Activation free energies, conformational behaviour and dynamics

Activation free energies, conformational behaviour and dynamics 

Molecular dynamics simulations of enzyme reactions have been performed successfully with semiempirical QM/MM methods [54,57,64,72] (see section 6). The sampling provided by such QM/MM molecular dynamics simulations may be used to calculate activation free energies (and to address dynamical effects on the reaction). Thus, semiempirical QM/MM simulations have an important role to play. It has been suggested that a mapping procedure can be used to calculate ab initio QM/MM reaction free energies from empirical valence bond simulations [39,176]. This approach shows promise, but calculation of energies within the QM system (as opposed to its interaction with its surroundings) from such a simulation remains problematic. 

In transition state theory, dynamic effects are included approximately by including a transmission coefficient in the rate expression [9]. This lowers the rate from its ideal maximum TS theory value, and should account for barrier recrossing by trajectories that reach the TS (activated complex) region but do not successfully cross to products (as all trajectories reaching this point are assumed to do in TS theory). The transmission coefficient can be calculated by activated molecular dynamics techniques, in which molecular dynamics trajectories are started from close to the TS and their progress monitored to find the velocity at which the barrier is crossed and the proportion that go on to react successfully [9,26,180]. It is not possible to study activated processes by standard molecular dynamics because barrier crossing events occur so rarely. One reason for the 

The interiors of proteins are more densely packed than liquids [181], and so the participation of the atoms of the protein surrounding the reactive system in an enzyme-catalysed reaction is likely to be at least as important as for a reaction in solution. There is experimental evidence which indicates that protein dynamics may modulate barriers to reaction in enzymes [10,11]. Ultimately, therefore, the effects of the dynamics of the bulk protein and solvent should be included in calculations on enzyme-catalysed reactions. Dynamic effects in enzyme reactions have been studied in empirical valence bond simulations Neria and Karplus [180] calculated a transmission coefficient of 0.4 for proton transfer in triosephosphate isomerase, a value fairly close to unity, and representing a small dynamical correction. Warshel has argued, based on EVB simulations of reactions in enzymes and in solution, that dynamical effects are similar in both, and therefore that they do not contribute to catalysis [39]. 

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