Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

Qianqian Wu,Tianhai Tian

doi:10.1038/srep31909

Abstract

To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. Among them, a widely used approach is delayed reaction for simplifying multistep reactions. However, recent research results suggest that a delayed reaction with constant time delay is unable to describe multistep reactions accurately. To address this issue, we propose a novel approach using state-dependent time delay to approximate multistep reactions. We first use stochastic simulations to calculate time delay arising from multistep reactions exactly. Then we design algorithms to calculate time delay based on system dynamics precisely. To demonstrate the power of proposed method, two processes of mRNA degradation are used to investigate the function of time delay in determining system dynamics. In addition, a multistep pathway of metabolic synthesis is used to explore the potential of the proposed method to simplify multistep reactions with nonlinear reaction rates. Simulation results suggest that the state-dependent time delay is a promising and accurate approach to reduce model complexity and decrease the number of unknown parameters in the models.

Highlights

To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models
We propose a new algorithm to calculate time delay in chemical reaction systems according to the system state
Using the process of multistep reaction systems as the test problem, we utilize both analytical solution of ordinary differential equation (ODE) model and stochastic simulation of chemical reaction systems to determine the relationship between the system state and value of time delay

Summary

Introduction

To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. A number of mathematical models in recent years have been designed to describe these multistep pathways accurately, due to the complex nature of molecular networks, more sophisticated models are needed to simplify the multistep reaction processes. Research work has been conducted for exact model reduction with time delay; and closed form distribution and extension have been derived for fully bi-directional monomolecular reactions[36,37] In spite of these advances, more work is still needed to address the issue of accuracy for modelling multistep reaction systems. In this work we will develop a new method using chemical reaction with state-dependent time delay to simplify multistep reaction systems accurately. The proposed method will be validated by two models for the degradation process of mRNA molecules and one model for multistep metabolic synthesis pathway

Methods

Results

Conclusion