# Re: [AMBER] Calculate lateral self-diffusion coefficient for POPE embedded protein system

From: Daniel Roe <daniel.r.roe.gmail.com>
Date: Thu, 31 Aug 2017 09:03:18 -0400

Hi,

On Wed, Aug 30, 2017 at 6:51 PM, carmine marco morgillo
<FnTcy.hotmail.it> wrote:
> Averaging the values of column#5 I would get the right hand of the Einstein equation (?).

The average is over particles, not time. The numbers being reported in
the output of 'stfcdiffusion' are averaged over selected atoms each
time step. To understand how to calculate the diffusion constant via
the Einstein relation it may help to think of an alternate
formulation:

2*n*D = lim(t->inf.)[MSD/t]

So what you need to get the diffusion coefficient is MSD vs. time. The
most common way to get this is to calculate the slope of the best-fit
line for MSD vs. time (you can do this in cpptraj with the 'regress'
Analysis command, or use your favorite math package/plotting program).
Then divide by 2*n (where n is the number of dimensions) and multiply
by 10.0 to convert from units of Ang^2/ps to cm^2/s. There is a
discussion of this in the cpptraj section of the Amber manual (28.9.21
diffusion). The calculation of the diffusion constant can be done
automatically by the 'diffusion' command but not yet by
'stfcdiffusion' (I'm working on eventually merging all the
functionality of the two commands).

Note also that diffusion in membrane systems can be a little trickier
to calculate properly, and you need to correct for periodic boundary
conditions and the very anisotropic nature of lipid diffusion. Rich
Pastor et al. have done a lot of interesting work in this area; see
e.g. http://pubs.acs.org/doi/abs/10.1021/acs.jpcb.6b09111 and
references therein.

Hope this helps,

-Dan

```--
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Daniel R. Roe
Laboratory of Computational Biology
National Institutes of Health, NHLBI
5635 Fishers Ln, Rm T900
Rockville MD, 20852
https://www.lobos.nih.gov/lcb
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Received on Thu Aug 31 2017 - 06:30:03 PDT
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