# [gmx-users] Dynamics cross correlation map

sukesh chandra gain sukesh at atc.tcs.com
Wed Mar 24 07:16:42 CET 2010

```Hi Tsjerk,

Thank you for your reply. May be I was not very clear with my previous post.
I am not looking for covariance / atomic covariances map (ie.,
covar.xpm/covara.xpm) which are generated by g_covar tool in GROMACS. I
am particularly trying to get correlation map (example:
http://www.pnas.org/content/102/4/994/F2.large.jpg,
http://www.pnas.org/content/99/26/16597/F3.small.gif). I hope there is a
difference between covariance matrix and correlation matrix.
The correlated motions between two atoms is calculated as the magnitude
of the co-relation coefficient between the atoms.  In case of a system
it can be assessed by examining the magnitude of all pairwise
cross-correlation coefficients. The cross-correlation coefficient,
C(i,j) for each pair of atoms i and j is calculated as:
C(i,j) = < delta r(i) * delta r(j) > / sqrt < sqr(delta r(i) ) > . sqrt
< sqr(delta r(j) ) > , where delta r(i) is the displacement from mean
position of the ith atom and < > symbol represents the time average.
This function returns a matrix of all atom-wise cross-correlations whose
elements, C(i,j), may be displayed in a graphical representation
frequently termed a dynamical cross-correlation map, or DCCM. If C(i,j)
= 1 the fluctuations of atoms i and j are completely correlated, if
C(i,j) = -1 the fluctuations of atoms i and j are completely
anticorrelated and if C(i,j) = 0 the fluctuations of i and j are not
correlated.
Now my query is there any tool like g_correlation
by which I can get the cross-correlation matrix from covariance matrix
or directly from trajectory file.

Ref:1. Hünenberger PH, Mark AE, van Gunsteren WF; Fluctuation and
cross-correlation analysis of protein motions observed in nanosecond
molecular dynamics simulations; JMB 1995; 252:492-503
2. Oliver F. Lange, H. Grubmüller; Generalized Correlation for
Biomolecular Dynamics; Proteins  2006; 62:1053-1061

Thank You,
Regards,
Sukesh

--
Sukesh Chandra Gain
TCS Innovation Labs
Tata Consultancy Services Ltd.