Free-energy profiles, computation methods

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... 

To evaluate solvent effeets, statistieal meehanical Monte Carlo simulations have been carried out. An important quantity to be computed is the potential of mean force, or free energy profile, as a funetion of the reaction coordinate, X, for a chemical reaction in solution using free energy perturbation method. (44) A straightforward approaeh is to determine free energy differences for incremental changes of certain geometrieal variables that characteristically reflect the... 

In the previous section we have outlined computational methods to accurately obtain free energy profiles as a function of an order parameter, E. On the one hand, these one-dimensional free energy profiles contain a wealth of information. On the other hand, the configuration space is of very high dimension and a one-dimensional order parameter might not be sufficient to construct... 

Computing Free-Energy Profiles Using Multidimensional Potentials of Mean Force and Polynomial Quadrature Methods... 

Solvent effects on chemical reactions are presently being studied intensively by molecular computer simulation methods. Outer sphere ET (e. g. Ref. [217-228]), ion transfer [229-232], proton transfer [233], and bondbreaking [234, 235] are among the reactions studied near electrodes and liquid-Kquid interfaces. Much of this work has been reviewed recently [170, 236, 237] and will therefore not be discussed here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

If the interactions between the polymer and the surface and those inside the bulk polymer liquid are known, computer simulations will be well suited to investigate the surface structure and thermodynamics. There are different techniques to measure the surface free energy by computer simulations. One method consists in integrating the difference between the perpendicular and parallel pressure profiles, (2) and P (z)... 

The Sj 2 reaction, X + RY XR + Y", has been simulated with MC equilibrium calculations by Jorgensen and coworkers [81, 82]. The procedure used by these authors involves three steps i) the lowest energy reaction path is determined for the in vacuo system by using ab initio molecular orbital calculations ii) inter-molecular potential functions are obtained to describe the interactions between the substrate and a solvent molecule these potentials depend on the internal structure of the substrate iii) MC simulations are carried out to determine the free energy profile for the reaction in solution. This is a difficult computational task since importance sampling methods are required to explore all the values of the reaction coordinate. A similar technique was used by Madura and Jorgensen [83] in simulating the nucleophilic addition of hydroxide ion to formaldehyde in the gas phase and in aqueous solution. 

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