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Learning the committor without collective variables

Nature Computational Science (2026)Cite this article

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Abstract

Here we introduce a graph neural network architecture built on geometric vector perceptrons to predict the committor function directly from atomic coordinates, bypassing the need for hand-crafted collective variables. The method offers atom-level interpretability, pinpointing the key atomic players in complex transitions without relying on prior assumptions. Applied across diverse molecular systems, the method accurately infers the committor function and highlights the importance of each heavy atom in the transition mechanism. It also yields precise estimates of the rate constants for the underlying processes. The proposed approach assists in understanding and modeling complex dynamics, by enabling collective-variable-free learning and automated identification of physically meaningful reaction coordinates of complex molecular processes.

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Fig. 1: qGNN.
Fig. 2: NANMA isomerization.

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Data availability

Due to the size of the dataset, all the data in this work are provided upon request. Nevertheless, the necessary configuration files for data reproducibility are available via Zenodo at https://doi.org/10.5281/zenodo.18259668 (ref. 49).

Code availability

All the codes generated in this work are available via Zenodo at https://doi.org/10.5281/zenodo.18259668 (ref. 49).

References

  1. Peters, B. Reaction coordinates and mechanistic hypothesis tests. Annu. Rev. Phys. Chem. 67, 669–690 (2016).

    Article  Google Scholar 

  2. E, W. & Vanden-Eijnden, E. Transition-path theory and path-finding algorithms for the study of rare events. Annu. Rev. Phys. Chem. 61, 391–420 (2010).

    Article  Google Scholar 

  3. Onsager, L. Initial recombination of ions. Phys. Rev. 54, 554–557 (1938).

    Article  Google Scholar 

  4. Berezhkovskii, A. & Szabo, A. One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions. J. Chem. Phys. 122, 014503 (2005).

    Article  Google Scholar 

  5. Roux, B. Transition rate theory, spectral analysis, and reactive paths. J. Chem. Phys. 156, 134111 (2022).

    Article  Google Scholar 

  6. van Erp, T. S., Moroni, D. & Bolhuis, P. G. A novel path sampling method for the calculation of rate constants. J. Chem. Phys. 118, 7762–7774 (2003).

    Article  Google Scholar 

  7. Best, R. B. & Hummer, G. Reaction coordinates and rates from transition paths. Proc. Natl Acad. Sci. USA. 102, 6732–6737 (2005).

    Article  Google Scholar 

  8. Peters, B. & Trout, B. L. Obtaining reaction coordinates by likelihood maximization. J. Chem. Phys. 125, 054108 (2006).

    Article  Google Scholar 

  9. Ma, A. & Dinner, A. R. Automatic method for identifying reaction coordinates in complex systems. J. Phys. Chem. B 109, 6769–6779 (2005).

    Article  Google Scholar 

  10. Krivov, S. V. On reaction coordinate optimality. J. Chem. Theory Comput. 9, 135–146 (2013).

    Article  Google Scholar 

  11. Rotskoff, G. M., Mitchell, A. R. & Vanden-Eijnden, E. Active importance sampling for variational objectives dominated by rare events: consequences for optimization and generalization. In Proc. 2nd Mathematical and Scientific Machine Learning Conference Vol. 145, (eds Bruna, J., Hesthaven, J. & Zdeborova, L.) 757–780 (PMLR, 2022).

  12. Ribeiro, J. M. L., Bravo, P., Wang, Y. & Tiwary, P. Reweighted autoencoded variational Bayes for enhanced sampling (RAVE). J. Chem. Phys. 149, 072301 (2018).

    Article  Google Scholar 

  13. Khoo, Y., Lu, J. & Ying, L. Solving for high-dimensional committor functions using artificial neural networks. Res. Math. Sci. 6, 1–13 (2019).

    Article  MathSciNet  Google Scholar 

  14. Lin, B. & Ren, W. A deep learning method for computing committor functions with adaptive sampling. SIAM J. Sci. Comput. 47, 1091–1114 (2025).

    Article  MathSciNet  Google Scholar 

  15. Prinz, J.-H. et al. Markov models of molecular kinetics: generation and validation. J. Chem. Phys. 134, 174105 (2011).

    Article  Google Scholar 

  16. Chen, H., Roux, B. & Chipot, C. Discovering reaction pathways, slow variables, and committor probabilities with machine learning. J. Chem. Theory Comput. 19, 4414–4426 (2023).

    Article  Google Scholar 

  17. Ansari, N., Rizzi, V. & Parrinello, M. Water regulates the residence time of benzamidine in trypsin. Nat. Commun. 13, 5438 (2022).

    Article  Google Scholar 

  18. Bonati, L., Trizio, E., Rizzi, A. & Parrinello, M. A unified framework for machine learning collective variables for enhanced sampling simulations: mlcolvar. J. Chem. Phys. 159, 014801 (2023).

    Article  Google Scholar 

  19. Zhang, J. et al. Descriptor-free collective variables from geometric graph neural networks. J. Chem. Theory Comput. 20, 10787–10797 (2024).

    Article  Google Scholar 

  20. Pengmei, Z., Lorpaiboon, C., Guo, S. C., Weare, J. & Dinner, A. R. Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamics. J. Chem. Phys. https://doi.org/10.1063/5.0244453 (2025).

  21. Eismann, S. et al. Hierarchical, rotation-equivariant neural networks to select structural models of protein complexes. Proteins Struct. Funct. Bioinform. 89, 493–501 (2020).

    Article  Google Scholar 

  22. Battaglia, P. W. et al. Relational inductive biases, deep learning, and graph networks. Preprint at https://arxiv.org/abs/1806.01261 (2018).

  23. Jing, B., Eismann, S., Soni, P. N. & Dror, R. O. Equivariant graph neural networks for 3D macromolecular structure. In Proc. 38th International Conference on Machine Learning https://doi.org/10.48550/arXiv.2106.03843 (2021).

  24. Townshend, R. J. L. et al. ATOM3D: tasks on molecules in three dimensions. In Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 1) Vol. 1 https://openreview.net/forum?id=FkDZLpK1Ml2 (2021).

  25. Megías, A. et al. Iterative variational learning of committor-consistent transition pathways using artificial neural networks. Nat. Comput. Sci. https://doi.org/10.1038/s43588-025-00828-3 (2025).

  26. Ajaz, A. et al. Concerted vs stepwise mechanisms in dehydro-Diels–Alder reactions. J. Org. Chem. 76, 9320–9328 (2011).

    Article  Google Scholar 

  27. Qiu, L., Pabit, S. A., Roitberg, A. E. & Hagen, S. J. Smaller and faster: the 20-residue trp-cage protein folds in 4 μs. J. Am. Chem. Soc. 124, 12952–12953 (2002).

    Article  Google Scholar 

  28. Lindorff-Larsen, K., Piana, S., Dror, R. O. & Shaw, D. E. How fast-folding proteins fold. Science 334, 517–520 (2011).

    Article  Google Scholar 

  29. Swenson, D. W. H., Prinz, J.-H., Noé, F., Chodera, J. D. & Bolhuis, P. G. OpenPathSampling: a Python framework for path sampling simulations. 1. Basics. J. Chem. Theory Comput. 15, 813–836 (2019).

    Article  Google Scholar 

  30. Chen, H. et al. A companion guide to the string method with swarms of trajectories: characterization, performance, and pitfalls. J. Chem. Theory Comput. 18, 1406–1422 (2022).

    Article  Google Scholar 

  31. Tiwary, P. & Berne, B. J. Spectral gap optimization of order parameters for sampling complex molecular systems. Proc. Natl Acad. Sci. USA 113, 2839–2844 (2016).

    Article  Google Scholar 

  32. Bannwarth, C. et al. Extended tight-binding quantum chemistry methods. Wiley Interdiscip. Rev. Comput. Mol. Sci. 11, 1493 (2021).

    Article  Google Scholar 

  33. Meuzelaar, H. et al. Folding dynamics of the trp-cage miniprotein: evidence for a native-like intermediate from combined time-resolved vibrational spectroscopy and molecular dynamics simulations. J. Phys. Chem. B 117, 11490–11501 (2013).

    Article  Google Scholar 

  34. Lloyd, S. Least squares quantization in pcm. IEEE Trans. Inf. Theory 28, 129–137 (1982).

    Article  MathSciNet  Google Scholar 

  35. Schütte, C., Noé, F., Lu, J., Sarich, M. & Vanden-Eijnden, E. Markov state models based on milestoning. J. Chem. Phys 134, 204105 (2011).

    Article  Google Scholar 

  36. Bicout, D. J. & Szabo, A. Electron transfer reaction dynamics in non-Debye solvents. J. Chem. Phys. 109, 2325–2338 (1998).

    Article  Google Scholar 

  37. Donati, L., Hartmann, C. & Keller, B. G. Girsanov reweighting for path ensembles and Markov state models. J. Chem. Phys. 146, 244112 (2017).

    Article  Google Scholar 

  38. Donati, L., Weber, M. & Keller, B. G. A review of Girsanov reweighting and of square root approximation for building molecular markov state models. J. Math. Phys. 63, 123306 (2022).

    Article  MathSciNet  Google Scholar 

  39. Glorot, X. & Bengio, Y. Understanding the difficulty of training deep feedforward neural networks. In Proc. Thirteenth International Conference on Artificial Intelligence and Statistics (eds Teh, Y. W. & Titterington, M.) Vol. 9, 249–256 (PMLR, 2010); https://proceedings.mlr.press/v9/glorot10a.html

  40. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://api.semanticscholar.org/CorpusID:6628106 (2014).

  41. Phillips, J. C. et al. Scalable molecular dynamics on CPU and GPU architectures with NAMD. J. Chem. Phys. 153, 044130 (2020).

    Article  Google Scholar 

  42. Fiorin, G. et al. Expanded functionality and portability for the Colvars library. J. Phys. Chem. B 128, 11108–11123 (2024).

    Article  Google Scholar 

  43. Fu, H., Shao, X., Cai, W. & Chipot, C. Taming rugged free energy landscapes using an average force. Acc. Chem. Res. 52, 3254–3264 (2019).

    Article  Google Scholar 

  44. Andersen, H. C. Rattle: a “velocity” version of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 52, 24–34 (1983).

    Article  Google Scholar 

  45. MacKerell, A. D. J. et al. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, 3586–3616 (1998).

    Article  Google Scholar 

  46. Maier, J. A. et al. ff14sb: Improving the accuracy of protein side chain and backbone parameters from ff99sb. J. Chem. Theory Comput. 11, 3696–3713 (2015).

    Article  Google Scholar 

  47. Fey, M. & Lenssen, J. E. Fast graph representation learning with pytorch geometric. Preprint at https://api.semanticscholar.org/CorpusID:70349949 (2019).

  48. an Rossum, G. & Drake, F. L. Python 3 Reference Manual (CreateSpace, 2009).

  49. GNN committor learning repository. Zenodo https://doi.org/10.5281/zenodo.18259668 (2025).

  50. Juraszek, J. & Bolhuis, P. G. Rate constant and reaction coordinate of Trp-cage folding in explicit water. Biophys. J. 95, 4246–4257 (2008).

    Article  Google Scholar 

Download references

Acknowledgements

C.C. acknowledges the European Research Council (project 101097272 ‘MilliInMicro’), the Université de Lorraine through its Lorraine Université d’Excellence initiative, and the Région Grand-Est (project ‘Respire’). C.C. also acknowledges the Agence Nationale de la Recherche under France 2030 (contract ANR-22-PEBB-0009) for support in the context of the MAMABIO project (B-BEST PEPR). A.M. is thankful for the support provided by Universidad Politécnica de Madrid through the ‘Programa Propio de Investigación’ grant EST-PDI-25-C0ON11-36-6WBGZ8, as well as the hospitality of Université de Lorraine during his stay.

Author information

Authors and Affiliations

  1. Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n∘7019, Université de Lorraine, Vandœuvre-lès-Nancy cedex, France

    Sergio Contreras Arredondo, Chenyu Tang, Radu A. Talmazan, Cheng Giuseppe Chen & Christophe Chipot

  2. Complex Systems Group and Department of Applied Mathematics, Universidad Politécnica de Madrid, Madrid, Spain

    Alberto Megías

  3. Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL, USA

    Christophe Chipot

  4. Theoretical and Computational Biophysics Group, Beckman Institute, and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Christophe Chipot

Authors
  1. Sergio Contreras Arredondo
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Contributions

C.C. conceived the idea, and designed and supervised the research. S.C.A. designed the neural network, developed the corresponding code and carried out the qGNN learnings. C.T., R.A.T. and C.G.C. performed the MD simulations. A.M. performed the shooting analysis of NANMA and worked on the theoretical framework. All the authors contributed in the writing of the manuscript and provided helpful discussions.

Corresponding author

Correspondence to Christophe Chipot.

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The authors declare no competing interests.

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Peer review information

Nature Computational Science thanks Han Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Trialanine conformational equilibrium.

Projection of learned committor q onto (ϕ1, ϕ3) (A), (ϕ1, ϕ2) (C) and (ϕ2, ϕ3) (D) space, from atomic coordinates of a biased trajectory of trialanine. Relative node sensitivity computed for a short biased simulation of 15 ns and a representation of the trialanine molecule where carbon atoms are represented in cyan, oxygen in red, nitrogen in blue and hydrogen in white (B).

Source data

Extended Data Fig. 2 Diels-Alder reaction.

Learned committor q, projected on (d1, d2)-space, from atomic coordinates of a biased trajectory of Diels–Alder system. The contour lines represent the free-energy surface (A). Relative node sensitivity analysis computed for a short biased simulation of 2 ns (B). A committor map learned using the variational committor network16 for this reaction is depicted for comparison (C). Furthermore, we show a sketch of the Diels–Alder system with the heavy atoms labelled as well as the distances used in the CV-projection. Carbon atoms are represented in cyan and hydrogen atoms in white(D).

Source data

Extended Data Fig. 3 Trp-cage reversible folding.

Learned committor q, projected on (RMSD, dend)-space,—where the RMSD is computed with respect to basin B—from atomic coordinates of an unbiased trajectory of Trp-cage system. (A). Relative node sensitivity computed for a short unbiased simulation of 50 ns (B). Sketch of Trp-cage protein with the three main distances between atoms (green spheres) d1, d2 and d3 (C). The projection of the committor onto the (d1,d2)-subspace (D). Conformations extracted from a clustering analysis in the vicinity of the separatrix, exhibiting distinct secondary-structure elements (E, I to IV). The Trp-cage representations are colour-coded by secondary structure: white for random coils, cyan for turns, yellow for β-sheets, and magenta for α-helices.

Source data

Supplementary information

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Source Data Fig. 2

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Source Data Extended Data Fig. 1

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Source Data Extended Data Fig. 2

Raw data for Extended Data Fig. 2.

Source Data Extended Data Fig. 3

Raw data for Extended Data Fig. 3.

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Contreras Arredondo, S., Tang, C., Talmazan, R.A. et al. Learning the committor without collective variables. Nat Comput Sci (2026). https://doi.org/10.1038/s43588-026-00958-2

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