[gmx-users] umbrella sampling

[chris.neale at utoronto.ca]

I've never actually reweighted with F-values. These are the values by  
which the component PMFs are shifted during WHAM after debiasing the  
umbrella potentials.

Look at equations 6 and 7 in "The multicanonical weighted histogram  
analysis method for the free-energy landscape along structural  
transition paths" Satoshi Ono, Nobuyuki Nakajima, Junichi Higo and  
Haruki Nakamura

My best guess is that you do it like this:

1. Run 1-D wham and obtain the F-values.

2. create an empty 3D histogram structure for z, rgyrA, and rgyrB.

3. Go through the data from each window and add a value to the  
appropriate location for [z,rgyrA,rgyrB]. This value is not the  
integer count 1. This value that you add to each histogram bin is a  
real number:

   1 * exp(-(1/RT)*-F) * exp(-(1/RT)*0.5K*(z-z0)^2

4. Now convert your histogram of probabilities to free energies dG=-RTln(P)

** To test this, project your 3-D free energy profile onto each  
dimension successively and compare it to (z) the profile from 1-D  
wham, and (rgyrA or rgyrB) the profile from 2-D wham with zero force  
constants as I outlined in my previous post.

PLEASE NOTE: this email outlines an *idea* of how to accomplish what  
you want. You must check the match for yourself.

Chris.

Qian Wang qwang at mail.uh.edu
Sat Jul 30 18:05:33 CEST 2011

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Thanks very much.
I am sorry I did not describe my question very clear. In my system, I  
am going to obtain three things. (1) the free energy versus distance,  
which I can obtain from g_wham. (2) the free energy versus, eg, the  
radius of gyration of the object A. (3) the 2-D free energy as a  
function of the radius of gyration of A and the radius of gyration of  
B. I do not know how to get (2) and (3).
Your first method can help me obtain (2), but I can not obtain (3)  
because then it needs a 3-D WHAM code, am I correct? For your second  
method, I do not quite understand how to re-weighting using the  
F-values from 1D-WHAM. Could you please explain it? Thanks.

Sincerely,
Qian

----- Original Message -----
From: chris.neale at utoronto.ca
Date: Friday, July 29, 2011 11:00 pm
Subject: [gmx-users] umbrella sampling
To: gmx-users at gromacs.org

> format your data for 2D-WHAM with 1D being the distance and the  
> 2nd-D being your other coordinate of interest. Specify a value of  
> zero for the force constants for your 2nd-D. Run 2D-WHAM. Boltzmann  
> project the 2D PMF onto your 2nd-D.
>
> I think you can also do essentially the same thing by re-
> weighting using the F-values from 1D-WHAM, but I find the above  
> method to be the simplest. It also provides you with a 2D free  
> energy profile, which can be informative both biologically and to  
> indicate on sampling problems.
>
> Note that you're very likely going to run into convergence problems  
> since your 2nd-D will rely on brute-force to converge, and worse:  
> the umbrellas in 1D can force the sampling in the 2nd-
> D to surmount energy barriers that might be circumvented in  
> unrestrained sampling.
>
> Chris.
>
> -- original message --
>
> Qian Wang wrote: