Efficient Finite-difference Methods for Sensitivity Analysis of Stiff Stochastic Discrete Models of Biochemical Systems

Abstract

In the study of Systems Biology it is necessary to simulate cellular processes and chemical reactions that comprise biochemical systems. This is achieved through a range of mathematical modeling approaches. Standard methods use deterministic differential equations, but because many biological processes are inherently probabilistic, stochastic models must be used to capture the random fluctuations observed in these systems. The presence of noise in a system can be a significant factor in determining its behavior. The Chemical Master Equation is a valuable stochastic model of biochemical kinetics. Models based on this formalism rely on physically motivated parameters, but often these parameters are not well constrained by experiments. One important tool in the study of biochemical systems is sensitivity analysis, which aims to quantify the dependence of a system's dynamics on model parameters. Several approaches to sensitivity analysis of these models have been developed. We proposed novel methods for estimating sensitivities of discrete stochastic models of biochemical reaction systems. We used finite-difference approximations and adaptive tau-leaping strategies to estimate the sensitivities for stiff stochastic biochemical kinetics models, resulting in significant speed-up in comparison with previously published approaches for a similar accuracy. We also developed an approach for estimating sensitivity coefficients involving adaptive implicit tau-leaping strategies. We provide a comparison of these methodologies in order to identify which approach is most efficient depending of the features of the model. These results can facilitate efficient sensitivity analysis, which can serve as a foundation for the formulation, characterization, verification and reduction of models as well as further applications to identifiability analysis.