Propagation of fluctuations in biochemical systems, II: Nonlinear chains

IET Systems Biology
David F Anderson, Jonathan C Mattingly

Abstract

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

Feb 15, 1974·European Journal of Biochemistry·R Heinrich, T A Rapoport
Jul 5, 2001·Proceedings of the National Academy of Sciences of the United States of America·M Thattai, A van Oudenaarden
Jul 7, 2005·Bulletin of Mathematical Biology·Chetan GadgilHans G Othmer
Feb 24, 2007·Bulletin of Mathematical Biology·Frithjof Lutscher
Nov 14, 2007·Epigenetics : Official Journal of the DNA Methylation Society·H Frederik NijhoutCornelia M Ulrich

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Citations

Apr 26, 2007·Bulletin of Mathematical Biology·David F AndersonMichael C Reed
Apr 13, 2012·PLoS Computational Biology·Rachael Hageman BlairGary A Churchill
Aug 17, 2018·Physical Review. E·Fabrizio Pucci, Marianne Rooman
Apr 9, 2019·Journal of the Royal Society, Interface·Fabrizio Pucci, Marianne Rooman

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