> On Feb 16, 2015, at 7:25 AM, Aditya Sarkar <aditya.molbio.gmail.com> wrote:
>
> Hi Jason,
>
> Thank you very much for your reply.
>
> What I understand from your answer is that the pressure can fluctuate from -1000 to 1000 bar and hence the average can not be always 1bar.
No, the average *will* be 1 bar (if your barostat is set to 1 bar, that is)... IF you run for an infinite length of time. What I’m saying is that since you are NOT simulating for an infinite length of time, your sample mean might not be equal to the “true” mean. The standard error of the mean (basically the standard deviation of your pressure distribution divided by the square root of the number of “independent” samples) will tell you the uncertainty of your sample mean compared to whatever the *true* mean is.
> As you suggested to look for standard error of mean pressure, i have note down the average pressure and their RMS fluctuation and these are:
RMS fluctuations are the wrong metric. You want to look at the standard deviation (or variance), which gives you the natural “spread” of your pressure distributions. The standard error of the mean will give you the “error bars” on your average pressure calculation.
>
> restart mean pressure RMS fluctuation
> ---------------------------------------------------------------------
> prodrun1 0.7 111.3
> prodrun2 -8.2 116.1
> ............
> prodrun36 11.5 108.5
>
> Do you want to say that the max and min of each mean value are actually within the range and hence the means does not differ significantly?
If your standard error of the mean is 50 bar, and your average pressure is 10 bar, then your 68% confidence interval that the *true* mean of the “correct” distribution is that the mean pressure is anywhere between -40 -- 60 bar. A 95% confidence interval requires you to go out 2 standard errors (or -90 -- 110 bar). See
http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule <
http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule> for example (keep in mind that you are looking at the distributions of sample means, not the actual pressure distribution, whose shape does not change with more data).
> If this is true that the pressure fluctuates so largely then why we use baostat at 1bar and use the constant pressure term (I am bit confused)???
You are getting “internal” pressure confused with “external” pressure. It is a common misconception, and occurs with thermostats as well. What the barostat or thermostat holds constant is the *external* pressure or heat bath that is coupled to your system (providing force against expansion or a reservoir to absorb or deposit excess heat energy). The measurements that sander and pmemd report are the instantaneous *internal* pressures and temperatures, which fluctuate normally over time. However, since they are coupled to the constant external thermodynamic controls, their *average* values will equal those.
So you set the barostat to 1 bar, because then you are exerting the force of 1 bar of (atmospheric) pressure on your system. Just like you use a thermostat to supply or absorb heat to maintain a constant *average* temperature inside the system.
Now water has a very (very) tiny isothermal compressibility, which means that you need *huge* pressure changes to trigger very small changes in volume (here is the equation for isothermal compressibility --
http://alcheme.tamu.edu/?page_id=755 <
http://alcheme.tamu.edu/?page_id=755> -- and you can look up the value for water in standard reference texts like the CRC). So setting the external pressure to 10 bar will have no measurable effect on the average volume (and therefore density) of your simulation (assuming a somewhat reasonable water model). But there is no reason *not* to use the experimental external pressure, which is why everybody uses 1 bar instead of 10.
> And one more silly request, can you suggest me books from which I can get these details regarding the MD simulation.
There are lots of good texts, each good for a different audience. I like the Allen and Tildesley (1984) book, but that is more of a technical text. The Leach book (
http://www.amazon.com/Molecular-Modelling-Principles-Applications-2nd/dp/0582382106/ref=sr_1_1?s=books&ie=UTF8&qid=1424092603&sr=1-1&keywords=andrew+leach+in+books <
http://www.amazon.com/Molecular-Modelling-Principles-Applications-2nd/dp/0582382106/ref=sr_1_1?s=books&ie=UTF8&qid=1424092603&sr=1-1&keywords=andrew+leach+in+books>) is also good, and may be more appropriate for a less technical audience.
However, what I discussed here isn’t actually specific to molecular simulation. It is standard thermodynamics and statistical thermodynamics, of which a good understanding is essential for making sense of these kinds of questions. Another good textbook that talks about the statistical mechanics of molecular simulation is the Tuckerman book (
http://www.amazon.com/Statistical-Mechanics-Molecular-Simulation-Graduate/dp/0198525265/ref=sr_1_1?s=books&ie=UTF8&qid=1424092726&sr=1-1&keywords=mark+tuckerman+in+books <
http://www.amazon.com/Statistical-Mechanics-Molecular-Simulation-Graduate/dp/0198525265/ref=sr_1_1?s=books&ie=UTF8&qid=1424092726&sr=1-1&keywords=mark+tuckerman+in+books>). I also like the MacQuarrie book(s), but Tuckerman’s focuses more on molecular simulation, which might help.
Hope this helps,
Jason
--
Jason M. Swails
BioMaPS,
Rutgers University
Postdoctoral Researcher
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Received on Mon Feb 16 2015 - 05:30:03 PST
