Determination of multiple steady states in a family of allosteric models for glycolysis

1998 ◽  
Vol 109 (19) ◽  
pp. 8485-8493 ◽  
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady States ◽  
Multiple Steady States

Determination of Multiple Steady States in an Active Membrane Transport Model

1999 ◽  
Vol 54 (3-4) ◽  
pp. 245-250 ◽  
Author(s):  
Hsing-Ya Li
Keyword(s):  
Membrane Transport ◽  
Transport Model ◽  
Steady States ◽  
Metabolic Energy ◽  
Multiple Steady States ◽  
Necessary And Sufficient Condition ◽  
Active Membrane ◽  
Positive Steady States ◽  
Necessary And Sufficient

A necessary and sufficient condition is applied to determine the possibility of multiple positive steady states in a complex, active membrane transport model with a cycle, which is performed by pump pro-teins coupled to a source of metabolic energy. A set of rate constants and two corresponding steady states are computed. Hysteresis phenomena are observed. A signature of multiplicity is derived, which can be applied in mechanism identifications if steady-state concentrations for some species are measured. The bifurcation of multiple steady states is also displayed.

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.

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