The Enhanced Finite State Projection algorithm, using conditional moment closure and time-scale separation

Abstract

The Chemical Master Equation (CME) is commonly used to describe the stochastic behavior of biomolecular systems. However, in general, the CME's dimension is very large or infinite, so analytical or even numerical solutions may be difficult to achieve. The truncation methods such as the Finite State Projection (FSP) algorithm alleviate this issue to some extent but not completely. To further resolve the computational issue, we propose the Enhanced Finite State Projection (EFSP) algorithm, in which the ubiquitous time-scale separation is utilized to reduce the dimension of the CME. Our approach combines the original FSP algorithm and the model reduction technique that we developed, to approximate an infinite dimensional CME with a finite dimensional CME that contains the slow species only. Unlike other time-scale separation methods, which rely on the fast-species counts' stationary conditional probability distributions, our model reduction technique relies on only the first few conditional moments of the fast-species counts. In addition, each iteration of the EFSP algorithm relies on the solution of the approximated CME that contains the slow species only, unlike the original FSP algorithm relies on the solution of the full CME. These two properties provide a significant computation advantage. The benefit of our algorithm is illustrated through a protein binding reaction example.