# [gmx-users] Re: PCA depends of the number of frames?

Ricardo Cuya Guizado rcuyag at hotmail.com
Mon Sep 26 14:54:28 CEST 2011

```Thanks Tsjerk
About my question...>> PCA depend of the number of frames?
>Yes, it does. This has, in fact, been pointed out in the early paperson PCA in MD
Please, Would you give me some references,

Ricardo

Hi Ricardo
> For the case (1) and (2) the most representative structure was used in the> option -s ( One that has the lowest rmsd with respect to the average of each> cluster).> In case (3) the initial structure of the MD was used in the option -s.
If all belong to the same system, it is better to use one referencestructure, to define the conformational space in the same way,allowing direct comparison.
> When I look the eigenvalues for the case (1) and (2), I found that the> eigenvalue is zero only after index="number of frames" (see below)> In the case (3) the distribution is smooth> I could expect a similar distribution for the case (1) and (2), because the> frames are representative of the dymanics of the protein.> Why this difference?> PCA depend of the number of frames?
Yes, it does. This has, in fact, been pointed out in the early paperson PCA in MD. I think it's best to read up more about PCA, includingsome introductory material from statistics. One thing I'll give awaythough... ;) Consider the motion of a particle in three dimensions. Ifyou have two frames, you can say something about motion along a line.You need two frames to say something about motion in a plane, and youneed at least three points to say something about motion in all threedimensions. Now in your case, each conformation is one point and theconformational space in which the point moves has 3N dimensions. Ifyou have two points, you can only say something about motion along aline, i.e., you have one component with nonzero eigenvector. Withthree points (conformations), you can obtain two eigenvectors, whichspan a plane, etc.
Hope it helps,
Tsjerk
-- Tsjerk A. Wassenaar, Ph.D.
post-doctoral researcherMolecular Dynamics Group* Groningen Institute for Biomolecular Research and Biotechnology* Zernike Institute for Advanced MaterialsUniversity of GroningenThe Netherlands
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