Modeling dynamics of FS Peptide

This example shows a typical, basic usage of MSMBuilder to model dynamics of a protein system.

MSMBuilder includes example datasets

The following cell loads an example protein dataset. In practice, you will generate your own dataset by running molecular dynamics (MD) on your system of interest. MSMBuilder does not run MD.



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# Download example dataset
from msmbuilder.example_datasets import FsPeptide
fs_peptide = FsPeptide(verbose=False)
xyz = fs_peptide.get().trajectories
print(fs_peptide.description())

Since the data was saved at 50 ps / frame, we only load every 10th frame (with a new frequency of 0.5/ns).



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xyz = [t[::10] for t in xyz]
print("{} trajectories".format(len(xyz)))
# msmbuilder does not keep track of units! You must keep track of your
# data's timestep
to_ns = 0.5
print("with length {} ns".format(set(len(x)*to_ns for x in xyz)))

Featurization

The raw (x, y, z) coordinates from the simulation do not respect the translational and rotational symmetry of our problem. A Featurizer transforms cartesian coordinates into other representations. Here we use the DihedralFeaturizer to turn our data into phi and psi dihedral angles. Observe that the 264*3-dimensional space is reduced to 84 dimensions



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from msmbuilder.featurizer import DihedralFeaturizer
featurizer = DihedralFeaturizer(types=['phi', 'psi'])
diheds = featurizer.fit_transform(xyz)

print(xyz[0].xyz.shape)
print(diheds[0].shape)

Preprocessing

Since the range of values in our raw data can vary widely from feature to feature, we can scale values to reduce bias. Here we use the RobustScaler to center and scale our dihedral angles by their respective interquartile ranges.



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from msmbuilder.preprocessing import RobustScaler
scaler = RobustScaler()
scaled_diheds = scaler.fit_transform(diheds)

print(diheds[0].shape)
print(scaled_diheds[0].shape)

Intermediate kinetic model: tICA

tICA is similar to principal component analysis (see "tICA vs. PCA" example). Note that the 84-dimensional space is reduced to 4 dimensions.



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from msmbuilder.decomposition import tICA
tica_model = tICA(lag_time=2, n_components=4)
# fit and transform can be done in seperate steps:
tica_model.fit(diheds)
tica_trajs = tica_model.transform(diheds)

print(diheds[0].shape)
print(tica_trajs[0].shape)

tICA Histogram

We can histogram our data projecting along the two slowest degrees of freedom (as found by tICA)



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%matplotlib inline
import msmexplorer as msme
import numpy as np
txx = np.concatenate(tica_trajs)
_ = msme.plot_histogram(txx)

Clustering

Conformations need to be clustered into states (sometimes written as microstates). We cluster based on the tICA projections to group conformations that interconvert rapidly. Note that we transform our trajectories from the 4-dimensional tICA space into a 1-dimensional cluster index.



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from msmbuilder.cluster import MiniBatchKMeans
clusterer = MiniBatchKMeans(n_clusters=100, random_state=42)
clustered_trajs = clusterer.fit_transform(tica_trajs)

print(tica_trajs[0].shape)
print(clustered_trajs[0].shape)



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from matplotlib import pyplot as plt
plt.hexbin(txx[:,0], txx[:,1], bins='log', mincnt=1, cmap='viridis')
plt.scatter(clusterer.cluster_centers_[:,0],
            clusterer.cluster_centers_[:,1], 
            s=100, c='w')

MSM

We can construct an MSM from the labeled trajectories



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from msmbuilder.msm import MarkovStateModel
msm = MarkovStateModel(lag_time=2, n_timescales=20)
msm.fit(clustered_trajs)



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assignments = clusterer.partial_transform(txx)
assignments = msm.partial_transform(assignments)
msme.plot_free_energy(txx, obs=(0, 1), n_samples=10000,
                      pi=msm.populations_[assignments],
                      xlabel='tIC 1', ylabel='tIC 2')
plt.scatter(clusterer.cluster_centers_[msm.state_labels_, 0],
            clusterer.cluster_centers_[msm.state_labels_, 1],
            s=1e4 * msm.populations_,       # size by population
            c=msm.left_eigenvectors_[:, 1], # color by eigenvector
            cmap="coolwarm",
            zorder=3) 
plt.colorbar(label='First dynamical eigenvector')
plt.tight_layout()



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msm.timescales_



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msme.plot_timescales(msm, n_timescales=5, ylabel='Implied Timescales ($ns$)')

Macrostate Model



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from msmbuilder.lumping import PCCAPlus
pcca = PCCAPlus.from_msm(msm, n_macrostates=4)
macro_trajs = pcca.transform(clustered_trajs)



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msme.plot_free_energy(txx, obs=(0, 1), n_samples=10000,
                      pi=msm.populations_[assignments],
                      xlabel='tIC 1', ylabel='tIC 2')
plt.scatter(clusterer.cluster_centers_[msm.state_labels_, 0],
            clusterer.cluster_centers_[msm.state_labels_, 1],
            s=50,
            c=pcca.microstate_mapping_,
            zorder=3
           )
plt.xlabel('tIC 1')
plt.ylabel('tIC 2')
plt.tight_layout()