Accelerated weight histogram method for exploring free energy landscapes

Abstract

Calculating free energies is an important and notoriously difficult task for molecular simulations. The rapid increase in computational power has made it possible to probe increasingly complex systems, yet extracting accurate free energies from these simulations remains a major challenge. Fully exploring the free energy landscape of, say, a biological macromolecule typically requires sampling large conformational changes and slow transitions. Often, the only feasible way to study such a system is to simulate it using an enhanced sampling method. The accelerated weight histogram (AWH) method is a new, efficient extended ensemble sampling technique which adaptively biases the simulation to promote exploration of the free energy landscape. The AWH method uses a probability weight histogram which allows for efficient free energy updates and results in an easy discretization procedure. A major advantage of the method is its general formulation, making it a powerful platform for developing further extensions and analyzing its relation to already existing methods. Here, we demonstrate its efficiency and general applicability by calculating the potential of mean force along a reaction coordinate for both a single dimension and multiple dimensions. We make use of a non-uniform, free energy dependent target distribution in reaction coordinate space so that computational efforts are not wasted on physically irrelevant regions. We present numerical results for molecular dynamics simulations of lithium acetate in solution and chignolin, a 10-residue long peptide that folds into a $\beta$-hairpin. We further present practical guidelines for setting up and running an AWH simulation.

12 pages, 6 figures

References in corpus (16)

• Canonical sampling through velocity-rescaling
• 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
• Simulated Tempering: A New Monte Carlo Scheme
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Equilibrium free energies from non-equilibrium metadynamics
• Extended Ensemble Monte Carlo
• Fast Algorithm to Calculate Density of States
• Replica exchange and expanded ensemble simulations as Gibbs sampling: Simple improvements for enhanced mixing
• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• Generalized-ensemble Monte carlo method for systems with rough energy landscape
• Optimal Modification Factor and Convergence of the Wang-Landau Algorithm
• Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics
• Improving the efficiency of extended ensemble simulations: The accelerated weight histogram method
• Intrinsic convergence properties of entropic sampling algorithms

Cited by in corpus (7)

• Heterogeneous Parallelization and Acceleration of Molecular Dynamics Simulations in GROMACS
• Specific interactions of peripheral membrane proteins with lipids: what can molecular simulations show us?
• Riemann metric approach to optimal sampling of multidimensional free-energy landscapes
• Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations
• Estimating thermodynamic expectations and free energies in expanded ensemble simulations: systematic variance reduction through conditioning
• Almost sure convergence of the accelerated weight histogram algorithm
• Comparison of Sampling Methods via Robust Free Energy Inference: Application to Calmodulin