Abstract
Mathematical model simulation is a useful method for understanding the complex behavior of a living system. The construction of mathematical models using comprehensive information is one of the techniques of model construction. Such a comprehensive knowledge-based network tends to become a large-scale network. As a result, the variation of analyses is limited to a particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we propose a contractive method that preserves the dynamic behavior of a large network. The method consists of the following two steps: comprehensive network building and network reduction. The reduction phase can extract network loop structures from a large-scale regulatory network, and the subnetworks were combined to preserve the dynamics of the original large-scale network. We confirmed that the extracted loop combination reproduced the known dynamics of HES1 and ASCL1 before and after differentiation, including oscillation and equilibrium of their concentrations. The model also reproduced the effects of the overexpression and knockdown of the Id2 gene. Our model suggests that the characteristic change in HES1 and ASCL1 expression in the large-scale regulatory network is controlled by a combination of four feedback loops, including a large loop, which has not been focused on. The model extracted by our method has the potential to reveal the critical mechanisms of neural differentiation. The method is applicable to other biological events.
Highlights
In the past few decades, biology has started to integrate a comprehensive knowledge of biological systems into biochemical networks and access the benefit of using it for mathematical modeling and simulation
We developed a new method that consists of comprehensive modeling and the reduction of a comprehensive network to analyze the dynamics of regulatory mechanisms of target reduction of a comprehensive network to analyze the dynamics of regulatory mechanisms of target phenomena
We modeled the differentiation of neural stem cells (NSCs) and analyzed the characteristic changes of dynamics during differentiation
Summary
In the past few decades, biology has started to integrate a comprehensive knowledge of biological systems into biochemical networks and access the benefit of using it for mathematical modeling and simulation. A whole-cell mathematical model of the bacterium Mycoplasma genitalium, which contains 525 genes, was built based on an enormous amount of experimental data and enabled the researchers to discover a new enzyme and some other suggestions [1]. Even if we build such a large-scale network, to translate it into equations and analyze them is still challenging, given that many parameters need to be determined in advance. Estimation of all the parameters of a whole-cell model has not yet been appropriately resolved [5].
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