Enzyme-catalyzed reactions, steady-state approximation

Appropriate expressions for the fluxes of each of the reactions in the system must be determined. Typically, biochemical reactions proceed through multiple-step catalytic mechanisms, as described in Chapter 4, and simulations are based on the quasi-steady state approximations for the fluxes through enzyme-catalyzed reactions. (See Section 3.1.3.2 and Chapter 4 for treatments on the kinetics of enzyme catalyzed reactions.)... 

The Michaelis-Menten mechanism of enzyme activity models the enzyme with one active site that, weakly and reversibly, binds a substrate in homogeneous solution. It is a three-step mechanism. The first and second steps are the reversible formation of the enzyme-substrate complex (ES). The third step is the decay of the complex into the product. The steady-state approximation is applied to the concentration of the intermediate (ES) and its use simplifies the derivation of the final rate expression. However, the justification for the use of the approximation with this mechanism is suspect, in that both rate constants for the reversible steps may not be as large, in comparison to the rate constant for the decay to products, as they need to be for the approximation to be valid. The simplest form of the mechanism applies only when A h 2> k. Neverthele.ss, the form of the rate equation obtained does seem to match the principal experimental features of enzyme-catalyzed reactions it explains why there is a maximum in the reaction rate and provides a mechanistic understanding of the turnover number. The model may be expanded to include multisubstrate reaction rate and provides a mechanistic understanding of the turnover number. The model may be expanded to include multisubstrate reactions and inhibition. 

The rate of a homogeneously or enzyme catalyzed reaction depends on the catalyst concentration Ccat even though the catalyst undergoes no net change. To relate Cx to Ccat, we use the steady-state approximation ... 

The steady state of B in the reaction A -> B C is short lived (see Fig. 1.15). However, for many reactions, such as enzyme-catalyzed reactions, the concentrations of important reaction intermediates are in a steady state. This allows for the use of steady-state approximations to obtain analytical solutions for the differential equations and thus enables estimation of the values of the rate constants. 

Rapid equilibrium conditions need not be assumed for the derivation of an enzyme catalysis model. A steady-state approximation can also be used to obtain the rate equation for an enzyme-catalyzed reaction. 

One kind of kinetics that uses the steady-state approximation is applied to enzyme-catalyzed reactions. Because enzymes (which are usually proteins) are very good catalysts, typically only a very small concentration is needed for a biochemical reaction to occur, and determination of the reaction kinetics focuses on following the change of concentration of the primary reactant, called the substrate. 

This is known as the quasi-steady state approximation, and is valid for enzyme catalyzed reactions if the total initial enzyme concentration is much less than the initial substrate concentration ([ lo maximum reaction rate v ua is equal to k[E]o (see equation (19.6)). When = [5], v = Vmax —see equation (19.1). 

Multiple complexes can be involved in some enzyme-catalyzed reactions. For the reaction sequence shown below, develop suitable rate expressions using (a) the Michaehs equilibrium approach and (b) the steady-state approximation for the complexes. 

The conclusion from all of this is that we do not live on a knife edge. We do not need natural selection to explain the observation that much of metabolism can be represented simply as a set of pools of major metabolites at approximately constant concentrations, with chemical flows between them that proceed at rates that over short timescales vary little or not at all. Systems of enzymes catalyzing diverse sets of reactions readily achieve steady states because that is almost an automatic property of such systems. Assigning kinetic properties haphazardly to all the enzymes in a system normally does not produce any exotic properties for the whole system as Kacser and Bums remarked three decades ago, almost any set of enzymes will generate a steady state with all fluxes in operation, with intermediate pools at their proper levels, and so on. So, desirable as these properties may be, we have no need to invoke natural selection to explain them. 

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