Unbiased Estimation of Parameter Sensitivities for Stochastic Chemical Reaction Networks

Estimation of parameter sensitivities for stochastic chemical reaction networks is an important and challenging problem. Sensitivity values are important in the analysis, modeling and design of chemical networks. They help in understanding the robustness properties of the system and also in identifying the key reactions for a given outcome. In a discrete setting, most of the methods that exist in the literature for the estimation of parameter sensitivities rely on Monte Carlo simulations along with finite difference computations. However these methods introduce a bias in the sensitivity estimate and in most cases the size or direction of the bias remains unknown, potentially damaging the accuracy of the analysis. In this paper, we use the random time change representation of Kurtz to derive an exact formula for parameter sensitivity. This formula allows us to construct an unbiased estimator for parameter sensitivity, which can be efficiently evaluated using a suitably devised Monte Carlo scheme. The existing literature contains only one method to produce such an unbiased estimator. This method was proposed by Plyasunov and Arkin and it is based on the Girsanov measure transformation. By taking a couple of examples we compare our method to this existing method. Our results indicate that our method can be much faster than the existing method while computing sensitivity with respect to a reaction rate constant which is small in magnitude. This rate constant could correspond to a reaction which is slow in the reference time-scale of the system. Since many biological systems have such slow reactions, our method can be a useful tool for sensitivity analysis.