Stochastic quasisteady state approximations for asymptotic solutions of the chemical master equation
In this paper, we propose two methods to carry out the quasisteady state approximation in stochastic models of enzyme catalytic regulation, based on WKB asymptotics of the chemical master equation or of the corresponding partial differential equation for the generating function. The first of the methods we propose involves the development of multiscale generalisation of a WKB approximation of the solution of the master equation, where the separation of time scales is made explicit which allows us to apply the quasisteady state approximation in a straightforward manner. To the lowest order, the multiscale WKB method provides a quasisteady state, Gaussian approximation of the probability distribution. The second method is based on the HamiltonJacobi representation of the stochastic process where, as predicted by large deviation theory, the solution of the partial differential equation for the corresponding characteristic function is given in terms of an effective action functional. The optimal transition paths between two states are then given by those paths that maximise the effective action. Such paths are the solutions of the Hamilton equations for the Hamiltonian associated to the effective action functional. The quasisteady state approximation is applied to the Hamilton equations thus providing an approximation to the optimal transitionmore »
 Authors:

^{[1]};
^{[2]}
 Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona) (Spain)
 (Barcelona) (Spain)
 Publication Date:
 OSTI Identifier:
 22252856
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 18; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; ALGORITHMS; ASYMPTOTIC SOLUTIONS; CATALYSIS; ENZYMES; FUNCTIONS; HAMILTONIANS; HAMILTONJACOBI EQUATIONS; MEANFIELD THEORY; SIMULATION; STOCHASTIC PROCESSES; WKB APPROXIMATION