Multiple free energies from a single simulation: Extending enveloping distribution sampling to nonoverlapping phase-space distributions

Abstract

A recently proposed method to obtain free energy differences for multiple end states from a single simulation of a reference state which was called enveloping distribution sampling (EDS) [J. Chem. Phys. 126, 184110 (2007)] is expanded to situations where the end state configuration space densities do not show overlap. It uses a reference state Hamiltonian suggested by Han in 1992 [Phys. Lett. A 165, 28 (1992)] in a molecular dynamics implementation. The method allows us to calculate multiple free energy differences "on the fly" from a single molecular dynamics simulation. The influence of the parameters on the accuracy and precision of the obtained free energy differences is investigated. A connection is established between the presented method and the Bennett acceptance ratio method. The method is applied to four two-state test systems (dipole inversion, van der Waals perturbation, charge inversion, and water to methanol conversion) and two multiple-state test systems [dipole inversion with five charging states and five (dis-)appearing water molecules]. Accurate results could be obtained for all test applications if the parameters of the reference state Hamiltonian were optimized according to a given algorithm. The deviations from the exact result or from an independent calculation were at most 0.6 kJ/mol. An accurate estimation of the free energy difference is always possible, independent of how different the end states are. However, the convergence times of the free energy differences are longer in cases where the end state configuration space densities do not show overlap [charge inversion, water to methanol conversion, (dis-)appearing water molecules] than in cases where the configuration space densities do show some overlap [(multiple) dipole inversion and van der Waals perturbation].

Comparison of enveloping distribution sampling and thermodynamic integration to calculate binding free energies of phenylethanolamine N-methyltransferase inhibitors

“…Two sets of parameters, a smoothness parameter s and a set of energy offsets E R , are introduced to ensure even sampling of all end states. 11 The optimized reference Hamiltonian H R = K R + V R has the generalized form, 13 where the kinetic terms K R are omitted for simplicity,…”

“…In addition, a new procedure to obtain the parameters of the reference state is proposed. Finally, the results are compared to those of EDS schemes introduced previously [11][12][13] and to those of TI.…”

“…The model Hamiltonian is either made dependent on a coupling parameter 16 λ and TI and its standard free enthalpy estimator is used or is formulated as the logarithm of a sum of exponentials of the end-state Hamiltonians as in EDS with the corresponding estimator. 11 Here, the methods TI and EDS are used to estimate the binding affinity of ten different tetrahydroisoquinoline derivatives to the protein phenylethanolamine N-methyltransferase (PNMT). For EDS, the performance using either a single or a dual topology implementation is investigated.…”

Monte Carlo Simulations of HIV Capsid Protein Homodimer

“…Although all-atom simulations have been successfully applied to validate the stability of capsid structures, 17 they would be very inefficient to reveal the spontaneous binding / unbinding of the proteins. In principle, when the bound structure is known, a variety of enhanced sampling methods 31,32 can be used to compute the free energy difference between the bound and unbound states, as similarly applied in the studies of ligand binding and conformational changes of small peptides 33 , as well as in QM/MM calculations 34,35 . Because the structures of free full-length CA dimers are unknown, however, these free-energy methods are not immediately applicable here, although they could be possibly used to examine the affinity of a given binding interface.…”

Communication: Estimating the initial biasing potential for λ-local-elevation umbrella-sampling (λ-LEUS) simulations via slow growth

“…These involve the definition of two Hamiltonians H A and H B corresponding to the topologically distinct physical end states A and B, respectively, of a molecular system, both being functions of the same set of degrees of freedom (Cartesian coordinates r and associated momenta p). While some methods like one-step perturbation 1, 2 (OSP) or enveloping distribution sampling 3,4 (EDS) only make use of these two end-state Hamiltonians, others require the introduction of an unphysical pathway connecting them. In this case, a coupling parameter λ is used to define a hybrid HamiltonianH(λ), equal to H A for λ = 0 and to H B for λ = 1.…”