Uni Bi mechanism

Let us consider an enzymatic reaction in which two substrates are utilized to from two products (in the nomenclature of enzyme reaction mechanisms this situation is referred to as a bi-bi mechanism). A reaction in which one substrate yields two products is referred to as a uni-bi mechanism, and one in which two substrates combine to form a single product is referred to as a bi-uni mechanism (see Copeland, 2000, for further details). For the purposes of illustration let us use the example of a group transfer reaction, in which a chemical species, X, is transferred from one substrate to the other in forming the products of the reaction ... 

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. 

A system for describing kinetic mechanisms for enzyme-catalyzed reactions . Reactants (ie., substrates) are symbolized by the letters A, B, C, D, eto., whereas products are designated by P, Q, R, S, etc. Reaction schemes are also identified by the number of substrates and products utilized (i.e.. Uni (for one), Bi (two), Ter (three occasionally Tri), Quad (four), Quin (five), etc. Thus, a two-substrate, three-product enzyme-catalyzed reaction would be a Bi Ter system. In addition, reaction schemes are identified by the pattern of substrate addition to the enzyme s active site as well as the release of products. For a two-substrate, one-product scheme in which either substrate can bind to the free enzyme, the enzyme scheme is designated a random Bi Uni mechanism. If the substrates bind in a distinct order (note that, in such cases, A binds before B for ordered multiproduct release, P is released prior to Q, etc.), the scheme would be ordered Bi Uni. If the binding scheme is different than the release of product, then that information should also be provided for example, a two-substrate, two-product reaction in which the substrates bind to the enzyme in an ordered fashion whereas the products are released randomly would be designated ordered on, random off Bi Bi scheme. If one or more Theorell-Chance steps are present, that information is also given (e.g., ordered Bi Bi-(Theorell-Chance)), with the prefixes included if there is more than one Theorell-Chance step. 

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... 

The Steady-State Mechanism If we consider the ordered Bi Uni mechanism with only one central complex. 

Rapid Equilibrium Case. In the absence of significant amounts of product (i.e., initial rate conditions thus, [P] 0), the rate expression for the rapid equilibrium random Bi Uni mechanism is v = Uniax[A][B]/(i iai b + i b[A] + i a[B] + [A][B]) where is the dissociation constant for the EA complex, and T b are the dissociation constants for the EAB complex with regard to ligands A and B, respectively, and Umax = 9[Etotai] where kg is the forward unimolecular rate constant for the conversion of EAB to EP. Double-reciprocal plots (1/v v. 1/[A] at different constant concentrations of B and 1/v v. 1/[B] at different constant concentrations of A) will be intersecting lines. Slope and intercept replots will provide values for the kinetic parameters. 

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... 

Overview of other bimolecular mechanisms The random bi-uni mechanism (random bi-substrate binding order with single product) has the form ... 

SLO follows an ordered, bi-uni mechanism, in which linoleic acid (LA) binds and reacts prior to O2 encounter [8], which has permitted a variety of steady-state and single-turnover studies into chemistry on SLO. The kinetic mechanism can be divided into a reductive half-reaction, described by the rate constant kcat/ffM(LA), and an oxidative half-reaction described by the rate constant fecat/KM(02). On the reductive half-reaction, SLO binds LA (ki), then the Fe +-OH cofactor abstracts the pro-S hydrogen from C-11 of LA (k2), forming a substrate-derived radical inter-... 

The binding of two substrates A and B to an enzyme may occur in a compulsory order or in a random order. If one product (uni) is formed out of two substrates (bi), the corresponding mechanisms are the ordered bi-uni mechanism and the random bi-uni mechanism , respectively (water is not regarded as a substrate). 

Corresponding to the above discussion about enzyme kinetics, the numerator is nearly identical for all different bi-bi-mechanisms (for bi-uni mechanisms, respectively), as the numerator characterizes the thermodynamic equilibrium of the reaction (which is independent of a kinetic mechanism). 

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,... 

Note, however, that the composition of denominator terms, in this respect, is not identical in Bi Bi and Bi Uni mechanisms (Section 9.4). 

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