Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks

Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.

A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis

Lattice kinetic Monte Carlo simulations have become a vital tool for predictive quality atomistic understanding of complex surface chemical reaction kinetics over a wide range of reaction conditions. In order to expand their practical value in terms of giving guidelines for the atomic level design of catalytic systems, it is very desirable to readily evaluate a sensitivity analysis for a given model. The result of such a sensitivity analysis quantitatively expresses the dependency of the turnover frequency, being the main output variable, on the rate constants entering the model. In the past, the application of sensitivity analysis, such as degree of rate control, has been hampered by its exuberant computational effort required to accurately sample numerical derivatives of a property that is obtained from a stochastic simulation method. In this study, we present an efficient and robust three-stage approach that is capable of reliably evaluating the sensitivity measures for stiff microkinetic models as we demonstrate using the CO oxidation on RuO₂(110) as a prototypical reaction. In the first step, we utilize the Fisher information matrix for filtering out elementary processes which only yield negligible sensitivity. Then we employ an estimator based on the linear response theory for calculating the sensitivity measure for non-critical conditions which covers the majority of cases. Finally, we adapt a method for sampling coupled finite differences for evaluating the sensitivity measure for lattice based models. This allows for an efficient evaluation even in critical regions near a second order phase transition that are hitherto difficult to control. The combined approach leads to significant computational savings over straightforward numerical derivatives and should aid in accelerating the nano-scale design of heterogeneous catalysts.