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Analysis of mode transitions in biological networks

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Abstract

This work presents a methodology for the analysis of mode transitions in biological networks. The proposed approach is predicated on the notion of orchestrating switching between the domains of attraction of the steady states of the constituent modes. Initially, the overall network is modeled as a switched nonlinear system that consists of multiple modes, each governed by a set of continuous-time differential equations. The transitions between the continuous modes are triggered by discrete events (changes in model parameters that correspond to alterations in physiological conditions). Then, following the characterization of the steady-state behavior of each mode, Lyapunov techniques are used to characterize the domains of attraction of the steady states. Finally, by analyzing how the domains of attraction of the various modes overlap with one other, a switching rule is derived to determine when, and if, a given mode transition at a given time results in the desired steady-state behavior. The proposed method is demonstrated using models of biological networks that arise in cell cycle regulation and the bacteriophage λ-switch system. © 2005 American Institute of Chemical Engineers AIChE J, 2005

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