Pseudo first-order reaction enzymatic

All enzymatic reactions are initiated by formation of a binary encounter complex between the enzyme and its substrate molecule (or one of its substrate molecules in the case of multiple substrate reactions see Section 2.6 below). Formation of this encounter complex is almost always driven by noncovalent interactions between the enzyme active site and the substrate. Hence the reaction represents a reversible equilibrium that can be described by a pseudo-first-order association rate constant (kon) and a first-order dissociation rate constant (kM) (see Appendix 1 for a refresher on biochemical reaction kinetics) ... 

Enzymatic assay methods are classified as fixed-time assays, fixed-change assays, or kinetic (initial rate) assays. Kinetic assays continuously monitor concentration as a function of time pseudo-first-order conditions generally apply up to 10% completion of the reaction to allow the initial reaction rate to be determined. If the initial substrate concentration is > 10Km, then the initial rate is directly proportional to enzyme concentration. At low initial substrate concentrations (< 0.1 Km), the initial rate will be directly proportional to initial substrate concentration (cf. Chapter 2). For enzyme quantitation, a plot of initial rate against [E] provides a linear... 

Because transition states may have lifetimes of only several nanoseconds, in most cases, it is impossible to observe them directly. However, there are numerous lines of evidence for the existence of a tetrahedral-like transition state for non-enzymatic ester hydrolysis a) substitution at a carbonyl group (as is the case of the hydrolysis of esters) most often proceeds by a tetrahedral mechanism, a second-order addition-elimination (for a review of this mechanism, see (23)) b) the kinetics are pseudo-first order either in the substrate or in the nucleophile, as predicted by the mechanism c) for the 180 labeled esters, the 180 isotope is detectable in both products (in a "normal" Sjj2 reaction all the 180 isotopes should remain in the acid functionality)(24) d) in a few cases tetrahedral intermediates have been isolated or detected spectrally (25). 

Richard (1984) has determined that TIM accelerates the rate of GAP to DHAP isomerization by almost 10 orders of magnitude over the rate enhancement provided by a simple base catalyst such as the acetate ion. Moreover, as indicated by the free energy profile, the enzymatic reaction rate is very fast in physical-chemical terms. kcat/Km (the pseudo first-order rate constant for the reaction of enzyme with substrate) in the thermodynamically favourable direction GAP to DHAP is 400,000,000 M Is 1, which is close to the expected diffusion-controlled limit. A Ferrari indeed ... 

It is obvious from the discussion above that any kinetic-based analytical procedure must take into account the degree of approximation made in the various rate equations with respect to the period of measurement, the relative initial concentrations of reactants, and, in some cases, the reversibility of the reactions. Care must be taken, for example, in using a pseudo-first-order method when the initial concentration of the unknown varies over several orders of magnitude the error introduced in assuming the validity of the pseudo-first-order approximation of Equation 18.8 is a function of [A]q. Although the reaction mechanisms and rate equations for enzymatic and other catalyzed reactions in general are somewhat more complex, similar assumptions and simplifications (and, therefore, restrictions in validity) apply to the rate-measurement techniques employed in the analytical use of these systems. 

In cases where the electron self-exchange through the redox mediator occurs very rapidly relative to either the enzymatic reaction rate with a natural electron acceptor or the rate of enzyme-mediator electron exchange, the electrode reaction will follow pseudo-first-order kinetics. Thus for the mediated enzymatic reaction described above, the overall reaction rate can be described by... 

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