Total Enzyme-substrate Complex Which Includes Product-destined Enzyme-substrate Complex

2019 ◽  
pp. 1-7
Author(s):  
Ikechukwu I. Udema
Keyword(s):  
Complex Formation ◽  
Maximum Velocity ◽  
Free Enzyme ◽  
Theoretical Research ◽  
Substrate Complex ◽  
Continuous Formation ◽  
Enzyme Substrate ◽  
The Difference ◽  
Total Enzyme

Background: There is no much interest in the determination of total enzyme-substrate complex concentration ([ES]T) which includes undissociated ES that is unaccounted for unlike the usual ES destined for transformation into free enzyme and product or substrate. The reason is speculatively as a result of the lack of awareness of such possibility via sequestration. Objectives: 1) To derive on the basis of both reverse – and standard – quasi-steady – state assumptions equations for the determination of [ES]T which is not restricted to the complex which dissociates to product/substrate and free enzyme and 2) quantitate the value of [ES]T. Methods: A theoretical research and experimentation using Bernfeld method to determine velocities of amylolysis with which to calculate relevant parameters. Results: The [EST] is < [E] ( i. e. [ET] - [ES]); [EST] decreased with increasing [ST] and increased with increasing concentration of enzyme [ET] while the velocity of amylolysis, v and maximum velocity of amylolysis, vmax expectedly increased with increasing [ET] and [ST]. Conclusion: The equations for the determination of the total enzyme-substrate complex, free enzyme without any complex formation before and after dissociation of enzyme-complex into product and/or substrate and free enzyme were derived. The difference, [ET] - [ES] is a heterogeneous mixture of undissociated ES and free enzyme without any complex formation. This is the case because [ES] which dissociates into product is only a part of the total enzyme-substrate complex. There is a continuous formation of ES during and at the expiry of the duration of assay as long as there is no total substrate depletion.

scholarly journals The Experimentally Determined Velocity of Catalysis could be Higher in the Absence of Sequestration

2019 ◽  
pp. 1-12
Author(s):  
Ikechukwu I. Udema ◽  
Abraham Olalere Onigbinde
Keyword(s):  
Maximum Velocity ◽  
Order Rate Constant ◽  
Free Enzyme ◽  
Theoretical Research ◽  
Coefficient Of Determination ◽  
First Order ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Pseudo First Order ◽  
The Relationship

Background: It is not unusual to observe calculated “total” free enzyme ([E]) in enzyme catalysed reaction, but this should include total enzyme-substrate complex ([EST]) which accounts for sequestration. Objectives: 1) To show indirectly that the velocities of catalytic action can be higher than experimentally observed velocities without sequestration and 2) redefine the relationship between velocity of hydrolysis with Michaelian enzyme and [E], where concentration of substrate, [ST] <  Michaelis-Menten constant, KM. Methods: A theoretical research and experimentation using Bernfeld method to determine velocities of amylolysis with which to mathematically calculate [EST] and the enzyme-substrate complex ([ES]) prepared for product, P, formation. Results: The [EST] is < [E]; [EST] and pseudo-first order constant, k decreased with increasing [ST] and increased with increasing concentration of enzyme [ET] while velocity amylolysis, v and maximum velocity of amylolysis, vmax expectedly increased with increasing [ET] and [ST]. Conclusion: The fact is that the [EST] is lower than what is usually referred to as free enzyme ([ET] - [ES]). Therefore, if the additional part of [EST] dissociated into product within the duration of assay, the velocity of amylolysis could be higher. The most important outcome and corollary when [KM] > [ST] is that v a 1/[E], v a [E][ST] and a quadratic relationship exists between pseudo-first order rate constant and maximum velocity of amylolysis; separately, v is not a [E] and if v a [ST] (if v/[ST] is constant with coefficient of determination = 1), then KM is not applicable.

scholarly journals Association-dissociation equations, distinct from Michaelis-Menten equation for the quantification of the net flux of reactants with or without immobiliser.

2020 ◽  
Vol 13 (1) ◽  
pp. 231-243
Author(s):  
Ikechukwu Iloh Udema
Keyword(s):  
Complex Formation ◽  
Physicochemical Properties ◽  
Time Dependent ◽  
Theoretical Research ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Enzymatic Action ◽  
Immobile Phase ◽  
Net Flux ◽  
Industrial Relevance

The formation of enzyme-substrate complex, often in connection with the adsorption of the enzyme leading to either partial immobilisation in which the enzymes are adsorbed on a colloid or total immobilisation in which the enzyme is adsorbed on a rigid immobile phase is the concern of some researchers. The interest in immobilised substrate common in biological system is not very common. The objectives of this theoretical research are the rederivation of the equations of association and dissociation of reactants in the presence of adsorbents, insoluble larger macro-or supra-molecule and elucidation of why such equations are important and generalisable. The derivations produced two different equations that describe mathematically the net flux of either the substrate where the enzyme is adsorbed or the net flux of the enzyme where the substrate is adsorbed. The derivation also produced equations of translational velocities, given the probabilities that reactions occur following complex formation or that an escape of bullet molecules or dissociation reactions occur. In conclusion two different equations need separate derivation for association and dissociation of reactants. The needs for the flux of reactants have both biological and industrial relevance, respectively due to importance of time-dependent digestive processes and for the optimisation of the production of desired products of enzymatic action. The equations describing net flux seem generalisable in that information about the physicochemical properties of both crowding agent and immobilisers may not be needed for calculations.

scholarly journals Derivable Equations and Issues Often Ignored in the Original Michaelis-Menten Mathematical Formalism

2019 ◽  
pp. 1-13
Author(s):  
Ikechukwu I. Udema
Keyword(s):  
Rate Constant ◽  
Product Formation ◽  
Theoretical Research ◽  
Quasi Steady State ◽  
Substrate Complex ◽  
The Core ◽  
Enzyme Substrate ◽  
Reverse Rate Constant ◽  
Core Issue

Background: There has been recent shift from the core issue of Michaelian kinetics to issues regarding various kinds of quasi-steady-state assumptions. Derivable equations with which to determine reverse rate constant for the dissociation of enzyme-substrate complex (ES) is given less attention. Objectives: The objectives of this research are: 1) to derive other equations from differential equations whose evaluation leads to MM equation and 2) quantify based on derived equations the kinetic parameters given less attention and duration of catalytic events. Methods: A major theoretical research and experimentation using Bernfeld method. Results and Discussion: The durations for ES dissociation (ESD) into free substrate, S and enzyme, E were much shorter than the duration of ESD into E and product, P in 3 minutes duration of assay with low [S]; it was the shortest and longest in 3 and 5 minutes durations respectively with high [S]. The durations of ESD into E and P was shortest in 3 minutes duration of assay with high [S]. The values of reverse rate constant, k-1 for ESD into S and E in 3 minutes duration of assay with high [S] was » the rate constant, k2 for product formation and they are much higher than in other duration of assay. Conclusion: The equations for the determination of the durations of various events, in a given catalytic cycle were derived. The various time regimes for each event and the rate constant for the dissociation of the ES can be graphically and calculationally determined as the case may be. Substrate concentration regime and duration of assay affects rate constants.

Optical Biosensors Based on Enzyme-Substrate Complex Formation

1994 ◽  
pp. 129
Author(s):  
D.A. Moss ◽  
A. Ritter ◽  
W. Andlauer ◽  
H.J. Ache
Keyword(s):  
Complex Formation ◽  
Optical Biosensors ◽  
Substrate Complex ◽  
Enzyme Substrate

The influence of pH and inhibitors on the kinetics of enzyme reactions involving two intermediates

1967 ◽  
Vol 45 (5) ◽  
pp. 539-546 ◽  
Author(s):  
Harvey Kaplan ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Ph Dependence ◽  
Free Enzyme ◽  
State Equations ◽  
Enzyme Reactions ◽  
Substrate Complex ◽  
Rate Determining Step ◽  
Enzyme Substrate ◽  
Special Cases ◽  
Influence Of Ph

General steady-state equations are worked out for enzyme reactions which occur according to the scheme [Formula: see text]Equations showing the pH dependence of the kinetic parameters are developed in a form which distinguishes between essential and nonessential ionizing groups. The pK dependence of [Formula: see text], the second-order constant extrapolated to zero substrate constant, gives pK values for groups which ionize on the free enzyme, but reveals such a pK only if the corresponding group is also involved in the breakdown of the Michaelis complex. General steady-state equations are also developed for the case in which an inhibitor can combine with the free enzyme, the enzyme–substrate complex, and also a second intermediate (e.g. an acyl enzyme). The equations are given in a form that is convenient for analyzing the experimental results, and a number of special cases are considered. It is shown how the type of inhibition depends not only on the nature of the inhibitor but also on that of the substrate, an important factor being the rate-determining step of the reaction. Examples of the various kinds of behavior are given.

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