2019/01/29 by Carlos Floyd, Floyd, Carlos, Garegin A. Papoian +3
Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · Chemistry · #Advanced Thermodynamics and Statistical Mechanics #Gene Regulatory Network Analysis #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.1901.10520
In modeling the interior of cells by simulating a reaction-diffusion master\nequation over a grid of compartments, one employs the assumption that the copy\nnumbers of various chemical species are small, discrete quantities. We show\nthat in this case, textbook expressions for the change in Gibbs free energy\naccompanying a chemical reaction or diffusion between adjacent compartments\nbecome inaccurate. We derive exact expressions for these free energy changes\nunder the assumption of discrete copy numbers and illustrate how these\nexpressions reduce to the textbook expressions under a series of successive\napproximations leveraging the relative sizes of the stoichiometric coefficients\nand the copy numbers of the solutes and solvent. Numerical results are\npresented to corroborate the claim that if the copy numbers are treated as\ndiscrete quantities, then only these more exact expressions lead to correct\nequilibrium behavior. The newly derived expressions are critical for correctly\ntracking dissipation and entropy production in mesoscopic simulations based on\nthe reaction-diffusion master equation formalism.\n