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N Sinitsyn, N Hengartner, and I Nemenman. Adiabatic coarse-graining and simulations of stochastic biochemical networks. Proc. Natl. Acad. Sci. (USA) 106:10546-10551, 2009. PDF, supplement, arXiv.
- We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian ﬂuctuations of the slow ones. Our approach is similar to the Born–Oppenheimer approximation in quantum mechanics and follows from the stochastic path integral representation of the cumulant generating function of reaction events. In applications with a small number of chemical reactions, it produces analytical expressions for cumulants of chemical ﬂuxes between the slow variables. This allows for a low-dimensional, interpretable representation and can be used for high-accuracy, low-complexity coarse-grained numerical simulations. As an example, we derive the coarse-grained description for a chain of biochemical reactions and show that the coarse-grained and the microscopic simulations agree, but the former is 3 orders of magnitude faster.