[gmx-users] Generating Structures from Covariance Matrix Eigenvectors

Robert Johnson bobjohnson1981 at gmail.com
Thu Feb 1 01:08:44 CET 2007

Hello everyone,
I'm new to Principle Components Analysis, so correct me if I'm wrong.
If you have a collection of protein structures from a replica exchange
calculation, for example, I believe you can reconstruct each of them
from its average structure by the following:

r(t) = <r> + p_1(t) v_1 + p2(t) v_2 + p_3(t) v_3 + ... + p_N(t) v_N

Here, r(t) is the protein configuration at time t, <r> is the average
structure, p_i(t) are the projections of the structure at time t on
the i-th eigenvector and v_i is the i-th eigenvector of the covariance
matrix. Of course, to capture the large scale motion, one would be
interested in only the first or second projections. For example, it
would be of interest to compute

r(t) = <r> + x v_1

Here, the value of x could be varied to observe the motion of the
protein along v_1.

I'm wondering if there is a feature in g_anaeig (or another program)
that does this? I didn't find this option, but thought I would ask to
make sure.

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