(695b) Hybrid, Multiscale Algorithm for Simulating Stochastic Systems

Several multiscale algorithms (1-5) have recently been proposed to overcome computational challenges in stochastic modeling, arising from separation of time scales. Essentially all these approaches extend the deterministic quasi-equilibrium (QE) approximation to stochastic processes. The probabilistic nature of stochastic equilibrium necessitates the use of a stochastic time-integrator (microsolver) to relax the fast species/network to its quasi-equilibrium distribution or low-dimensional manifold. The choice of the microsolver in most existing multiscale algorithms is based on a priori assumptions about the population scales. These assumptions may have negative implications on the efficiency and/or accuracy of these methods. For example, the exact stochastic simulation algorithm (SSA) accurately relaxes the fast network to its quasi-equilibrium state, but is computationally expensive when the populations of the fast species are large (4, 5). On the other hand, using the approximate chemical Langevin equation as the microsolver will be inaccurate when the fast network involves low populations (3, 6).

In this talk we present a new, multiscale stochastic algorithm wherein the microsolver is decided on-the-fly, without sacrificing speed or accuracy of the simulation. Specifically, the algorithm seamlessly switches between coarse-grained Monte Carlo and exact SSA methods, as well as stiff and non-stiff algorithms based on instantaneous probability-based conditions. Integrating this adaptive approach with a new relaxation criterion enabled us to reduce the computational load of our original multiscale Monte Carlo algorithm (5) by more than factor of 10, while maintaining simulation accuracy at all scales.

Disparity in time scales is commonly encountered in intracellular signaling networks, rendering their simulation via SSA intractable. Various such networks from biology, such as the heat shock response and gene expression models, will be presented to demonstrate the strengths of this new hybrid, multiscale approach.

References

1. T. Cao, D. T. Gillespie, L. R. Petzold, Journal of Computational Physics 206, 395-411 (2005).

2. C. V. Rao, A. P. Arkin, Journal of Chemical Physics 118, 4999-5010 (2003).

3. H. Salis, Y. Kaznessis, Journal of Chemical Physics 122, 054103-1-13 (2005).

4. H. Salis, Y. Kaznessis, Journal of Chemical Physics 123, 214106 (2005).

5. A. Samant, D. G. Vlachos, J. Chem. Phys. 123, 14114 (2005).

6. E. L. Haseltine, J. B. Rawlings, Journal of Chemical Physics 117, 6959-6969 (2002).