Variance-covariance and cross-correlation analysis

carma again :

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

and for cross-correlations :

carma -v -cov -dot -norm -write CA.psf CA.dcd
gv CA.dcd.varcov.ps

giving something like :

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), 44 and depicts a correlation matrix derived from an NMR ensemble for the B1 domain of protein G :

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 :

#
# 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
#

giving something like :

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 :

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 :

Using this sigmoidal weighting has been incorporated to carma. Just use a '-sigm λ' flag in the spirit of :

carma -v -cov -dot -norm -sigm 5.5 -write CAs.dcd CAs.psf

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

#
# 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
#

Giving :

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