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Studying genetic regulatory networks at the molecular level: Delayed reaction stochastic models

Authors: Rui Zhu, Andre S. Ribeiro, Dennis Salahub, and Stuart A. Kauffman

Ref.: Journal of Theoretical Biology 246(4), 725-745 (2007)

Abstract: Current advances in molecular biology enable us to access the rapidly increasing body of genetic information and, guided by models, we can understand further the world of genes. It is still challenging to model gene systems at the molecular level. Here, we propose two types of reaction kinetic models for constructing genetic networks. One is based on delayed effective reactions, each modeling a biochemical process like transcription without involving intermediate reactions. The other is based on delayed virtual reactions, each being converted from a mathematical function to model a biochemical function like gene inhibition. The latter stochastic models are derived from the corresponding mean-field models. The former ones are composed of single gene expression modules. We thus design a model of gene expression. This model is verified by our simulations using a delayed Gillespie algorithm, which accurately reproduces the stochastic kinetics in a recent experimental study. Various simplified versions of the model, including a widely used one in the literature, are given and evaluated. It is found that the literature model may cause significant errors in quantitative studies. We then use the two methods to study the genetic toggle switch and the repressilator. We define the “on” and “off” states of genes and extract the binary code from the stochastic time series. The binary code can be accurately described by the corresponding Boolean network models in certain conditions. We discuss these conditions, suggesting a method to connect Boolean network models, mean-field models, and stochastic chemical models in studying genetic networks.