# [gmx-users] Dynamics cross correlation map

Tsjerk Wassenaar tsjerkw at gmail.com
Wed Mar 24 10:37:53 CET 2010

```Hi Sukesh,

Great. This makes things much clearer. So basically what you'd need to
do is to divide each i,j-th element of the covariance matrix you
obtained (covar.dat) by the sqrt of the  ii-th and jj-th diagonal
element. That will commonly turn a covariance matrix into a
correlation matrix. But, that also happens to be what the modified
version of g_covar provided by Ran does. I think it's still on the
contributions page.

Just one more thing, the generalized correlation of Lange and
Grubmueller is a bit of a different thing. Might also be handy though.
In stead of calculating the correlation as the normalized product
moment, they have a similarity parameter that measures how close the
actual distribution of measurements is to the one you'd get if the
measurements were uncorrelated (mutually independent). This
compensates for non-linear relationships between variables.

Cheers,

Tsjerk

On Wed, Mar 24, 2010 at 7:16 AM, sukesh chandra gain <sukesh at atc.tcs.com> wrote:
> 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.
> Phone:  +91 40 6667 3572
>
> --
> gmx-users mailing list    gmx-users at gromacs.org
> http://lists.gromacs.org/mailman/listinfo/gmx-users
> Please search the archive at http://www.gromacs.org/search before posting!
> Please don't post (un)subscribe requests to the list. Use the www interface
> or send it to gmx-users-request at gromacs.org.
>

--
Tsjerk A. Wassenaar, Ph.D.

post-doctoral researcher
Molecular Dynamics Group
Groningen Institute for Biomolecular Research and Biotechnology
University of Groningen
The Netherlands

```