Michaelis parameters

While the Michaelis parameters are an important guide as to the integrity of the adsorbed sample, they are not of primary concern. By contrast, voltammetry reveals activity as a function of potential which can be varied and tuned to control and probe the enzyme in different ways. We will see that many enzymes display a "potential optimum , i.e. they have maximum activity at a particular potential. Many enzymes operate well in both redox directions, and the "bias can be measured precisely by running the voltammetry in the presence of both oxidised and reduced substrates. The exact form of the catalytic wave provides important mechanistic details, and this is often more easily analysed by taking the derivative of the catalytic current (dz/d ). 

Procedure Maximum velocity Michaelis parameter Permeability ... 

Now, one can proceed one step further by grouping the rate constants in the form of Michaelis parameters ... 

Briggs Haldane (1925) removed the restrictive assumption that the enzyme-substrate complex is in equilibrium with free enzyme and substrate and introduced the steady state model, which gives the Michaelis parameters, ATm and a more complex meaning. The principles of steady state kinetics of enzyme reactions can be demonstrated with the more realistic, though still oversimplified, model of Haldane (1930). This contains the minimum number of intermediates, namely enzyme-substrate and enzyme-product complexes ... 

Now we can see what happens to when the rate limiting step is changed between those controlled by k2j to Atj, that is from the chemical transformation to product dissociation. When Aj, then we obtain the Michaelis parameters of equation (3.3.17). However, if A 2j A j, then we obtain... 

Some further comments are necessary to define the units and dimensions of the Michaelis parameters. As stated above, the has the units of a dissociation constant (concentration) and this remains so, regardless of its complexity in terms of many rate constants and v have the dimensions... 

Criteria for the validity of the steady state assumption can be obtained operationally by consideration of how to obtain correct values for initial rates and their use in the evaluation of the Michaelis parameters. Before going into these practical considerations some reference should be made to theoretical treatments of steady state conditions (see Segel, 1975 Wong, 1975). We use the simple form, equation (3.3.19), for saturation kinetics, differentiating to obtain a relation between the change in the steady state intermediate Ce (0 and in Cs(0 with time. 

However, the above equations will only give reasonable values for the parameters in the unlikely case when the reaction is both essentially irreversible and not subject to product inhibition. Much more complex equations with many more parameters have to be used fora fit of the whole time course of the reaction to a realistic mechanism. There are hazards, too, in the determination of true initial rates. It is necessary to check that the change in substrate concentration during the period of initial rate measurement is sufficiently small so that the observed rate is the correct one for each specified value of Cs(0). After a preliminary estimate for and one can readily calculate whether these parameters would cause a significant deviation from true linearity of initial rates, that is adherence to the steady state condition because of the difference in substrate concentration at the beginning and end of the measurement. This must not be left to the appearance of the initial slope. It is also important, for the correct evaluation of the Michaelis parameters, to heed the advice of Dowd Riggs (1965) that the range of Cg(0) must straddle both sides of by a factor of 10. 

If the Michaelis parameters for the forward reaction under conditions Cp(t) = 0 and for the reverse reaction under conditions cg(0)=0 are substituted in equation (3.3.26), the following useful expression is obtained... 

This is exactly what the Haldane relations demonstrate for the sequence of intermediates in enzyme reactions. They are useful criteria when changing Michaelis parameters are compared to the equilibrium constant for an enzyme catalysed reaction. We shall return to this problem in section 5.1, when we discuss how transient kinetic analysis can be used to determine the equilibrium constants of individual steps. In this connection the equations which express the concentrations of the intermediates in terms of the fraction of total amount of enzyme in the reaction mixture will turn out to be useful. Many enzyme reactions can be studied in both directions and the two sets of parameters for the reactions starting on either side (with S or P as the substrate) - Kh, and - give further insight. 

Taking the expressions for the Michaelis parameters derived for the three step mechanism, with only the first step reversible (p. 83), we obtain... 

As noted in a number of sections of this volume, the nomenclature of enzymology has been adopted for the description of reactions of receptors in general. Competitive, non-competitive and uncompetitive inhibitors are classified in terms of their effects on the Michaelis parameters and... 

The other Michaelis parameter, F,nax cat E(0)> not affected by a competitive inhibitor. The clear distinction of competitive inhibition from any other is that, on substrate saturation, the resulting maximum velocity is always the same, regardless of inhibitor concentration. 

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