necessarily constitute ‘primary’ abilities of living machines, as both occur, in life on Earth, as homeostatic adaptable activities of the self-constructing organization that produces components whose interactions realize that organization, along with its homeostatic adaptability. On other worlds, living systems need not necessarily grow or reproduce, so long as they can, in some way, construct the components that can self-organize to construct the organization that can produce those components, including the system’s own boundary whose character enables its individuality and access to resources and a waste disposal.

Scientists can model and even synthesize experimental living machines that satisfy the basic criteria of a self-constructing self-perpetuating homeostatic machine (see^[89]).

Access to resources alone cannot carry the day for a self-constructing homeostatic machine. It must have the ability, as part of its self-constructed organization, to recognize the resources it needs in order to sustain its organization. Recognition, however mediated, implies a type of ‘cognition’. In that case, for living machines to have an organization that produces the components that self-construct their-own component-producing organization, that organization must devote some of its activities to a type of cognition that enables it to recognize import resources and dispose of waste.

Those considerations dictate that a full description, or definition, of a living machine include the following:

• An organization of components capable of producing and reproducing, cyclically, the components that self-organize to construct the organization of components that produces those components;

• The components produced must self-construct a boundary between the machine and the environment, of a nature that enables the machine to trade with the environment, acquiring the materials and/or energy required to sustain its self-perpetuating organization;

• The components produced must self-construct an organization that has the cognitive ability to recognize the resources it needs to import and the wastes it needs to export.

• The components produced must self-construct an organization that has the homeostatic ability to ‘correct’/’accommodate’ perturbations of the organization, or to reorganize appropriately to sustain a self-perpetuating organization;^[90]

With those conditions realized, we can then ask about the details of the mechanisms or conditions that effect that realization in Earth’s living machines, whose components are molecules that self-construct networks comprising an organization that recursively constructs its components of such nature that the organization they produce can operate autonomously with homeostatic adaptability to sustain or reorganize itself as a cognizing compartmented system capable of escaping thermodynamic equilibrium through repeated self-reproduction.

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As an academic discipline, systems biology aims to explain, predict and control the properties, functions and behaviors^[91] of biological systems — complex assemblages of interrelated, dynamically interacting, coordinated and hierarchically organized naturally selected components^[92] generated over evolutionary time by natural biochemical and biological experiments.^[93]  Biological systems studied range from the level of the molecular subsystems of cells (e.g., mitochondrial production of versatilely usable energy; circuits regulating gene expression; cell-to-cell and within-cell signaling (communicational) pathways); to the Earth's biosphere, and include a large number of intermediate system levels (e.g., unicellular organisms, multicellular organisms, ecosystems).

Systems biology developed as a scientific endeavor in part because of the recognition that knowledge of the properties of a system’s components alone, however complete, could not yield an explanation of the organized functioning of the system, which depends not only on the properties of the system’s components, but also on how they interrelate and interact in the spatiotemporal domain, and on how the organized functioning of the system itself influences the properties and interactions of the components. Unpredictable novel properties of systems emerge from its dynamic organization, whose understanding require a ‘holistic’ ^[94] approach in addition to the traditional ‘reductionistic’^[94] approach.

Systems biologists try to achieve their aims in part through developing models (descriptions, representations, simulations) of systems — various kinds types of models, including graphical, mathematical and computer-based simulation models. The models aspire to 'describe' systems, or 'translate' them into the known 'language' of the model, to enable interpretation of the systems' components' interrelations by human cognition. The models aspire to do that sufficiently well to account for experimentally derived data about a system’s interacting components, and allow predictions of the system's properties, functions and behaviors in response to given stimuli or given sets of conditions. Systems biologists use sophisticated mathematical, statistical and computational tools in diverse modeling approaches, in mathematical network analyses, in computer simulations, in design and building synthetic networks from biomolecules, and, iteratively, incorporating new data derived from systems-analysis-inspired further experimentation.

Modeling permits a kind of formal integrative analysis of a biological system that also enables the development of conceptual frameworks to integrate large amounts of data and identify gaps in the information known about a system. Without models, the human mind can comprehend little of the organization as a whole of a complex living system. In speaking specifically about cellular signaling pathways, Weng et al. put it this way: There is simply too much essential detail in biological signaling for the unaided human mind to organize and understand.^[95]

Systems biologists often work with non-biological scientists, from a variety of disciplines, in developing models and conceptual frameworks. Some of those non-biological disciplines (e.g., mathematics, physics and chemistry) have developed systems approaches to explore systems in their domains.

No definition or succinct description can capture the breadth and depth of the interdisciplinary enterprise of systems biology. Indeed, historian and philosopher of science Evelyn Fox Keller argues that “so far, ‘systems biology’ is a concept waiting for definition".^[96]  This article elaborates on the above description of the discipline.

MCA

Computerized mathematical modeling of metabolic networks (Metabolic Control Analysis) began as early as 1960^[97], further advancing in the early 1970s, with the aim of quantifying the effect of the differing chemical reactions in the network on the concentrations of the network metabolites and on the flow of metabolites through the network, in particular in response to various perturbations (see review by Visser and Heijnen^[98]).

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Pliny the Elder (23-79 C.E.), Roman encyclopedist of ancient European science, wrote:

But it is the fact, that every moment of our existence we are distrusting the power and the majesty of Nature, if the mind, instead of grasping her in her entirety, considers her only in detail.^[99]

Re swimbladder exaptation^[100]

Some refer to biological homeostatic devices as ‘Bernard Machines’. ^[101]

Claude Bernard (1813-1878), a French physiologist studying rabbits and other mammals, first enunciated the concept that dynamic physiological mechanisms continually operate to maintain stability of an animal’s internal environment (‘milieu intérieur’). Bernard stated: “The fixity of the internal environment is the condition for free life.”^[102]

Systems biology developed as a scientific endeavor in part because of the recognition that knowledge of the properties of a system’s components alone, however complete, could not yield an explanation of the organized functioning of the system, which depends not only on the properties of the system’s components, but also on how they interrelate and interact in the spatiotemporal domain, and on how the organized functioning of the system itself influences the properties and interactions of the components. Unpredictable novel properties of systems emerge from its dynamic organization, whose understanding require a ‘holistic’ ^[94] approach in addition to the traditional ‘reductionistic’^[94] approach.

Aristotle on gender.^[103]

The Fourth Great Awakening and the Future of Egalitarianism (book by Robert William Fogel)

Writing the book of that title published in 2000 C.E.,^[104]  Robert William Fogel, who received the Nobel Prize in Economics in 1993, surveys the see-saw cyclical relationships among fervent religion, politics, legislative policies, and public interest throughout the course of American history. In the process, he presents a synthesis of American history in the domains of technological advances, consequences of those advances on social, economic, religious and political life, and the course of egalitarianism for Americans. He argues that at least three periods of surges in religious fervor and organization (’awakenings’) have occurred in American history, each greatly influencing the political process and leading to major changes in legislation and governmental policies satisfying the religious fervor, subsequently leading to backlash reactions that resulted in new political and legislative changes. He argues that a fourth great awakening began in the 1960s and 1970s and continues into the present (early 21st century).

Phases of the Great Awakenings

One can get the gist of Fogel’s main argument from a table shown on the publisher’s website The Phases of the Four Great Awakenings website, reproduced below. The chart shows the phases of the four great awakenings, including for each the dates, the phases and nature of the religious revivals, of their rising political effect, and of increasing challenge to the revival’s political program.:

Courtesy University of Chicago Press, http://www.press.uchicago.edu/Misc/Chicago/256626.html

[View larger image]

The publisher’s website, The Phases of the Four Great Awakenings introduces Fogel’s argument as follows:

To understand what is taking place today (2000 C.E.), we need to understand the nature of the recurring political-religious cycles called "Great Awakenings." Each lasting about 100 years, Great Awakenings consist of three phases, each about a generation long…A cycle begins with a phase of religious revival, propelled by the tendency of new technological advances to outpace the human capacity to cope with ethical and practical complexities that those new technologies entail. The phase of religious revival is followed by one of rising political effect and reform, followed by a phase in which the new ethics and politics of the religious awakening come under increasing challenge and the political coalition promoted by the awakening goes into decline. These cycles overlap, the end of one cycle coinciding with the beginning of the next.

In 2007 C.E., it does not seem disputable that a fervent religious revival of evangelicalism and Christian fundamentalism prevails among a large segment of the United States population.^[105]  Nor does it seem disputable that to some extent scientific and technological advances, in particular in biology (e.g., promotion of Darwinism and evolutionary biology, embryonic stem cell research technologies, ‘morning-after pill’, etc.) fosters that revival. Advocating religious ideals, President George W. Bush has opposed embryonic stem cell research, and otherwise has been accused by scientists of ignoring scientific evidence that does not accord with Administrative policy.^[106]

An annotated table of contents

• Introduction: The Egalitarian Creed in America

• Egalitarianism comprises both ‘material’ egalitarianism but also ‘immaterial’, or 'spiritual', egalitarianism, the latter including such things as sense of purpose, vision of opportunity, self-esteem, sense of discipline and thirst for knowledge. The overlapping cycles in religion and politics — the four great awakenings reflect the struggle for egalitarianism in America, a basic creed of the American value system.

• The Fourth Great Awakening, the Political Realignment of the 1990s, and the Potential for Egalitarian Reform

• The great awakenings represent reform movements where an ethical and programmatic phase leads to political reform, both arising out of a lag between the consequences of technological change and the adjustments to that change by institutions and government. The first great awakening (beginning ca. 1730s) led to the American Revolution and the establishment of democracy. The second (beginning ca. 1800), led to the Civil War and abolition of slavery, and religion-based efforts to achieve equality of opportunity. The third (beginning ca. 1890), concerned with how to reform vice-ridden cities, with the moral implications of an amoral Darwinism, and with growing labor disputes, ultimately led to the New Deal and the Great Society and the rise of the welfare state. The fourth (beginning ca. 1960-70), led to a focus on spiritual reform. "One cannot understand current political and ethical trends, or properly forecast future economic developments, without understanding the cycles in religious feeling in American history and the social, economic, and political reform movements that they have generated." (page 17)

• Technological Change, Cultural Transformations, and Political Crises

• Discusses technological change as a double-edged sword, bringing economic growth and greater material egalitarianism, but also problems: cheaper alcohol available to urban poor; cheaper ocean transportation facilitating waves of immigration and its social and economic consequences, lowering wages and raising unemployment; manufacturing economies of scale destroying small businesses; advances in medicine and surgery outpacing ethical guidelines for their implementation. First paragraph chapter:

The ethical crises, religious upsurge, and programmatic demands that heralded the opening decades of the Fourth Great Awakening were precipitated by a series of major technological breakthroughs that destabil¬ized prevailing culture. Some of those unsettling advances were in energy production (particularly nuclear energy), information retrieval, and communications. The unprecedented extension of control of human biology, particularly in the fields of reproductive technology and organ transplantation, also provoked widespread concern. The new technological breakthroughs raised profoundly difficult ethical and practical issues, including many that had never been considered previously, such as how to dispose of large quantities of radioactive waste. Among those who worried about these issues, some became alarmed that humanity was heading toward disaster, led by corrupt or mindless scientists and business leaders.

• The Triumph of the Modern Egalitarian Ethic

• Emphasis in the third great awakening (beginning ca. 1890) on equality of life condition rather than on equality of opportunity. Part of the second great awakening: justice for native Americans, women’s rights, temperance, voting rights for women and blacks, expansion of education, income taxes, entitlement programs, restriction of immigration and child labor.

• The Egalitarian Revolution of the Twentieth Century

• An evaluation of the egalitarian reforms of the third great awakening (ca. 1890-1960). The successes and failures of policy changes, the relationship between the rapid pace of technology and the rigidities of the political process.

• The Emergence of a Postmodern Egalitarian Agenda

• The new agenda of the fourth great awakening (beginning ca. 1960-70): the necessity to overcome severe misallocations of immaterial resources, the problems involved, the paths to solution. “Central to the new reforms is a vast expansion of higher education and a variety of new educational forms geared to the needs of alienated young people and the elderly.”

• Afterword: Whither Goes Our World?

• A prediction of a rosier economic and egalitarian future.

• Acknowledgments, Appendices, Notes, References, Index

References

Citations and Notes

References

Citations and Notes