Parameter estimation in stochastic chemical kinetic models using derivative free optimization and bootstrapping

• This paper presents a novel method of parameter estimation for stochastic chemical kinetic models.
• These models arise naturally in the modeling of small scale chemical reactors or biological processes.
• The method uses tools from statistics, probability theory and numerical optimization.
• The combination leads to an accurate and reliable method.

Recent years have seen increasing popularity of stochastic chemical kinetic models due to their ability to explain and model several critical biological phenomena. Several developments in high resolution fluorescence microscopy have enabled researchers to obtain protein and mRNA data on the single cell level. The availability of these data along with the knowledge that the system is governed by a stochastic chemical kinetic model leads to the problem of parameter estimation. This paper develops a new method of parameter estimation for stochastic chemical kinetic models. There are three components of the new method. First, we propose a new expression for likelihood of the experimental data. Second, we use sample path optimization along with UOBYQA-Fit, a variant of Powell's unconstrained optimization by quadratic approximation, for optimization. Third, we use a variant of Efron's percentile bootstrapping method to estimate the confidence regions for the parameter estimates. We apply the parameter estimation method in an RNA dynamics model of Escherichia coli. We test the parameter estimates obtained and the confidence regions in this model. The testing of the parameter estimation method demonstrates the efficiency, reliability, and accuracy of the new method.