core set Markov state models

[anyschaefer]

Hey,

I would like to have an overview of the current software that is able to generate core set MSMs with milestoning.
Specifically, I am looking for a set up that creates the transition matrix with the time-lagged correlation between forward $m_i^+(t)$ and backward $m_i^-(t)$ milestoning processes, with time $t$ and lagtime $\tau$ .
Basically, I need two main steps:
the projection of discrete trajectory of length $N$ into the milestoning processes

$$m_i^-(t) = \cases{1 & \text{if process is in core set i}\cr 1 & \text{if process came from core set i}\cr 0 & \text{otherwise}}$$

$$m_i^+(t) = \cases{1 & \text{if process is in core set i}\cr 1 & \text{if process go core set i}\cr 0 & \text{otherwise}}$$

and the estimation of the count matrix, with elements

$$\frac{1}{N-\tau} \sum_t m_i^-(t)m_j^+(t+\tau)$$

I know that pyemma has implemented the milestoning method, but if I understand it correctly it is only based on the backward process, right?
Have you integrated the method in deeptime?

All the best,
Joana

[thempel]

Hi Joana,
Yes, the pyemma implementation is based on the backward process only. If I remember correctly, this required some discrete trajectory filtering but otherwise used the same ML-MSM estimator for obtaining the transition matrix from the that. Not sure if there were some unresolved questions regarding the combination of the reversible MSM estimator with the forward-backward formalism that you are describing above. In any case, I don't think it was ever ported to deeptime, even though in my opinion, core-set MSMs are a super useful tool especially for large systems / noisy data.
Cheers,
Tim

[anyschaefer]

Hey Tim,
okay thanks!
We have developed a routine for core set MSMs (kellerlab) in recent years. I would be interested in transferring this to deeptime and directly integrating the reweighting. I'm so curious to see how this works with larger systems.
I'm thinking of extending count_matrix with a new function, and I need to implement the trajectory projection. Can you guide me where to find your discretization methods?
All the best,
joana

[thempel]

Sure! I am not sure if I understand everything correctly though. What you describe as a count matrix in your original post looks like it is normalized -- is it a count matrix or an ML transition matrix estimator? And: What kind of trajectory projection are you doing, i.e., is it a continuous to core-set map or do you start from raw discrete trajectories and discard some states and lump others into core-sets?

Based on my current understanding, this could be a possible implementation:

• Implement functions that extract the forward and backward trajectories from the raw discrete trajectories likely belong into deeptime/markov/_discrete_states.py (I am not sure what this class here is used for, but the place seems right.)
• EITHER A): Extend TransitionCountEstimator's count method (deeptime/markov/_transition_counting.py#L589) with a new kwarg, maybe milestoning_method. Functions from 1) can be used to combine resulting forward and backward trajectories into a count matrix here. Extend the API to treat milestone trajectories and allow access to this new kwarg from top level API of MSM methods.
• OR B): Create a new class, MilestoningTransitionCountEstimator or so, that implements your method. This should inherit most things from the other default estimator. IMO this could be a cleaner solution, but would require some way of accessing different estimators from the top level API. Maybe @clonker has an opinion on that.

Finally some amazing code from pyemma -- maybe some of it can be recycled.

• Possibly efficient implementation of assigning unassigned states to cores:
  https://github.com/markovmodel/PyEMMA/blob/3327f28b49e388e1ce4a6a83ab2f0c0ac7ca5050/pyemma/msm/estimators/_dtraj_stats.py#L131-L138
• Function that assigns microstates to core-sets: https://github.com/markovmodel/PyEMMA/blob/3327f28b49e388e1ce4a6a83ab2f0c0ac7ca5050/pyemma/util/discrete_trajectories.py#L227
• Some unit test cases: https://github.com/markovmodel/PyEMMA/blob/3327f28b49e388e1ce4a6a83ab2f0c0ac7ca5050/pyemma/util/tests/test_discrete_trajectories.py#L199