Steady-State Random Bi Uni

Occasionally rate expressions are described as 1/1, 2/1, etc., functions, referring to the maximum power of the substrate concentration in the numerator (N) and denominator (D). For example, consider the case of the steady-state random Bi Uni mechanism. The reciprocal form of the rate expression (at constant [B]) has the general form of 1/v = ( o + a[A] -t da2[A] )/ (na[A] + na2[A] ) where the Rvalues are collections of rate constants. If both the numerator and denominator of this reciprocal form of the rate expression are divided by the substrate concentration raised to the highest power in which it appears (in this case, [A] ), then the numerator has a term in 1/[A] (as well as 1/[A] and 1/[A]°) whereas the denominator has terms in 1/[A] and 1/[A]°. Thus, this rate expression is a 2/1 function. See Multisubstrate Mechanisms... 

Let us take the last example in Table 1, the Steady-State Random Bi Uni mechanism. The number of enzyme species or comers in the basic figure is four and the number of lines is five. Thus,... 

If the breakdown of the central complex in bisubstrate reactions is not the sole rate-limiting step, than the rate equation becomes quite complex. For example, consider the Steady-State Random Bi Uni system shown below ... 

An enzyme-catalyzed reaction involving two substrates and one product. There are two basic Bi Uni mechanisms (not considering reactions containing abortive complexes or those catagorized as Iso mechanisms). These mechanisms are the ordered Bi Uni scheme, in which the two substrates bind in a specific order, and the random Bi Uni mechanism, in which either substrate can bind first. Each of these mechanisms can be either rapid equilibrium or steady-state systems. 

Steady-State Expression. In the absence of significant amounts of product, P (thus, initial rate conditions in which [P] 0), the steady-state expression for the random Bi Uni mechanism having two central complexes... 

Restricting ourselves to the rapid equilibrium approximation (as opposed to the steady-state approximation) and adopting the notation of Cleland [158 160], the most common enzyme-kinetic mechanisms are shown in Fig. 8. In multisubstrate reactions, the number of participating reactants in either direction is designated by the prefixes Uni, Bi, or Ter. As an example, consider the Random Bi Bi Mechanism, depicted in Fig. 8a. Following the derivation in Ref. [161], we assume that the overall reaction is described by vrbb = k+ [EAB — k EPQ. Using the conservation of total enzyme... 

An enzyme-catalyzed reaction scheme in which the two substrates (A and B) can bind in any order, resulting in the formation of a single product of the enzyme-catalyzed reaction (hence, this reaction is the reverse of the random Uni Bi mechanism). Usually the mechanism is distinguished as to being rapid equilibrium (/.c., the ratedetermining step is the central complex interconversion, EAB EP) or steady-state (in which the substrate addition and/or product release steps are rate-contributing). See Multisubstrate Mechanisms... 

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