Using BME with PRE data

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Dear developer,
Thank you for bringing the Bayesian maximum entropy approach to the MD community. I have previously used the BME method with NMR NOE data and found good success. I am now trying to use BME with PRE data.

I have calculated the gamma value per frame from a set of long Gaussian accelerated MD simulations of a IDP bound to a folded protein. We have experimental PRE data for each residue in the IDP from four different PRE probes at different positions on the folded partner. What I am looking for is to use BME to derive weights for the MD ensemble that agree with the experimental PRE.

The potential issue is, the relationship between gamma and PRE intensity ratio is an exponential one where very small values of PRE ratios result from very large values of gamma. Here is the relation between gamma and PRE ratio from the DEERpredict article:

Since the BME weight optimization happens using the gamma values (range of gamma is from 0 - Inf), this seems to be an issue, where very large values of gamma in certain frames may dominate the averages and introduce large errors in the derived weights. One way to address this might be to cap the gamma values at an arbitrary threshold before running the BME optimization, but I was wondering if you have any better ideas.

Thanks in advance. I hope, I could explain the problem sufficiently. If not, feel free to let me know.

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To add to this, I am not sure if the assumption of normally distributed noise, that is used in the BME cost function, would be valid when using gamma values. My guess, probably not.