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

Abstract

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 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 E. 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.

A framework supporting multi-compartment stochastic simulation and parameter optimisation for investigating biological system development

“…To summarise, we believe that the subject is well-established for deterministic models. On the other hand, we also found some recent works that tackle stochastic models, 30,50–52 even though the problem of parameter estimation for such kind of models is not yet a routine. The property of stochasticity makes indeed the exploration of the landscape even more difficult, mainly because: (i) the objective function is computed as the average value (or another statistic) of diverse simulation runs, which can induce a rugged landscape and/or with a lot of plateaus; (ii) the solution returned by the algorithm is an estimator of the actual solution, therefore it is necessarily affected by an error.…”

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

“…Classical bootstrapping with data replication and resampling to enable repeated estimations is described in (Vanlier et al, 2013). Confidence intervals of parameter estimates can be obtained using bootstrapping (Joshia et al, 2006;Srivastavaa and Rawlingsb, 2014). Bootstrapping can be used to improve efficiency in recomputing model trajectories (Lindera and Rempala, 2015).…”

Optimal Design of Experiments Based on Bootstrapping

“…Bootstrapping wurde z. B. von Srivastave und Rawlings verwendet, um Vertrauensintervalle von Parametern kinetischer Modelle ableitungsfrei zu berechnen. Banks et al verwendeten Bootstrapping zur Schätzung von Parametervarianzen unter Verwendung heteroskedastischen Messrauschens.…”