Sampling methods and free energy estimators for computer simulations: development and applications.
Edoardo Giovannelli · Florence Research (University of Florence) · 2018
Strategies extending the range of application of nonequilibrium work theorems [Phys.Rev. E, 2000, 61, 2361] and improving the efficiency of the related computational techniques are developed and tested.The Configurational Domains Transitions scheme, based on steps consisting of transition kernels alternated to relaxation kernels, performs nonequilibrium paths connecting two states with arbitrary shape and size in the space of the collective coordinates, giving access to their free energy difference.The method can be viewed as a generalization of the Steered Molecular Dynamics [Phys.Rev. E, 2008, 677, 016709].Moreover, Annealed Importance Sampling [Stat.Comput., 2001, 11, 125] is reviewed, from the perspective of nonequilibrium path-ensemble averages.The equivalence of Neal and Crooks treatments highlights the generality of the method, which goes beyond the mere thermal protocols.A temperature schedule based on a constant cooling rate outperforms stepwise cooling schedules.Furthermore, the Path-Linked Domains scheme is proposed as an alternative approach to estimate free energy differences between conformational states, defined in terms of collective coordinates of the molecular system.The computational protocol is organized into three independent stages.Two of them consist of independent simulations Abstract aimed at sampling the states of interest.Free energy evaluation is completed by estimation of the potential of mean force difference between two arbitrary points of the configurational surface, located around the target domains.Finally, the developed algorithms are adapted to the context of ligand-receptor equilibria, in order to evaluate absolute binding free energies of noncovalent complexes.We have developed two approaches, termed binded-domain and single-point alchemical-path schemes, based on the possibility of performing alchemical trajectories during which the ligand is constrained to fixed positions relative to the receptor.The first scheme exploits Configurational Domains Transitions framework to estimate the free energy difference between the coupled and uncoupled states of the ligand-receptor complex.On the other side, the single-point scheme resembles the Path Linked Domains procedure, originally conceived in the context of conformational equilibria, to avoid the calculation of the binding-site volume by introducing an additional equilibrium simulation of ligand and receptor in the bound state.The extra computational effort required by the second scheme leads to a significant improvement of accuracy in the free energy estimates.However, comparison with experimental data and previous molecular dynamics simulation studies confirm the validity of both nonequilibrium-alchemical methodologies.