**From:** Rudy Richardson (*rjrich_at_umich.edu*)

**Date:** Thu Sep 22 2022 - 16:36:11 CDT

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Hi Kelly,

I agree with Josh. One approach for dealing with autocorrelation in

time series data such as MD trajectories is to use block averaging:

Flyvbjerg, H., and Petersen, H.G. (1989). Error estimates on averages

of correlated data. J. Chem. Phys. 91, 461-466. doi: 10.1063/1.457480.

There are functions for this in R:

Huais, P.Y. (2022). R-function: block_average.

https://urldefense.com/v3/__https://github.com/phuais/block_average__;!!DZ3fjg!-9yWk-1p1Kcp_qjgiQLaiOtdLDFSbdV6qQyH3JrSZnVBAXivXdtd5ZV0N_cXoghOMaivBkV_OWLfaNo9ylA$

and I think in Python and Matlab as well. A plot of SEM vs block size

fits an exponential function with a plateau -- the plateau value gives

the optimal block size. In a recent MD simulation that I did, I found

that I needed a rather large block size of 10 to 20 ns, depending on

the parameter being assessed.

Best regards,

Rudy

Rudy J. Richardson, ScD, DABT

Molecular Simulations Laboratory

Room M6065 SPH-II 2029

University of Michigan

1415 Washington Heights

Ann Arbor, MI 48109-2029 USA

Email: rjrich_at_umich.edu

On Thu, Sep 22, 2022 at 5:00 PM Mcguire, Kelly <klmcguire_at_ucsd.edu> wrote:

*>
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*> Thanks for the response. I am using a 10 ps decorrelation time which was recommended in a couple of publications. I could bump that up.
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*>
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*> Sent via the Samsung Galaxy S22 5G, an AT&T 5G smartphone
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*> ________________________________
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*> From: Josh Vermaas <vermaasj_at_msu.edu>
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*> Sent: Thursday, September 22, 2022 1:15:36 PM
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*> To: namd-l_at_ks.uiuc.edu <namd-l_at_ks.uiuc.edu>; Mcguire, Kelly <klmcguire_at_UCSD.EDU>
*

*> Subject: Re: namd-l: MMPBSA Question
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*>
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*> Hi Kelly,
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*>
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*> Would you expect your standard deviation to go down with more frames/data points? The standard deviation measures in some general sense how far away a typical measurement is away from the mean of a measurement. If you took 1000 samples from a gaussian distribution, the standard deviation would be basically the same as if you took 1,000,000 samples. The standard error of the mean does decrease with increasing number of samples.
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*>
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*> The better question I think is how many actually independent samples you have in your 5000 DCD frames. CaFE is assuming something like a ~100ps decorrelation time between frames. Is that enough? No idea, but technically you want independent samples when calculating a standard error.
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*>
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*> -Josh
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*>
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*> On 9/22/22 1:56 PM, Mcguire, Kelly wrote:
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*>
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*> Question about standard deviations with MMPBSA. Should I use millions of snapshots for better standard deviations. I ran a 10 nanosecond simulation of my protein-peptide complex (2 fs timesteps, saved to dcd every 1000 steps). That would be 5,000 frames total in the DCD. I used CaFE and NAMD to get my MMPBSA result (single trajectory method). For CaFE I used stride 5 for the trajectory so that I would use a frame every 10 ps, thus a total of 1,000 frames for the MMPBSA calculation. My result is in the attached file. I get -29.3 kcal/mol with a standard deviation of 11.5. That's a large standard deviation. But, my standard error seems decent (11.5/sqrt(1,000) = 0.37), which appears to be what others report for these calculations instead of the standard deviation. So is this a good result for a single trajectory only using 1,000 frames for the calculation, or do I really still need to use millions of frames? Thanks!
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*>
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*>
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*>
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*>
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*> Dr. Kelly McGuire
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*> Herzik Lab - Postdoc
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*> Chemistry/Biochemistry Department
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*> Natural Science Building, 4104A, 4106A, 4017
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*>
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*>
*

*> --
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*> Josh Vermaas
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*>
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*> vermaasj_at_msu.edu
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*> Assistant Professor, Plant Research Laboratory and Biochemistry and Molecular Biology
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*> Michigan State University
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*> vermaaslab.github.io
*

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