# Re: [AMBER] autocorr of hydrogen bonds

From: Tom Kurtzman <simpleliquid.gmail.com>
Date: Tue, 30 Aug 2016 11:07:36 -0400

Hi Roman, in response to your comment "In my opinion this is not possible
since the track is made of 0 and 1, so the autocorrelation cannot be < 0."

Often correlation functions (including autocorrelation functions) are
normalized so that their initial values are 1 and absence of correlation is
zero so instead of calculating

<A(t)A(t')> they actually calculate This is the same as calculating
<[A(t) -<A>][A(t')-<A>]> = <A(t)A(t')> - <A>^2. This allows for negative
numbers and ensures that the limit as t --> \infty is zero. Often the
function is then divided by its initial value to give an initial value
(upper bound) value of unity.

For the no-covariance calculation, I assume that the average values are not
subtracted and hence the limit and infinite time approaches <A>^2 which is
positive.

It is not unusual for autocorrelation functions to have negative values nor
to have long time non-zero tails (the velocity autocorrelation function is
a famous example of both of these) however, I'm not sure whether the long
time tail you are seeing is

1) real
2) fluctuations about zero due to sampling limitations (noise)
3) an artifact of an incorrectly calculated quantity.

Without seeing the data, I would initially suspect it's just noise.

Tom

On Mon, Aug 29, 2016 at 9:05 AM, Osman, Roman <roman.osman.mssm.edu> wrote:

> Hello Amberites,
>
> I was wondering whether anybody has used an autocorrelation of hydrogen
> bonds.
> Here is a cpptraj input that I ran:
>
> # Read in trajectory
>
> trajin mcmrjp_free_nw.dcd
>
> hbond HB out mcmrjp_free_hb.dat :17,252,67,206,159,272,27,32,
> 228,245,262,267,165
> ,183,34,138,239,290,39,143,207,204,162 series uuseries mcmrjp_free_hb.dat
> avgout
> mcmrjp_free_avg.dat printatomnum
> run
> runanalysis lifetime HB[solutehb] out mcmrjp_free_lifet.dat
> autocorr HB[solutehb] out mcmrjp_free_auc.dat lagmax 14500
> run
>
>
> The surprising thing is that I get in the aucorrelation function negative
> numbers towards the end of the track.
> In my opinion this is not possible since the track is made of 0 and 1, so
> the autocorrelation cannot be < 0.
>
> In fact if I run with
> autocorr HB[solutehb] out mcmrjp_free_auc.dat lagmax 14500 nocovar
>
> The autocorrelations become positive.
>
> Am I doing something wrong?
>
> Thanks for your help.
>
> PS: I can provide the trajectory (large) and the output from the
> autocorrelation.
>
> Roman Osman
> Professor of Structural and Chemical Biology
> Mount Sinai School of Medicine
> New York, NY 10029
> (212) 659-8627
> roman.osman.mssm.edu<mailto:roman.osman.mssm.edu>
>
>
> _______________________________________________
> AMBER mailing list
> AMBER.ambermd.org
> http://lists.ambermd.org/mailman/listinfo/amber
>

--
************************************************
Tom Kurtzman, Ph.D.
Assistant Professor
Department of Chemistry
Lehman College, CUNY
250 Bedford Park Blvd. West
Bronx, New York 10468
718-960-8832
http://www.lehman.edu/faculty/tkurtzman/
<http://www.lehman.edu/faculty/tkurtzman/index.html>
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Received on Tue Aug 30 2016 - 09:30:03 PDT
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