Biological systems are wonderfully complex. In order to gain a better understanding on how the complexity dictates the biological functions and gives rise to different cellular phenotypes, it is important to investigate the underlying dynamic interactions of the biomolecular components. These interactions are governed by random events and thus stochastic models are needed to gain fundamental insight.
We have developed a closure scheme method that solves the master equation of stochastic chemical reaction models . The method postulates that only a finite number of probability moments is necessary to capture all of the system’s information, which can be achieved by maximizing the information entropy of the system.
Using the closure scheme, we examine the behavior of the stochastic Schlögl model, a toy, bistable chemical reaction network. We examine the behavior of the system with changes in the kinetic constants and focus on when the bifurcation to bistability occurs. Besides, we present an analysis of how the stochastic model behaves as the system approaches the thermodynamic limit.
Finally, we discuss the implementation of more advanced numerical methods in order to improve the convergence of the algorithm.
1. Smadbeck P, Kaznessis YN, "A Closure Scheme for Chemical Master Equations", Proc Natl Acad Sci U S A. 2013 Aug 27; 110(35): 14261-5 10.1073/pnas.1306481110
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