Quasi-steady state assumptions for non-isolated enzyme-catalysed reactions

Stoleriu, Iulian; Davidson, Fordyce A.; Liu, Junli

doi:10.1007/s00285-003-0225-7

Cited by 35 publications

(55 citation statements)

References 7 publications

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“…Therefore, although the saturation and regulation features of enzymatic rate laws cannot be immediately described by mass-action kinetics [28], they are the consequences of the mass-action kinetics in which the concentrations of all forms of an enzyme are limited. Enzymatic kinetics are usually derived from traditional mass-action kinetics together with simplifying assumptions such as the existence of a quasi-steady state [29,30]. At the level of enzymatic reactions, the kinetic rate laws exhibit some special features such as saturation and regulation [28].…”

Section: Discussionmentioning

confidence: 99%

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

Liu¹

2006

Biophysical Chemistry

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Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe 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 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.3

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Section: Discussionmentioning

confidence: 99%

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

Liu¹

2006

Biophysical Chemistry

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“…The phase space trajectories for system (7) and the same system with the QSSA applied (15) are shown in Fig. 3.…”

Section: Discussionmentioning

confidence: 99%

“…In recent years, special attention has been paid to the conditions for the validity of the QSSA in both closed [9,11] and open [15,16] mechanisms. However, there has been little interest in understanding the impact of the QSSA on the analysis of the dynamical behaviour of biochemical pathways.…”

Section: Discussionmentioning

confidence: 99%

“…This states that c′ ≈ 0. From this we find an expression for c in terms of s (14) We substitute this back into what remains of the system to give (15) We have reduced the system from three species to two.…”

Section: Applying the Qssa To The Open Mechanismmentioning

confidence: 99%

“…Over the last 10 years, we have determined the timescales of the reacting species and validity of the QSSA in isolated enzyme reactions [8,11,13,14]. Recently, the effects of substrate input on the validity of the QSSA for open enzyme reactions has also been considered [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Use and abuse of the quasi-steady-state approximation

Flach

Schnell

2006

IEE Proc. Syst. Biol.

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The transient kinetic behaviour of an open single enzyme, single substrate reaction is examined. The reaction follows the Van Slyke-Cullen mechanism, a spacial case of the Michaelis-Menten reaction. The analysis is performed both with and without applying the quasi-steady-state approximation. The analysis of the full system shows conditions for biochemical pathway coupling, which yield sustained oscillatory behaviour in the enzyme reaction. The reduced model does not demonstrate this behaviour. The results have important implications in the analysis of open biochemical reactions and the modelling of metabolic systems.

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Mathematical modelling of methanol poisoning with impulsive dosing of antidote therapeutics to prevent toxicity

Ghosh

Roy

2018

Math Methods in App Sciences

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The harmful use of methanol is a worldwide problem resulting in millions of deaths, including thousands of young lives lost. Although methanol itself may be harmless, it is oxidized to formaldehyde and, further, it breaks down to formic acid, which is lethal for humans with high concentration. The primary treatment of methanol poisoning is the administration of ethanol to slow down the formation of toxic metabolites by competitive substitution of the methanol due to its intrinsic binding affinity. Moreover, supportive role of administering sodium bicarbonate in the patient assists the neutralization of the metabolic acidosis in human for the accumulation of formic acid. In this research article, we formulate a mathematical model to study the effect of co-administration of ethanol and sodium bicarbonate to treat methanol toxicity. This treatment procedure may help the health workers to provide at least a basic emergency care to minimize the death toll in the remote and distant places. The experimental data were used to acquire the model generated time and dosing prediction through which patient is to be benefited in obtaining the normalcy within minimum therapy time. KEYWORDSalcohol dehydrogenase, aldehyde dehydrogenase, competitive inhibition, ethanol, impulsive differential equation, methanol, sodium bicarbonate, supportive therapy 9176

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Quasi-steady state assumptions for non-isolated enzyme-catalysed reactions

Cited by 35 publications

References 7 publications

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

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

Use and abuse of the quasi-steady-state approximation

Mathematical modelling of methanol poisoning with impulsive dosing of antidote therapeutics to prevent toxicity

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