[gmx-developers] Energy and Foreign Lambdas and Hamiltonian Replica Exchange

[Berk Hess]

Matt Wyczalkowski wrote:

>
>>> I would say this is very easy, less than a day. But maybe I am 
>>> overly optimistic,
>>> since I know the code. This involves no real changes to the code, 
>>> since you just
>>> do the acceptance based on the same potential energy of normal REMD.
>>> There are only some checks that need to be changed.
>>>
>>> But I don't see for what kind of systems such a RE would help.
>>> Or is this not for free energy differences and do you want to use 
>>> lambda
>>> to lower barriers?
>>>
>> IIRC this requires evaluating the energy at a different lambda than 
>> the one assigned to the processor(s). Maybe someone can post the 
>> exchange probability criterion.
>>
>> It is all about sampling of course, and this kind of approach is also 
>> used in constant pH MD (with implicit solvent) and in Van Gunsterens 
>> switching between coarse grained and atomistic MD. A more general 
>> setup for all these REMD variants would be useful therefore. One 
>> could also envision REMD in two dimensions (e.g. T and lambda).
>
> The exchange probability for a Hamiltonian Replica Exchange swap 
> between systems a and b is,
>
> P_swap = min[1,exp(-beta dU)]
>
> where
>
> dU = U(l_a,X_b) + U(l_b,X_a) - U(l_a,X_a) - U(l_b,X_b)
>
> is the total energy change of the two systems combined due to the 
> swap; U is the potential of configuration X parameterized by lambda 
> (l).  Clearly, it is necessary to evaluate the energy of a given 
> system at a different ('foreign') lambda -- this is the same 
> requirement as was discussed with respect to the Bennett Acceptance 
> Ratio and Free Energy Perturbation.
>
> I have implemented this in another piece of software before 
> (http://towhee.sourceforge.net) and so have a reasonable idea of what 
> it will involve, but I am just now starting to look at Gromacs code.  
> Once I get a feel for what is involved, and if it doesn't seem overly 
> daunting, I will have more specific questions.  For the time being, 
> however, I am wondering if I should be focusing my attention on the 
> 3.2.2 or the CVS HEAD versions of the codebase?
>
There is nearly no difference between the two as far as the replica 
stuff is concerned.
It will be more work to (correctly) extract the foreign lambda energy 
than it is to modify
the actual exchange criterion. Erik did some work on foreign lambda 
calculations,
but I don't know what the status of that is.

I guess the head branch would be the better option, especially if you 
want to run
each replica over multiple cpu's.

Berk.