Mathematics of small stochastic reaction networks: A boundary layer theory for eigenstate analysis

Eric Mjolsness, Upendra Prasad

Research output: Contribution to journalArticlepeer-review

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Abstract

We study and analyze the stochastic dynamics of a reversible bimolecular reaction A B C called the trivalent reaction. This reaction is of a fundamental nature and is part of many biochemical reaction networks. The stochastic dynamics is given by the stochastic master equation, which is difficult to solve except when the equilibrium state solution is desired. We present a novel way of finding the eigenstates of this system of difference-differential equations, using perturbation analysis of ordinary differential equations arising from approximation of the difference equations. The time evolution of the state probabilities can then be expressed in terms of the eigenvalues and the eigenvectors.

Original languageEnglish
Article number104111
JournalJournal of Chemical Physics
Volume138
Issue number10
DOIs
StatePublished - 14 Mar 2013

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