DETERMINING THE CONTRIBUTIONS OF CONSTRAINTS IN FREE-ENERGY CALCULATIONS - DEVELOPMENT, CHARACTERIZATION, AND RECOMMENDATIONS

We develop and/or characterize three methods for determining the contr ibutions of constraints in free energy calculations. A new method for determining such contributions in thermodynamic integration (TI) calcu lations, the potential forces (PF) method, is developed and compared t o a second method, the constraint forces (CF) method. Both methods are also compared to a previously described technique for calculating suc h contributions in free energy perturbation (FEP) simulations. We find that the TI/PF protocol is considerably more efficient than the TI/CF method, and is preferred except in cases where the constraints contri buting to the free energy are part of a closed ring. Compared to TI/PF , the FEP method is shown to be relatively poor for generating potenti al of mean force (PMF) curves, though the FEP method is suitable for d etermining the ''PMF bond contribution'' in compositional free energy changes. PMF curves for a system of two neon atoms in a periodic box o f water have been derived. The convergence behavior of the free energy derivative partial derivative G/partial derivative R, where R is a di stance constraint, has been examined in detail for this system. As muc h as a nanosecond of molecular dynamics sampling can be required to de rive a fully converged value for this derivative at a single (lambda) point. We have determined the sampling ratio for partial derivative G/ partial derivative R as a function of Ne-Ne distance for a 295 water ( 21 angstrom/side) periodic water box, and conclude that for free energ y changes where long-distance constraint contributions are being deter mined, a minimum of 0.7 ps of sampling should be performed per window. When constraint contributions arise from short distances (such as whe n the PMF bond contribution is being calculated), correlation in the c onstraint derivative series dies out relatively quickly and the minimu m sampling-then dictated by correlation in the nonbonded series-should be about 0.6 ps.