Solvation Energies by Free-Energy Perturbation Methods

CALCULATION OF SOLVATION ENERGIES BY FREE-ENERGY PERTURBATION METHODS 

Direct Calculations of Free Energy Converge Very Siowiy 

With a realistic solvent model, we can explore the properties of solvated molecules. As before, we take a classical approach by adding the solute-solvent interaction term (USs) to the potential surface of the system and write 

The term Uss is the solvent-solvent interaction term [the Unb and Uqq terms of eq. (3.1)] and t/ind is the induced dipoles three-body term which includes now the field both from the solute and the solvent. With a potential surface for a solvated solute we can address the important issue of evaluating solvation energies. In principle, one can try to evaluate the average poten- 

One may also try to evaluate solvation-free energies by using the corresponding partition function through the formula (Ref. 4) 

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The free energy perturbation calculations on mutation of the central statine residue of pepstatin to its dehydroxy and other derivatives were carried out using the window method. The crystal structure reported by Suguna et al.l4 l5was used for these calculations. In most simulations, the mutations were achieved either in 101 or 51 windows with 0.4 ps of equilibration and 0.4 ps of data collection at each window. The calculation for each mutation was repeated in water to determine the difference in the free energies of solvation and to complete the thermodynamic cycle. 

The effects of solvation have been studied by an implementation of an ellipsoid cavity model into Kohn-Sham theory [94]. The lowering of the activation energy by water solvation of the allyl vinyl ether has been calculated to be 0.3 kcal/mol by this method. This value is considerably lower than the results from other calculations on the same system using cavity models [95], free energy perturbation [96], or QM/MM calculations [97] as well as the values... 

Bash et al. (1987) applied the thermodynamic perturbation method to complexes of thermolysin with a phosphonamidate [Cbz-Gly -(NH)-Leu-Leu] and the corresponding phosphonate inhibitor [Cbz-Gly -(0)-Leu-Leu]. The perturbation was carried out by using 20 windows, with 2-psec molecular dynamics simulations in each window. Computations were for the ligand in solution and bound to the enzyme. The solvation of the enzyme was represented by a spherical cap of 168 water molecules about the bound inhibitor. The difference in free energy of binding of the two inhibitors was calculated to be 4.38 kcal/mol, to be compared with the experimental value, 4.10 kcal/mol. These calculations point out the importance of solvation effects, which are seen in the 3.4 kcal/mol difference between the NH and O forms of the inhibitor. 

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