Multi-Equilibrium Property of Metabolic Networks:MMN Module
This paper studies the multi-equilibrium property of multiple substrate or multiple product modules with no inhibition (MMN modules).The rates of the metabolic reactions are characterized by Michaelis-Menten kinetics.A uni fied model is given for MMN modules by using a set of nonlinear ordinary differential equations (ODEs)with multi-variables.It is shown that the injectivity of the ODE is equivalent to the non-singularity of its Jacobian matrix,and an easy-to-verify suf ficient and necessary condition is obtained.For a general class of MMN modules named α -MMN modules,a criterion of injectivity based on topology structure is given,with which it is shown that a speci fic class of α -MMN modules cannot produce multiple equilibria,and the equilibrium if existent is asymptotically stable.
GUO Jin ZHANG Ji-Feng
Key Laboratory of Systems and Control,Institute of Systems Science,Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100190,P.R.China
国际会议
The 30th Chinese Control Conference(第三十届中国控制会议)
烟台
英文
1-6
2011-07-01（万方平台首次上网日期，不代表论文的发表时间）