Biased Sampling of Nonequilibrium Trajectories:  Can Fast Switching Simulations Outperform Conventional Free Energy Calculation Methods?

Oberhofer, Harald; Dellago, Christoph; Geissler, Phillip L.

doi:10.1021/jp044556a

Cited by 171 publications

(204 citation statements)

References 36 publications

Supporting

Mentioning

202

Contrasting

Order By: Relevance

“…The Jarzynski equality, on the other hand, can in principle be used to calculate the PMF. However it is well-known [12,13,14,15] that the exponential average in the Jarzynski equality depends crucially on a small fraction of realizations that transiently violate the second law of thermodynamics. Since such "magic" realizations are very unlikely to occur among a collection of fast rate realizations, it is clear that the potential of mean force cannot be determined accurately by the direct application of the Jarzynski equality.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the potential of mean force from nonequilibrium measurements via maximum likelihood estimators

Chelli¹,

Marsili²,

Procacci³

2008

Phys. Rev. E

View full text Add to dashboard Cite

We present an approach to the estimate of the potential of mean force along a generic reaction coordinate based on maximum likelihood methods and path-ensemble averages in systems driven far from equilibrium. Following similar arguments, various free energy estimators can be recovered, all providing comparable computational accuracy. The method, applied to the unfolding process of the α-helix form of an alanine deca-peptide, gives results in good agreement with thermodynamic integration.

show abstract

Section: Introductionmentioning

confidence: 99%

Calculation of the potential of mean force from nonequilibrium measurements via maximum likelihood estimators

Chelli¹,

Marsili²,

Procacci³

2008

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes such as Wang-Landau sampling.In recent years increasing attention has been paid to the possibility of studying equilibrium thermodynamical processes by means of non-equilibrium processes [1,2,3,4,5]. A major breakthrough in this field is the work of Jarzynski [2] who has demonstrated that it is possible to estimate the free energy difference between two states as a suitable average of the work done on the system by forcing the transition in a finite time.…”

mentioning

confidence: 99%

Equilibrium Free Energies from Nonequilibrium Metadynamics

2006

View full text Add to dashboard Cite

In this paper we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to a model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes such as Wang-Landau sampling.In recent years increasing attention has been paid to the possibility of studying equilibrium thermodynamical processes by means of non-equilibrium processes [1,2,3,4,5]. A major breakthrough in this field is the work of Jarzynski [2] who has demonstrated that it is possible to estimate the free energy difference between two states as a suitable average of the work done on the system by forcing the transition in a finite time.More recently, two of us have introduced, on a more empirical basis, the metadynamics method [6] in which the free energy as a function of one or more collective variables (CVs) is obtained from a non-equilibrium simulation. In this method, the dynamics of a system at finite temperature is biased by a history-dependent potential constructed as the sum of Gaussians centered on the trajectory of the CVs. After a transient period, the free energy dependence on the CVs can be estimated as the negative of the bias potential. This method is closely related to the local elevation method [7], to coarse molecular dynamics [8,9] and to the adaptive-force bias method [10]. Moreover, as described in Ref.[11], metadynamics can be viewed as a finite temperature extension of the Wang-Landau approach [12], where the density of states of a system is estimated by a Monte Carlo procedure in which the acceptance probability of a move is modified every time a configuration is explored. The practical validity of the metadynamics method has been demonstrated in a number of applications to real problems [6,11,13,14,15,16,17,18,19,20], and an empirical way to evaluate the error has been suggested in Ref. [21]. Attempts at a more formal approach have so far been frustrated by the lack of a formalism capable of handling a non-Markovian process [22].The problem of working with history-dependent dynamics is that the forces (or the transition probabilities) on the system depend explicitly on its history. Hence it is not a priori clear if, and in which sense, the system can reach a stationary state under the action of these dynamics. In this Letter we introduce a formalism that allows us to demonstrate that this is indeed the case, at least when the evolution of the system is of the Langevin type. We introduce a novel mapping of the history-dependent evolution into a Markovian process in the original variable and in an auxiliary field that keeps track of the configurations visited. Using this mapping we are able to validate rigorously the metadynamics method. In particular, we show that the average over several independent simulat...

show abstract

“…a statistics that is both inherently noisy and biased, even if the spread of the work data is only moderately larger than k B T . [54][55][56][57][58] In case of Gaussian work distributions for the (forward) annihilation process, the Crooks theorem [40],…”

Section: Basic Theorymentioning

confidence: 99%

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

Procacci

2016

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

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.

show abstract

Biased Sampling of Nonequilibrium Trajectories: Can Fast Switching Simulations Outperform Conventional Free Energy Calculation Methods?

Cited by 171 publications

References 36 publications

Calculation of the potential of mean force from nonequilibrium measurements via maximum likelihood estimators

Calculation of the potential of mean force from nonequilibrium measurements via maximum likelihood estimators

Equilibrium Free Energies from Nonequilibrium Metadynamics

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

Contact Info

Product

Resources

About