Efficient Finite Difference Method for Computing Sensitivities of Biochemical Reactions

Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking stochastic noise into account. This paper proposes a new finite difference method for efficiently computing sensitivities of biochemical reactions. We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes. The exactness of the simulation is reserved by applying the rejection-based mechanism. For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to computing sensitivities of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks. We benchmark our method on biological reaction models to prove its applicability and efficiency.Comment: 29 pages with 6 figures, 2 table

Tree-Based Search for Stochastic Simulation Algorithm

In systems biology, the cell behavior is governed by a series of biochemical reactions. The stochastic simulation algorithm (SSA), which was introduced by Gillespie, is a standard method to properly realize the dynamic and stochastic nature of such systems. In general, SSA follows a two-step approach: finding the next reaction firing, and updating the system accordingly. In this paper we apply the Huffman tree, an optimal tree for data compression, so to improve the search for the next reaction firing