Quantitative Biology

, Volume 1, Issue 1, pp 50–53 | Cite as

Stochastic physics, complex systems and biology

Perspective

Abstract

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod’s necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibria, spontaneous random “mutations” and “adaptations”. On an evolutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.

References

  1. 1.
    Mackey, M. C. (1989) The dynamic origin of increasing entropy. Rev. Mod. Phys., 61, 981–1015.CrossRefGoogle Scholar
  2. 2.
    Ge, H., Pressé, S., Ghosh, K. and Dill, K. A. (2012) Markov processes follow from the principle of maximum caliber. J. Chem. Phys., 136, 064108.PubMedCrossRefGoogle Scholar
  3. 3.
    Hopfield, J. J. (1994) Physics, computation, and why biology looks so different? J. Theor. Biol., 171, 53–60.CrossRefGoogle Scholar
  4. 4.
    Knight, J. (2002) Physics meets biology: bridging the culture gap. Nature, 419, 244–246.PubMedCrossRefGoogle Scholar
  5. 5.
    Prigogine, I. and Stengers, I. (1984) Order Out of Chaos: Man’s New Dialogue with Nature. Boulder, CO: New Sci. Lib. Shambhala.Google Scholar
  6. 6.
    Haken, H. (1983) Synergetics, An Introduction: Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology. 3rd rev. enl. ed. New York: Springer-Verlag.Google Scholar
  7. 7.
    Lasota, A. and Mackey, M. C. (1994) Chaos, Fractals and Noise: Stochastic Aspects of Dynamics. New York: Springer-Verlag.Google Scholar
  8. 8.
    Abarbanel, H. D. I., Brown, R., Sidorowich, J. and Tsimring, L. (1993) The analysis of observed chaotic data in physical systems. Rev. Mod. Phys., 65, 1331–1392.CrossRefGoogle Scholar
  9. 9.
    Tong, H. (1993) Non-Linear Time Series: A Dynamical System Approach. UK: Oxford University Press.Google Scholar
  10. 10.
    Qian, H., Shi, P.-Z. and Xing, J. (2009) Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity. Phys. Chem. Chem. Phys., 11, 4861–4870.PubMedCrossRefGoogle Scholar
  11. 11.
    Qian, H. (2011) Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reactions systems — an analytical theory. Nonlinearity, 24, R19–R49.CrossRefGoogle Scholar
  12. 12.
    Wax, N. (1954) Selected Papers on Noise and Stochastic Processes. New York: Dover Pubns.Google Scholar
  13. 13.
    Onsager, L. and Machlup, S. (1953) Fluctuations and irreversible processes. Phys. Rev., 91, 1505–1512.CrossRefGoogle Scholar
  14. 14.
    Fox, R. F. (1978) Gaussian stochastic processes in physics. Phys. Rep., 48, 179–283.CrossRefGoogle Scholar
  15. 15.
    Ge, H. and Qian, H. (2011) Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond. J. R. Soc. Interface, 8, 107–116.PubMedCrossRefGoogle Scholar
  16. 16.
    Qian, H. and Ge, H. (2012) Mesoscopic biochemical basis of isogenetic inheritance and canalization: stochasticity, nonlinearity, and emergent landscape. Mol. Cell. Biomech., 9, 1–30.PubMedGoogle Scholar
  17. 17.
    Monod, J. (1972) Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology. New York: Vintage Books.Google Scholar
  18. 18.
    Shapiro, B. E. and Qian, H. (1997) A quantitative analysis of single protein-ligand complex separation with the atomic force microscope. Biophys. Chem., 67, 211–219.PubMedCrossRefGoogle Scholar
  19. 19.
    Moore, P. B. (2012) How should we think about the ribosome? Annu. Rev. Biophys., 41, 1–19.PubMedCrossRefGoogle Scholar
  20. 20.
    Phillips, R. and Quake, S. R. (2006) The biological frontier of physics. Phys. Today, 59, 38–43.CrossRefGoogle Scholar
  21. 21.
    Bustamante, C., Liphardt, J. and Ritort, F. (2005) The nonequilibrium thermodynamics of small systems. Phys. Today, 58, 43–48.CrossRefGoogle Scholar
  22. 22.
    Qian, H. (2012) Hill’s small systems nanothermodynamics: a simple macromolecular partition problem with a statistical perspective. J. Biol. Phys., 38, 201–207.PubMedCrossRefGoogle Scholar
  23. 23.
    Westerhoff, H. V. and Palsson, B. Ø. (2004) The evolution of molecular biology into systems biology. Nat. Biotechnol., 22, 1249–1252.PubMedCrossRefGoogle Scholar
  24. 24.
    Qian, H. (2012) Cooperativity in cellular biochemical processes: noiseenhanced sensitivity, fluctuating enzyme, bistability with nonlinear feedback, and other mechanisms for sigmoidal responses. Annu. Rev. Biophys., 41, 179–204.PubMedCrossRefGoogle Scholar
  25. 25.
    Beard, D. A. and Kushmerick, M. J. (2009) Strong inference for systems biology. PLoS Comput. Biol., 5, e1000459.PubMedCrossRefGoogle Scholar
  26. 26.
    Koonin, E. V. (2009) Darwinian evolution in the light of genomics. Nucleic Acids Res., 37, 1011–1034.PubMedCrossRefGoogle Scholar
  27. 27.
    Alberts, B. (1998) The cell as a collection of protein machines: preparing the next generation of molecular biologists. Cell, 92, 291–294.PubMedCrossRefGoogle Scholar
  28. 28.
    Elowitz, M. B., Levine, A. J., Siggia, E. D. and Swain, P. S. (2002) Stochastic gene expression in a single cell. Science, 297, 1183–1186.PubMedCrossRefGoogle Scholar
  29. 29.
    Cai, L., Friedman, N. and Xie, X. S. (2006) Stochastic protein expression in individual cells at the single molecule level. Nature, 440, 358–362.PubMedCrossRefGoogle Scholar
  30. 30.
    Kirschner, M. W. and Gerhart, J. C. (2005) The Plausibility of Life: Resolving Darwin’s Dilemma. New Haven, CT: Yale University Press.Google Scholar
  31. 31.
    Ge, H. and Qian, H. (2010) Physical origins of entropy production, free energy dissipation, and their mathematical representations. Phys. Rev. E, 81, 051133.CrossRefGoogle Scholar
  32. 32.
    Zhang, X.-J., Qian, H. and Qian, M. (2012) Stochastic theory of nonequilibrium steady states and its applications (Part I). Phys. Rep., 510, 1–86.CrossRefGoogle Scholar
  33. 33.
    Ge, H., Qian, M. and Qian, H. (2012) Stochastic theory of nonequilibrium steady states (Part II): Applications in chemical biophysics. Phys. Rep., 510, 87–118.CrossRefGoogle Scholar
  34. 34.
    Jiang, D.-Q., Qian, M. and Qian, M.-P. (2004) Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems (Lecture Notes in Mathematics, Vol. 1833). Berlin: Springer-Verlag.CrossRefGoogle Scholar
  35. 35.
    Von Bertalanffy, L. (1950) The theory of open systems in physics and biology. Science, 111, 23–29.CrossRefGoogle Scholar
  36. 36.
    Qian, H. (2007) Phosphorylation energy hypothesis: open chemical systems and their biological functions. Annu. Rev. Phys. Chem., 58, 113–142.PubMedCrossRefGoogle Scholar
  37. 37.
    Wang, J., Xu, L. and Wang, E. K. (2008) Potential landscape and flux framework of nonequilibrium networks: robustness, dissipation, and coherence of biochemical oscillations. Proc. Natl. Acad. Sci. USA, 105, 12271–12276.PubMedCrossRefGoogle Scholar
  38. 38.
    Wang, J., Zhang, K. and Wang, E. K. (2010) Kinetic paths, time scale, and underlying landscapes: a path integral framework to study global natures of nonequilibrium systems and networks. J. Chem. Phys., 133, 125103.PubMedCrossRefGoogle Scholar
  39. 39.
    Wang, J., Zhang, K., Xu, L. and Wang, E. K. (2011) Quantifying the Waddington landscape and biological paths for development and differentiation. Proc. Natl. Acad. Sci. USA, 108, 8257–8262.PubMedCrossRefGoogle Scholar
  40. 40.
    Ge, H. and Qian, H. (2012) Analytical mechanics in stochastic dynamics: most probable path, large-deviation rate function and Hamilton-Jacobi equation. Int. J. Mod. Phys. B, 26, 1230012.CrossRefGoogle Scholar
  41. 41.
    Hanahan, D. and Weinberg, R. A. (2000) The hallmarks of cancer. Cell, 100, 57–70.PubMedCrossRefGoogle Scholar
  42. 42.
    Ao, P., Galas, D., Hood, L. and Zhu, X.-M. (2008) Cancer as robust intrinsic state of endogenous molecular-cellular network shaped by evolution. Med. Hypotheses, 70, 678–684.PubMedCrossRefGoogle Scholar
  43. 43.
    Ewens, W. J. (2004) Mathematical Population Genetics I. Theoretical Introduction. New York: Springer.CrossRefGoogle Scholar
  44. 44.
    Ao, P. (2005) Laws in Darwinian evolutionary theory. Phys. Life Rev., 2, 117–156.CrossRefGoogle Scholar
  45. 45.
    Ao, P. (2008) Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics. Commun. Theor. Phys., 49, 1073–1090.PubMedCrossRefGoogle Scholar
  46. 46.
    Qian H. (2012) A decomposition of irreversible diffusion processes without detailed balance. arXiv.org/abs/1204.6496.Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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