# [gmx-users] number of lambda values

David Mobley dmobley at gmail.com
Mon Jun 5 19:10:03 CEST 2006

```Soren,

>  Given a certain amount of time and computer power available, is it better
> in general to do short simulations for many lambda values or to do long
> simulations for fewer lambda values?

This is a really good question, and one that is hard to answer
generally (that is, the answer is probably somewhat system-dependent).
Here are a couple considerations:

1) You need enough lambda values to ensure good phase space overlap
from one lambda value to the next, otherwise the results you get will
be meaningless (all of the FEP/TI type expressions require sufficient
overlap between the  Hamiltonians of interest). Bennett Acceptance
Ratio (a type of FEP) is somewhat more efficient and may require
slightly fewer lambda values. It is probably nontrivial to figure out
how many lambda values is "enough", either. The approach I would
typically take for a particular problem is to start with lots of
lambda values for a "typical" problem of that type, and compute the
"correct" answer, and then reduce the number of lambda values until
the answer starts to deteriorate, then add a couple back in and use
that number.
2) Regardless of whether you have enough lambda values, if your
simulations are not long enough, your results will be meaningless.
Your simulations should probably be at least 10x the typical
For example, if you are calculating binding free energies of a ligand,
and the ligand has two different sub-conformations it can occupy in
the binding site, and the timescale for switching between these is 100
ps, you would need to run at least 1 ns at each lambda value to ensure
you have time to sample each conformation a sufficient number of
times. In the extreme case, suppose you started with only one of these
conformations and ran 50 ps, observing no swaps -- instead of
computing the binding free energy of the ligand, you would compute
what the binding free energy would have been if the ligand could only
occupy one conformation in the binding site. This could be not at all
related to the correct binding free energy.

Anyway, that all basically boils down to this: If the transformation
you are doing is "hard" (like turning off LJ interactions for some
atoms in your system), (1) dictates that you will need a relatively
large number of lambda values, since the phase space changes a great
deal, and if the system you are looking at has long correlation times,
(2) dictates that you will need long simulations. You need to do some
investigation to see what your problem is like. I would especially
recommend looking at correlation times. Maybe run out one or two
really long MD trajectories to get an idea of some of the relevant

I would also recommend not thinking of it so much as an optimization
problem of, "How do I best use X amount of computer time?" but, "How
much computer time will I have to spend where to get my statistical
uncertainty down to X in the most efficient way?" Depending on your
system, (1) and (2) may dictate that the amount of computer time you
need to spend is more than you actually want to spend. Then you have
to decide, basically, how big of error bars you are willing to
tolerate.

David Mobley
UCSF
>
>  Thanks for all the good advices on the list,
>  Soren
>
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