Computational Methods for Modeling Multistep Reactions and Parameter Inference in Transcriptional Processes

Abstract

A major task in Systems Biology is to conduct accurate mechanistic simulations of multistep reactions. The simulation of a biological process from experimental data requires detailed knowledge of its model structure and kinetic parameters. Despite advances in experimental techniques, estimating unknown parameter values from observed data remains a bottleneck for obtaining accurate simulation results. Therefore, the goal is to focus on development of computationally efficient parameter inference methods for characterizing transcriptional bursting process, for inferring unknown kinetic parameters, given single-cell time-series data. Many biochemical events involve multistep reactions. One of the most important biological processes in gene expression, which involve multistep reactions, is the transcriptional process. Models for multistep reactions necessarily need multiple states, and it is a challenge to compute model parameters that best agree with experimental data. To address this issue, first, a novel model reduction strategy is devised, representing several number of promoter OFF states by a single state, accompanied by specifying a time delay for burst frequency. This model approximates complex promoter switching behavior with Erlang-distributed ON/OFF times. To explore combined effects of parameter inference and simulation, using this model reduction, two inference methods are developed namely, Delay-Bursty MCEM and Clumped-MCEM. These methods are applied to time-series data of endogenous mouse glutaminase promoter to validate model assumptions and infer the values of kinetic parameters. Simulation results are summarized below: 1. Models with multiple OFF states produce behaviour that is most consistent with experimental data and the bursting kinetics are promoter specific. 2. Delay-Bursty MCEM and Clumped-MCEM inference are more efficient for time-series data. The comparison with the state-of-the-art Bursty iMCEM2 method shows that Delay-Bursty MCEM and Clumped-MCEM produce similar numerical accuracy. However, these methods are better in terms of efficiency. Delay-Bursty MCEM reduces computational cost by 37:44% as compared to Bursty MCEM2. Clumped-MCEM reduces computational cost by 57:58% when compared with Bursty MCEM2 and 32:19% when compared with Delay-Bursty MCEM.