Dror, R. O., Dirks, R. M., Grossman, J. P., Xu, H. & Shaw, D. E. Biomolecular simulation: a computational microscope for molecular biology. Annu. Rev. Biophys. 41, 429–452 (2012).
Google Scholar
Chipot, C. Free energy methods for the description of molecular processes. Annu. Rev. Biophys. 52, 113–138 (2023).
Google Scholar
Kang, C. et al. Convergence is not correctness: context-dependent performance of enhanced-sampling methods across biological complexity. Nat. Commun. 17, 6245 (2026).
Ho, J., Jain, A. N. & Abbeel, P. Denoising diffusion probabilistic models. In Proc. Advances in Neural Information Processing Systems Vol. 33 (eds Larochelle, H. et al.) 6840–6851 (Curran Associates, 2020).
Roux, B. Transition rate theory, spectral analysis, and reactive paths. J. Chem. Phys. 156, 134111 (2022).
Google Scholar
Lindorff-Larsen, K., Piana, S., Dror, R. O. & Shaw, D. E. How fast-folding proteins fold. Science 334, 517–520 (2011).
Google Scholar
Jung, H. et al. Machine-guided path sampling to discover mechanisms of molecular self-organization. Nat. Comput. Sci. 3, 334–345 (2023).
Google Scholar
Shaw, D. E. et al. Anton 3: twenty microseconds of molecular dynamics simulation before lunch. In Proc. International Conference for High Performance Computing, Networking, Storage and Analysis (eds de Supinski, B. R., Hall, M. W. & Gamblin, T.) 1:1–1:11 (Association for Computing Machinery, 2021).
Ren, W. & Vanden-Eijnden, E. Finite temperature string method for the study of rare events. J. Phys. Chem. B 109, 6688–6693 (2005).
Google Scholar
Pan, A. C., Sezer, D. & Roux, B. Finding transition pathways using the string method with swarms of trajectories. J. Phys. Chem. B 112, 3432–3440 (2008).
Google Scholar
Miao, M. et al. Avoiding non-equilibrium effects in adaptive biasing force calculations. Mol. Simul. 47, 390–394 (2021).
Google Scholar
Vanden-Eijnden, E. & Tal, F. A. Transition state theory: variational formulation, dynamical corrections, and error estimates. J. Chem. Phys. 123, 184103 (2005).
Google Scholar
He, Z., Chipot, C. & Roux, B. Committor-consistent variational string method. J. Phys. Chem. Lett. 13, 9263–9271 (2022).
Google Scholar
Horvath, F. et al. STIM1 transmembrane helix dimerization captured by AI-guided transition path sampling. Proc. Natl Acad. Sci. USA 122, e2506516122 (2025).
Google Scholar
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).
Google Scholar
Megías, A. et al. Iterative variational learning of committor-consistent transition pathways using artificial neural networks. Nat. Comput. Sci. 5, 592–602 (2025).
Google Scholar
Giuseppe Chen, C. et al. Following the committor flow: a data-driven discovery of transition pathways. J. Chem. Theory Comput. 22, 1258–1265 (2026).
Google Scholar
Contreras Arredondo, S. et al. Learning the committor without collective variables. Nat. Comput. Sci. 6, 350–357 (2026).
Google Scholar
Noé, F., Olsson, S., Köhler, J. & Wu, H. Boltzmann generators: sampling equilibrium states of many-body systems with deep learning. Science 365, eaaw1147 (2019).
Google Scholar
Jing, B., Stärk, H., Jaakkola, T. & Berger, B. Generative modeling of molecular dynamics trajectories. In Proc. Advances in Neural Information Processing Systems Vol. 37 (eds Globerson, A. et al.) 40534–40564 (Curran Associates, 2024).
Lewis, S. et al. Scalable emulation of protein equilibrium ensembles with generative deep learning. Science 389, eadv9817 (2025).
Google Scholar
Thiemann, F. L. et al. Force-free molecular dynamics through autoregressive equivariant networks. Nat. Mach. Intell. 8, 764–776 (2026).
Google Scholar
Seong, K., Park, S., Kim, S., Kim, W. Y. & Ahn, S. Transition path sampling with improved off-policy training of diffusion path samplers. In Proc. International Conference on Learning Representations Vol. 2025 (eds Yue, Y. et al.) 93040–93062 (ICLR, 2025).
Raja, S. et al. Action-minimization meets generative modeling: efficient transition path sampling with the Onsager–Machlup functional. In Proc. 42nd International Conference on Machine Learning Vol. 267 (eds Singh, A. et al.) 50972–51008 (PMLR, 2025).
Kania, S., Webber, R. J., Simpson, G., Aristoff, D. & Zuckerman, D. M. Randomized Iterative trajectory reweighting for steady-state distributions without discretization error. Proc. Natl Acad. Sci. USA 123, e2529246123 (2026).
Google Scholar
Bolhuis, P. G., Dellago, C., Geissler, P. L. & Chandler, D. Transition path sampling: throwing ropes over mountains in the dark. J. Phys. Condens. Matter 12, A147–A152 (2000).
Google Scholar
Juraszek, J. & Bolhuis, P. G. Sampling the multiple folding mechanisms of Trp-cage in explicit solvent. Proc. Natl Acad. Sci. USA 103, 15859–15864 (2006).
Google Scholar
Chen, H. & Chipot, C. Chasing collective variables using temporal data-driven strategies. QRB Discov. 4, e2 (2023).
Google Scholar
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).
Google Scholar
Roh, S.-H. et al. Cryo-EM and MD infer water-mediated proton transport and autoinhibition mechanisms of the Vo complex. Sci. Adv. 6, eabb9605 (2020).
Google Scholar
Blanc, F. E. C. & Hummer, G. Mechanism of proton-powered c-ring rotation in a mitochondrial ATP synthase. Proc. Natl Acad. Sci. USA 121, e2314199121 (2024).
Google Scholar
Zhou, R. Trp-cage: folding free energy landscape in explicit water. Proc. Natl Acad. Sci. USA 100, 13280–13285 (2003).
Google Scholar
Marinelli, F., Pietrucci, F., Laio, A. & Piana, S. A kinetic model of Trp-cage folding from multiple biased molecular dynamics simulations. PLoS Comput. Biol. 5, e1000452 (2009).
Google Scholar
Sidky, H., Chen, W. & Ferguson, A. L. High-resolution Markov state models for the dynamics of Trp-cage miniprotein constructed over slow folding modes identified by state-free reversible VAMPnets. J. Phys. Chem. B 123, 7999–8009 (2019).
Google Scholar
Klingenberg, M. The ADP and ATP transport in mitochondria and its carrier. Biochim. Biophys. Acta Biomembr. 1778, 1978–2021 (2008).
Google Scholar
Kunji, E. R. & Ruprecht, J. J. The mitochondrial ADP/ATP carrier exists and functions as a monomer. Biochem. Soc. Trans. 48, 1419–1432 (2020).
Google Scholar
Tamura, K. & Hayashi, S. Atomistic modeling of alternating access of a mitochondrial ADP/ATP membrane transporter with molecular simulations. PLoS One 12, 1–21 (2017).
Google Scholar
Pietropaolo, A., Pierri, C. L., Palmieri, F. & Klingenberg, M. The switching mechanism of the mitochondrial ADP/ATP carrier explored by free-energy landscapes. Biochim. Biophys. Acta Bioenerg. 1857, 772–781 (2016).
Google Scholar
Yao, S. et al. Mechanistic insights into multiple-step transport of mitochondrial ADP/ATP carrier. Comput. Struct. Biotechnol. J. 20, 1829–1840 (2022).
Google Scholar
Yi, Q. et al. Molecular dynamics simulations on apo ADP/ATP carrier shed new lights on the featured motif of the mitochondrial carriers. Mitochondrion 47, 94–102 (2019).
Google Scholar
Springett, R., King, M. S., Crichton, P. G. & Kunji, E. R. Modelling the free energy profile of the mitochondrial ADP/ATP carrier. Biochim. Biophys. Acta Bioenerg. 1858, 906–914 (2017).
Google Scholar
Okazaki, K.-I. et al. Mechanism of the electroneutral sodium/proton antiporter PaNhaP from transition-path shooting. Nat. Commun. 10, 1742 (2019).
Google Scholar
Thompson, M. J. et al. Asynchronous subunit transitions prime acetylcholine receptor activation. Science 391, eadw1264 (2025).
Google Scholar
Lev, B. et al. String method solution of the gating pathways for a pentameric ligand-gated ion channel. Proc. Natl Acad. Sci. USA 114, E4158–E4167 (2017).
Google Scholar
Bergh, C., Heusser, S. A., Howard, R. & Lindahl, E. Markov state models of proton- and pore-dependent activation in a pentameric ligand-gated ion channel. eLife 10, e68369 (2021).
Google Scholar
Ajaz, A. et al. Concerted vs stepwise mechanisms in dehydro-Diels-Alder reactions. J. Org. Chem. 76, 9320–9328 (2011).
Google Scholar
Biroli, G. & Kurchan, J. Metastable states in glassy systems. Phys. Rev. E 64, 016101 (2001).
Google Scholar
Yang, S., Banavali, N. K. & Roux, B. Mapping the conformational transition in Src activation by cumulating the information from multiple molecular dynamics trajectories. Proc. Natl Acad. Sci. USA 106, 3776–3781 (2009).
Google Scholar
Moradi, M. & Tajkhorshid, E. Mechanistic picture for conformational transition of a membrane transporter at atomic resolution. Proc. Natl Acad. Sci. USA 110, 18916–18921 (2013).
Google Scholar
Shaw, D. E. et al. Anton, a special-purpose machine for molecular dynamics simulation. Commun. ACM 51, 91–97 (2008).
Google Scholar
Sipka, M., Dietschreit, J. C. B., Grajciar, L. & Gomez-Bombarelli, R. Differentiable simulations for enhanced sampling of rare events. In Proc. 40th International Conference on Machine Learning Vol. 202 (eds Krause, A. et al.) 31990–32007 (PMLR, 2023).
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).
Google Scholar
Belkacemi, Z., Gkeka, P., Lelièvre, T. & Stoltz, G. Chasing collective variables using autoencoders and biased trajectories. J. Chem. Theory Comput. 18, 59–78 (2022).
Google Scholar
Frassek, M., Arjun, A. & Bolhuis, P. G. An extended autoencoder model for reaction coordinate discovery in rare event molecular dynamics datasets. J. Chem. Phys. 155, 064103 (2021).
Google Scholar
Zou, Z., Wang, D. & Tiwary, P. A graph neural network-state predictive information bottleneck (GNN-SPIB) approach for learning molecular thermodynamics and kinetics. Digit. Discov. 4, 211–221 (2025).
Google Scholar
Strahan, J., Finkel, J., Dinner, A. R. & Weare, J. Predicting rare events using neural networks and short-trajectory data. J. Comput. Phys. 488, 112152 (2023).
Google Scholar
Kang, P., Trizio, E. & Parrinello, M. Computing the committor with the committor to study the transition state ensemble. Nat. Comput. Sci. 4, 451–460 (2024).
Google Scholar
Costa, A. d. S., Ponnapati, M., Rubin, D., Smidt, T. & Jacobson, J. Accelerating protein molecular dynamics simulation with DeepJump. Preprint at https://doi.org/10.48550/arXiv.2509.13294 (2025).
Song, J., Meng, C. & Ermon, S. Denoising diffusion implicit models. In Proc. International Conference on Learning Representations (ICLR) (eds Oh, A., Murray, N. & Titov, I.) 1–20 (ICLR, 2021).
Schlitter, J., Engels, M. & Krüger, P. Targeted molecular dynamics: a new approach for searching pathways of conformational transitions. J. Mol. Graph. 12, 84–89 (1994).
Google Scholar
Schütt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A. & Müller, K.-R. SchNet–a deep learning architecture for molecules and materials. J. Chem. Phys. 148, 241722 (2018).
Vaswani, A. et al. Attention is all you need. In Proc. Advances in Neural Information Processing Systems Vol. 30 (eds Guyon, I. et al.) 5998–6008 (Curran Associates, 2017).
Post, M. & Hummer, G. AI-guided transition path sampling of lipid flip-flop and membrane nanoporation. Nat. Commun. 17, 224 (2026).
Google Scholar
Breebaart, R. S., Lazzeri, G., Covino, R. & Bolhuis, P. G. Understanding mechanisms of molecular rare events from start to finish. Phys. Rev. Lett. 136, 168001 (2026).
Clevert, D.-A., Unterthiner, T. & Hochreiter, S. Fast and accurate deep network learning by exponential linear units (ELUs). In Proc. 4th International Conference on Learning Representations (ICLR) (eds Bengio, Y. & LeCun, Y.) 1–14 (ICLR, 2016).
Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. In Proc. 3rd International Conference on Learning Representations (ICLR) (eds Bengio, Y. & LeCun, Y.) 1–15 (ICLR, 2015).
Phillips, J. C. et al. Scalable molecular dynamics on CPU and GPU architectures with NAMD. J. Chem. Phys. 153, 044130 (2020).
Google Scholar
Huang, J. et al. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods 14, 71–73 (2017).
Google Scholar
Pebay-Peyroula, E. et al. Structure of mitochondrial ADP/ATP carrier in complex with carboxyatractyloside. Nature 426, 39–44 (2003).
Google Scholar
Webb, B. & Sali, A. Comparative protein structure modeling using MODELLER. Curr. Protoc. Bioinformatics 54, 5–6 (2016).
Google Scholar
Ruprecht, J. J. et al. The molecular mechanism of transport by the mitochondrial ADP/ATP carrier. Cell 176, 435–447 (2019).
Google Scholar
Smart, O. S., Neduvelil, J. G., Wang, X., Wallace, B. A. & Sansom, M. S. P. HOLE: a program for the analysis of the pore dimensions of ion channel structural models. J. Mol. Graph. 14, 354–360 (1996).
Google Scholar
