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Matrix Network: A New Data Structure for Efficient Enumeration of Microstates of a Genetic Regulatory Network

Stochastic processes play an important role in gene regulatory networks. For many years, methods and algorithms have been developed to solve the problems regarding stochastic mechanisms in the cellular reaction system. Discrete Chemical Master Equation (dCME) is a method developed to analyze biological networks by computing the exact probability distribution of the microstates. With this method, because all computations and analyses of probability distribution can be processed based on the enumerated microstates, network microstates enumeration has been considered as a significant and prerequisite step. However, there is no efficient enumeration method. Applications will perform poorly when enumeration must address a complex or large network. To improve these microstate computation and analysis methods, we propose an efficient algorithm to enumerate microstates using Matrix Network, a new data structure we designed. Unlike traditional methods that perform the enumeration using simulation to apply reactions, the proposed approach utilizes the correlation of the microstate values and the geometric structure of the microstate map to accelerate the enumeration computation. In this paper, the theoretical basis, features and algorithms of Matrix Network are discussed. Moreover, sample applications demonstrating computation and analysis using Matrix Network are provided.