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On 26/09/2011 10:54 PM, Ricardo Cuya Guizado wrote:
<blockquote cite="mid:COL117-W2008977BD0FA47407B8FAD4F30@phx.gbl"
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Thanks Tsjerk
<div><br>
</div>
<div>About my question...</div>
<div>
<div>>> PCA depend of the number of frames?</div>
<div><br>
</div>
<div>and your answer:</div>
<div><br>
</div>
<div>>Yes, it does. This has, in fact, been pointed out in
the early papers</div>
<div>on PCA in MD</div>
</div>
<div><br>
</div>
<div>Please, Would you give me some references,</div>
</div>
</blockquote>
<br>
See manual section 8.10 and references, or the references in the
literature of work similar to that which you intend to do...<br>
<br>
Mark<br>
<blockquote cite="mid:COL117-W2008977BD0FA47407B8FAD4F30@phx.gbl"
type="cite">
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<div><br>
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<div><br>
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<div>Ricardo</div>
<div><br>
</div>
<div><br>
<div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px; ">Hi
Ricardo</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
For the case (1) and (2) the most representative
structure was used in the</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
option -s ( One that has the lowest rmsd with respect
to the average of each</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
cluster).</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
In case (3) the initial structure of the MD was used
in the option -s.</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">If
all belong to the same system, it is better to use one
reference</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">structure,
to define the conformational space in the same way,</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">allowing
direct comparison.</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
When I look the eigenvalues for the case (1) and (2),
I found that the</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
eigenvalue is zero only after index="number of frames"
(see below)</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
In the case (3) the distribution is smooth</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
I could expect a similar distribution for the case (1)
and (2), because the</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
frames are representative of the dymanics of the
protein.</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
Why this difference?</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">>
PCA depend of the number of frames?</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">Yes,
it does. This has, in fact, been pointed out in the
early papers</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">on
PCA in MD. I think it's best to read up more about
PCA, including</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">some
introductory material from statistics. One thing I'll
give away</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">though...
;) Consider the motion of a particle in three
dimensions. If</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">you
have two frames, you can say something about motion
along a line.</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">You
need two frames to say something about motion in a
plane, and you</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">need
at least three points to say something about motion in
all three</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">dimensions.
Now in your case, each conformation is one point and
the</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">conformational
space in which the point moves has 3N dimensions. If</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">you
have two points, you can only say something about
motion along a</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">line,
i.e., you have one component with nonzero eigenvector.
With</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">three
points (conformations), you can obtain two
eigenvectors, which</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">span
a plane, etc.</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">Hope
it helps,</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">Tsjerk</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">-- </span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">Tsjerk
A. Wassenaar, Ph.D.</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;"><br>
</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">post-doctoral
researcher</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">Molecular
Dynamics Group</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">*
Groningen Institute for Biomolecular Research and
Biotechnology</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">*
Zernike Institute for Advanced Materials</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">University
of Groningen</span></font></div>
<div><font class="Apple-style-span" face="Tahoma"><span
class="Apple-style-span" style="font-size: 13px;">The
Netherlands</span></font></div>
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