Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling

1977/02/01 by G.M. Torrie, G. M. Torrie, J.P. Valleau +1 · 6,281 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Hybrid Monte Carlo #Importance sampling #Markov chain Monte Carlo #Mathematics #Monte Carlo integration #Monte Carlo method #Monte Carlo method in statistical physics #Phase Equilibria and Thermodynamics #Physics #Rejection sampling #Sampling (signal processing) #Statistical physics #Statistics #Theoretical and Computational Physics #Umbrella sampling

paper · doi:10.1016/0021-9991(77)90121-8

published in Journal of Computational Physics 23(2), 187-199 (Elsevier BV)

openalex publication_date 1977/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Cited by

• Multi-body effects in a coarse-grained protein force field
• Can a coarse-grained water model capture the key physical features of the hydrophobic effect?
• Experimental Parameterization of an Energy Function for the Simulation of Unfolded Proteins
• A cavity-biased (T, V, μ) Monte Carlo method for the computer simulation of fluids
• Backbone-mediated weakening of pairwise interactions enables percolation in peptide-based mimics of protein condensates
• Microtubule dynamics are defined by conformations and stability of clustered protofilaments
• Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint
• Hyperspatial Sampling: Circumventing Free-Energy Barriers via Replica Exchange with Extra Dimensions
• FES-FM: Free Energy Surface Sampling via Reduced Flow Matching
• ATLAS: A Foundation Neural Sampler for Amorphous Materials
• Deep learning of committor and explainable artificial intelligence analysis for identifying reaction coordinates
• Stochastic Resetting: A Non-Equilibrium Framework for Prediction, Inference and Design
• Computational Methods for Modeling Lipid-Mediated Active Pharmaceutical Ingredient Delivery
• Fast parameterization of Martini3 models for fragments and small molecules
• Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models
• A Bayesian Approach to Interpret Time-Resolved Experiments Using Molecular Simulations
• Permeability Benchmarking: Guidelines for Comparing in Silico, in Vitro, and in Vivo Measurements
• Analysis and sampling of molecular simulations with adversarial autoencoders
• PLUMED Tutorials: a collaborative, community-driven learning ecosystem
• Neural Network Potential with Multi-Resolution Approach Enables Accurate Prediction of Reaction Free Energies in Solution
• Partition Function Estimation Using Analog Quantum Processors
• Dual-LAO for calculating fast and robust relative binding free energies of simple and complex transformations
• Efficient Monte-Carlo sampling of metastable systems using non-local collective variable updates
• Lambda-ABF-OPES: Faster Convergence with High Accuracy in Alchemical Free Energy Calculations
• Exact fluctuation relation for open systems beyond the Zwanzig FEP equation
• Refining Machine Learning Potentials through Thermodynamic Theory of Phase Transitions
• From Static Pathways to Dynamic Mechanisms: A Committor-Based Data-Driven Approach to Chemical Reactions
• Large-Scale Molecular Dynamics Simulations for Highly Parallel Infrastructures
• Automated Prediction of Thermodynamic Properties via Bayesian Free-Energy Reconstruction from Molecular Dynamics
• Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
• Toward an FPGA-based dedicated computer for molecular dynamics simulations
• Active Importance Sampling for Variational Objectives Dominated by Rare Events: Consequences for Optimization and Generalization
• Entangled Schrödinger Bridge Matching
• Free-energy REconstruction from Stable Clusters (FRESC): A new method to evaluate nucleation barriers from simulation
• Transformer Atomic Cluster Expansion: TRACE
• Grand canonical Monte Carlo and deep learning assisted enhanced sampling to characterize the distribution of Mg2+ and influence of the Drude polarizable force field on the stability of folded states of the twister ribozyme
• Understanding Mobile Particles in Solid-State Materials: From the Perspective of Potential Energy Surfaces
• Human cytomegalovirus deploys molecular mimicry to recruit VPS4A to sites of virus assembly
• Acceleration of Molecular Simulations by Parametric Time-Lagged tSNE Metadynamics
• Calculating Free-Energy Differences Using an Average Force: A Tutorial for Adaptive Biasing Force Simulations
• Effect of Glycosylation on the Reorganization at the Active Site of Human Carbonic Anhydrase IX
• Human cytomegalovirus deploys molecular mimicry to recruit VPS4A to sites of virus assembly
• AI‐Physics‐Experiment Trinity for Integrated Protein Dynamics Modeling
• Thermodynamics and the global optimization of Lennard-Jones clusters
• Machine learning approaches for analyzing and enhancing molecular dynamics simulations
• Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems
• An Introduction to Monte Carlo Simulation of Statistical physics Problem
• Machine Learning the Entropy to Estimate Free Energy Differences without Sampling Transitions
• Gaussian Process Regression for Materials and Molecules
• On Free Energy Calculations in Drug Discovery
• Challenges and opportunities for machine learning potentials in transition path sampling: alanine dipeptide and azobenzene studies
• Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials
• Analyzing Molecular Dynamics Trajectories Thermodynamically through Artificial Intelligence
• Rotation of crystal seed during early stages of growth reveals the anisotropy of glass matrix
• Enhanced Sampling Algorithms
• Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics
• Optimal parallelisation strategies for flat histogram Monte Carlo sampling
• The dawn of alchemical free-energy methods in biomolecular simulations
• Marginal Girsanov Reweighting: Stable Variance Reduction for Long-Timescale Dynamics from Biased Simulation
• Markov models of molecular kinetics: Generation and validation
• Annealed importance sampling
• Adaptive Resetting for Informed Search Strategies and the Design of Non-equilibrium Steady-states
• Redox-Activated Proton Transfer through a Redundant Network in the Q o Site of Cytochrome bc 1
• DFTB+, a software package for efficient approximate density functional theory based atomistic simulations
• Crystallization of a polymer on a surface
• Intercalation Favors DNA Covalent Photobinding in Photoresponsive Dual PDT/PCT Bimetallic Assemblies
• On the reproducibility of free energy surfaces in machine-learned collective variable spaces
• Protonation and magnesium ions shape the transition state diversity of phosphoanhydride hydrolysis in water
• Markov State Model Approach to Simulate Self-Assembly
• Unraveling the mechanisms of spinigerin: A promising antimicrobial peptide against antibiotic resistance through molecular dynamics simulations
• Machine learning of slow collective variables and enhanced sampling via spatial techniques
• Machine learning coarse-grained potentials of protein thermodynamics
• A unified framework for data-driven construction of stochastic reduced models with state-dependent memory
• Enhanced Sampling in the Age of Machine Learning: Algorithms and Applications
• Software update: The ORCA program system—Version 5.0
• Hybrid Monte Carlo Metadynamics (hybridMC-MetaD)
• Metropolis and Wang-Landau Algorithms
• Importance sampling methods for Bayesian discrimination between embedded models
• Intramolecular transformation of an antifungal antibiotic nystatin A1 into its isomer, iso‐nystatin A1 – structural and molecular modeling studies
• Peptidyl nitroalkene inhibitors of main protease rationalized by computational and crystallographic investigations as antivirals against SARS-CoV-2
• Computational study of the mechanism of a polyurethane esterase A (PueA) from Pseudomonas chlororaphis
• Cation-DNA outer sphere coordination in DNA polymorphism
• Secondary finite-size effects and multi-barrier free energy landscapes in molecular simulations of hindered ion transport
• Improving sampling of binding free energy differences between covalently bound ligands in alternate binding pockets using MT-REXEE
• Constructing Generalized Sample Transition Probabilities with Biased Simulations
• Pseudo-grand canonical molecular dynamics via volumetrically controlled osmotic pressure
• Reversible self-assembly of patchy particles into monodisperse icosahedral clusters
• Exploiting the synergy between computational and experimental biophysics for efficient cancer drug development
• Learning to Fold Proteins Using Energy Landscape Theory
• Computer simulations of the mechanism of thickness selection in polymer crystals
• Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• A molecular density functional theory to study solvation in water
• Machine learning approaches for analyzing and enhancing molecular dynamics simulations
• Latent Thermodynamic Flows: Unified Representation Learning and Generative Modeling of Temperature-Dependent Behaviors from Limited Data
• Free energy calculations and unbiased dynamics reveal a continuous liquid-liquid transition in water no man's land
• Automated exploration of the low-energy chemical space with fast quantum chemical methods
• A Bayesian approach for extracting free energy profiles from cryo-electron microscopy experiments using a path collective variable
• Electrochemistry-Enhanced Dynamic Paths Sampling Unveiling Nuclear Quantum Effects in Electrocatalysis
• Fokker-Planck Score Learning: Efficient Free-Energy Estimation under Periodic Boundary Conditions
• High-Throughput Computation of Anharmonic Low-Frequency Protein Vibrations
• Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
• Adsorption Behavior of Organic Corrosion Inhibitors on Metal Surfaces—Some New Insights from Molecular Simulations
• Scalable molecular dynamics with NAMD
• Statistical Mechanics: Theory and Molecular Simulation
• Breaking the Curse of Dimensionality: Solving Configurational Integrals for Crystalline Solids by Tensor Networks
• CN101 - A Digital Thermodynamic Computer for Generative AI
• Structural mechanism of Fab domain dissociation as a measure of interface stability
• Hamiltonian replica exchange augmented with diffusion-based generative models and importance sampling to assess biomolecular conformational basins and barriers
• Direct numerical computation of disorder parameters
• Split Sampling: Expectations, Normalisation and Rare Events
• On the 3d Ising Spin Glass
• Monte Carlo likelihood inference for missing data models
• MOLECULARTHEORY OFHYDROPHOBICEFFECTS: “She is too mean to have her name repeated.”
• Being curious about the answers to questions: novelty search with learned attention
• Generative Replica-Exchange: A Flow-based Framework for Accelerating Replica Exchange Simulations
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Multicanonical Study of the 3D Ising Spin Glass
• Multicanonical multigrid Monte Carlo method
• Free energy reconstruction from steered dynamics without post-processing
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Monte Carlo study of the phase structure of compact polymer chains
• Biological and synthetic membranes: What can be learned from a coarse-grained description?
• The confined-deconfined interface tension in quenched QCD using the histogram method
• Multidimensional replica-exchange method for free-energy calculations
• A variational conformational dynamics approach to the selection of collective variables in metadynamics
• Statistically optimal analysis of samples from multiple equilibrium states
• A probabilistic approach to system-environment coupling
• Lateral organization, bilayer asymmetry, and inter-leaflet coupling of biological membranes
• Magnetic Susceptibility of Strongly Interacting Matter across the Deconfinement Transition
• Algorithmic aspects of multicanonical simulations
• Calculating free-energy profiles in biomolecular systems from fast nonequilibrium processes
• Equilibrium free-energy differences at different temperatures from a single set of nonequilibrium transitions
• Monte Carlo methods in statistical physics: Mathematical foundations and strategies
• Review and comparison of equations of state for the Lennard-Jones fluid
• Reducing Weighted Ensemble Variance With Optimal Trajectory Management
• Superposition Enhanced Nested Sampling
• Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data
• Insights into DNA-mediated interparticle interactions from a coarse-grained model
• Modular Markov chain Monte Carlo with application to multimodal sampling
• Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional
• Polyformer: a generative framework for thermodynamic modeling of polymeric molecules
• Adaptive umbrella sampling: Self-consistent determination of the non-Boltzmann bias
• Probability Distributions for Complex Systems: Adaptive Umbrella Sampling of the Potential Energy
• Rare Event Analysis of Large Language Models
• Measuring the convergence of Monte Carlo free-energy calculations
• Parallel excluded volume tempering for polymer melts
• Scaling of the atmosphere of self-avoiding walks
• NUCLEAR PROPERTIES AND FUTURE PLAN OF HIGH-FLUX REACTOR.
• A perturbative solution to metadynamics ordinary differential equation
• Studying functional dynamics in bio-molecules using accelerated molecular dynamics
• The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities
• Spin-glass overlap barriers in three and four dimensions
• Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions
• Method to study relaxation of metastable phases: Macroscopic mean-field dynamics
• From populations to absolute binding affinities in molecular simulations: exact volumetric terms and practical estimators
• Ice formation on kaolinite: Insights from molecular dynamics simulations
• Learning free energy landscapes using artificial neural networks
• Homogeneous and heterogeneous nucleation of Lennard-Jones liquids
• A variational approach to nucleation simulation
• Simultaneous Determination of Protein Structure and Dynamics using Cryo-Electron Microscopy
• Effects of co-ordination number on the nucleation behaviour in many-component self-assembly
• Follow the MEP: Scalable Neural Representations for Minimum-Energy Path Discovery in Molecular Systems
• Phase behaviours of superionic water at planetary conditions
• A numerically stable algorithm for integrating Bayesian models using Markov melding
• Coarse-graining strategy for molecular pair interactions: A reaction coordinate study for two- and three-dimensional systems
• New algorithm to investigate neural networks
• Multicanonical recursions
• Coarse-grained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment
• Prospects of Quantum Computing for Molecular Sciences
• Modelling Toehold-Mediated RNA Strand Displacement
• A nucleotide-level coarse-grained model of RNA
• First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions
• Characteristic of Bennett’s acceptance ratio method
• Computing the absolute Gibbs free energy in atomistic simulations: Applications to defects in solids
• Seeding approach to bubble nucleation in superheated Lennard-Jones fluids
• Conformational Entropy as Collective Variable for Proteins
• Long-Range Ionic and Short-Range Hydration Effects Govern Strongly Anisotropic Clay Nanoparticle Interactions
• Phase and vacancy behaviour of hard “slanted” cubes
• Non-equilibrium by molecular dynamics: a dynamical approach
• Analysis of key parameters for molecular dynamics of pMHC molecules
• Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding
• Unraveling Mg2+–RNA binding with atomistic molecular dynamics
• EXTENDED ENSEMBLE MONTE CARLO
• Enzymes: An integrated view of structure, dynamics and function. [europepmc]
• Statistically optimal analysis of samples from multiple equilibrium states. [europepmc]
• Generic coarse-grained model for protein folding and aggregation. [europepmc]
• Free energy of conformational transition paths in biomolecules: the string method and its application to myosin VI. [europepmc]
• Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation. [europepmc]
• Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations. [europepmc]
• Computational methods in drug discovery. [europepmc]
• Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations. [europepmc]
• Dynamic Docking: A Paradigm Shift in Computational Drug Discovery. [europepmc]
• RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview. [europepmc]
• Bridging Molecular Docking to Molecular Dynamics in Exploring Ligand-Protein Recognition Process: An Overview. [europepmc]
• Temperature-Controlled Liquid-Liquid Phase Separation of Disordered Proteins. [europepmc]
• Molecular Docking: Shifting Paradigms in Drug Discovery. [europepmc]
• Pitfalls of the Martini Model. [europepmc]
• Molecular basis of force-from-lipids gating in the mechanosensitive channel MscS. [europepmc]
• Harnessing Conformational Plasticity to Generate Designer Enzymes. [europepmc]
• Does SARS-CoV-2 Bind to Human ACE2 More Strongly Than Does SARS-CoV? [europepmc]
• Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation. [europepmc]
• The Role of Machine Learning in the Understanding and Design of Materials. [europepmc]
• Free energy of proton transfer at the water-TiO 2 interface from ab initio deep potential molecular dynamics. [europepmc]
• Revealing the molecular mechanisms of proteolysis of SARS-CoV-2 M pro by QM/MM computational methods. [europepmc]
• Mechanism of inhibition of SARS-CoV-2 M pro by N3 peptidyl Michael acceptor explained by QM/MM simulations and design of new derivatives with tunable chemical reactivity. [europepmc]
• Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems. [europepmc]
• Gaussian Process Regression for Materials and Molecules. [europepmc]
• Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy. [europepmc]