Stability Analysis of Hybrid Gene Regulatory Network Models with Intercellular Diverse Slow and Fast Dynamics

M. Mahmoud (USA)


Gene Regulatory Network, Biomedical Imaging,


To construct an accurate Gene Regulatory Network (GRN) model, large number of variables and chemical reactions in a cell are to be considered. The hybrid stochastic nature of a GRN model allows the consideration of several time scales representing different biological reactions contained in a cell, such as the slow time scale for transcription and translation processes as compared to that of phosphoryla tion, dimerization or binding reactions of transcription. In this work, the effect of combining slow with fast biological processes within a cell on the stochastic stability of the con structed hybrid Gene Regulatory Network (HGRN) model is investigated. A slow reaction in a cell is represented by a process with a large time delay in its response, whereas a fast reaction has a response with a short time delay. In this article, a mathematical representation for the time-delays of fast and slow reactions is developed. The modeling of time delay is represented a stochastic Markovian process with ex ponential holding time functions. Conditions for asymptotic exponential stochastic stability for a HGRN model is exam ined under large and short time delays. A numerical example is used to demonstrate the theoretical results.

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