Questions about umbrella sampling and wham analysis

[Zheng Ruan]

Hi Plumed Users,

I'm trying to perform wham analysis on my 2D umbrella sampling trajectory to extract PMF. However, I had a question about using the wham-2d utility of Grossfield Lab.

My umbrella sampling consists of 59 biased simulations constrained at various CV points using the harmonic function. In the plumed tutorial, I read "An often misunderstood fact about WHAM is that data of the different trajectories can be mixed and it is not necessary to keep track of which restraint was used to produce every single frame." But this is the input for the wham.cpp program in the tutorial (https://plumed.github.io/doc-v2.4/user-doc/html/belfast-4.html). Does that mean I can concatenate all my simulations together to use the wham-2d? Specifically, the documentation for wham-2d requires a meta file that includes the time series data file and the associated CV centers and spring constants. Should the time series data contain the combined CV values of all my umbrella simulations or just the simulation data for the specific simulation constrained under that CV points?

Also, I read some wham equations contains a statistical inefficiency term gi. Right now, I'm using all my MD snapshots for wham calculation. This may cause a non-optimal estimate of the PMF since some of my data points are correlated. I want to know how people overcome this problem. Is there any existing software/programs that I can try?

Thank you!

Ruan

[Giovanni Bussi]

Hi,

About analysis with wham-2d: I think you should check the documentation of that software. WHAM equations do not require you to know where each frame came from. However, a specific analysis tool might be written in a way that separated trajectories should be provided. In the WHAM script we use in the tutorial, a concatenated trajectory is sufficient.

About correlation: my experience is that this is not a problem. WHAM expressions can be derived using a maximum likelihood approach. The derivation is similar to the one you can use to show that the best estimator of the population of one bin for a single replica calculation is given by the fraction of frames falling in the bin. So, my understanding is that correlation time is not a problem. However, I might misinterpret some subtleties and I would be happy to be contradicted.

The real point is how to compute errors. Do not assume frames are independent. Block analysis is more robust. Still, if you don't initialize replicas well also block analysis underestimate the error (see an example here: https://www.ncbi.nlm.nih.gov/pubmed/26051557 , but I am sure you can find others)

Giovanni

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[Zheng Ruan]

Hi Giovanni,

Thank you for the quick reply. I will look into the block analysis for error analysis.

Ruan

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