Graph-theoretic analysis of multistationarity using degree theory

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• 作者：Carsten Conradi^a ; ^{carsten.conradi@htw-berlin.de} ; Maya Mincheva^b ; ^{mincheva@math.niu.edu}
• 关键词：Biochemical mechanisms ; Mass-action kinetics ; Multistationarity ; Bipartite graph ; MAPK network
• 刊名：Mathematics and Computers in Simulation
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：133
• 期：Complete
• 页码：76-90
• 全文大小：423 K
• 卷排序：133

文摘

Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems, since they are large, nonlinear and contain many unknown parameters. Mass action biochemical mechanisms can be represented by a directed bipartite graph with species and reaction nodes. Graph-theoretic methods can then be used to assess the potential of a given biochemical mechanism for multistationarity by identifying structures in the bipartite graph referred to as critical fragments. In this article we present a graph-theoretic method for conservative biochemical mechanisms characterized by bounded species concentrations, which makes the use of degree theory arguments possible. We illustrate the results with an example of a mitogen-activated protein kinases (MAPK) network.