Comparison of three enveloping distribution sampling Hamiltonians for the estimation of multiple free energy differences from a single simulation

Abstract

We test the performance of three different reference state Hamiltonians for enveloping distribution sampling (EDS). EDS is an implementation of umbrella sampling which allows estimation of various free energy differences "on the fly" from a single simulation. This is achieved by construction of a reference state, which envelopes the regions of configuration space important to the various end states of interest. The proposed Hamiltonians differ in the way energy barriers separating these regions of configuration space are reduced. The test system consisted of 17 disubstituted benzenes in water and in complex with alpha-cyclodextrin. The calculated free energy differences correlate with thermodynamic integration results (R(2) > 0.99 for the ligands in water and R(2) > 0.98 for the ligands in complex with alpha-cyclodextrin). One of the reference state Hamiltonians outperformed the others in sampling the configuration space important to the various end states. In this reference state not all barriers between all pairs of states are reduced. Instead a minimum spanning tree of states is calculated, which connects states that are "closest" in configuration space.