Frontiers in Computational and Systems Biology pp 175-201

Part of the Computational Biology book series (COBO, volume 15)

Irreversible Stochastic Processes, Coupled Diffusions and Systems Biochemistry


  1. 1.
    M.-P. Qian and M. Qian. The decomposition into a detailed balance part and a circulation part of an irreversible stationary Markov chain. Sci Sin A, 22:69–79, 1979. Google Scholar
  2. 2.
    M.-P. Qian and M. Qian. Circulation for recurrent Markov chain. Z Wahrscheinlichkeitstheor Verw Geb, 59:203–210, 1982. MATHCrossRefGoogle Scholar
  3. 3.
    Y. Zhang, M.-P. Qian, Q. Ouyang, M. Deng, F. Li, and C. Tang. Stochastic model of yeast cell-cycle network. Physica, 219:35–39, 2006. MathSciNetMATHGoogle Scholar
  4. 4.
    E. Schrödinger. What is Life? Cambridge University Press, Cambridge, 1944. Google Scholar
  5. 5.
    P.J. Choi, L. Cai, K. Frieda, and X.S. Xie. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science, 322:442–446, 2008. CrossRefGoogle Scholar
  6. 6.
    M.W. Deem. Mathematical adventures in biology. Phys Today, January: 42–47, 2007. (Feature article). Google Scholar
  7. 7.
    D.A. Beard and H. Qian. Chemical Biophysics: Quantitative Analysis of Cellular System. Cambridge University Press, London, 2008. MATHCrossRefGoogle Scholar
  8. 8.
    M. Qian and B. Zhang. Multi-dimensional coupled diffusion process. Acta Math Appl Sin, 2:168–179, 1984. Google Scholar
  9. 9.
    Z. Guo, M. Qian, and M.-P. Qian. Minimal coupled diffusion process. Acta Math Appl Sin, 3:58–69, 1987. MATHGoogle Scholar
  10. 10.
    F. Zhang. Exponential convergence of coupled diffusion processes. J Math Phys, 46:063304, 2005. MathSciNetCrossRefGoogle Scholar
  11. 11.
    G.E. Briggs and J.B.S. Haldane. A note on the kinetics of enzyme action. Biochem J, 19:338–339, 1925. Google Scholar
  12. 12.
    I.H. Segel. Enzyme Kinetics, Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. Wiley-Interscience, New York, 1993. Google Scholar
  13. 13.
    X.S. Xie and H.P. Lu. Single-molecule enzymology. J Biol Chem, 274:15967–15970, 1999. CrossRefGoogle Scholar
  14. 14.
    H. Qian. Open-system nonequilibrium steady state: statistical thermodynamics, fluctuations, and chemical oscillations. J Phys Chem B, 110:15063–15074, 2006. CrossRefGoogle Scholar
  15. 15.
    H. Qian. Cooperativity and specificity in enzyme kinetics: a single-molecule time-based perspective. Biophys J, 95:10–17, 2008. CrossRefGoogle Scholar
  16. 16.
    D.-Q. Jiang, M. Qian, and M.-P. Qian. Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems. Springer, New York, 2004. MATHCrossRefGoogle Scholar
  17. 17.
    K. Kamata, M. Mitsuya, T. Nishimura, J. Eiki, and Y. Nagata. Structural basis for allosteric regulation of the monomeric allosteric enzyme human glucokinase. Structure, 429–438, 2004. Google Scholar
  18. 18.
    G.R. Welch. The Fluctuating Enzyme. Wiley, New York, 1986. Google Scholar
  19. 19.
    J.A. Hanson, H. Yang, et al.. Illuminating the mechanistic roles of enzyme conformational dynamics. Proc Natl Acad Sci, 104:18055–18060, 2007. CrossRefGoogle Scholar
  20. 20.
    H. Qian and P.-Z. Shi. Fluctuating enzyme and its biological functions: positive cooperativity without multiple states. J Phys Chem B, 113:2225–2230, 2009. CrossRefGoogle Scholar
  21. 21.
    H. Qian. The mathematical theory of molecular motor movement and chemomechanical energy transduction. J Math Chem, 27(3), 2000. Google Scholar
  22. 22.
    F. Jacob and J. Monod. Genetic regulatory mechanisms in the synthesis of proteins. J Mol Biol, 3:318–356, 1961. CrossRefGoogle Scholar
  23. 23.
    H. Qian, M. Qian, and X. Tang. Thermodynamics of the general diffusion process: Time-reversibility and entropy production. J Stat Phys, 107:1129–1141, 2002. MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    H. Qian, P.-Z. Shi, and J. Xing. Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity. Phys Chem Chem Phys, 11:4861–4870, 2009. CrossRefGoogle Scholar
  25. 25.
    R.B. Lehoucq, D.C. Sorensen, and C. Yang. ARPACK User’s Guide. Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Method. SIAM, Philadelphia, 1998. CrossRefGoogle Scholar
  26. 26.
    E.V. Koonin. Darwinian evolution in the light of genomics. Nucleic Acids Res, 37:1011–1034, 2009. CrossRefGoogle Scholar
  27. 27.
    W.J. Ewens. Mathematical Population Genetics, 2nd edition. Springer, Berlin, 2004. MATHCrossRefGoogle Scholar
  28. 28.
    J.H. Gillespie. The Causes of Molecular Evolution. Oxford University Press, London, 1991. Google Scholar
  29. 29.
    J. Schnakenberg. Network theory of microscopic and macroscopic behaviour of master equation systems. Rev Mod Phys, 48:571–585, 1976. MathSciNetCrossRefGoogle Scholar
  30. 30.
    K. Tomita and H. Tomita. Irreversible circulation of fluctuation. Prog Theor Phys, 51:1731–1749, 1974. CrossRefGoogle Scholar
  31. 31.
    R.K.P. Zia and B. Schmittmann. Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states. J Stat Mech Theor Exp, 07012, 2007. Google Scholar
  32. 32.
    D. Andrieux and P. Gaspard. Fluctuation theorem for currents and Schnakenberg network theory. J Stat Phys, 127:107–131, 2007. MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    G. Nicolis and I. Prigogine. Self-Organization in Nonequilibrium Systems. Wiley-Interscience, New York, 1977. MATHGoogle Scholar
  34. 34.
    T.L. Hill. Free Energy Transduction in Biology: The Steady-state Kinetic and Thermodynamic Formalism. Academic Press, New York, 1977. Google Scholar
  35. 35.
    M. Qian, G.X. Wang, and X.J. Zhang. Stochastic resonance on a circle without excitation: Physical investigation and peak frequency formula. Phys Rev E, 62:6469, 2000. CrossRefGoogle Scholar
  36. 36.
    H. Qian and M. Qian. Pumped biochemical reactions, nonequilibrium circulation, and stochastic resonance. Phys Rev Lett, 84:2271–2274, 2000. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

Personalised recommendations