Sensitivity analysis and principal component analysis in free energy calculations

Recent publications have suggested that the systematic sensitivity analysis approach (SSAP) commonly used in engineering problems and atomic/molecular scattering problems is also useful for analyzing structural relationships and estimating the uncertainties of results from molecular mechanics and free energy calculations. Here we demonstrate that, by performing a principal component analysis (PCA) of the results from a sensitivity analysis, it is possible to identify a subset of parameters (possibly small in many instances) of a potential energy function that are most important in determining the value of a free energy difference (ΔA = A₂ - A₁ where A₂ and A₁ correspond to the free energy of system 2 and system 1, respectively) Consequently, the uncertainty of ΔA due to the use of nonoptimal parameters of a potential energy function is mainly determined by the uncertainties of a smaller number of parameters of the potential energy function. We also show that the SSAP and the PCA methods can help to choose experimental data to use for the refinement of the parameters of a potential energy unction In general, a PCA allows for the identification of the set(s) of parameters that act in a correlated fashion to most (or best) influence the observables. A PCA may also be applied to molecular mechanics, and the concepts may be generalized to the analysis of molecular dynamics.