Software and online documentation

Python package for estimation, validation and analysis of kinetic models from molecular dynamics data. Currently supports:

  • Markov (state) models (MSMs)

  • time-lagged independent component analysis (TICA)

  • Transition path theory (TPT)

  • Variational Approach (VA)


As published papers cannot be updated or deleted, the scientific literature is cluttered with inconsistent and outdated information. This project is an attempt to present our collected knowledge on conformation dynamics, Markov models and related methods in an up-to-date and consistent manner.


BHMM is a python package for both maximum likelihood and Bayesian estimates of Hidden Markov models. Suitable for analyzing both, experimental and simulation data. Currently supports:

Jointly developed by John Chodera and Frank NoƩ

The transition-based reweighting analysis method (TRAM) gives optimal estimates of thermodynamics and kinetics given simulations at different thermodynamic states. For example, you can use it to combine direct MD simulations and enhanced sampling simulations (umbrella sampling, REMD) to get the full kinetics. TRAM is a generalization to both reweighting estimators such as WHAM, MBAR and to reversible Markov models.


We have derived a variational principle of conformation dynamics: Markov models, TICA and other models that linearly combine basis functions will underestimate the true timescales and eigenvalues. We have derived a general variational approach to optimally approximate conformation dynamics of molecules which is analogous to the generalized Ritz method in quantum mechanics. Markov models and TICA are special cases of our theory.

Variational Approach (VA)

Time-lagged independent component analysis (TICA) is a data transformation / dimension reduction method that projects high- dimensional time series e.g. from molecular dynamics to a slow subspace. Amongst linear projection methods, TICA is optimal in identifying good "reaction coordinates" and very useful as a preprocessing method for Markov state modeling. Originally invented by Molgedey and Schuster, adapted and exploited for molecular dynamics independently by us and the Pande group.