Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching

Quantitative Biology

Volumn 2, Issue 1, 2014, Pages 47-53

  Qian, Hong ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

diversity; fundamental theorem of natural selection; population dynamics

Indexed keywords

EID: 84923267299     PISSN: 20954689     EISSN: 20954697     Source Type: Journal    
DOI: 10.1007/s40484-014-0028-4     Document Type: Article

References (53)

1. Haldane, J. B. S. (1924) A mathematical theory of natural and artificial selection. Trans. Cambridge Philos. Soc, 23, 19–41
2. Fisher, R. A. (1930) The Genetical Theory of Natural Selection. Oxford: Clarendon Press
3. Wright, S. (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proc. Sixth Intern. Congress Genet. 1, 356–366
4. Crow, J. F. and Kimura, M. (1970) An Introduction to Population Genetics Theory. Caldwell: Harper & Row
5. Roughgarden, J. (1979) Theory of Population Genetics and Evolutionary Ecology: An Introduction. New York: Macmillan Publishers.
6. Felsenstein, J. (2011) Theoretical Evolutionary Genetics. Online Books, http://evolution.gs.washington.edu/pgbook/pgbook.pdf
7. Ewens, W. J. (2013) Mathematics, genetics and evolution. Quant. Biol, 1, 9–31
8. Qian, H. (2011) Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—An analytical theory. Nonlinearity, 24, R19–R49
9. Qian, H., Qian, M. and Tang, X. (2002) Thermodynamics of the general diffusion process: Time-reversibility and entropy production. J. Stat. Phys., 107, 1129–1141
10. Ge, H. and Qian, H. (2010) Physical origins of entropy production, free energy dissipation, and their mathematical representations. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 81, 051133
11. Esposito, M. and Van den Broeck, C. (2010) Three detailed fluctuation theorems. Phys. Rev. Lett., 104, 090601
12. Seifert, U. (2012) Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys., 75, 126001
13. Qian, H. and Kou, S. C. (2014) Statistics and related topics in singlemolecule biophysics. Ann. Rev. Stat. Appl, 1, 465–492
14. Zheng, Q. (1999) Progress of a half century in the study of the Luria-Delbrück distribution. Math. Biosci., 162, 1–32
15. Chang, H. H., Hemberg, M., Barahona, M., Ingber, D. E. and Huang, S. (2008) Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature, 453, 544–547
16. Gupta, P. B., Fillmore, C. M., Jiang, G., Shapira, S. D., Tao, K., Kuperwasser, C. and Lander, E. S. (2011) Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell, 146, 633–644
17. Huang, S. (2012) The molecular and mathematical basis of Waddington’s epigenetic landscape: a framework for post-Darwinian biology? BioEssays, 34, 149–157
18. Wang, J., Zhang, K., Xu, L. and Wang, E. (2011) Quantifying the Waddington landscape and biological paths for development and differentiation. Proc. Natl. Acad. Sci. U.S.A., 108, 8257–8262
19. Huang, S. (2012) Tumor progression: chance and necessity in Darwinian and Lamarckian somatic (mutationless) evolution. Prog. Biophys. Mol. Biol., 110, 69–86
20. Wang, G., Zhu, X., Hood, L. and Ao, P. (2013) From phage lambda to human cancer: endogenous molecular-cellular network hypothesis. Quant. Biol, 1, 32–49
21. 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
22. Wang, J., Xu, L. and Wang, E. (2008) Potential landscape and flux framework of nonequilibrium networks: robustness, dissipation, and coherence of biochemical oscillations. Proc. Natl. Acad. Sci. U.S.A., 105, 12271–12276
23. Ge, H., Wu, P., Qian, H. and Xie, X. S. (2013) A gene regulation theory for spontaneous transition between cellular phenotypes under nonequilibrium steady-state conditions. (Manuscript in preparation)
24. Zhou, D., Wu, D.-M., Li, Z., Qian, M.-P. and Zhang, M. Q. (2013) Population dynamics of cancer cells with cell state conversions. Quant. Biol, 1, 201–208
25. Eigen, M. and Schuster, P. (1979) The Hypercycle: A Principle of Natural Self-Organization. Berlin: Springer-Verlag
26. van Nimwegen, E., Crutchfield, J. P. and Huynen, M. (1999) Neutral evolution of mutational robustness. Proc. Natl. Acad. Sci. U.S.A., 96, 9716–9720
27. Kussell, E. and Leibler, S. (2005) Phenotypic diversity, population growth, and information in fluctuating environments. Science, 309, 2075–2078
28. Mustonen, V. and Lässig, M. (2010) Fitness flux and ubiquity of adaptive evolution. Proc. Natl. Acad. Sci. U.S.A., 107, 4248–4253
29. Price, G. R. (1972) Fisher’s ‘fundamental theorem’ made clear. Ann. Hum. Genet., vn36, 129–140
30. Edwards, A. W. F. (1994) The fundamental theorem of natural selection. Biol. Rev. Camb. Philos. Soc., 69, 443–474
31. Qian, H. (2014) The zeroth law of thermodynamics and volume-preserving conservative system in equilibrium with stochastic damping. Phys. Lett. A, 378, 609–616
32. Ao, P. (2008) Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics. Commun. Commun Theor Phys, 49, 1073–1090
33. Zhang, F., Xu, L., Zhang, K., Wang, E. and Wang, J. (2012) The potential and flux landscape theory of evolution. J. Chem. Phys., 137, 065102
34. Iwasa, Y. (1988) Free fitness that always increases in evolution. J. Theor. Biol., 135, 265–281
35. Maddox, J. (1991) Is Darwinism a thermodynamic necessity? Nature, 350, 653
36. Varadhan, S. R. S. (2012) Book review: Large deviations for stochastic processes. Am. Math. Soc, 49, 597–601
37. Voigt, J. (1981) Stochastic operators, information, and entropy. Commun. Math. Phys., 81, 31–38
38. Mackey, M. C. (1989) The dynamic origin of increasing entropy. Rev. Mod. Phys., 61, 981–1015
39. Qian, H. (2001) Relative entropy: free energy associated with equilibrium fluctuations and nonequilibrium deviations. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 63, 042103
40. Cover, T.M. and Thomas, J. A. (1991) Elements of Information Theory. New York: John Wiley & Sons
41. Onsager, L. (1931) Reciprocal relations in irreversible processes. I. Phys. Rev., 37, 405–426
42. Price, G. R. (1972) Extension of covariance selection mathematics. Ann. Hum. Genet., 35, 485–490
43. 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
44. 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
45. van Valen, L. (1973) A new evolutionary law. Evolu. Th., 1, 1–30
46. Ao, P. (2005) Laws in Darwinian evolutionary theory. Phys. Life Rev., 2, 117–156
47. Schrödinger, E. (1944) What is Life? London: Cambridge University Press
48. Qian, H. (2007) Phosphorylation energy hypothesis: open chemical systems and their biological functions. Annu. Rev. Phys. Chem., 58, 113–142
49. Qian, H. (2013) A decomposition of irreversible diffusion processes without detailed balance. J. Math. Phys., 54, 053302
50. Lotka, A. J. (1922) Contribution to the energetics of evolution. Proc. Natl. Acad. Sci. U.S.A., 8, 147–151
51. Lotka, A. J. (1922) Natural selection as a physical principle. Proc. Natl. Acad. Sci. U.S.A., 8, 151–154
52. Kirschner, M. W. and Gerhart, J. C. (2005) The Plausibility of Life: Resolving Darwin’s Dilemma. New Haven: Yale University Press
53. Kauffman, S. A. (1993) The Origins of Order: Self-Organization and Selection in Evolution. New York: Oxford University Press