期刊
MATHEMATICAL BIOSCIENCES
卷 241, 期 1, 页码 1-23出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2012.08.002
关键词
Reaction network; Bistability; Persistence; Concordant; Systems biology; Species-Reaction Graph
资金
- NSF [EF-1038394]
- NIH [1R01GM086881-01]
- Emerging Frontiers
- Direct For Biological Sciences [1038394] Funding Source: National Science Foundation
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies within the very broad and natural weakly monotonic class. In particular, multiple equilibria are precluded, as are degenerate positive equilibria. Moreover, under certain circumstances, also related to concordance, all real eigenvalues associated with a positive equilibrium are negative. Although concordance of a reaction network can be decided by readily available computational means, we show here that, when a nondegenerate network's Species-Reaction Graph satisfies certain mild conditions, concordance and its dynamical consequences are ensured. These conditions are weaker than earlier ones invoked, to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance. Because the Species-Reaction Graph resembles pathway depictions often drawn by biochemists, results here expand the possibility of inferring significant dynamical information directly from standard biochemical reaction diagrams. (C) 2012 Elsevier Inc. All rights reserved.
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