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Everything everywhere all at once: a probability-based enhanced sampling approach to rare events

Nature Computational Science volume 5, pages 582–591 (2025)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

The problem of studying rare events is central to many areas of computer simulations. We recently proposed an approach to solving this problem that involves computing the committor function, showing how it can be iteratively computed in a variational way while efficiently sampling the transition state ensemble. Here we greatly improve this procedure by combining it with a metadynamics-like enhanced sampling approach in which a logarithmic function of the committor is used as a collective variable. This procedure leads to an accurate sampling of the free energy surface in which transition states and metastable basins are studied with the same thoroughness. We show that our approach can be used in cases with the possibility of competing reactive paths and metastable intermediates. In addition, we demonstrate how physical insights can be obtained from the optimized committor model and the sampled data, thus providing a full characterization of the rare event under study.

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Fig. 1: Schematic representation of enhanced sampling framework.
Fig. 2: Müller–Brown potential.
Fig. 3: Alanine dipeptide.
Fig. 4: Asymmetric double-path potential.
Fig. 5: Chignolin folding.
Fig. 6: OAMe–G2 binding.

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Data availability

Training and simulation data and inputs are available on GitHub56 and on Zenodo57. Source data are provided with this paper.

Code availability

The code for the training of the NN-based committor model alongside didactic tutorials is available through the open-source mlcolvar library55, which is the preferred way to access the most updated code. To obtain the results reported in the manuscript, version 1.2.2 was used and a frozen version is also available on Zenodo57. The PLUMED58,59 interface for the application of the bias is available on GitHub56 and on Zenodo57.

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Acknowledgements

We are grateful to L. Bonati, A. Rizzi, J. Zhang, U. Raucci, A. Triveri and F. Mambretti for discussions and feedback about this manuscript.

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Author notes

  1. These authors contributed equally: Enrico Trizio, Peilin Kang.

Authors and Affiliations

  1. Atomistic Simulations, Italian Institute of Technology, Genova, Italy

    Enrico Trizio, Peilin Kang & Michele Parrinello

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  1. Enrico Trizio
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  3. Michele Parrinello
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Contributions

All the authors equally contributed to the manuscript by conceptualizing the project, developing the theoretical methodologies and participating in the writing of the manuscript. Specifically, E.T. and P.K. developed the code for the training of the committor function and conducted the computational simulations.

Corresponding authors

Correspondence to Peilin Kang or Michele Parrinello.

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The authors declare no competing interests.

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Peer review information

Nature Computational Science thanks Samik Bose, Carme Rovira, and Omar Valsson for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team.

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Extended data

Extended Data Fig. 1 Convergence of ΔG.

Convergence with simulation time of the estimate for the folding energy of chignolin (A) and the binding energy of the G2 ligand to the OAMe octa-acid guest (B). The average estimates from independent simulations for each system (3 for chignolin, 4 for OAMe-G2) are reported as a blue solid line, whereas the uncertainty, computed as the standard deviation over the three replicas, is depicted as a shaded blue region. The reference values are provided as gray dashed lines, and the 0.5 kBT interval around the reference is marked by gray dotted lines. For chignolin, that is the unbiased estimate from ref. 33, for the calixarene, an estimate obtained using the enhanced sampling setup of ref. 38.

Source Data

Supplementary information

Supplementary Information

Supplementary Figs. 1–9, Tables 1–6 and simulation computational details.

Reporting Summary

Peer Review File

Source data

Source Data Fig. 2

Muller–Brown potential. a, Scatter plot data, reference potential isoline data, reference and learned committor data. b, Sampling distribution data. c, Free energy surface data.

Source Data Fig. 3

Alanine. a, Free energy surface isoline data, sampling distribution data. b, Free energy surface isoline data, Kolmogorov distribution data. c, Sampling distribution data. d, Free energy surface data, reference line TSE.

Source Data Fig. 4

Double-path potential. a, Potential isoline data, learned committor data. b, Potential isoline data, Kolmogorov distribution data. c, Potential isoline data, computed free energy surface data.

Source Data Extended Data Fig. 1

a, ΔG data (time, avg, s.d., ref. value) for chingolin. b, ΔG data (time, avg, s.d., ref. value) for calixarene.

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Trizio, E., Kang, P. & Parrinello, M. Everything everywhere all at once: a probability-based enhanced sampling approach to rare events. Nat Comput Sci 5, 582–591 (2025). https://doi.org/10.1038/s43588-025-00799-5

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