Biological robustness


Robustness is a ubiquitously observed property of biological systems. It is considered to be a fundamental feature of complex evolvable systems. It is attained by several underlying principles that are universal to both biological organisms and sophisticated engineering systems. Robustness facilitates evolvability and robust traits are often selected by evolution. Such a mutually beneficial process is made possible by specific architectural features observed in robust systems. But there are trade-offs between robustness, fragility, performance and resource demands, which explain system behaviour, including the patterns of failure. Insights into inherent properties of robust systems will provide us with a better understanding of complex diseases and a guiding principle for therapy design.

Key Points

  • Robustness is a ubiquitous feature of biological systems. It ensures that specific functions of the system are maintained despite external and internal perturbations. System control, alternative (or fail-safe) mechanisms, modularity and decoupling are the underlying mechanisms that produce robustness.

  • Robustness facilitates the evolvability of complex dynamic systems. Evolution, given enough time, might select a robust trait that is tolerant against environmental perturbations. This interlinks the properties of robustness and evolvability. Robustness is ubiquitous in biological systems that have evolved.

  • There are specific architectural requirements for robust and evolvable systems — genetic buffering, robust modules and bow-tie architecture. These architectural requirements are the basis for the system's robustness against environmental perturbations, but congruent with genetic perturbations; they facilitate generation of a flexible phenotype.

  • Systems that are robust involve intrinsic trade-offs. Enhanced robustness against certain perturbations has to be balanced by extreme fragility elsewhere. This robust yet fragile nature, predicted by the highly optimized tolerance (HOT) theory, is a fundamental property of the system that has been optimally designed or has evolved to cope with perturbations. There are also other trade-offs in the system's performance and resource demands.

  • Diseases can be thought of in terms of the exposed fragility of robust yet fragile systems. The design of effective countermeasures requires proper understanding of a system's behavioural and failure patterns. Diabetes mellitus, cancer and HIV infection represent the typical failure of such a system that requires systematic countermeasures to control robustness of an epidemic state. Countermeasures include systematic intervention to control a system's dynamics, attack fragility or introduce decoys to re-establish control.

  • Developing a theory of biological robustness with a solid mathematical foundation that can realistically represent biological systems is a difficult challenge. Research into non-linear dynamics, control theory and non-equilibrium theory is urgently required, but it has to be careful to capture the essential structural complexity and heterogeneity of biological systems.

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Figure 1: Robust reactions of the system: to stay or to change.
Figure 2: Explaining robustness — the aeroplane example.
Figure 3: The architectural framework of robust evolvable systems.


  1. 1

    Kitano, H. Systems biology: a brief overview. Science 295, 1662–1664 (2002).

  2. 2

    Kitano, H. Computational systems biology. Nature 420, 206–210 (2002).

  3. 3

    Little, J. W., Shepley, D. P. & Wert, D. W. Robustness of a gene regulatory circuit. EMBO J. 18, 4299–4307 (1999).

  4. 4

    Ptashne, M. A Genetic Switch: Gene Control and Phage λ (Blackwell Scientific, Oxford, 1987).

  5. 5

    Zhu, X. M., Yin, L., Hood, L. & Ao, P. Calculating biological behaviors of epigenetic states in the phage λ life cycle. Funct. Integr. Genomics 4, 188–195 (2004).

  6. 6

    Santillan, M. & Mackey, M. C. Why the lysogenic state of phage λ is so stable: a mathematical modeling approach. Biophys. J. 86, 75–84 (2004).

  7. 7

    Alon, U., Surette, M. G., Barkai, N. & Leibler, S. Robustness in bacterial chemotaxis. Nature 397, 168–171 (1999). A seminal research paper on the robust adaptation observed in bacterial chemotaxis.

  8. 8

    Barkai, N. & Leibler, S. Robustness in simple biochemical networks. Nature 387, 913–917 (1997).

  9. 9

    Yi, T. M., Huang, Y., Simon, M. I. & Doyle, J. Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc. Natl Acad. Sci. USA 97, 4649–4653 (2000).

  10. 10

    von Dassow, G., Meir, E., Munro, E. M. & Odell, G. M. The segment polarity network is a robust developmental module. Nature 406, 188–192 (2000). A study that suggests that the modular robust network contributes to pattern formation during embryogenesis in D. melanogaster.

  11. 11

    Ingolia, N. T. Topology and robustness in the Drosophila segment polarity network. PLoS Biol. 2, e123 (2004).

  12. 12

    Barkai, N. & Shilo, B. Modeling pattern formation: counting to two in the Drosophila egg. Curr. Biol. 12, R493 (2002).

  13. 13

    Houchmandzadeh, B., Wieschaus, E. & Leibler, S. Establishment of developmental precision and proportions in the early Drosophila embryo. Nature 415, 798–802 (2002).

  14. 14

    Kitano, H. Cancer robustness: tumour tactics. Nature 426, 125 (2003).

  15. 15

    Kitano, H. Cancer as a robust system: implications for anticancer therapy. Nature Rev. Cancer 4, 227–235 (2004). A theoretical proposal to approach cancer treatment from the aspect of robustness.

  16. 16

    Kitano, H. et al. Metabolic syndrome and robustness trade–offs. Diabetes 53, (Suppl. 3), 1–10 (2004).

  17. 17

    Morohashi, M. et al. Robustness as a measure of plausibility in models of biochemical networks. J. Theor. Biol. 216, 19–30 (2002).

  18. 18

    Borisuk, M. T. & Tyson, J. J. Bifurcation analysis of a model of mitotic control in frog eggs. J. Theor. Biol. 195, 69–85 (1998).

  19. 19

    Rao, C. V., Kirby, J. R. & Arkin, A. P. Design and diversity in bacterial chemotaxis: a comparative study in Escherichia coli and Bacillus subtilis. PLoS Biol. 2, e49 (2004).

  20. 20

    McAdams, H. H. & Arkin, A. It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 15, 65–69 (1999).

  21. 21

    Rao, C. V., Wolf, D. M. & Arkin, A. P. Control, exploitation and tolerance of intracellular noise. Nature 420, 231–237 (2002).

  22. 22

    McAdams, H. H. & Shapiro, L. Circuit simulation of genetic networks. Science 269, 650–656 (1995).

  23. 23

    Arkin, A., Ross, J. & McAdams, H. H. Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected Escherichia coli cells. Genetics 149, 1633–1648 (1998).

  24. 24

    McAdams, H. H. & Arkin, A. Stochastic mechanisms in gene expression. Proc. Natl Acad. Sci. USA 94, 814–819 (1997).

  25. 25

    Bagowski, C. P., Besser, J., Frey, C. R. & Ferrell, J. E. Jr. The JNK cascade as a biochemical switch in mammalian cells: ultrasensitive and all-or-none responses. Curr. Biol. 13, 315–320 (2003).

  26. 26

    Ferrell, J. E. Jr. Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr. Opin. Cell. Biol. 14, 140–148 (2002).

  27. 27

    Tyson, J. J., Chen, K. & Novak, B. Network dynamics and cell physiology. Nature Rev. Mol. Cell Biol. 2, 908–916 (2001).

  28. 28

    Freeman, M. Feedback control of intercellular signalling in development. Nature 408, 313–319 (2000). A comprehensive review of how feedback control contributes to robustness and pattern formation during development.

  29. 29

    Agrawal, A. A. Phenotypic plasticity in the interactions and evolution of species. Science 294, 321–326 (2001).

  30. 30

    West-Eberhard, M. J. Developmental Plasticity and Evolution (Oxford Univ. Press, Oxford, 2003).

  31. 31

    Schlichting, C. & Pigliucci, M. Phenotypic Evolution: A Reaction Norm Perspective (Sinauer Associates Inc., Sunderland, Massachusetts, 1998).

  32. 32

    Schwob, E. & Nasmyth, K. CLB5 and CLB6, a new pair of B cyclins involved in DNA replication in Saccharomyces cerevisiae. Genes Dev. 7, 1160–1175 (1993).

  33. 33

    Kellis, M., Birren, B. W. & Lander, E. S. Proof and evolutionary analysis of ancient genome duplication in the yeast Saccharomyces cerevisiae. Nature 428, 617–624 (2004).

  34. 34

    Langkjaer, R. B., Cliften, P. F., Johnston, M. & Piskur, J. Yeast genome duplication was followed by asynchronous differentiation of duplicated genes. Nature 421, 848–852 (2003).

  35. 35

    Ohno, S. Evolution by Gene Duplication (Springer, Berlin, 1970).

  36. 36

    Gu, X. Evolution of duplicate genes versus genetic robustness against null mutations. Trends Genet. 19, 354–356 (2003).

  37. 37

    Gu, Z. et al. Role of duplicate genes in genetic robustness against null mutations. Nature 421, 63–66 (2003).

  38. 38

    Nowak, M. A., Boerlijst, M. C., Cooke, J. & Smith, J. M. Evolution of genetic redundancy. Nature 388, 167–171 (1997).

  39. 39

    Berg, J., Tymoczko, J. & Stryer, L. Biochemistry 5th edn (W. H. Freeman, 2002).

  40. 40

    DeRisi, J. L., Iyer, V. R. & Brown, P. O. Exploring the metabolic and genetic control of gene expression on a genomic scale. Science 278, 680–686 (1997).

  41. 41

    Edwards, J. S. & Palsson, B. O. Robustness analysis of the Escherichia coli metabolic network. Biotechnol. Prog. 16, 927–939 (2000).

  42. 42

    Edwards, J. S., Ibarra, R. U. & Palsson, B. O. In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nature Biotechnol. 19, 125–130 (2001).

  43. 43

    Conant, G. C. & Wagner, A. Convergent evolution of gene circuits. Nature Genet. 34, 264–266 (2003).

  44. 44

    Teichmann, S. A. & Babu, M. M. Gene regulatory network growth by duplication. Nature Genet. 36, 492–496 (2004).

  45. 45

    Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. From molecular to modular cell biology. Nature 402, 47–52 (1999). An influential article that stresses the importance of a system-based approach in biology, with particular emphasis on modularity.

  46. 46

    Schlosser, G. & Wagner, G. (eds.) Modularity in Development and Evolution (Univ. Chicago Press, Chicago, 2004). An edited collection of papers on modularity in biological systems that provides up-to-date discussions of the issue.

  47. 47

    Baldwin, C. & Clark, K. Design Rules, Vol. 1: The Power of Modularity (MIT Press, Cambridge, Massachusetts, 2000).

  48. 48

    Simon, H. The Sciences and the Artificial 3rd edn (MIT Press, Cambridge, Massachusetts, 1996).

  49. 49

    McAdams, H. H., Srinivasan, B. & Arkin, A. P. The evolution of genetic regulatory systems in bacteria. Nature Rev. Genet. 5, 169–178 (2004).

  50. 50

    Spirin, V. & Mirny, L. A. Protein complexes and functional modules in molecular networks. Proc. Natl Acad. Sci. USA 100, 12123–12128 (2003).

  51. 51

    Rutherford, S. L. & Lindquist, S. Hsp90 as a capacitor for morphological evolution. Nature 396, 336–342 (1998).

  52. 52

    Queitsch, C., Sangster, T. A. & Lindquist, S. Hsp90 as a capacitor of phenotypic variation. Nature 417, 618–624 (2002).

  53. 53

    Rutherford, S. L. Between genotype and phenotype: protein chaperones and evolvability. Nature Rev. Genet. 4, 263–274 (2003). This article describes issues to do with genetic buffering, particularly involving hsp90, and outlines the implications of such phenomena.

  54. 54

    Waddington, C. H. The Strategy of the Genes: a Discussion of Some Aspects of Theoretical Biology (Macmillan, New York, 1957).

  55. 55

    Kimura, M. Preponderance of synonymous changes as evidence for the neutral theory of molecular evolution. Nature 267, 275–276 (1977).

  56. 56

    Kimura, M. The neutral theory of molecular evolution. Sci. Am. 241, 98–100, 102, 108 passim (1979).

  57. 57

    Hartman, J. L. 4th, Garvik, B. & Hartwell, L. Principles for the buffering of genetic variation. Science 291, 1001–1004 (2001).

  58. 58

    Bergman, A. & Siegal, M. L. Evolutionary capacitance as a general feature of complex gene networks. Nature 424, 549–552 (2003).

  59. 59

    Kitami, T. & Nadeau, J. H. Biochemical networking contributes more to genetic buffering in human and mouse metabolic pathways than does gene duplication. Nature Genet. 32, 191–194 (2002).

  60. 60

    Siegal, M. L. & Bergman, A. Waddington's canalization revisited: developmental stability and evolution. Proc. Natl Acad. Sci. USA 99, 10528–10532 (2002).

  61. 61

    Lev Bar-Or, R. et al. Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study. Proc. Natl Acad. Sci. USA 97, 11250–11255 (2000).

  62. 62

    Lahav, G. et al. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nature Genet. 36, 147–150 (2004).

  63. 63

    Kirschner, M. & Gerhart, J. Evolvability. Proc. Natl Acad. Sci. USA 95, 8420–8427 (1998). An influential article that discusses the various molecular and system mechanisms that contribute to the evolvability of organisms. Together with their book (reference 64), basic issues and perspectives are presented.

  64. 64

    Gerhart, J. & Kirschner, M. Cells, Embryos, and Evolution: Toward a Cellular and Developmental Understanding of Phenotypic Variation and Evolutionary Adaptability (Blackwell Science, Malden, Massachusetts, 1997).

  65. 65

    Broder, A. et al. in The Nineth International World Wide Web Conference 309–320 (Elsevier Science, Amsterdam, 2000).

  66. 66

    Csete, M. E. & Doyle, J. Bow ties, metabolism and disease. Trends Biotechnol. 22, 446–450 (2004).

  67. 67

    de Visser, J. et al. Evolution and detection of genetics robustness. Evolution 57, 1959–1972 (2003). A summary of workshop discussions on evolvability and robustness, which are relevant to current discussions.

  68. 68

    Eldar, A. et al. Robustness of the BMP morphogen gradient in Drosophila embryonic patterning. Nature 419, 304–308 (2002).

  69. 69

    Nieuwkoop, P. D. Pattern formation in artificially activated ectoderm (Rana pipiens and Ambystoma punctatum). Dev. Biol. 7, 255–279 (1963).

  70. 70

    Nieuwkoop, P. D. Inductive interactions in early amphibian development and their general nature. J. Embryol. Exp. Morphol. 89, S333–S347 (1985).

  71. 71

    Pires-daSilva, A. & Sommer, R. J. The evolution of signalling pathways in animal development. Nature Rev. Genet. 4, 39–49 (2003).

  72. 72

    Carroll, S., Grenier, J. & Weatherbee, S. From DNA to Diversity: Molecular Genetics and the Evolution of Animal Design (Blackwell, Oxford, 2001). This book describes the role of toolkit and co-option in development.

  73. 73

    Wagner, G. P., Amemiya, C. & Ruddle, F. Hox cluster duplications and the opportunity for evolutionary novelties. Proc. Natl Acad. Sci. USA 100, 14603–14606 (2003).

  74. 74

    Gehring, W. J. Master Control Genes in Development and Evolution: The Homeobox Story (Yale Univ. Press, New Haven; London, 1998).

  75. 75

    Lewis, E. B. A gene complex controlling segmentation in Drosophila. Nature 276, 565–570 (1978).

  76. 76

    Kaufman, T. C., Seeger, M. A. & Olsen, G. Molecular and genetic organization of the antennapedia gene complex of Drosophila melanogaster. Adv. Genet. 27, 309–362 (1990).

  77. 77

    Struhl, G. A homoeotic mutation transforming leg to antenna in Drosophila. Nature 292, 635–638 (1981).

  78. 78

    Halder, G., Callaerts, P. & Gehring, W. J. Induction of ectopic eyes by targeted expression of the eyeless gene in Drosophila. Science 267, 1788–1792 (1995).

  79. 79

    Taniguchi, T. & Takaoka, A. A weak signal for strong responses: interferon-α/β revisited. Nature Rev. Mol. Cell Biol. 2, 378–386 (2001).

  80. 80

    Bhalla, U. S. & Iyengar, R. Robustness of the bistable behavior of a biological signaling feedback loop. Chaos 11, 221–226 (2001).

  81. 81

    Wagner, G. P. & Altenberg, L. Complex adaptations and the evolution of evolvability. Evolution 50, 967–976 (1996).

  82. 82

    Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N. & Barabasi, A. L. The large-scale organization of metabolic networks. Nature 407, 651–654 (2000).

  83. 83

    Barabasi, A. L. & Oltvai, Z. N. Network biology: understanding the cell's functional organization. Nature Rev. Genet. 5, 101–113 (2004). A good summary of the scale-free network in biology by the originator of the idea.

  84. 84

    Albert, R., Jeong, H. & Barabasi, A. L. Error and attack tolerance of complex networks. Nature 406, 378–382 (2000).

  85. 85

    Ma, H. W. & Zeng, A. P. The connectivity structure, giant strong component and centrality of metabolic networks. Bioinformatics 19, 1423–1430 (2003).

  86. 86

    van Nimwegen, E. Scaling laws in the functional content of genomes. Trends Genet. 19, 479–484 (2003).

  87. 87

    van Nimwegen, E. in Power Laws, Scale–free Networks, and Genome Biology (ed. Koonin, E. V.) (Landes Bioscience, in the press).

  88. 88

    Ashburner, M. et al. Gene ontology: tool for the unification of biology. The Gene Ontology Consortium. Nature Genet. 25, 25–29 (2000).

  89. 89

    Jordan, J. D., Landau, E. M. & Iyengar, R. Signaling networks: the origins of cellular multitasking. Cell 103, 193–200 (2000).

  90. 90

    Jordan, J. D. & Iyengar, R. Modes of interactions between signaling pathways. Biochem. Pharmacol. 55, 1347–1352 (1998).

  91. 91

    Hermans, E. Biochemical and pharmacological control of the multiplicity of coupling at G-protein-coupled receptors. Pharmacol. Ther. 99, 25–44 (2003).

  92. 92

    Werry, T. D., Wilkinson, G. F. & Willars, G. B. Mechanisms of cross-talk between G-protein-coupled receptors resulting in enhanced release of intracellular Ca2+. Biochem. J. 374, 281–296 (2003).

  93. 93

    Vassilatis, D. K. et al. The G protein-coupled receptor repertoires of human and mouse. Proc. Natl Acad. Sci. USA 100, 4903–4908 (2003).

  94. 94

    Mattick, J. S. RNA regulation: a new genetics? Nature Rev. Genet. 5, 316–323 (2004).

  95. 95

    Mattick, J. S. Non-coding RNAs: the architects of eukaryotic complexity. EMBO Rep. 2, 986–991 (2001).

  96. 96

    Mattick, J. S. Challenging the dogma: the hidden layer of non-protein-coding RNAs in complex organisms. Bioessays 25, 930–939 (2003).

  97. 97

    Schreiber, S. L. & Bernstein, B. E. Signaling network model of chromatin. Cell 111, 771–778 (2002).

  98. 98

    Carroll, S. B. Chance and necessity: the evolution of morphological complexity and diversity. Nature 409, 1102–1109 (2001).

  99. 99

    Carlson, J. M. & Doyle, J. Highly optimized tolerance: a mechanism for power laws in designed systems. Phys. Rev. E 60, 1412–1427 (1999).

  100. 100

    Carlson, J. M. & Doyle, J. Complexity and robustness. Proc. Natl Acad. Sci. USA 99 (Suppl 1), 2538–2545 (2002). An introductory article on the highly optimized tolerance (HOT) theory.

  101. 101

    Barabasi, A. L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999).

  102. 102

    Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality. Phys. Rev. A 38, 364–374 (1988).

  103. 103

    Csete, M. E. & Doyle, J. C. Reverse engineering of biological complexity. Science 295, 1664–1669 (2002). An inspiring piece that discusses the complexity of biological systems from engineering and control-theory perspective.

  104. 104

    Lamport, L., Shostak, R. & Pease, M. The Byzantine generals problem. ACM Trans. Program. Lang. Sys. 4, 382–401 (1982).

  105. 105

    Cassel, D. & Pfeuffer, T. Mechanism of cholera toxin action: covalent modification of the guanyl nucleotide-binding protein of the adenylate cyclase system. Proc. Natl Acad. Sci. USA 75, 2669–2673 (1978).

  106. 106

    Moss, J. & Vaughan, M. Guanine nucleotide-binding proteins (G proteins) in activation of adenylyl cyclase: lessons learned from cholera and 'travelers' diarrhea'. J. Lab. Clin. Med. 113, 258–268 (1989).

  107. 107

    Harris, A. L. Hypoxia — a key regulatory factor in tumour growth. Nature Rev. Cancer 2, 38–47 (2002).

  108. 108

    Bingle, L., Brown, N. J. & Lewis, C. E. The role of tumour-associated macrophages in tumour progression: implications for new anticancer therapies. J. Pathol. 196, 254–265 (2002).

  109. 109

    Hasty, J., McMillen, D. & Collins, J. J. Engineered gene circuits. Nature 420, 224–230 (2002).

  110. 110

    McMichael, A. J. & Rowland-Jones, S. L. Cellular immune responses to HIV. Nature 410, 980–987 (2001).

  111. 111

    McCune, J. M. The dynamics of CD4+ T-cell depletion in HIV disease. Nature 410, 974–979 (2001).

  112. 112

    Richman, D. D. HIV chemotherapy. Nature 410, 995–1001 (2001).

  113. 113

    Pomerantz, R. J. HIV: a tough viral nut to crack. Nature 418, 594–595 (2002).

  114. 114

    Dropulic, B., Hermankova, M. & Pitha, P. M. A conditionally replicating HIV-1 vector interferes with wild-type HIV-1 replication and spread. Proc. Natl Acad. Sci. USA 93, 11103–11108 (1996).

  115. 115

    Weinberger, L. S., Schaffer, D. V. & Arkin, A. P. Theoretical design of a gene therapy to prevent AIDS but not human immunodeficiency virus type 1 infection. J. Virol. 77, 10028–10036 (2003).

  116. 116

    Mautino, M. R. & Morgan, R. A. Gene therapy of HIV-1 infection using lentiviral vectors expressing anti-HIV-1 genes. AIDS Patient Care STDS 16, 11–26 (2002).

  117. 117

    von Bertalanffy, L. General System Theory: Foundations, Development, Applications (George Braziller Inc., New York, 1976).

  118. 118

    Wiener, N. Cybernetics: or Control and Communication in the Animal and the Machine (MIT Press, Cambridge, Massachusetts, 1948).

  119. 119

    Doyle, J., Glover, K., Khargonekar, P. & Francis, B. State-space solutions to standard H2 and H1 control problems. IEEE Trans. Automat. Control 34, 831–847 (1989).

  120. 120

    Ma, L. & Iglesias, P. A. Quantifying robustness of biochemical network models. BMC Bioinformatics 3, 38 (2002).

  121. 121

    Haken, H. Synergetics — An Introdution 2nd edn (Springer, Berlin, 1978).

  122. 122

    Prajna, S. & Papachristodoulou, A. in Proceedings of American Control Conference 2779–2784 (IEEE, Denver, Colorado, 2003).

  123. 123

    Prajna, S., Papachristodoulou, A. & Parrilo, P. A. in Proceedings of IEEE Conference on Decision and Control 741–746 (IEEE, Las Vegas, 2002).

  124. 124

    Chen, K. C. et al. Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell 15, 3841–3862 (2004).

  125. 125

    Martins, N. C. & Dahleh, M. A. in Forty-Second Annual Allerton Conference on Communication, Control, and Computing (Univ. Illinois, Urbana-Champaign, 2004).

  126. 126

    Martins, N. C., Dahleh, M. A. & Elia, N. in IEEE Conference on Decision and Control (IEEE, Nassau, The Bahamas, in the press).

  127. 127

    Prigogine, I. & Defay, R. Chemical Thermodynamics (Everett, Longmans Geeen, London, 1954).

  128. 128

    Prigogine, I., Lefever, R., Goldbeter, A. & Herschkowitz-Kaufman, M. Symmetry breaking instabilities in biological systems. Nature 223, 913–916 (1969).

  129. 129

    Prigogine, I., Nicolis, G. & Babloyantz, A. Nonequilibrium problems in biological phenomena. Ann. NY Acad. Sci. 231, 99–105 (1974).

  130. 130

    Nicolis, G. & Prigogine, I. Self-Organization in Non–Equilibrium Systems: From Dissipative Structures to Order Through Fluctuations (J. Wiley & Sons, New York, 1977).

  131. 131

    Ao, P. Potential in stochastic differential equations: novel construction. J. Phys. A 37, L25–L30 (2004).

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I would like to thank members of the Sony Computer Science laboratories, Inc. and ERATO-SORST Kitano Symbiotic Systems Project for their fruitful discussions, John Doyle and Marie Csete for critical reading of the initial version of this article, a number of colleagues who discussed the article, and anonymous referees for informative comments. This research is, in part, supported by the ERATO-SORST programme (run by the Japan Science and Technology Agency) of the Systems Biology Institute, the Center of Excellence programme, the special coordination funds (Ministry of Education, Culture, Sports, Science, and Technology) to Keio University and the Air Force Office of Scientific Research (AFOSR/AOARD).

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