Regularized Maximum Likelihood Estimation of Sparse Stochastic Monomolecular Biochemical Reaction Networks

Abstract

A sparse parameter estimation method is proposed for identifying a stochastic monomolecular biochemical reaction network system. Identification of a reaction network can be achieved by estimating a sparse parameter matrix containing the reaction network structure and kinetics information. Stochastic dynamics of a biochemical reaction network system is usually modeled by a chemical master equation, which is composed of several ordinary differential equations describing the time evolution of probability distributions for all possible states. This paper considers closed monomolecular reaction systems for which an exact analytical solution of the corresponding chemical master equation is available. The estimation method presented in this paper incorporates the closed-form solution into a regularized maximum likelihood estimation (MLE) for which model complexity is penalized, whereas most of existing studies on sparse reaction network identification use deterministic models for regularized least-square estimation. A simulation result is provided to verify performance improvement of the presented regularized MLE over the least squares (LSE) based on a deterministic mass-average model in the case of a small population size. Improved reaction structure detection is achieved by adding a penalty term for ℓ1 regularization to the exact maximum likelihood function.