Dehydrogenases initial rate equations

The initial rate equation is again of the form of Eq. (1) with the kinetic coefficients as in Table I, which shows that the mechanism differs from the simple ordered mechanism in three important respects. First, the isomerization steps are potentially rate-limiting evidence for such a rate-limiting step not attributable to product dissociation or the hydride-transfer step (fc) has been put forward for pig heart lactate dehydrogenase 25). Second, Eqs. (5) and (6) no longer apply in each case the function of kinetic coefficients will be smaller than the individual velocity constant (Table I). Third, because < ab/ a< b is smaller than it may also be smaller than the maximum specific rate of the reverse reaction that is, one of the maximum rate relations in Eq. (7) need not hold 26). This mechanism was in fact first suggested to account for anomalous maximum rate relations obtained with dehydrogenases for which there was other evidence for an ordered mechanism 27-29). 

Since the initial rate equation for a random mechanism, Eq. (13), is not of the linear form of Eq. (1), it can account for rate cooperativity with appropriate values for the rate constants (6,30,149) and has been suggested for isocitrate dehydrogenases (lJf2,150). It does not require that there be more than one active center in the enzyme molecule nor cooperative equilibrium binding of substrates or modifiers. An alternative to this purely kinetic explanation is that there are two or more active... 

At very high substrate concentrations deviations from the classical Michaelis-Menten rate law are observed. In this situation, the initial rate of a reaction increases with increasing substrate concentration until a limit is reached, after which the rate declines with increasing concentration. Substrate inhibition can cause such deviations when two molecules of substrate bind immediately, giving a catalytically inactive form. For example, with succinate dehydrogenase at very high concentrations of the succinate substrate, it is possible for two molecules of substrate to bind to the active site and this results in non-functional complexes. Equation S.19 gives one form of modification of the Michaelis-Menten equation. 

Fia. 32. Reaction of lactate dehydrogenase with NAD and lactate at pH 6 monitored by nucleotide absorbance, nucleotide fluorescence, and protein fluorescence, The derivative plots on the right represent the initial transient approach to a steady-state rate of NADH production for nucleotide absorbance and fluorescence. To obtain the derivative plot for protein fluorescence, the fluorescence was measured as a fraction of the fluorescence of unliganded enzyme at each time, and the fractional fluorescence was then converted into fractional saturation of the enzyme with ligand by using the equation F " = 1 — a(l — x) (see Section II,D,1). Steady-state rate (s.s.) was 4.8 sec h... 

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