MBG wiki: Editing Variance-covariance and cross-correlation analysis

/carma/ again :

<code>
carma -v -cov -write CA.psf CA.dcd
gv CA.dcd.varcov.ps
carma -v -cov -dot -write CA.psf CA.dcd
gv CA.dcd.varcov.ps
</code>

and for cross-correlations :

<code>
carma -v -cov -dot -norm -write CA.psf CA.dcd
gv CA.dcd.varcov.ps
</code>

giving something like :

[[image: cross-correlation image]]

Variance-covariance and correlation images do benefit from the inclusion of colour. The reason, of course, is that you can use the hue to differentiate between correlated and anti-correlated motions. For example, the image below is from Fig.1 of Lange, Grubmuller & de Groot, /Angew. Chem. Int. Ed./ (2005), <b>44</b> and depicts a correlation matrix derived from an NMR ensemble for the B1 domain of protein G :

[[image: Protein G, NMR correlation matrix]]

You can produce such a figure from the raw data produced by /carma/ using programs with /gnuplot/ or /kuplot/. For example, using /gnuplot/ it will be something like :

<code>
#
# carma -v -cov -dot -norm -write CAs.dcd CAs.psf
# cat > script

set pm3d
set view 0,0
set size square 3.0,3.0
unset key
set output 'coloured.png'
set terminal png large crop
set palette defined ( 0 "blue", 1 "cyan", 2 "green", 3 "yellow", 4 "red" )
splot [0:55] [0:55] "CAs.dcd.varcov.dat" matrix with pm3d palette

<CTRL-D>
#
# gnuplot < script
# display coloured.png
#
</code>

giving something like :

[[image: variance covariance color map from carma and gnuplot]]

If you want to artificially increase the contrast of the image, there is the standard way of multiplying the correlation coefficients with the sigmoidal function :
\[
W(x) = \frac{2}{1+\exp(-\lambda x)}-1
\]

where λ is an adjustable parameter determining the contrast. The following plots of W(x) and of a map calculated with different values for λ may shed some light :

[[image: covariance maps calculated with different lambda values]]

Using this sigmoidal weighting has been incorporated to /carma/. Just use a '-sigm λ' flag in the spirit of :
<code>
carma -v -cov -dot -norm -sigm 5.5 -write CAs.dcd CAs.psf
</code>

Needless to say that there are numerous /gnuplot/ options that you can play with. For example :

<code>
#
# cat > script

set pm3d
set view 0,0
set size square 3.0,3.0
unset key
set output 'coloured.png'
set terminal png giant crop
set dgrid3d 112,112,8
splot [0:55] [0:55] "CAs.dcd.varcov.dat" matrix with pm3d palette

<CTRL-D>
#
# gnuplot < script
# display coloured.png
#
</code>

Giving :

[[image: variance covariance color map from carma and gnuplot sigmoidal weights 2]]

If you feel that these graphs are boring, you can always do much better with /dx/ :

[[image: variance covariance color map from carma and dx]]

Summary:

This change is a minor edit.

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