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).
Chipot, C. Free energy methods for the description of molecular processes. Annu. Rev. Biophys. 52, 113–138 (2023).
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).
Lindorff-Larsen, K., Piana, S., Dror, R. O. & Shaw, D. E. How fast-folding proteins fold. Science 334, 517–520 (2011).
Jung, H. et al. Machine-guided path sampling to discover mechanisms of molecular self-organization. Nat. Comput. Sci. 3, 334–345 (2023).
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).
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).
Miao, M. et al. Avoiding non-equilibrium effects in adaptive biasing force calculations. Mol. Simul. 47, 390–394 (2021).
Vanden-Eijnden, E. & Tal, F. A. Transition state theory: variational formulation, dynamical corrections, and error estimates. J. Chem. Phys. 123, 184103 (2005).
He, Z., Chipot, C. & Roux, B. Committor-consistent variational string method. J. Phys. Chem. Lett. 13, 9263–9271 (2022).
Horvath, F. et al. STIM1 transmembrane helix dimerization captured by AI-guided transition path sampling. Proc. Natl Acad. Sci. USA 122, e2506516122 (2025).
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).
Megías, A. et al. Iterative variational learning of committor-consistent transition pathways using artificial neural networks. Nat. Comput. Sci. 5, 592–602 (2025).
Giuseppe Chen, C. et al. Following the committor flow: a data-driven discovery of transition pathways. J. Chem. Theory Comput. 22, 1258–1265 (2026).
Contreras Arredondo, S. et al. Learning the committor without collective variables. Nat. Comput. Sci. 6, 350–357 (2026).
Noé, F., Olsson, S., Köhler, J. & Wu, H. Boltzmann generators: sampling equilibrium states of many-body systems with deep learning. Science 365, eaaw1147 (2019).
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).
Thiemann, F. L. et al. Force-free molecular dynamics through autoregressive equivariant networks. Nat. Mach. Intell. 8, 764–776 (2026).
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).
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).
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).
Chen, H. & Chipot, C. Chasing collective variables using temporal data-driven strategies. QRB Discov. 4, e2 (2023).
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).
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).
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).
Zhou, R. Trp-cage: folding free energy landscape in explicit water. Proc. Natl Acad. Sci. USA 100, 13280–13285 (2003).
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).
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).
Klingenberg, M. The ADP and ATP transport in mitochondria and its carrier. Biochim. Biophys. Acta Biomembr. 1778, 1978–2021 (2008).
Kunji, E. R. & Ruprecht, J. J. The mitochondrial ADP/ATP carrier exists and functions as a monomer. Biochem. Soc. Trans. 48, 1419–1432 (2020).
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).
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).
Yao, S. et al. Mechanistic insights into multiple-step transport of mitochondrial ADP/ATP carrier. Comput. Struct. Biotechnol. J. 20, 1829–1840 (2022).
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).
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).
Okazaki, K.-I. et al. Mechanism of the electroneutral sodium/proton antiporter PaNhaP from transition-path shooting. Nat. Commun. 10, 1742 (2019).
Thompson, M. J. et al. Asynchronous subunit transitions prime acetylcholine receptor activation. Science 391, eadw1264 (2025).
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).
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).
Ajaz, A. et al. Concerted vs stepwise mechanisms in dehydro-Diels-Alder reactions. J. Org. Chem. 76, 9320–9328 (2011).
Biroli, G. & Kurchan, J. Metastable states in glassy systems. Phys. Rev. E 64, 016101 (2001).
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).
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).
Shaw, D. E. et al. Anton, a special-purpose machine for molecular dynamics simulation. Commun. ACM 51, 91–97 (2008).
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).
Belkacemi, Z., Gkeka, P., Lelièvre, T. & Stoltz, G. Chasing collective variables using autoencoders and biased trajectories. J. Chem. Theory Comput. 18, 59–78 (2022).
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).
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).
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).
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).
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).
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).
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).
Huang, J. et al. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods 14, 71–73 (2017).
Pebay-Peyroula, E. et al. Structure of mitochondrial ADP/ATP carrier in complex with carboxyatractyloside. Nature 426, 39–44 (2003).
Webb, B. & Sali, A. Comparative protein structure modeling using MODELLER. Curr. Protoc. Bioinformatics 54, 5–6 (2016).
Ruprecht, J. J. et al. The molecular mechanism of transport by the mitochondrial ADP/ATP carrier. Cell 176, 435–447 (2019).
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).