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Dissipation and maintenance of stable states in an enzymatic system: Analysis and simulation

Liu, JL

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The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. An essential assumption for constraint-based analysis is the formation of a stable steady state. This work investigates dissipation and maintenance of stable states in a simple reversible enzymatic reaction with substrate inhibition. Under mass-action kinetics, the conditions under which the reaction maintains a stable steady state are analytically derived and numerically confirmed. It is shown that, in order to maintain a steady state in the regulated reaction, maximal enzyme activity must be much higher than input rate. Moreover, it is revealed that requirements for large enzyme activity are due to substrate inhibition. It is suggested that high activities of enzymes may play a vital role in protecting a stable state from its catastrophic collapse, giving an additional explanation to an intriguing problem—why the activities of some enzymes greatly exceed the flux capacity of a pathway. In addition, dissipation of the enzymatic reaction is analysed. It is shown that the collapse of stable states is always associated with a point at which dissipation is the highest. Therefore, in order to maintain a stable state, dissipation of the reaction must be less than a critical value. Moreover, although external forcing may not change net mass flow, it may lead to collapse of stable states. Furthermore, when stable states collapse at a critical forcing amplitude and period, dissipation also reaches a highest value. It is concluded that collapse of stable steady state in the enzyme system with substrate inhibition always corresponds to critical points at which dissipation is highest, regardless if the reaction is forced or not. Therefore, for the substrate inhibited reaction, maintenance of stable states is intrinsically related to level of dissipation.


Liu, J. (2006). Dissipation and maintenance of stable states in an enzymatic system: Analysis and simulation. Biophysical Chemistry, 120(3), 207-214.

Journal Article Type Article
Publication Date Apr 1, 2006
Deposit Date Feb 12, 2009
Publicly Available Date Feb 12, 2009
Journal Biophysical Chemistry
Print ISSN 0301-4622
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 120
Issue 3
Pages 207-214
Keywords Constraint-based analysis, Stable steady states, Dissipation, Excess of enzyme activities, Forced reactions, Kinetic constraints, Complex metabolic networks, Biochemical networks, Pathway analysis, Thermodynamic efficiency, Substrate-inhibition.


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