Nonequilibrium Candidate Monte Carlo Simulations with Configurational Freezing Schemes

Local Resampling Trick for Focused Molecular Dynamics

We describe a method that focuses sampling effort on a user-defined selection of a large system, which can lead to substantial decreases in computational effort by speeding up the calculation of nonbonded interactions. A naive approach can lead to incorrect sampling if the selection depends on the configuration in a way that is not accounted for. We avoid this pitfall by introducing appropriate auxiliary variables. This results in an implementation that is closely related to "configurational freezing" and "elastic barrier dynamical freezing." We implement the method and validate that it can be used to supplement conventional molecular dynamics in free energy calculations (absolute hydration and relative binding).

Fragment Pose Prediction Using Non-equilibrium Candidate Monte Carlo and Molecular Dynamics Simulations

Part of early stage drug discovery involves determining how molecules may bind to the target protein. Through understanding where and how molecules bind, chemists can begin to build ideas on how to design improvements to increase binding affinities. In this retrospective study, we compare how computational approaches like docking, molecular dynamics (MD) simulations, and a non-equilibrium candidate Monte Carlo (NCMC)-based method (NCMC + MD) perform in predicting binding modes for a set of 12 fragment-like molecules, which bind to soluble epoxide hydrolase. We evaluate each method's effectiveness in identifying the dominant binding mode and finding additional binding modes (if any). Then, we compare our predicted binding modes to experimentally obtained X-ray crystal structures. We dock each of the 12 small molecules into the apo-protein crystal structure and then run simulations up to 1 μs each. Small and fragment-like molecules likely have smaller energy barriers separating different binding modes by virtue of relatively fewer and weaker interactions relative to drug-like molecules and thus likely undergo more rapid binding mode transitions. We expect, thus, to see more rapid transitions between binding modes in our study. Following this, we build Markov State Models to define our stable ligand binding modes. We investigate if adequate sampling of ligand binding modes and transitions between them can occur at the microsecond timescale using traditional MD or a hybrid NCMC+MD simulation approach. Our findings suggest that even with small fragment-like molecules, we fail to sample all the crystallographic binding modes using microsecond MD simulations, but using NCMC+MD, we have better success in sampling the crystal structure while obtaining the correct populations.

Binding Modes of Ligands Using Enhanced Sampling (BLUES): Rapid Decorrelation of Ligand Binding Modes via Nonequilibrium Candidate Monte Carlo

Accurately predicting protein-ligand binding affinities and binding modes is a major goal in computational chemistry, but even the prediction of ligand binding modes in proteins poses major challenges. Here, we focus on solving the binding mode prediction problem for rigid fragments. That is, we focus on computing the dominant placement, conformation, and orientations of a relatively rigid, fragment-like ligand in a receptor, and the populations of the multiple binding modes which may be relevant. This problem is important in its own right, but is even more timely given the recent success of alchemical free energy calculations. Alchemical calculations are increasingly used to predict binding free energies of ligands to receptors. However, the accuracy of these calculations is dependent on proper sampling of the relevant ligand binding modes. Unfortunately, ligand binding modes may often be uncertain, hard to predict, and/or slow to interconvert on simulation time scales, so proper sampling with current techniques can require prohibitively long simulations. We need new methods which dramatically improve sampling of ligand binding modes. Here, we develop and apply a nonequilibrium candidate Monte Carlo (NCMC) method to improve sampling of ligand binding modes. In this technique, the ligand is rotated and subsequently allowed to relax in its new position through alchemical perturbation before accepting or rejecting the rotation and relaxation as a nonequilibrium Monte Carlo move. When applied to a T4 lysozyme model binding system, this NCMC method shows over 2 orders of magnitude improvement in binding mode sampling efficiency compared to a brute force molecular dynamics simulation. This is a first step toward applying this methodology to pharmaceutically relevant binding of fragments and, eventually, drug-like molecules. We are making this approach available via our new Binding modes of ligands using enhanced sampling (BLUES) package which is freely available on GitHub.

Driving Structural Transitions in Molecular Simulations Using the Nonequilibrium Candidate Monte Carlo

Hybrid simulation procedures which combine molecular dynamics with Monte Carlo are attracting increasing attention as tools for improving the sampling efficiency in molecular simulations. In particular, encouraging results have been reported for nonequilibrium candidate protocols, in which a Monte Carlo move is applied gradually, and interleaved with a process that equilibrates the remaining degrees of freedom. Although initial studies have uncovered a substantial potential of the method, its practical applicability for sampling structural transitions in macromolecules remains incompletely understood. Here, we address this issue by systematically investigating the efficiency of the nonequilibrium candidate Monte Carlo on the sampling of rotameric distributions of two peptide systems at atomistic resolution both in vacuum and explicit solvent. The studied systems allow us to directly probe the efficiency with which a single or a few slow degrees of freedom can be driven between well-separated free-energy minima and to explore the sensitivity of the method toward the involved free parameters. In line with results on other systems, our study suggests that order-of-magnitude gains can be obtained in certain scenarios but also identifies challenges that arise when applying the procedure in explicit solvent.

Simulations in generalized ensembles through noninstantaneous switches

Generalized-ensemble simulations, such as replica exchange and serial generalized-ensemble methods, are powerful simulation tools to enhance sampling of free energy landscapes in systems with high energy barriers. In these methods, sampling is enhanced through instantaneous transitions of replicas, i.e., copies of the system, between different ensembles characterized by some control parameter associated with thermodynamical variables (e.g., temperature or pressure) or collective mechanical variables (e.g., interatomic distances or torsional angles). An interesting evolution of these methodologies has been proposed by replacing the conventional instantaneous (trial) switches of replicas with noninstantaneous switches, realized by varying the control parameter in a finite time and accepting the final replica configuration with a Metropolis-like criterion based on the Crooks nonequilibrium work (CNW) theorem. Here we revise these techniques focusing on their correlation with the CNW theorem in the framework of Markovian processes. An outcome of this report is the derivation of the acceptance probability for noninstantaneous switches in serial generalized-ensemble simulations, where we show that explicit knowledge of the time dependence of the weight factors entering such simulations is not necessary. A generalized relationship of the CNW theorem is also provided in terms of the underlying equilibrium probability distribution at a fixed control parameter. Illustrative calculations on a toy model are performed with serial generalized-ensemble simulations, especially focusing on the different behavior of instantaneous and noninstantaneous replica transition schemes.

Annealed importance sampling with constant cooling rate

Annealed importance sampling is a simulation method devised by Neal [Stat. Comput. 11, 125 (2001)] to assign weights to configurations generated by simulated annealing trajectories. In particular, the equilibrium average of a generic physical quantity can be computed by a weighted average exploiting weights and estimates of this quantity associated to the final configurations of the annealed trajectories. Here, we review annealed importance sampling from the perspective of nonequilibrium path-ensemble averages [G. E. Crooks, Phys. Rev. E 61, 2361 (2000)]. The equivalence of Neal's and Crooks' treatments highlights the generality of the method, which goes beyond the mere thermal-based protocols. Furthermore, we show that a temperature schedule based on a constant cooling rate outperforms stepwise cooling schedules and that, for a given elapsed computer time, performances of annealed importance sampling are, in general, improved by increasing the number of intermediate temperatures.

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

The equation of state of bulk materials is achieved via thermodynamic derivatives of the free energy yielded by nonequilibrium transformations and Jarzynski equality.