ESTIMATING THE RELATIVE FREE-ENERGY OF DIFFERENT MOLECULAR-STATES WITH RESPECT TO A SINGLE REFERENCE STATE

We have investigated the feasibility of predicting free energy differe nces between a manifold of molecular states from a single simulation o r ensemble representing one reference state. Two formulas that are bas ed on the so-called lambda-coupling parameter approach are analyzed an d compared: (i) expansion of the free energy F(lambda) into a Taylor s eries around a reference state (lambda = 0), and (ii) the so-called fr ee energy perturbation formula. The results obtained by these extrapol ation methods are compared to exact (target) values calculated by ther modynamic integration for mutations in two molecular systems: a model dipolar diatomic molecule in water, and a series of para-substituted p henols in water. For moderate charge redistribution (approximate to 0. 5 e), both extrapolation methods reproduce the exact free energy diffe rences. For free energy changes due to a change of atom type or size, the Taylor expansion method fails completely, while the perturbation f ormula yields moderately accurate predictions. Both extrapolation meth ods fail when a mutation involves the creation or deletion of atoms, d ue to the poor sampling in the reference state simulation of the confi gurations that are important in the end states of interest. To overcom e this sampling difficulty, a procedure based on the perturbation form ula and on biasing the sampling in the reference state is proposed, in which soft-core interaction sites are incorporated into the Hamiltoni an of the reference state at positions where atoms are to be created o r deleted. For mutations going from p-methylphenol to the other five d ifferently para-substituted phenols, the differences in free energy ar e correctly predicted using extrapolation based on a single simulation of a biased, non-physical reference state. Since a large number of mu tations can be investigated using a recorded trajectory of a single si mulation, the proposed method is potentially viable in practical appli cations such as drug design.