Accurate parametric sensitivity of stochastic biochemical systems

Farid Gassoumov

doi:10.32920/ryerson.14644161

Abstract

Computational and Systems Biology are experiencing a rapid development in recent years. Mathematical and computational modelling are critical tools for studying cellular dynamics. Molecular interactions in a cell may display significant random fluctuations when some key species have low amounts (RNA, DNA), making the traditional model of the deterministic reaction rate equations insufficient. Consequently, stochastic models are required to accurately represent the biochemical system behaviour. Nonetheless, stochastic models are more challenging to simulate and analyse than the deterministic ones. Parametric sensitivity is a powerful tool for exploring the system behaviour, such as system robustness with respect to perturbations in its parameters. We present an accurate method for estimating parametric sensitivities for stochastic discrete models of biochemical systems using a high order Coupled Finite Difference scheme and illustrate its advantages compared to the existing techniques

Highlights

One of the most accurate models for describing the stochastic chemical kinetics of well-stirred systems is by the Chemical Master Equation (CME)
Stochastic modelling and simulation have been extensively employed for studying significant problems in Computational and Systems Biology, such as genetic regulatory networks, signalling pathways and cellular dynamics
The Chemical Master Equation is a stochastic discrete model which may be applied to generic biochemical systems, in particular to those with some low molecular amounts of some species

Summary

Introduction

One of the most accurate models for describing the stochastic chemical kinetics of well-stirred systems is by the Chemical Master Equation (CME). In a well-stirred system of constant volume, most of the molecular collisions that take place are elastic, resulting in the positions of the molecules becoming uniformly randomized in space, and the velocities thermally randomized in accordance with the Maxwell-Boltzmann distribution [23]. This will allow to forgo tracking the positions and the velocities of the molecules and focus entirely on the changes in the molecular populations, significantly simplifying the mathematical model. The propensity for the first order reaction implies that the probability of it taking place is directly proportional to the number of molecules of species Sm available in the system. The propensity for the dimerization reaction when two identical chemical species interact, can be understood from combinatorics

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