Abstract
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation approximation of the paths. In this paper, multiscale methods for approximating paths are used to formulate different strategies for estimating the dynamics by diffusion processes. We then analyze how efficient and accurate these methods are in a range of different scenarios and compare their respective advantages and disadvantages to other methods proposed to analyze multiscale chemical networks.
Highlights
A well-mixed chemically reacting system in a container of volume V is described, at time t, by its N -dimensional state vector (1.1)X(t) ≡ [X1(t), X2(t), . . . , XN (t)], where N is the number of chemical species in the system and Xi(t) ∈ N0, i = 1, 2, . . . , N, is the number of molecules of the ith chemical species at time t
In this paper we have introduced two new methods for approximating the dynamics of slow variables in multiscale stochastic chemical networks: the nested multiscale algorithm (NMA) and quasi-steady state multiscale algorithm (QSSMA)
These new methods combine ideas from the constrained multiscale algorithm (CMA) [5], with ideas used in existing methods for speeding up the Gillespie stochastic simulation algorithm (SSA) for multiscale systems [8, 2]
Summary
A well-mixed chemically reacting system in a container of volume V is described, at time t, by its N -dimensional state vector (1.1). The idea of the NSSA is to approximate the effective propensities of the slow reactions in order to compute trajectories only on the slow state space This is done by using short bursts of stochastic simulation of the fast reaction subsystem. The NMA is approximating the effective propensity of the slow reactions by using a QSSA, so that all that needs to be computed is the expectation of the propensities with respect to the invariant distribution of the fast subsystem The analytical solution of the steady-state CME is given by the following multivariate Poisson distribution [19]:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
