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References

The methods Trails-MD builds on, with primary references. Cite the relevant ones alongside Trails-MD (see CITATION.cff).

Markov state models

  • Prinz, J.-H. et al. Markov models of molecular kinetics: Generation and validation. J. Chem. Phys. 134, 174105 (2011).
  • Husic, B. E. & Pande, V. S. Markov state models: From an art to a science. J. Am. Chem. Soc. 140, 2386–2396 (2018).
  • Röblitz, S. & Weber, M. Fuzzy spectral clustering by PCCA+. Adv. Data Anal. Classif. 7, 147–179 (2013). (PCCA+ metastable decomposition.)

Weighted ensemble & kinetics

  • Huber, G. A. & Kim, S. Weighted-ensemble Brownian dynamics simulations for protein association reactions. Biophys. J. 70, 97–110 (1996). (WE split/merge.)
  • Zwier, M. C. et al. WESTPA: An interoperable, highly scalable software package for weighted ensemble simulation and analysis. J. Chem. Theory Comput. 11, 800–809 (2015).
  • Russo, J. D. et al. WESTPA 2.0: High-performance upgrades for weighted ensemble simulations and analysis. J. Chem. Theory Comput. 18, 6494–6509 (2022).
  • Hill, T. L. Free Energy Transduction and Biochemical Cycle Kinetics. Springer (1989). (Steady-state flux / MFPT = 1/flux.)

Dimensionality reduction / collective variables

  • Pérez-Hernández, G. et al. Identification of slow molecular order parameters for Markov model construction (TICA). J. Chem. Phys. 139, 015102 (2013).
  • Schwantes, C. R. & Pande, V. S. Improvements in Markov state model construction reveal many non-native interactions in the folding of NTL9. J. Chem. Theory Comput. 9, 2000–2009 (2013). (TICA.)
  • Bonati, L., Piccini, G. & Parrinello, M. Deep learning the slow modes for rare events sampling (Deep-TICA). PNAS 118, e2113533118 (2021).
  • Bonati, L., Rizzi, V. & Parrinello, M. Data-driven collective variables for enhanced sampling (Deep-LDA). J. Phys. Chem. Lett. 11, 2998–3004 (2020).
  • Mardt, A. et al. VAMPnets for deep learning of molecular kinetics. Nat. Commun. 9, 5 (2018).
  • Wang, D. & Tiwary, P. State predictive information bottleneck (SPIB). J. Chem. Phys. 154, 134111 (2021).
  • Time-lagged (variational) autoencoders: Wehmeyer, C. & Noé, F. Time-lagged autoencoders. J. Chem. Phys. 148, 241703 (2018).

Software

  • Hoffmann, M. et al. Deeptime: a Python library for machine learning dynamical models from time series data. Mach. Learn.: Sci. Technol. 3, 015009 (2022).
  • Eastman, P. et al. OpenMM 8. J. Phys. Chem. B 128, 109–116 (2024).
  • Michaud-Agrawal, N. et al. MDAnalysis: A toolkit for the analysis of molecular dynamics simulations. J. Comput. Chem. 32, 2319–2327 (2011).