As stochastic simulations become increasingly common in biological research, tools for analysis of such systems are in demand. The deterministic analog to stochastic models, a set of probability moment equations equivalent to the Chemical Master Equation (CME), offers the possibility of a priori analysis of systems without the need for computationally costly Monte Carlo simulations. Despite the drawbacks of the method, in particular non-linearity in even the simplest of cases, the use of moment equations combined with moment-closure techniques has been used effectively in many fields. The techniques currently available to generate moment equations rely upon analytical expressions that are not efficient upon scaling. Additionally, the resulting moment-dependent matrix is lower diagonal and demands massive memory allocation in extreme cases. Here it is demonstrated that by utilizing factorial moments and the probability generating function (the Z-transform of the probability distribution) a recursive algorithm is produced. The resulting method is scalable and particularly efficient when high-order moments are required. The matrix produced is banded and often demands substantially less memory resources.
Bibliographical noteFunding Information:
This work was supported by a grant from the National Institute of Health (American Recovery and Reinvestment Act grant GM086865 ) and a grant from the National Science Foundation ( CMET-064472 ) with computational support from the Minnesota Supercomputering Institute (MSI).
- Computational chemistry
- Mathematical modeling
- Moments and probability
- Numerical analysis
- Stochastic simulation