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Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNAs or proteins. Several approaches including Stochastic Master Equation (SME) and Probabilistic Boolean Network (PBN) have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that SME is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, PBN captures only the coarse-scale stochastic properties of the system. We propose a new approximation of the SME model that is able to capture the finer details of the modeled system including bi-stabilities and oscillatory behavior, and yet has a significantly lower computational complexity. We represent the system using tensors and apply Zassenhaus formula to approximate the exponential of a sum of matrices as a product of matrices. Simulation results of the new method on four different biological benchmark systems illustrate performance comparable to detailed SME models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.
Nonlinear approximation, Computing Methodologies, Simulation, Modeling, and Visualization, Types of Simulation, Discrete event, Mathematics of Computing, Numerical Analysis, Approximation

R. Pal and M. U. Caglar, "Stochastic Model Simulation Using Kronecker Product Analysis and Zassenhaus Formula Approximation," in IEEE/ACM Transactions on Computational Biology and Bioinformatics.
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