Abstract

Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.

Highlights

  • Modelling and simulation of cellular processes are subjects of significant interest in fields such as Computational and Systems Biology

  • We provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved

  • Among the most effective and accurate finite-difference parametric estimators for stochastic discrete models of biochemical systems are the Common Random Number (CRN) method due to Rathinam et al [18] and the Coupled Finite-Difference (CFD) scheme proposed by Anderson [17]

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Summary

Introduction

Reduction techniques for deterministic models of biochemical systems include species and reaction lumping methods [6] [7], sensitivity analysis based schemes [8] and time-scale analysis based strategies [9] [10]. Local sensitivity analysis of models of biochemical systems measures the variation of the system’s state with small perturbations in model’s parameters [11]. This paper proposes a new technique for reducing the complexity of stochastic discrete models of homogeneous biochemical networks. We shall apply a strategy akin to that proposed in [8] for reducing continuous deterministic models of chemical reactions This strategy ensures that the simplified biochemical system retains the stability and nonlinear properties of the original network.

Chemical Master Equation
Gillespie’s Algorithm
Sensitivity Analysis
Model Reduction
Numerical Examples
Infectious Disease Model
Gemcitabine Model
Conclusions
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