[gmx-users] Re: Cross-correlation maps

[Mark Abraham]

On 28/08/2012 3:09 PM, James Starlight wrote:
> Hi Tsjerk!
>
> Normally during analysis of the MD trajectory I've observed frequent
> side-chain fluctuations (ps timescale) cased by the temperature motion
> of the atoms as well as larger-scale backbone motions ( on the ns
> time).
>
> The ps  side-chains motions are known to especially increase total
> enthropy of the system in comparison to the backbone dynamics where
> such factor is less meaningful. Also there is suggestion that such
> enthropy-dominated motions could be functional-relevant due to
> possible coperativity of that process ( e.g fluctuations in one side
> of protein case increase dynamics in another part of such molecule
> without visible pathways between both parts )

So you're looking for correlated motion of atoms distant in space. That 
will appear as off-diagonal entries in the correlation matrix. Think 
about what sort of correlation matrices and eigenstructure you would 
expect for a system of a small number of SHM oscillators under different 
sorts of correlation conditions. Then worry about proteins.

> The main goal of my study to find out such coperativity in some
> proteins. So I want to detect such coperativity in fluctuations of the
> side-chains. As I've found the only way to do it is the calculation of
> the cross-correlation maps.

Cross-correlation is an analysis distinct from looking at off-diagonal 
(a.k.a. "cross") elements of a correlation matrix.

>   When I've performed PCA of my 100ns
> trajectory and examined filtered.xtc trajectory consisted of first 50
> principal components) I didt observed any fluctuations of the
> side-chains ( only backbone motions were presented) So I could
> calculate only correlations in the backbone atoms motions. Is there
> any way to observe such cross-correlations for side chains as well ?

Did you construct a correlation matrix from side chain atoms?

Mark

>
> James
>
> 2012/8/27, Tsjerk Wassenaar <tsjerkw at gmail.com>:
>> Hi James,
>>
>> Correlation is covariance normalized to variance. So you'll need the
>> covariance matrix anyway. But what exactly due you mean with the loss of
>> information, which you could solve with correlations?
>>
>> Cheers,
>>
>> Tsjerk
>>
>> On Aug 27, 2012 4:01 PM, "James Starlight" <jmsstarlight at gmail.com> wrote:
>>
>> Mark,
>>
>> Is there any way to calculate such cross-correlations without
>> calculation of the covariance matrix ( from the MD trajectory
>> indirectly) ?
>> I've noticed that after processind of my trajectory with PCA method
>> some dynamics ( e.g fluctuations of the side-chains) are lost even
>> when I've analysed filtered.xtc from the first 50 principal
>> components. How I should analyse possible cross-correlations of the
>> fluctuations of the side-chains?
>>
>> James
>>
>> 2012/8/27 Mark Abraham <Mark.Abraham at anu.edu.au>:
>>
>>> On 24/08/2012 4:51 PM, James Starlight wrote: >> >> up :) >> It's
>> appeared two additional question...
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