An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions

The Journal of Chemical Physics
Ramon Grima

Abstract

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at bot...Continue Reading

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Citations

Apr 12, 2012·Nature Communications·Rajesh RamaswamyRamon Grima
Dec 7, 2013·BMC Genomics·Philipp ThomasRamon Grima
Jul 19, 2012·BMC Systems Biology·Jürgen PahleAlan J McKane
Aug 31, 2013·PloS One·Javad NoorbakhshPankaj Mehta
Jan 1, 2014·PloS One·Diana MonteolivaLuis Diambra
Jul 6, 2014·PLoS Computational Biology·Jan HasenauerFabian J Theis
Oct 14, 2011·The Journal of Chemical Physics·Andre Leier, Tatiana T Marquez-Lago
Feb 24, 2011·The Journal of Chemical Physics·Anshuman J DasK S Narayan
Sep 4, 2012·The Journal of Chemical Physics·Peter Keller, Angelo Valleriani
Jul 27, 2012·The Journal of Chemical Physics·R GrimaT J Newman
Sep 8, 2011·The Journal of Chemical Physics·Ramon GrimaArthur V Straube
Sep 1, 2014·The Journal of Chemical Physics·David SchnoerrRamon Grima
Dec 10, 2015·The Journal of Chemical Physics·Stephen SmithRamon Grima
Jun 26, 2013·Bulletin of Mathematical Biology·Raffaele BasileNikola Popović
Jan 1, 2011·Scientific Reports·Rajesh Ramaswamy, Ivo F Sbalzarini
Dec 3, 2013·The FEBS Journal·Ramon GrimaSantiago Schnell
Jul 9, 2013·Journal of Theoretical Biology·Philipp ThomasRamon Grima
Oct 22, 2013·Physical Chemistry Chemical Physics : PCCP·Márcio MourãoSantiago Schnell
May 6, 2016·Journal of the Royal Society, Interface·Stephen SmithRamon Grima
Jul 23, 2016·PLoS Computational Biology·Fabian FröhlichJan Hasenauer
Apr 28, 2017·PloS One·Johannes FalkBarbara Drossel
May 12, 2017·PLoS Computational Biology·Nick E PhillipsMagnus Rattray
Jul 3, 2017·The Journal of Chemical Physics·Basil S Bayati
Mar 27, 2018·PloS One·Sayuri Katharina Hortsch, Andreas Kremling
Dec 6, 2017·PLoS Computational Biology·Oleksandr OstrenkoIvo F Sbalzarini
Nov 16, 2018·Statistical Methods in Medical Research·Christoph ZimmerReza Yaesoubi
Apr 4, 2019·Journal of the Royal Society, Interface·Zhixing Cao, Ramon Grima
Apr 13, 2018·Bulletin of Mathematical Biology·Per Lötstedt
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ramon Grima
Jan 18, 2017·PLoS Computational Biology·Christoph ZimmerTed Cohen
Sep 9, 2017·Bioinformatics·Atefeh KazeroonianJan Hasenauer
Nov 28, 2018·Journal of Mathematical Biology·E MorakiK J Painter

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