Abstract
BackgroundA fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems. Among them, a key question is how to use simplified reactions to describe the chemical events of multi-step reactions that are ubiquitous in biochemistry and biophysics. To address this issue, a widely used approach in literature is to use one-step reaction to represent the multi-step chemical events. In recent years, a number of modelling methods have been designed to improve the accuracy of the one-step reaction method, including the use of reactions with time delay. However, our recent research results suggested that there are still deviations between the dynamics of delayed reactions and that of the multi-step reactions. Therefore, more sophisticated modelling methods are needed to accurately describe the complex biological systems in an efficient way.ResultsThis work designs a two-variable model to simplify chemical events of multi-step reactions. In addition to the total molecule number of a species, we first introduce a new concept regarding the location of molecules in the multi-step reactions, which is the second variable to represent the system dynamics. Then we propose a simulation algorithm to compute the probability for the firing of the last step reaction in the multi-step events. This probability function is evaluated using a deterministic model of ordinary differential equations and a stochastic model in the framework of the stochastic simulation algorithm. The efficiency of the proposed two-variable model is demonstrated by the realization of mRNA degradation process based on the experimentally measured data.ConclusionsNumerical results suggest that the proposed new two-variable model produces predictions that match the multi-step chemical reactions very well. The successful realization of the mRNA degradation dynamics indicates that the proposed method is a promising approach to reduce the complexity of biological systems.
Highlights
A fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems
A new two-variable model The starting-point of this research work is the chemical events with multi-step reactions
Using the total molecule number and total length of molecules, we proposed a two-variable model to reduce the complexity of the multi-step reactions
Summary
A fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems. One of the major challenges in systems biology is how to use simple mathematical models to describe complex biological systems. To address this issue, a number of modelling techniques have been designed. A widely used approach is to use one-step reaction to represent multi-step reactions, which is called slow reaction This technique is very important because recent theoretical and experimental studies have shown that a wide variety of biochemical events involve multistep reactions [3]. The major aim of this research work is to design simplified models to accurately characterize biological systems with multi-step reactions
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