# Re: Retrieving standard deviation values while using collective variables (ABF)

From: Jerome Henin (jhenin_at_cmm.chem.upenn.edu)
Date: Thu Nov 26 2009 - 09:04:19 CST

Yes, the system force is an instantaneous quantity, it is output as a
function of time. What you say is precisely what makes the error
analysis particularly complex. The data used to compute the estimate
in a given bin is a combination of multiple blocks of data, which were
collected each time the coordinate visited that particular bin. So the
problem it to do a time correlation analysis on a time series that
consists of little contiguous pieces with gaps inbetween (when the
colvar was in other bins).

One possibility is to merge all these little series into one, and
analyze correlations within this large series. In practice, you'd do
that by matching the force trajectory and the colvar trajectory
(that's the info you're missing, from what you wrote), and sorting the
force data depending on what bin the colvar was visiting at the time
it was collected.

Otherwise, you'd have to formulate assumptions on the nature of
correlations. It is tempting to assume that successive visits of the
bin are decorrelated, but that's unlikely to be true.

Yet another approach is to run a separate simulation for the sole
purpose of studying time correlations. In that kind of simulation, the
colvar can be confined to just one bin, so that a single, contiguous
time-series is obtained.

I warned you it was somewhat complex. The truth is, error analysis in
biomolecular free energy calculations is never simple. When it is,
it's wrong.

You should also look at this paper (if you haven't already):

and our 2004 paper, which references it and adds some details.

Best,
Jerome

2009/11/26 Hugh Martin <hughtendo_at_gmail.com>:
> Thanks for the response, yes sorry I was referring the free energy
> derivative.
>
> I produced the system force from a simulation to see if I could reconcile
> the data with the PMF output, but it seems that the outputSystemForce data
> correlates to the timestep rather than to the reaction coordinate (which the
> PMF corresponds to). Thus, given that the nature of ABF/colvar simulations
> means that the position of the pulling atom does not correlate to a
> particular timstep or timestep bin (compared to, say, constant
> velocity-SMD), I can't see a way to use the data to produce useful error
> bars on the free energy derivative output.
>
> I'm just wondering if I'm out of options here, and should maybe look to
> other measures of error/deviation?
>
>
> Many thanks,
>
> Hugh
>
>
> 2009/11/10 Jerome Henin <jhenin_at_cmm.chem.upenn.edu>
>>
>> Hi,
>>
>> If you are talking about the standard deviation for the free energy
>> derivative, it is not available directly. The reason for that is, that
>> quantity is not useful on its own, but only within a somewhat complex
>> error analysis that should include time correlations. Hence, such an
>> analysis requires the time series of the system force (or
>> instantaneous colvar force, or whatever you call it). That quantity
>> will be output if you include the outputSystemForce keyword in your
>> colvar blocks.
>> http://www.ks.uiuc.edu/Research/namd/2.7b1/ug/node48.html
>>
>> Best,
>> Jerome
>>
>>
>> 2009/11/10 Hugh Martin <hughtendo_at_gmail.com>:
>> > Hello,
>> >
>> > I'm using NAMD2.7b1 and the collective variables implementation in order
>> > to
>> > perform ABF simulations. I was wondering if there is a way to output the
>> > standard deviation of each point (bin). I see that there is an option
>> > for
>> > "runAve" which calculates the standard deviation of the running average,
>> > but
>> > I don't see an option for the standard deviation of each point/bin. Is
>> > this
>> > possible?
>> >
>> > Many thanks,
>> >
>> > Hugh
>> >
>
>

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