Markov state models are a statistical tool for analysing molecular simulations which has met with lots of success. The Model class here, encapsulates all functionallity for the calculation of Markov models while hiding unnecessary details under the hood. It uses PyEMMA [1] internally to calculate Markov models.
References
PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models. Martin K. Scherer et al. JCTC 2015.
Bases: object
Constructor for the Model class.
data (MetricData
object) – A MetricData
object containing the discretized trajectories
Example
>>> model = Model(data)
Methods
Attributes
The transition probability matrix
Conducts a Chapman-Kolmogorow test.
Mapping of microstates to clusters
Numpy array which at index i has the index of the cluster corresponding to microstate i.
Produces a deep copy of the object
data – A copy of the current object
Model
object
Examples
>>> model2 = model.copy()
Given an MSM this function detects the states belonging to a core set and returns a new model consisting only of these states.
threshold (float) – Membership probability threshold over which microstates belong to the core of a macrostate
newmodel – A new model object
frames (list) – A list of the frames that were kept in the new model
Creates a new state. Works both for new clusters and macrostates.
If creating a new cluster, it just reassigns the given frames to the new cluster. If creating a new macrostate, it removes the given microstates from their previous macrostate, creates a new one and assigns them to it.
Obtain and plot the equilibrium probabilities of each macrostate
eq – An array of equilibrium probabilities of the macrostates
ndarray
Examples
>>> model = Model(data)
>>> model.markovModel(100, 5)
>>> model.eqDistribution()
Get samples of MSM states in Molecule classes
states (ndarray, optional) – A list of states to visualize
statetype (['macro','micro','cluster'], optional) – The type of state to visualize
wrapsel (str, optional, default='protein') – Atom selection string to use for wrapping. See more here
alignsel (str, optional, default='name CA') – Atom selection string used for aligning all frames. Set to None to disable aligning. See more here
alignmol (Molecule
object) – A reference molecule onto which to align all others
samplemode (['weighted','random'], optional, default='weighted') – How to obtain the samples from the states
numsamples (int) – Number of samples (conformations) for each state.
simlist (numpy.ndarray of Sim
objects) – Optionally pass a different (but matching, i.e. filtered) simlist for creating the Molecules.
mols – A list of Molecule
objects containing the samples of each state
ndarray of Molecule
objects
Examples
>>> model = Model(data)
>>> model.markovModel(100, 5)
>>> mols = model.getStates()
>>> for m in mols:
>>> m.view()
Load a MetricData
object from disk
filename (str) – Path to the saved MetricData object
Examples
>>> model = Model()
>>> model.load('./model.dat')
Mapping of clusters to microstates
Numpy array which at index i has the index of the macrostate corresponding to cluster i. Clusters which were not connected and thus are not in the model have a macrostate value of -1.
Mapping of microstates to macrostates
Numpy array which at index i has the index of the macrostate corresponding to microstate i.
Number of macrostates
Build a Markov model at a given lag time and calculate metastable states
lag (int) – The lag time at which to calculate the Markov state model. The units are specified with the units argument.
macronum (int) – The number of macrostates (metastable states) to produce
units (str) – The units of lag. Can be ‘frames’ or any time unit given as a string.
sparse (bool) – Make the transition matrix sparse. Useful if lots (> 4000) states are used for the MSM. Warning: untested.
Examples
>>> model = Model(data)
>>> model.markovModel(150, 4) # 150 frames lag, 4 macrostates
Heuristic for getting the lagtime before a timescale drops.
It calculates the last lagtime before a drop occurs in the first implied timescale due to disconnected states. If the top timescale is closer to the second top timescale at the previous lagtime than to itself at the previous lagtime it means that a drop occured. The lagtime before the drop is returned.
lags (np.ndarray or list) – A list of lag times for which to calculate the implied timescales
ml – The maximum lagtime before a drop occurs in the top timescale
Examples
>>> model = Model(data)
>>> model.maxConnectedLag(list(range(1, 100, 5)))
Mapping of clusters to microstates
Numpy array which at index i has the index of the microstate corresponding to cluster i. Clusters which were not connected and thus are not in the model have a microstate value of -1.
Number of microstates
Plots the free energy surface on any given two dimensions. Can also plot positions of states on top.
dimX (int) – Index of projected dimension to use for the X axis.
dimY (int) – Index of projected dimension to use for the Y axis.
temperature (float) – Simulation temperature.
states (bool) – If True, will plot scatter plot of microstates coloured by macro state on top of FES.
s (float) – Marker size for states.
cmap – Sets the Matplotlib colormap for both fescmap and statescmap
fescmap – Matplotlib colormap for the free energy surface
statescmap – Matplotlib colormap for the states
plot (bool) – If the method should display the plot of the FES
save (str) – Path of the file in which to save the figure
data (MetricData
object) – Optionally you can pass a different MetricData object than the one used to build the model. For example
if the user wants to build a model on distances but wants to plot the FES on top of RMSD values. The
MetricData object needs to have the same simlist as the Model.
Examples
>>> import matplotlib as plt
>>> model.plotFES(0, 1, 300)
>>> model.plotFES(2, 3, 300, data=otherdata, states=True, fescmap=plt.cm.gray)
Plot the implied timescales of MSMs of various lag times
lags (list) – Specify explicitly at which lag times to compute the timescales.
minlag (float) – The minimum lag time for the timescales. Used in combination with maxlag and numlags.
maxlag (float) – The maximum lag time for the timescales. If None will default to the mode length of the trajectories.
numlags (int) – The number of points to place between minlag and maxlag.
units (str) – The units of lag. Can be ‘frames’ or any time unit given as a string.
errors (errors) – Calculate errors using Bayes (Refer to pyEMMA documentation)
nits (int) – Number of implied timescales to calculate. Default: all
results (bool) – If the method should return the calculated implied timescales
plot (bool) – If the method should display the plot of implied timescales
save (str) – Path of the file in which to save the figure
njobs (int) – Number of parallel jobs to spawn for calculation of timescales. Negative numbers are used for spawning jobs as many as CPU threads. -1: for all CPUs -2: for all except one etc.
ylog (bool) – Set to False to get linear y axis instead of logarithmic
If given results=True this method will return the following data
its (np.ndarray) – The calculated implied timescales. 2D array with dimensions (len(lags), nits)
lags (np.ndarray) – A list of the lag times that were used to calculate the implied timescales
Examples
>>> model = Model(data)
>>> model.plotTimescales()
>>> model.plotTimescales(lags=list(range(1,100,5)))
>>> model.plotTimescales(minlag=0.1, maxlag=20, numlags=25, units='ns')
Samples frames from a set of states
states (Union[list, int]) – A list of state indexes from which we want to sample
frames (Union[None, int, list]) – An integer with the number of frames we want to sample per state or a list of same length as states which contains the number of frames we want from each of the states. If set to None it will return all frames of the states.
statetype (['micro','macro','cluster'], optional) – The type of state we want to sample from.
replacement (bool) – If we want to sample with or without replacement.
samplemode (['random','even','weighted']) – What sampling strategy to use. For statetype == ‘macro’ this can be set to ‘even’ to sample evenly from all microstates in the macrostate or to ‘weighted’ to sample proportional to the equilibium probability of each microstate in the macrostate.
allframes (bool) – Deprecated. Use frames=None instead.
absframes (numpy.ndarray) – An array which contains for each state an array containing absolute trajectory frames
relframes (numpy.ndarray) – An array which contains for each state a 2D array containing the trajectory ID and frame number for each of the sampled frames
Examples
>>> model = Model(data)
>>> model.markovModel(100, 5)
>>> model.sampleStates(range(5), [10, 3, 2, 50, 1]) # Sample from all 5 macrostates
>>> model.sampleStates(range(model.micronum), samplesnum, statetype='micro') # Sample from all microstates
Save a Model
object to disk
filename (str) – Path of the file in which to save the object
Examples
>>> model = Model(data)
>>> model.markovModel(100, 5)
>>> model.save('./model.dat')
Visualize macro/micro/cluster states in VMD
states (ndarray, optional) – A list of states to visualize
statetype (['macro','micro','cluster'], optional) – The type of state to visualize
protein (bool, optional) – Set to True to enable pure protein system visualization
ligand (str, optional) – Atom selection string for the ligand. See more here
viewer (VMD
object, optional) – A viewer in which to visualize the states
mols (ndarray, optional) – An array of Molecule
objects to visualize
numsamples (int) – Number of samples (conformations) for each state.
wrapsel (str, optional, default='protein') – Atom selection string to use for wrapping. See more here
alignsel (str, optional, default='name CA') – Atom selection string used for aligning all frames. See to None to disable aligning. See more here
simlist (numpy.ndarray of Sim
objects) – Optionally pass a different (but matching, i.e. filtered) simlist for visualizing the states.
Examples
>>> model = Model(data)
>>> model.markovModel(100, 5)
>>> model.viewStates(protein=True)
>>> model.viewStates(ligand='resname MOL')
Calculates properties of the states.
Calculates properties of data corresponding to states. Can calculate for example the mean distances of atoms in a state, or the standard deviation of the RMSD in a state.
reference (Model
object or MetricData
object) – A model containing the state definitions or a MetricData object containing cluster definitions
data (MetricData
object) – A projection corresponding to the conformations in the states of the model. The data and the model need to share
the same simlist
states (list) – A list of the states for which we want to calculate the properties
statetype (['macro','micro','cluster']) – The state type
weighted (bool) – If the properties of the macrostates should be calculated as the weighted average of their microstates, where the weights are the equilibrium probabilities of the microstates
method – A function pointer for the method that calculates our desired property. e.g. np.mean, np.std
axis (int) – On which axis of the data the method should operate on
existing (bool) – Not used
target – Not used
statistic – A list which contains in each element the desired statistic of a specific state specifies in states
Examples
>>> data = MetricDistance.project(sims, 'protein and name CA', 'resname MOL')
>>> model = Model(data)
>>> model.markovModel(100, 5)
>>> # Get the standard deviation of distances in all macrostates
>>> getStateStatistic(model, data, list(range(5)), method=np.std)
Accumulate values of macrostates from a microstate array
model (Model
object) – The model which to use to accumulate
microvalue (ndarray) – An array of values corresponding to the microstates of the model
macrovalue – An array of values corresponding to the macrostates of the model
ndarray