Subnetwork Analysis for the Determination of Multiple Steady States in Complex Reaction Networks

2000 ◽  
Vol 39 (9) ◽  
pp. 3291-3297 ◽  
Author(s):  
Hsing-Ya Li ◽  
Pang-Yen Ho
Keyword(s):  
Steady States ◽  
Reaction Networks ◽  
Multiple Steady States ◽  
Complex Reaction ◽  
Subnetwork Analysis

A Positive Real Eigenvalue Condition for the Determination of Unstable Steady States in Chemical Reaction Networks

2008 ◽  
Vol 63 (12) ◽  
pp. 778-790
Author(s):  
An-Chong Chao ◽  
Hsing-Ya Li ◽  
Guo-Syong Chuang ◽  
Pang-Yen Ho
Keyword(s):  
Steady State ◽  
Chemical Reaction ◽  
Steady States ◽  
Reaction Networks ◽  
Real Eigenvalue ◽  
Multiple Steady States ◽  
Positive Real ◽  
Unstable Steady State ◽  
Eigenvalue Condition

The interesting dynamical behaviours exhibiting in chemical reaction systems, such as multiple steady states and undamped oscillations, often result from unstable steady states. A positive real eigenvalue condition is proposed which gives a necessary and sufficient condition for the determination of an unstable steady state having a positive real eigenvalue in general isothermal reaction networks. Formulas are developed to construct an unstable steady state and a set of positive rate constants. The applications are illustrated by three examples. Two give rise to oscillations and one admits multiple steady states.

The Determination of Multiple Steady States in Two Families of Biological Systems

2004 ◽  
Vol 59 (3) ◽  
pp. 136-146
Author(s):  
Guo-Syong Chuang ◽  
Pang-Yen Ho ◽  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Transport Model ◽  
Biological Systems ◽  
Linear Equations ◽  
Steady States ◽  
Metabolic Energy ◽  
Mass Action ◽  
Multiple Steady States ◽  
Mass Action Kinetics ◽  
Subnetwork Analysis

The capacity of computational multiple steady states in two biological systems are determined by the Deficiency One Algorithm and the Subnetwork Analysis. One is a bacterial glycolysis model involving the generation of ATP, and the other one is an active membrane transport model, which is performed by pump proteins coupled to a source of metabolic energy. Mass action kinetics, is assumed and both models consist of eight coupled non-linear equations. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability and hysteresis are discussed. The bifurcation of multiple steady states is also displayed. A signature of multiplicity is derived, which can be applied to mechanism identifications if steady state concentrations for some species are measured. The capacity of steady state multiplicity is extended to their families of reaction networks.

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