Metadynamics with adaptive Gaussians

Abstract

Metadynamics is an established sampling method aimed at reconstructing the free-energy surface relative to a set of appropriately chosen collective variables. In standard metadynamics the free-energy surface is filled by the addition of Gaussian potentials of pre-assigned and typically diagonal covariance. Asymptotically the free-energy surface is proportional to the bias deposited. Here we consider the possibility of using Gaussians whose variance is adjusted on the fly to the local properties of the free-energy surface. We suggest two different prescriptions: one is based on the local diffusivity and the other on the local geometrical properties. We further examine the problem of extracting the free-energy surface when using adaptive Gaussians. We show that the standard relation between the bias and the free energy does not hold. In the limit of narrow Gaussians an explicit correction can be evaluated. In the general case we propose to use instead a relation between bias and free energy borrowed from umbrella sampling. This relation holds for all kinds of incrementally deposited bias. We illustrate on the case of alanine dipeptide the advantage of using adaptive Gaussians in conjunction with the new free-energy estimator both in terms of accuracy and speed of convergence.

Reprinted (adapted) with permission from J. Chem. Theory Comput., DOI: 10.1021/ct3002464. Copyright (2012) American Chemical Society

References in corpus (5)

• Escaping free-energy minima
• Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
• An efficient, multiple range random walk algorithm to calculate the density of states
• Equilibrium free energies from non-equilibrium metadynamics
• A self-learning algorithm for biased molecular dynamics

Cited by in corpus (43)

• PLUMED 2: New feathers for an old bird
• Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration
• Rethinking Metadynamics: from bias potentials to probability distributions
• Caliber based spectral gap optimization of order parameters (SGOOP) for sampling complex molecular systems
• Neural networks-based variationally enhanced sampling
• Folding of guanine quadruplex molecules -- funnel-like mechanism or kinetic partitioning? An overview from MD simulation studies
• Enhanced Conformational Sampling using Replica Exchange with Collective-Variable Tempering
• Free Energy Landscape of GAGA and UUCG RNA Tetraloops
• Analyzing and biasing simulations with PLUMED
• Unravelling Mg${}^{2+}$-RNA binding with atomistic molecular dynamics
• Learning Free Energy Landscapes Using Artificial Neural Networks
• Empirical corrections to the Amber RNA force field with Target Metadynamics
• The solid-liquid interfacial free energy out of equilibrium
• Making the best of a bad situation: a multiscale approach to free energy calculation
• Multiscale reweighted stochastic embedding (MRSE): Deep learning of collective variables for enhanced sampling
• Reweighting of molecular simulations with explicit-solvent SAXS restraints elucidates ion-dependent RNA ensembles
• Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics
• Riemann metric approach to optimal sampling of multidimensional free-energy landscapes
• Metadynamics of paths
• Time-independent free energies from metadynamics via Mean Force Integration
• Metadynamics sampling in atomic environment space for collecting training data for machine learning potentials
• The Reaction Mechanism of the Azide-Alkyne Huisgen Cycloaddition
• Adding alchemical variables to metadynamics to enhance sampling in free energy calculations
• Bridging the gap between atomistic and macroscopic models of homogeneous nucleation
• Same and interconvertible high-pressure ice phases
• Conformational Entropy as Collective Variable for Proteins
• Computing committors via Mahalanobis diffusion maps with enhanced sampling data
• The Gibbs free energy of homogeneous nucleation: from atomistic nuclei to the planar limit
• Assessing models of force-dependent unbinding rates via infrequent metadynamics
• A perturbative solution to metadynamics ordinary differential equation
• Nucleation rates from small scale atomistic simulations and transition state theory
• Multistate metadynamics for automatic exploration of conical intersections
• Enhanced Sampling for Free Energy Profiles with Post-Transition-State Bifurcations
• $\mu$-tempered metadynamics: Artifact independent convergence times for wide hills
• Can molecular dynamics be used to simulate biomolecular recognition?
• Exploring Conformational Landscapes Along Anharmonic Low-Frequency Vibrations
• Metadynamics for Automatic Sampling of Quantum Property Manifolds: Exploration of Molecular Biradicality Landscapes
• A hybrid molecular dynamics/atomic-scale finite element method for quasi-static atomistic simulations at finite temperature
• Exploration vs Convergence Speed in Adaptive-bias Enhanced Sampling
• Fast Sampling of Protein Conformational Dynamics
• Advantages of multi-dimensional biasing in accelerated dynamics: application to the calculation of the acid $p{K}_a$ for acetic acid
• Improving the Efficiency of Variationally Enhanced Sampling with Wavelet-Based Bias Potentials
• Dissociation of Liquid Water on Defective Rutile TiO2 (110) Surfaces Using Ab-Initio Molecular Dynamics Simulations