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Propagation of fluctuations in biochemical systems, II: nonlinear chains

Propagation of fluctuations in biochemical systems, II: nonlinear chains

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We consider biochemical reaction chains and investigate how random external fluctuations, as characterised by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of molecules is high enough so that the behaviour of the concentrations of the system is well approximated by differential equations. We conclude that the variances and coefficients of variation of the fluxes will decrease as one moves down the chain and, through an example, show that there is no corresponding result for the variances of the concentrations of the chemical species. We also prove that the fluctuations of the fluxes as characterised by their time averages decrease down reaction chains. The results presented give insight into how biochemical reaction systems are buffered against external perturbations solely by their underlying graphical structure and point out the benefits of studying the out-of-equilibrium dynamics of systems.

References

    1. 1)
      • R. Heinrich , T.A. Rapoport . A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur. J. Biochem. , 89 - 95
    2. 2)
      • M. Feinberg . Chemical reaction network structure and the stability of complex isothermal reactors - I. the deficiency zero and deficiency one theorems: review article 25. Chem. Eng. Sci. , 2229 - 2268
    3. 3)
      • E. Weinan , J.C. Mattingly . Ergodicity for the Navier–Stokes equation with degenerate random forcing: finite-dimensional approximation. Comm. Pure Appl. Math. , 11 , 1386 - 1402
    4. 4)
      • M. Delbr̈uck . Statistical fluctuations in autocatalytic reactions. J. Chem. Phys. , 120 - 124
    5. 5)
      • P. Billingsley . (1991) Convergence of probability measures.
    6. 6)
      • H. Kacser , J.A. Burns . The control of flux. Symp. Soc. Exper. Biol. , 65 - 104
    7. 7)
      • M. Thattai , A. van Oudenaarden . Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. USA , 15 , 8614 - 8619
    8. 8)
      • Anderson, D.F.: `Stochastic perturbations of biochemical reaction systems', 2005, PhD, Duke University.
    9. 9)
      • S.P. Meyn , R.L. Tweedie . (1996) Markov chains and stochastic stability.
    10. 10)
      • S.P. Meyn , R.L. Tweedie . Stability of Markovian processes III. Adv. Appl. Probab. , 3 , 518 - 548
    11. 11)
      • J.C. Mattingly , A.M. Stuart , D.J. Highman . Ergodicity for sdes and approximations: locally Lipschitz vector fields and degenerate noise. Stochastic Process. Appl. , 2 , 185 - 232
    12. 12)
    13. 13)
      • H.F. Nijhout , M.C. Reed , D.F. Anderson , J.C. Mattingly , S.J. James , C.M. Ulrich . Long-range allosteric interactions between the folate and methionine cycles stabilize DNA methylation reaction rate. Epigenetics , 81 - 87
    14. 14)
      • C. Gadgil , H. Othmer , C.H. Lee . A stochastic analysis of chemical firstorder reaction networks. Bull. Math. Biol. , 901 - 946
    15. 15)
      • D.F. Anderson , J.C. Mattingly , H.F. Nijhout , M.C. Reed . Propagation of fluctuations in biochemical systems, I: Linear SSC networks. Bull. Math. Biol.
    16. 16)
      • A. Lasota , M.C. Mackey . (1994) Chaos, fractals, and noise: stochastic aspects of dynamics.
    17. 17)
      • M. Feinberg . (1979) Lectures on chemical reaction networks, Delivered at the Mathematics Research Center.
    18. 18)
      • I.M. Krieger , P.J. Gans . First-order stochastic processes. J. Chem. Phys. , 1 , 247 - 250
    19. 19)
      • F.J.M. Horn , R. Jackson . General mass action kinetics. Arch. Rat. Mech. Anal. , 81 - 116
    20. 20)
      • M. Hairer . Ergodicity of stochastic differential equations driven by fractional Brownian motion. Ann. Probab. , 2 , 703 - 758
    21. 21)
      • L. Rey-Bellet , L.E. Thomas . Exponential convergence to nonequilibrium stationary states in classical statistical mechanics. Comm. Math. Phys. , 2 , 305 - 329
    22. 22)
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