CONVERGENCE PROPERTIES OF FREE-ENERGY CALCULATIONS - ALPHA-CYCLODEXTRIN COMPLEXES AS A CASE-STUDY

By considering all possible mutations among four para-substituted phen ols, p-chlorophenol, p-methylphenol, p-cyanophenol, and p-methoxypheno l, which bind as inclusion compounds in alpha-cyclodextrin, the conver gence properties of thermodynamic integration free energy calculations using slow growth as compared to numerical quadrature are investigate d and interpreted in terms of structural and dynamical properties of t he molecular system. It is shown that a systematic increase in the cal culated hysteresis can be expected with increasing simulation time in slow-growth calculations if the system is perturbed faster than the ra te at which the various states that make up the equilibrium ensemble a re sampled. Using numerical quadrature the effects of nonequilibrium c an be largely separated from the effects of insufficient sampling. It is shown, however, that the apparent degree of convergence when using numerical quadrature does not necessarily reflect the accuracy of the calculation. The utility of formulating closed cycles in both the boun d and unbound states as a means of determining the minimum error in a given calculation is demonstrated. The effects of the choice of pathwa y and of the choice of integration scheme on convergence within closed cycles are also discussed. Finally, the quality of the force field us ed and the relative importance of the force field as opposed to sampli ng considerations are assessed by comparing the estimated free energy differences to experimental data. It is shown that a meaningful apprai sal of a specific force field cannot be made independent of sampling c onsiderations. A modification to the GROMOS force field that improved the agreement between the calculated and experimental free energies fo r the mutation of p-chlorophenol to p-methylphenol is also proposed.