The dynamics of single enzyme reactions: A reconsideration of Kramers' model for colored noise processes

2008 ◽  
Vol 129 (7) ◽  
pp. 075104 ◽  
Author(s):  
Srabanti Chaudhury ◽  
Debarati Chatterjee ◽  
Binny J. Cherayil
Keyword(s):  
Colored Noise ◽  
Enzyme Reactions ◽  
Kramers Model ◽  
Single Enzyme

A kinetic analysis of coupled sequential enzyme reactions

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>

A kinetic analysis of coupled sequential enzyme reactions

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>

Kinetics of Single-Enzyme Reactions on Vesicles: Role of Substrate Aggregation

2015 ◽  
Vol 10 (02) ◽  
pp. 69-83 ◽  
Author(s):  
Vladimir P. Zhdanov
Keyword(s):  
Lipid Membranes ◽  
Lipid Vesicles ◽  
Enzymatic Reactions ◽  
Enzyme Dynamics ◽  
Special Issue ◽  
Enzyme Reactions ◽  
And Function ◽  
Single Enzyme

Enzymatic reactions occurring in vivo on lipid membranes can be influenced by various factors including macromolecular crowding in general and substrate aggregation in particular. In academic studies, the role of these factors can experimentally be clarified by tracking single-enzyme kinetics occurring on individual lipid vesicles. To extend the conceptual basis for such experiments, we analyze herein the corresponding kinetics mathematically with emphasis on the role of substrate aggregation. In general, the aggregation may occur on different length scales. Small aggregates may e.g. contain a few proteins or peptides while large aggregates may be mesoscopic as in the case of lipid domains which can be formed in the membranes composed of different lipids. We present a kinetic model describing comprehensively the effect of aggregation of the former type on the dependence of the reaction rate on substrate membrane concentration. The results obtained with physically reasonable parameters indicate that the aggregation-related deviations from the conventional Michaelis–Menten kinetics may be appreciable. [Formula: see text]Special Issue Comments: This theoretical article is focused on single-enzyme reactions occurring in parallel with substrate aggregation on individual vesicles. This subject is related to a few Special Issue articles concerning enzyme dynamics6,7 and function8 and mathematical aspects of stochastic kinetics.9

Mass transfer and biochemical reaction in enzyme membrane reactor systems—I. Single enzyme reactions

1973 ◽  
Vol 28 (4) ◽  
pp. 1013-1020 ◽  
Author(s):  
W.R. Vieth ◽  
A.K. Mendiratta ◽  
A.O. Mogensen ◽  
R. Saini ◽  
K. Venkatasubramanian
Keyword(s):  
Mass Transfer ◽  
Membrane Reactor ◽  
Biochemical Reaction ◽  
Enzyme Membrane Reactor ◽  
Enzyme Reactions ◽  
Single Enzyme

scholarly journals Quantitative determination of the steady-state kinetics of multienzyme reactions using the algebraic rate equations for the component single-enzyme reactions

1993 ◽  
Vol 291 (2) ◽  
pp. 585-593 ◽  
Author(s):  
C D Stoner
Keyword(s):  
Steady State ◽  
Direct Calculation ◽  
Rate Equations ◽  
Maximum Efficiency ◽  
Control Analysis ◽  
Flux Control ◽  
Enzyme Reactions ◽  
Dependent Variables ◽  
The Individual ◽  
Single Enzyme

Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.

Modeling Trienzyme Biosensor at Internal Diffusion Limitation

2004 ◽  
Vol 9 (2) ◽  
pp. 139-144 ◽  
Author(s):  
J. Kulys
Keyword(s):  
Immobilized Enzymes ◽  
Internal Diffusion ◽  
Significant Response ◽  
Diffusion Limitation ◽  
Enzyme Reactions ◽  
Substrate Conversion ◽  
Apparent Stability ◽  
Biosensor Response

A model of biosensor containing three immobilized enzymes utilizing consecutive substrate conversion in the chain was developed. The modeling was performed at an internal diffusion limitation and a steadystate condition. The calculations showed that significant response of biosensors was produced if diffusion modules were larger than 1 for all enzyme reactions. Due to diffusion limitation the apparent stability of biosensor response increased many times in comparison to stability of the most labile enzyme of the chain.

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