Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions

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

doi:10.1007/s00285-004-0282-6

Cited by 22 publications

(40 citation statements)

References 13 publications

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“…13). The question that we address in the rest of this communication is the following: Given that the condition γ 1 is satisfied, what is the variance of the noise about the mean concentrations as predicted by the reduced and full master equations?…”

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confidence: 99%

Communication: Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

Thomas

Straube

Grima

2011

The Journal of Chemical Physics

106

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It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation

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confidence: 99%

Communication: Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

Thomas

Straube

Grima

2011

The Journal of Chemical Physics

106

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“…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%

“…We investigate the stability of the steady state by evaluating the Jacobian there (16) where α = ((e 0 − v * ) 2 /e 0 ) > 0. This then gives the following stability formula (17) We see that the quadratic expression has only positive terms and so the only solution is found for Re(λ) < 0.…”

Section: Discussionmentioning

confidence: 99%

“…An example might be v i (p) = 1 − cos(p) [16]. This is difficult to justify biologically: the supply and sink functions matching exactly would either be a strange coincidence or a strongly connected system.…”

Section: Mass Conservationmentioning

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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Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions

Abstract: In this paper we investigate the validity of a quasi-steady state assumption in approximating Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions that are subject to periodic substrate input.

Cited by 22 publications

References 13 publications

Communication: Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

Communication: Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

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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