Nonequilibrium candidate Monte Carlo is an efficient tool for equilibrium simulation

Nilmeier, Jerome P.; Crooks, Gavin E.; Minh, David D. L.; Chodera, John D.

doi:10.1073/pnas.1106094108

Cited by 109 publications

(196 citation statements)

References 67 publications

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“…In order to maintain detailed balance, the velocity must be inverted if the proposed state is rejected [12], which may lead to increased correlation times. Applied to single time steps, this is essentially the idea behind the generalized hybrid Monte Carlo (GHMC integrator [12,35], and when applied to trajectory segments, this is the idea behind work-bias Monte Carlo [40] and nonequilibrium-candidate MonteCarlo [41] simulations. In either case, Metropolization results in an MCMC process that samples the true equilibrium distribution.…”

Section: Recovering Equilibrium Statistics From Nonequilibrium Simentioning

confidence: 99%

Using Nonequilibrium Fluctuation Theorems to Understand and Correct Errors in Equilibrium and Nonequilibrium Simulations of Discrete Langevin Dynamics

2013

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Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite-time-step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that, even with a time-independent Hamiltonian, finite-time-step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate worklike quantity is defined-here called the shadow work-recently developed nonequilibrium fluctuation theorems can be used to measure or correct for the errors introduced by the use of finite time steps. In particular, we demonstrate that amending estimators based on nonequilibrium work theorems to include this shadow work removes the time-stepdependent error from estimates of free energies. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying sizes. While these deviations can be large, they can be eliminated altogether by Metropolization or greatly diminished by small reductions in the time step. Through this connection with driven processes, further developments in nonequilibrium fluctuation theorems can provide additional analytical tools for dealing with errors in finite-time-step integrators.

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Section: Recovering Equilibrium Statistics From Nonequilibrium Simentioning

confidence: 99%

Using Nonequilibrium Fluctuation Theorems to Understand and Correct Errors in Equilibrium and Nonequilibrium Simulations of Discrete Langevin Dynamics

2013

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“…It is worth noting that fast switching ideas have not only been applied to the calculation of free energies, but have also been combined with existing sampling methods to enhance the efficiency of the simulation. For instance, non-equilibrium switches have been used to improve the acceptance probability of replica exchange simulations [79,80] and to generate trial configurations for Monte Carlo simulations [81,82]. Conversely, waste-recycling Monte Carlo [37] can be adapted for the calculation of free energies from non-equilibrium switching simulations [36].…”

Section: Discussionmentioning

confidence: 99%

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Dellago

Hummer

2013

Entropy

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As shown by Jarzynski, free energy differences between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crooks fluctuation theorem, provide the basis for the computation of free energy differences from fast switching molecular dynamics simulations, in which an external parameter is changed at a finite rate, driving the system away from equilibrium. In this article, we first briefly review the Jarzynski identity and the Crooks fluctuation theorem and then survey various algorithms building on these relations. We pay particular attention to the statistical efficiency of these methods and discuss practical issues arising in their implementation and the analysis of the results.

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“…This has been obverved previously with NCMC, 44,51 and in our case might arise from the asymmetric work distributions associated with removing and restoring the ligand's interactions 92 Figure 4: Acceptance probability for toluene as a function of the amount of NCMC relaxation. The acceptance probability-also referred to as the acceptance rate-is shown on a log scale as a function of the total number of NCMC switching steps per cycle, for toluene in the L99A site of T4 lysozyme.…”

Section: Variations In the Ncmc Protocol Dramatically Impact Move Accmentioning

confidence: 99%

“…We believe this relative advantage of standard MC may be a peculiarity of toluene in this particular binding site (which is relatively large compared to the size of toluene, and known to be especially rigid 5,68,94,95 ), and not representative of typical MC performance in condensed phase systems. 44 To further test the relative performance of MC and NCMC, we examined performance of NCMC versus MC move proposals for a larger ligand in the lysozyme binding site, 3-iodotoluene; we find that the presence of the bulky iodo substituent dramatically impairs acceptance of MC moves, presumably due to the larger size of the ligand relative to the size of the binding site (see Section 2.9 for methods). 3-iodotoluene is another known binder in the lysozyme L99A site; however, due to its lack of symmetry, we are unable to take advantage of ligand symmetry to provide a simple metric for convergence of binding mode populations.…”

Section: Ncmc Does Not Compare As Favorably To MC For Toluene But Ncmentioning

confidence: 99%

“…(NCMC) couples MD with the benefits of MC and yields more efficient sampling Nonequilibrium Candidate Monte Carlo (NCMC) provides a framework for translating insight about the system (in the form of a naïve Monte Carlo proposals) into practical algorithms 44 that retain some of the advantages of Monte Carlo while providing dramatically higher acceptance. The motivation is that it can be easier to construct a finite-time proposal process (a nonequilibrium "protocol") that achieves high acceptance rates with short correlation times than to construct a successful instantaneous proposal.…”

Section: Nonequilibrium Candidate Monte Carlomentioning

confidence: 99%

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

Gill¹,

Lim²,

Grinaway³

et al. 2018

Preprint

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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, fragmentlike 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 timescales, 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 two orders of magnitude improvement in binding mode sampling efficiency compared to a brute force molecular dynamics simulation. This is a first step towards 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.

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Nonequilibrium candidate Monte Carlo is an efficient tool for equilibrium simulation

Abstract: [39][41] www.pnas.org/cgi

Cited by 109 publications

References 67 publications

Using Nonequilibrium Fluctuation Theorems to Understand and Correct Errors in Equilibrium and Nonequilibrium Simulations of Discrete Langevin Dynamics

Using Nonequilibrium Fluctuation Theorems to Understand and Correct Errors in Equilibrium and Nonequilibrium Simulations of Discrete Langevin Dynamics

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

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

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