[gmx-users] Generating Structures from Covariance Matrix Eigenvectors
David van der Spoel
spoel at xray.bmc.uu.se
Thu Feb 1 08:20:01 CET 2007
Robert Johnson wrote:
> 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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David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596, 75124 Uppsala, Sweden
phone: 46 18 471 4205 fax: 46 18 511 755
spoel at xray.bmc.uu.se spoel at gromacs.org http://folding.bmc.uu.se
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