Second order rate constants enzyme-substrate complex formation

Specificity constant Defined as kcJKm. It is a pseudo-second-order rate constant which, in theory, would be the actual rate constant if formation of the enzyme-substrate complex were the rate-determining step. 

The kinetics of the formation and decay of the observed intermediates through the formation of Q show no concentration dependence on either O2 or methane [15, 26] (O formation is presumably dependent on O2 concentration, but this has not been directly confirmed). In contrast, Q decay is linearly dependent on methane concentration indicating that this is the step where substrates react with the enzyme. Other substrates also accelerate Q decay, and the second order rate constant for the process depends on the specific substrate used. When nitrobenzene is used as a substrate, the decay of Q leads to the formation of another chromophoric intermediate, which we term compound T (T) for the terminal complex [15]. Chemical quench experiments showed that T is the nitrophenol (product) complex of... 

The right hand side of this equation can be rearranged to expose the relation of one or other rate constant to the rest. It is, however, readily ascertained that k jK gives a minimum value for kf2- This has been widely used as an estimate for the rate of substrate binding from steady state kinetic investigations. During the detailed discussion of the rate of collision complex formation (section 7.4), criteria will be discussed which help to decide how close k K is, in different systems, to the true second order rate constant characteristic of the first step of enzyme-substrate complex formation. 

Table 7.3. Second order rate constants for enzyme-substrate complex formation"...

In the absence of an enzyme, the reaction rate v is proportional to the concentration of substance A (top). The constant k is the rate constant of the uncatalyzed reaction. Like all catalysts, the enzyme E (total concentration [E]t) creates a new reaction pathway, initially, A is bound to E (partial reaction 1, left), if this reaction is in chemical equilibrium, then with the help of the law of mass action—and taking into account the fact that [E]t = [E] + [EA]—one can express the concentration [EA] of the enzyme-substrate complex as a function of [A] (left). The Michaelis constant lknow that kcat > k—in other words, enzyme-bound substrate reacts to B much faster than A alone (partial reaction 2, right), kcat. the enzyme s turnover number, corresponds to the number of substrate molecules converted by one enzyme molecule per second. Like the conversion A B, the formation of B from EA is a first-order reaction—i. e., V = k [EA] applies. When this equation is combined with the expression already derived for EA, the result is the Michaelis-Menten equation. 

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