Adaptive integration method for Monte Carlo simulations

Fasnacht, Marc; Swendsen, Robert H.; Rosenberg, John M.

doi:10.1103/physreve.69.056704

Cited by 45 publications

(70 citation statements)

References 42 publications

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“…(3), the AIM method satisfies detailed balance only asymptotically. In other words, once the ∆F estimate fully converges, the value of δF is correct, and detailed balance is satisfied 8,31 .…”

Section: B Adaptive Integrationmentioning

confidence: 99%

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Comparison of free energy methods for molecular systems

Ytreberg

Swendsen

Zuckerman

2006

The Journal of Chemical Physics

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144

148

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We present a detailed comparison of computational efficiency and precision for several free energy difference (∆F ) methods. The analysis includes both equilibrium and non-equilibrium approaches, and distinguishes between uni-directional and bi-directional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration and single-ensemble path sampling, to more established methodologies. As test cases, we study relative solvation free energies, of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation ∆F estimates as compared to other methods used in this report, while also offering rapid estimation of ∆F . The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the uni-directional, "fast-growth" non-equilibrium case. Closer examination of the path sampling approach on a twodimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.

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Section: B Adaptive Integrationmentioning

confidence: 99%

“…We are particularly interested in assessing recently proposed methods 8,9 in comparison to established techniques. Thus, the purpose of this study is to provide a careful comparison of the efficiency and precision of several ∆F methods.…”

Section: Introductionmentioning

confidence: 99%

Comparison of free energy methods for molecular systems

Ytreberg

Swendsen

Zuckerman

2006

The Journal of Chemical Physics

Self Cite

144

148

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“…6 In this method, we focus on one order parameter, λ, of the system that leads to the most significant barriers.…”

Section: Introductionmentioning

confidence: 99%

Markov Chains of Infinite Order and Asymptotic Satisfaction of Balance: Application to the Adaptive Integration Method

Earl

Deem

2005

J. Phys. Chem. B

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Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.

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“…The latter is often related to the presence of secondary poses (RL) i that may emerge especially at small λ values, [14,33] [36] To overcome this serious problem and unpredictable behavior, in a parallel environment, alchemical transformations can be coupled to Generalized Ensemble techniques whereby each replica of the system performs a random walk in the λ domain with λ moving according to a Metropolis criterion, so as to make the λ probability distribution flat on the whole [0,1] λ interval. These methods are termed λ-hopping schemes and use either Hamiltonian Replica Exchange (HREM) [22], Serial Generalized Ensemble (SGE) methodologies [50] or Adaptive Integration Schemes (AIM) [15,33] and are all aimed at defeating the convergence problems induced by the existence of meta-stable conformational states of the bound ligand along the alchemical path. In the HREM implementation, no bias potential is needed in the transition probability, while in SGE or AIM, the bias potential (i.e.…”

Section: Systemsmentioning

confidence: 99%

“…In the last two decades, in the context of atomistic molecular dynamics (MD) simulations with explicit solvent, various computational techniques have been devised to compute the absolute binding free energies with unprecedented accuracy such as the Double Decoupling method (DDM), [8] Potential of Mean Force (PMF) [9,10], Metadynamics [11][12][13] or generalized ensemble approaches (GE) like the Binding Energy Distribution Analysis (BEDAM) [14], the Adaptive Integration Method [15], or the Energy Driven Undocking scheme. [16] All these methodologies bypass the sampling limitations that are inherent to classical molecular dynamics simulations in drug receptor systems by appropriately modifying the interaction potential and/or by invoking geometrical restraints so as to force the binding/unbinding event in a simulation time scale typically in the order of the nanoseconds.…”

Section: Introductionmentioning

confidence: 99%

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

Procacci

2016

Phys. Chem. Chem. Phys.

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In this contribution I critically revise the alchemical reversible approach in the context of the statistical mechanics theory of non covalent bonding in drug receptor systems. I show that most of the pitfalls and entanglements for the binding free energies evaluation in computer simulations are rooted in the equilibrium assumption that is implicit in the reversible method. These critical issues can be resolved by using a non-equilibrium variant of the alchemical method in molecular dynamics simulations, relying on the production of many independent trajectories with a continuous dynamical evolution of an externally driven alchemical coordinate, completing the decoupling of the ligand in a matter of few tens of picoseconds rather than nanoseconds. The absolute binding free energy can be recovered from the annihilation work distributions by applying an unbiased unidirectional free energy estimate, on the assumption that any observed work distribution is given by a mixture of normal distributions, whose components are identical in either direction of the non-equilibrium process, with weights regulated by the Crooks theorem. I finally show that the inherent reliability and accuracy of the unidirectional estimate of the decoupling free energies, based on the production of few hundreds of non-equilibrium independent sub-nanoseconds unrestrained alchemical annihilation processes, is a direct consequence of the funnel-like shape of the free energy surface in molecular recognition. An application of the technique on a real drug-receptor system is presented in the companion paper.

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Adaptive integration method for Monte Carlo simulations

Cited by 45 publications

References 42 publications

Comparison of free energy methods for molecular systems

Comparison of free energy methods for molecular systems

Markov Chains of Infinite Order and Asymptotic Satisfaction of Balance: Application to the Adaptive Integration Method

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

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