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Analysis of mode transitions in biological networks
Author(s) -
ElFarra Nael H.,
Gani Adiwinata,
Christofides Panagiotis D.
Publication year - 2005
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.10499
Subject(s) - steady state (chemistry) , nonlinear system , mode (computer interface) , work (physics) , control theory (sociology) , attraction , lyapunov function , statistical physics , biological network , biological system , set (abstract data type) , topology (electrical circuits) , computer science , mathematics , physics , chemistry , quantum mechanics , artificial intelligence , biology , linguistics , philosophy , control (management) , combinatorics , programming language , operating system
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