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2024-04-23
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2024-04-22
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 : <gnuplot> plot [-1.0:1.0] 2/(1+exp(-5.5*x))-1; </gnuplot> [[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]]
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