"Mathematical Modeling and Computational Simulation of Gene Regulatory Networks"
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Mathematical modeling is to approximate a real world system, i.e., cell, to an extent the prediction can be made and tested against observable properties of the system. Therefore, the sophistication of the model is tied to that of techniques to make observations of the system. More sophisticated model may lead the development of better measurement technique and/or vice versa. Recently, new technologies that make possible genomic and proteomic profiling of cellular behavior have been developed, providing enormous amount of information for cellular behavior. These genomic and proteomic observations could and have successfully been used to identify molecular markers for certain kinds of disease such as cancers. However, the monitoring and modeling of genetic regulatory behavior of cell could benefit most from it. Therefore, the need for the mathematical models to better describe cellular behavior is inevitable. Among them are Boolean network, Bayesian network, and ODE-based gene regulatory network modeling. Bayesian network is to Boolean network is promising for qualitative and deterministic description of biological system and can be extended to describe stochastic behavior of gene regulatory controls and to consider the perspective of biological context. It is also critical to study systemic behavior of cellular system by analyzing both dynamic and steady state behaviors. Markov chain simulation has been shown to be a useful tool for this kind of study. An application to gene expression profiles of melanoma and glioma systems, some interesting observations were made from these mathematical modeling and computational simulation studies.