3.4.3 Running the aMD
Calculations
Once the aMD parameters are defined, we run 200 ns of aMD
production with the same conditions of cMD. In addition to the
boost of the aMD, we use the power of GPUs to significantly
increase the conformational sampling in an acceptable total simula-
tion time. Additional aMD productions can be launched from the
output of the previous run.3.4.4 Analyzing the aMD
Results
Principal Component
Analysis: Preliminaries
When using a biased molecular dynamics method to enhance the
conformational sampling of a protein, one important analysis step is
to assess whether the obtained conformational ensemble is a con-
sistent and robust representation of the accessible conformations of
the protein. This implies to identify the largest motions in the
protein, more precisely the protein regions whose movements con-
tribute the most to explain the conformational diversity. From a
mathematical point of view, a trajectory can be viewed as a matrix of
atomic coordinates where each line corresponds to a conformation
(snapshot) of the system at a timet(the individuals) and each
column corresponds to the considered xyz coordinates of protein
atoms (the variables). Extracting the variables that contribute to the
largest motions in protein (variance) over a long timescale (number
of individuals) and spatial scale (number of variables) is a common
task in multivariate statistical analysis. For this purpose, dimension-
ality reduction methods are particularly suited to achieve a reduc-
tion in the number of variables. Among them, the principal
component analysis (PCA) is a linear dimensionality reduction
technique that linearly combines the set of variables into a reduced
number of uncorrelated variables called principal components
(PCs), consisting of five major steps:- Calculation of the covariance matrix: from the atomic coordi-
nate matrix of the trajectory, a variance-covariance matrix is
calculated. - Diagonalization of the covariance matrix: in order to
de-correlate variables, we seek to minimize the covariance
between variables that is the off-diagonal entries of the covari-
ance matrix. Conversely, the diagonal entries, corresponding to
the variance, shall be maximized since they correspond to
interesting dynamics in the system. Note that the variance is a
special case of covariance when the two variables are identical.
Since minimizing the covariance consists in being as close to
zero as possible, we are then looking to diagonalize the covari-
ance matrix. - Extraction of the principal components: the columns of the
transformation matrix, that is the matrix having served to
diagonalize the covariance matrix, are the eigenvectors of the
new basis. These eigenvectors are the principal components of
the PCA space.
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