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

[Ricardo Cuya Guizado]

PCA depend of the number of frames?
Dear users  I did a test with three sets of frames
(1) 13 frames  From X-ray(2) 28 frames  From X-ray(3) 1000 frames From MD
In each case translations and rotations were eliminated.then g_covar was applied to obtain the covariance matrix
 g_covar -f sample.xtc -s representative.tpr -o eig_sample.xvg -xpm covar_sample.xpm 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.
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 smoothI 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?
A plot with the eigenvalues and cumulative number is available in this limk.
http://www.4shared.com/file/c4sQQd9U/cumulative.html?
In the plot Cluster (1) is case (1)            Cluster (2) is case (2)                X1          is case (3)
Sincerely yours
Ricardo

caso (1)
@    title "Eigenvalues of the covariance matrix"@    xaxis  label "Eigenvector index"@    yaxis  label "(nm\S2\N)"@TYPE xy         1 3.21824         2 1.59207         3 0.7186         4 0.603902         5 0.555743         6 0.479754         7 0.412325         8 0.345979         9 0.282516        10 0.269861        11 0.260193        12 0.209889        13 1.96752e-15   *IN THIS INDEX THE EIGENVALUES IS CLOSE TO ZEROM COINCIDENT WITH THE NUMBER OF FRAMES        14 1.62777e-15        15 1.5654e-15        16 1.3087e-15        17 9.35402e-16        18 9.04299e-16        19 6.71342e-16        20 6.64882e-16


caso (2) Obtained from X-ray
@    title "Eigenvalues of the covariance matrix"@    xaxis  label "Eigenvector index"@    yaxis  label "(nm\S2\N)"@TYPE xy         1 0.283967         2 0.0952257         3 0.0743586         4 0.0598192         5 0.0450539         6 0.0410722         7 0.0301708         8 0.0262085         9 0.0240471        10 0.0175948        11 0.0147602        12 0.0140895        13 0.011544        14 0.0107718        15 0.00884784        16 0.00851068        17 0.00748592        18 0.00662536        19 0.00645983        20 0.00609032        21 0.00516941        22 0.00404203        23 0.00373644        24 0.00336767        25 0.00299449        26 0.00227847        27 0.00156805        28 -3.86967e-05  *IN THIS INDEX THE EIGENVALUES IS CLOSE TO ZEROM COINCIDENT WITH THE NUMBER OF FRAMES        29 1.04056e-07        30 -2.72851e-08	caso (3)

@    title "Eigenvalues of the covariance matrix"@    xaxis  label "Eigenvector index"@    yaxis  label "(nm\S2\N)"@TYPE xy         1 3.03786         2 1.27271         3 0.53899         4 0.423554         5 0.27003         6 0.260328         7 0.220423         8 0.191197         9 0.168856        10 0.152404        11 0.128236        12 0.126204        13 0.110368        14 0.092775        15 0.0885705        16 0.0750595        17 0.0696554        18 0.0627624        19 0.0532074        20 0.0513393        21 0.0474214        22 0.0463299        23 0.0432387        24 0.0403574        25 0.0392867        26 0.0352699        27 0.0333476        28 0.0319553        29 0.0308987        30 0.0306235        31 0.027971        32 0.0268982        33 0.0258224        34 0.0249171        35 0.0234315        36 0.0221298        37 0.0217099        38 0.0202486        39 0.0196283        40 0.0191729        41 0.018719        42 0.0185378        43 0.0176382        44 0.0174487        45 0.0165635        46 0.0161611        47 0.015876        48 0.0155579        49 0.0147515        50 0.0139361...


 		 	   		  
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