Enzyme catalysis, activation energy reaction mechanism

First-order rate constants are used to describe reactions of the type A — B. In the simple mechanism for enzyme catalysis, the reactions leading away from ES in both directions are of this type. The velocity of ES disappearance by any single pathway (such as the ones labeled k2 and k3) depends on the fraction of ES molecules that have sufficient energy to get across the specific activation barrier (hump) and decompose along a specific route. ES gets this energy from collision with solvent and from thermal motions in ES itself. The velocity of a first-order reaction depends linearly on the amount of ES left at any time. Since velocity has units of molar per minute (M/min) and ES has units of molar (M), the little k (first-order rate constant) must have units of reciprocal minutes (1/min, or min ). Since only one molecule of ES is involved in the reaction, this case is called first-order kinetics. The velocity depends on the substrate concentration raised to the first power (v = /c[A]). 

EPSP synthase catalyzes the synthesis of EPSP by an addition-elimination reaction through the tetrahedral intermediate shown in Fig. 2a. This enzyme is on the shikimate pathway for synthesis of aromatic amino acids and is the target for the important herbicide, glyphosate, which is the active ingredient in Roundup (The Scotts Company EEC, Marysville, OH). Transient-state kinetic studies led to proof of this reaction mechanism by the observation and isolation of the tetrahedral intermediate. Moreover, quantification of the rates of formation and decay of the tetrahedral intermediate established that it was tmly an intermediate species on the pathway between the substrates (S3P and PEP) and products (EPSP and Pi) of the reaction. The chemistry of this reaction is interesting in that the enzyme must first catalyze the formation of the intermediate and then catalyze its breakdown, apparently with different requirements for catalysis. Quantification of the rates of each step of this reaction in the forward and reverse directions has afforded a complete description of the free-energy profile for the reaction and allows... 

Despite all the problems inherent to QM/CM approaches, some extremely interesting and perceptive work has been described in the literature recently in which all sorts of approaches have been used, improvements introduced and results obtained ([351, 372] and references therein). The study of enzyme catalysed reaction mechanisms, the calculation of relative binding free energies of substrates and inhibitor, and the determination of proton transfer processes in enzymatic reactions, are all good examples of enzyme-ligand interactions studies. Even though Warshel s EVB method [349] probably remains the most practical QM/CM approach for the study of enzyme catalysis, very useful work has been reported on enzyme catalysed reactions ([381] for an excellent review-[238, 319, 382-384]). This is a consequence of the accuracy of QM to treat the active site and inhibitor/substrate and the viability of classical mechanics to model the bulk of the enzyme not directly involved in the chemical reaction. 

Apart from technical considerations, it is important to identify what mechanistic questions can be addressed by the calculations. For example, different possible candidates for an active site base could be compared, or perhaps the stability of various proposed intermediates could be studied. There is a wealth of unanswered questions regarding aspects of specific enzyme reaction mechanisms, and also on the general principles of enzyme catalysis (e.g. what factors or interactions are most important in reducing the activation energy, how the enzyme reaction compares to the equivalent reaction in solution, etc.). Different types of calculation, within the QM/MM framework, may be required to address different types of question, as demonstrated by the variety of applications and approaches described in section 6. Consider what... 

Enzyme catalysis is achieved by a variety of mechanisms including both noncovalent and covalent interactions. Enzymes reduce the activation energy for the reaction they catalyze. 

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