THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method
Abstract
The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free‐energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built‐in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free‐energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Final relative free energy differences were calculated with WHAM, and statistical errors were estimated using bootstrapping.
“Final relative free energy differences were calculated with WHAM144, and statistical errors were estimated using bootstrapping.”
From EXOSC3 G191 Variants Trigger System-Wide Recalibration of RNA Processing Machinery (2026) · cites this paper as [144]
Cited by
Sorted by citations
‘Improved parameters for the Martini coarse-grained protein force field’
de Jong, D. H., Singh, G., Bennett, W. F. D., Arnarez, C., Wassenaar, T. A., Schäfer, L. V., Periole, X., Tieleman, D. P., & Marrink, S. J. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300646g · Cited by 1,486 · see citing works
Dill, K. A., Ozkan, S. B., Shell, M. S., & Weikl, T. R. (2008) · Annual Review of Biophysics · doi:10.1146/annurev.biophys.37.092707.153558 · Cited by 1,163 · see citing works
Extreme disorder in an ultrahigh-affinity protein complex
Borgia, A., Borgia, M. B., Bugge, K., Kissling, V. M., Heidarsson, P. O., Fernandes, C. B., Sottini, A., Soranno, A., Buholzer, K. J., Nettels, D., et al. (2018) · Nature · doi:10.1038/nature25762 · Cited by 653 · see citing works
Standard Binding Free Energies from Computer Simulations: What Is the Best Strategy?
Gumbart, J. C., Roux, B., & Chipot, C. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct3008099 · Cited by 343 · see citing works
Synergistic lipid compositions for albumin receptor mediated delivery of mRNA to the liver
Miao, L., Lin, J., Huang, Y., Li, L., Delcassian, D., Ge, Y., Shi, Y., & Anderson, D. G. (2020) · Nature Communications · doi:10.1038/s41467-020-16248-y · Cited by 343 · see citing works
Mobley, D. L., Chodera, J. D., & Dill, K. A. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2221683 · Cited by 316 · see citing works
Kollman, P., Dixon, R., Cornell, W., Fox, T., Chipot, C., & Pohorille, A. (1997) · Computer Simulation of Biomolecular Systems · doi:10.1007/978-94-017-1120-3_2 · Cited by 242 · see citing works
Self-citationMolecular driving forces determining potassium channel slow inactivation
Cordero-Morales, J. F., Jogini, V., Lewis, A., Vásquez, V., Cortes, D. M., Roux, B., & Perozo, E. (2007) · Nature Structural & Molecular Biology · doi:10.1038/nsmb1309 · Cited by 236 · see citing works
Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory
Cournia, Z., Allen, T. W., Andricioaei, I., Antonny, B., Baum, D., Brannigan, G., Buchete, N.-V., Deckman, J. T., Delemotte, L., del Val, C., et al. (2015) · The Journal of Membrane Biology · doi:10.1007/s00232-015-9802-0 · Cited by 235 · see citing works
Using AMBER18 for Relative Free Energy Calculations
Song, L. F., Lee, T.-S., Zhu, C., York, D. M., & Merz, K. M. (2019) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.9b00105 · Cited by 234 · see citing works
A gate in the selectivity filter of potassium channels
Bernèche, S., & Roux, B. (2005) · Structure · doi:10.1016/j.str.2004.12.019 · Cited by 214 · see citing works
Using sketch-map coordinates to analyze and bias molecular dynamics simulations
Tribello, G. A., Ceriotti, M., & Parrinello, M. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1201152109 · Cited by 202 · see citing works
Computational prediction of protein–protein binding affinities
Siebenmorgen, T., & Zacharias, M. (2020) · WIREs Computational Molecular Science · doi:10.1002/wcms.1448 · Cited by 184 · see citing works
“The weighted-histogram analysis method 127,128 or related algorithms are then used to calculate a potential of mean force (PMF) along the RC.”
MethodMartinek, T., Duboué-Dijon, E., Timr, Š., Mason, P. E., Baxová, K., Fischer, H. E., Schmidt, B., Pluhařová, E., & Jungwirth, P. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5006779 · Cited by 114 · see citing works
Collective action of water molecules in zeolite dealumination
Nielsen, M., Hafreager, A., Brogaard, R. Y., De Wispelaere, K., Falsig, H., Beato, P., Van Speybroeck, V., & Svelle, S. (2019) · Catalysis Science & Technology · doi:10.1039/c9cy00624a · Cited by 76 · see citing works
Quantifying the topography of the intrinsic energy landscape of flexible biomolecular recognition
Chu, X., Gan, L., Wang, E., & Wang, J. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1220699110 · Cited by 62 · see citing works
Cheng, Y., Zhang, Y., & McCammon, J. A. (2006) · Protein Science · doi:10.1110/ps.051852306 · Cited by 62 · see citing works
Hamm, L. M., Wallace, A. F., & Dove, P. M. (2010) · The Journal of Physical Chemistry B · doi:10.1021/jp9108893 · Cited by 61 · see citing works
Periole, X. (2017) · Chemical Reviews · doi:10.1021/acs.chemrev.6b00344 · Cited by 58 · see citing works
Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression
Stecher, T., Bernstein, N., & Csányi, G. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500438v · Cited by 56 · see citing works
Kinetic pathways of water exchange in the first hydration shell of magnesium
Schwierz, N. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5144258 · Cited by 52 · see citing works
Prinz, J.-H., Chodera, J. D., Pande, V. S., Swope, W. C., Smith, J. C., & Noé, F. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3592153 · Cited by 52 · see citing works
Nucleotide modifications and tRNA anticodon–mRNA codon interactions on the ribosome
Allnér, O., & Nilsson, L. (2011) · RNA · doi:10.1261/rna.029231.111 · Cited by 50 · see citing works
Shen, Z., Szlufarska, I., Brown, P. E., & Xu, H. (2015) · Langmuir · doi:10.1021/acs.langmuir.5b02025 · Cited by 31 · see citing works
Lenk, T., Rabet, S., Sprick, M., Raabe, G., & Schröder, U. (2023) · ChemPhysChem · doi:10.1002/cphc.202200614 · Cited by 26 · see citing works
Reactive force fields for aqueous and interfacial magnesium carbonate formation
Zare, S., & Qomi, M. J. A. (2021) · Physical Chemistry Chemical Physics · doi:10.1039/d1cp02627e · Cited by 24 · see citing works
Jeon, J., & Shell, M. S. (2012) · Biophysical Journal · doi:10.1016/j.bpj.2012.03.019 · Cited by 16 · see citing works
Ohnuki, J., Jaunet-Lahary, T., Yamashita, A., & Okazaki, K.-I. (2024) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c03052 · Cited by 14 · see citing works
EXOSC3 G191 Variants Trigger System-Wide Recalibration of RNA Processing Machinery
Wijeratne, H. R. S., Runnebohm, A. M., Barron, M. P., Hampton, A. J., Li, R., Peck Justice, S. A., Lenceski, S. H., Rooney, J. D., Smith-Kinnaman, W. R., Chang, G. S., et al. (2026) · doi:10.64898/2026.01.26.701775 · Cited by 1 · see citing works
“Final relative free energy differences were calculated with WHAM 144 , and statistical errors were estimated using bootstrapping.”
- Authors
- Kumar, S., Rosenberg, J. M., Bouzida, D., Swendsen, R. H., & Kollman, P. A.
- Affiliations
- University of Pittsburgh (US)
- Carnegie Mellon University (US)
- University of California, San Francisco (US)
- Corresponding author
- Rosenberg, John M.
- Venue
- Journal of Computational Chemistry
- Publisher
- Wiley
- Published
- 1992-10
- Volume
- 13
- Issue
- 8
- Pages
- 1011-1021
- ISSN
- 0192-8651 (ISSN-L)
- 1096-987X
- OpenAlex
- W2112154906
- Cited by
- 6,808
- References
- 0
- Citations by year
- 2026: 330 · 2025: 388 · 2024: 395 · 2023: 365 · 2022: 407 · 2021: 450 · 2020: 392 · 2019: 390 · 2018: 388 · 2017: 369 · 2016: 346 · 2015: 311 · 2014: 328 · 2013: 286 · 2012: 261
- FWCI
- 2.02
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Computational Chemistry (publishedVersion)
- Topics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Keywords
- weighted histogram analysis method, free energy calculation, umbrella sampling, potential of mean force, sampling error estimation, deoxyadenosine, molecular mechanics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review