MarkovStateModel¶

Reversible Markov State Model

This model fits a first-order Markov model to a dataset of integer-valued timeseries. The key estimated attribute, transmat_ is a matrix containing the estimated probability of transitioning between pairs of states in the duration specified by lag_time.

Unless otherwise specified, the model is constrained to be reversible (satisfy detailed balance), which is appropriate for equilibrium chemical systems.:

MarkovStateModel(lag_time=1, n_timescales=None, reversible_type='mle',
                 ergodic_cutoff='on', prior_counts=0, sliding_window=True,
                 verbose=True)

Parameters¶

lag_time: The lag time of the model
n_timescales: The number of dynamical timescales to calculate when diagonalizing the transition matrix. If not specified, it will compute n_states - 1
reversible_type: Method by which the reversibility of the transition matrix is enforced. ‘mle’ uses a maximum likelihood method that is solved by numerical optimization, and ‘transpose’ uses a more restrictive (but less computationally complex) direct symmetrization of the expected number of counts.
ergodic_cutoff: Only the maximal strongly ergodic subgraph of the data is used to build an MSM. Ergodicity is determined by ensuring that each state is accessible from each other state via one or more paths involving edges with a number of observed directed counts greater than or equal to ergodic_cutoff. By setting ergodic_cutoff to 0 or ‘off’, this trimming is turned off. Setting it to ‘on’ sets the cutoff to the minimal possible count value.
prior_counts: Add a number of “pseudo counts” to each entry in the counts matrix after ergodic trimming. When prior_counts == 0 (default), the assigned transition probability between two states with no observed transitions will be zero, whereas when prior_counts > 0, even this unobserved transitions will be given nonzero probability.
sliding_window: Count transitions using a window of length lag_time, which is slid along the sequences 1 unit at a time, yielding transitions which contain more data but cannot be assumed to be statistically independent. Otherwise, the sequences are simply subsampled at an interval of lag_time.
verbose: Enable verbose printout

References¶

[1]	Prinz, Jan-Hendrik, et al. “Markov models of molecular kinetics: Generation and validation.” J Chem. Phys. 134.17 (2011): 174105.

[2]	Pande, V. S., K. A. Beauchamp, and G. R. Bowman. “Everything you wanted to know about Markov State Models but were afraid to ask” Methods 52.1 (2010): 99-105.

Attributes¶

n_states_: The number of states in the model
mapping_: Mapping between “input” labels and internal state indices used by the counts and transition matrix for this Markov state model. Input states need not necessarily be integers in (0, ..., n_states_ - 1), for example. The semantics of mapping_[i] = j is that state i from the “input space” is represented by the index j in this MSM.
countsmat_: Number of transition counts between states. countsmat_[i, j] is counted during fit(). The indices i and j are the “internal” indices described above. No correction for reversibility is made to this matrix.
transmat_: Maximum likelihood estimate of the reversible transition matrix. The indices i and j are the “internal” indices described above.
populations_: The equilibrium population (stationary eigenvector) of transmat_