A kinetic analysis of coupled sequential enzyme reactions

10.26434/chemrxiv.5746065.v1 ◽

2018 ◽

Author(s):

Justin Eilertsen ◽

Santiago Schnell

Keyword(s):

Enzyme Assay ◽

Sequential Reaction ◽

Enzyme Reactions ◽

Indicator Reaction ◽

Single Substrate ◽

Complex Sequences ◽

Catalyzed Reactions ◽

Enzyme Catalyzed Reactions ◽

Single Enzyme

<div>As a case study, we consider a coupled enzyme assay of sequential enzyme reactions obeying the Michaelis-Menten reaction mechanism. The sequential reaction consists of a single-substrate, single enzyme non-observable reaction followed by another single-substrate, single enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction becomes the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the sequential reaction is described by a pair of interacting Michaelis-Menten equations. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

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A kinetic analysis of coupled (or auxiliary) enzyme reactions

10.26434/chemrxiv.5746065 ◽

2018 ◽

Cited By ~ 1

Author(s):

Justin Eilertsen ◽

Santiago Schnell

Keyword(s):

Enzyme Assay ◽

Slow Variable ◽

Indicator Reaction ◽

Single Substrate ◽

Complex Sequences ◽

Catalyzed Reactions ◽

Enzyme Catalyzed Reactions ◽

Coupled Reaction ◽

Single Enzyme

<div>As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis-Menten equations. Moreover, we show that when the indicator reaction is slow, the quasi-steady-state dynamics are governed by two fast variables and two slow variables, and when the indicator reaction is fast, the dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

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A kinetic analysis of coupled (or auxiliary) enzyme reactions

10.26434/chemrxiv.5746065.v3 ◽

2018 ◽

Author(s):

Justin Eilertsen ◽

Santiago Schnell

Keyword(s):

Enzyme Assay ◽

Slow Variable ◽

Indicator Reaction ◽

Single Substrate ◽

Complex Sequences ◽

Catalyzed Reactions ◽

Enzyme Catalyzed Reactions ◽

Coupled Reaction ◽

Single Enzyme

<div>As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis-Menten equations. Moreover, we show that when the indicator reaction is slow, the quasi-steady-state dynamics are governed by two fast variables and two slow variables, and when the indicator reaction is fast, the dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

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Thermokinetic studies of the product inhibition of single-substrate, enzyme-catalyzed reactions

Thermochimica Acta ◽

10.1016/0040-6031(95)02513-8 ◽

1995 ◽

Vol 268 ◽

pp. 27-35 ◽

Cited By ~ 7

Author(s):

Yi Liang ◽

Cunxin Wang ◽

Dingquan Wu ◽

Songsheng Qu

Keyword(s):

Product Inhibition ◽

Single Substrate ◽

Catalyzed Reactions ◽

Enzyme Catalyzed Reactions

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Theory on the rate equation of Michaelis-Menten type single-substrate enzyme catalyzed reactions

10.1101/143396 ◽

2017 ◽

Author(s):

Rajamanickam Murugan

Keyword(s):

Steady State ◽

Critical Parameters ◽

Rate Equations ◽

Differential Rate ◽

Single Substrate ◽

Progress Curve ◽

Catalyzed Reactions ◽

Space Dynamics ◽

Time Required ◽

Enzyme Catalyzed Reactions

AbstractAnalytical solution to the Michaelis-Menten (MM) rate equations for single-substrate enzyme catalysed reaction is not known. Here we introduce an effective scaling scheme and identify the critical parameters which can completely characterize the entire dynamics of single substrate MM enzymes. Using this scaling framework, we reformulate the differential rate equations of MM enzymes over velocity-substrate, velocity-product, substrate-product and velocity-substrate-product spaces and obtain various approximations for both pre- and post-steady state dynamical regimes. Using this framework, under certain limiting conditions we successfully compute the timescales corresponding to steady state, pre- and post-steady states and also compute the approximate steady state values of velocity, substrate and product. We further define the dynamical efficiency of MM enzymes as the ratio between the reaction path length in the velocity-substrate-product space and the average reaction time required to convert the entire substrate into product. Here dynamical efficiency characterizes the phase-space dynamics and it would tell us how fast an enzyme can clear a harmful substrate from the environment. We finally perform a detailed error level analysis over various pre- and post-steady state approximations along with the already existing quasi steady state approximations and progress curve models and discuss the positive and negative points corresponding to various steady state and progress curve models.

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