Free energy calculations endpoints

In the present case, each endpoint involves—in addition to the fully interacting solute—an intact side chain fragment without any interactions with its environment. This fragment is equivalent to a molecule in the gas phase (acetamide or acetate) and contributes an additional term to the overall free energy that is easily calculated from ideal gas statistical mechanics [18]. This contribution is similar but not identical at the two endpoints. However, the corresponding contributions are the same for the transfonnation in solution and in complex with the protein therefore, they cancel exactly when the upper and lower legs of the thermodynamic cycle are subtracted (Fig. 3a). 

Hansch incorporated several chemical/physical chemical characteristics into this approach (4). He found Log P values (log octanol/water portion coefficient) were usually applicable with other parameters, such as Hammet linear free-energy relationships and Van der Waals radii selectively applicable. Continued work in this area by Hansch and other workers (5) has expanded the number of relevant characteristics to include molecular orbital calculations and diffusion parameters. Still, this quantitative approach embodies continuous parameters as an endpoint, a parametric philosophy. 

Figure 16.2 A thermodynamic cycle. If the path being used to calculate free energy moves horizontally employing methods like MM-PBSA, MM-GBSA or LIE, these calculations are referred to as endpoint calculations . Until recently, endpoint calculations were considered better suited for diverse ligands. If the path used to calculate free energy is vertical, methods like FEP, TI or NE are employed. These calculations are referred to as alchemical transformation calculations because ligand 1 is transformed through a series of steps into ligand 2.

In many cases, one would like to calculate not only the total free energy, but also the entropic and enthalpic contributions thereto. Knowledge of these components can frequently lead to better understanding of the underlying reasons for molecular preferences, e.g., differences in the binding efficacies of related ligands. Obviously, we can attempt to determine AH between two endpoint A states 0 and 1 as the directly calculated difference in their potential energies ... 

Another measure of error that is applicable to FEP simulations can be obtained from so-called double wide sampling . At each point (other than the endpoints) in the windowing chain during FEP, one can actually calculate two free energy differences one in the A. A. -F 5A direction, and one in the A A — 5A direction. The respective delta free energies are given by... 

One should experiment with the various options available for reducing sampling errors at endpoints where atoms are being introduced or removed from the system. A variety of choices exist for this (bond shrinking, alternative k scaling, a shift (unction in the non-bonded potential, etc.). Some combination of these choices will probably allow more efficient calculation of the free energy. 

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