Enzyme mechanisms, free energy

Jorgensen et al. [49] developed a combined quantum mechanical and molecular mechanical approach for study of organic reactions and applied it with success to many solution reactions. Inspired by this Kollman et al. [50, 51] developed the approach further for study of enzyme reactions. This quantum mechanical/free energy (QM/... 

A new, more general, way to combine ab initio quantum mechanical calculations with classical mechanical free-energy perturbation approach (QM/FE approach) to calculate the energetics of enzyme-catalysed reactions and the same reaction in solution has been reported." The calculated free energies were in fairly good agreement with the experimental data for the activation energies of the first test case, amide hydrolysis in trypsin and in aqueous solution. 

Kollman, P. A. Kuhn, B. Donini, O. Perakyla, M. Stanton, R. Bakowies, D. Elucidating the nature of enzyme catalysis utiUzing a new twist on an old methodology Quantum mechanical-free energy calculations on chemical reactions in enzymes and in aqueous solution, Acc. Chem. Res. 2000, 34, 72-79. 

For enzyme-catalyzed reactions, we consider the unimolecular rate constant for the chemical step, which is the reaction of the Michaelis complex. The EA-VTST/OMT method involves a two-stage or three-stage procedure, where the third stage is optional. In stage one, a user-defined, physically meaningful reaction coordinate is used to calculate a one-dimensional potential of mean force. This provides a classical mechanical free energy of activation along that coordinate that is used to identify a transition state ensemble. In... 

A final important area is the calculation of free energies with quantum mechanical models [72] or hybrid quanmm mechanics/molecular mechanics models (QM/MM) [9]. Such models are being used to simulate enzymatic reactions and calculate activation free energies, providing unique insights into the catalytic efficiency of enzymes. They are reviewed elsewhere in this volume (see Chapter 11). 

Since work with the radical clock substrate probes indicated important differences in the hydroxylation mechanisms for M. capsulatus (Bath) and M. trickosporium OB3b, work with (R) and (S)-[1-2H,1-3H]ethane with both enzymes was carried out (93, 94). With M. tri-chosporium OB3b, approximately 65% of the product displays retention of stereochemistry (93). A rebound rate constant of 2 - 6 x 1012 s-1 was calculated, assuming a free energy change of 0.5 kcal mole-1 for rotation about the C-C bond (94). This estimate approaches the value obtained from the radical clock substrate probe analysis (59). 

This chapter reviewed some of our group s contributions to the development and application of QM/MM methods specifically as applied to enzymatic reactions, including the use of sequential MD/QM methods, the use of effective fragment potentials for reaction mechanisms, the development of the new QM/MM interface in Amber, as well as the implementation and optimization of the SCC-DFTB method in the Amber program. This last implementation allows the application of advanced MD and sampling techniques available in Amber to QM/MM problems, as exemplified by the potential and free energy surface surfaces for the reaction catalyzed by the Tripanosoma cruzi enzyme /ram-sialidasc shown here. 

In our simulations of histone modifying enzymes, the computational approaches centered on the pseudobond ab initio quantum mechanical/molecular mechanical (QM/MM) approach. This approach consists of three major components [20,26-29] a pseudobond method for the treatment of the QM/MM boundary across covalent bonds, an efficient iterative optimization procedure which allows for the use of the ab initio QM/MM method to determine the reaction paths with a realistic enzyme environment, and a free energy perturbation method to take account... 

With the characterized mechanism, the next key question is the origin of its catalytic power. A prerequisite for this investigation is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio QM/MM approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9... 

Cummins, P.L. Gready, J.E., Computational methods for the study of enzymic reaction mechanisms III a perturbation plus QM/MM approach for calculating relative free energies of protonation, J. Comp. Chem. 2005, 26, 561-568. 

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