[gmx-users] Free energy calculation

David Mobley dmobley at gmail.com
Mon Aug 6 17:58:57 CEST 2007

```Hi,

> I need to calculate the free energy of complex formation between protein A and ligand B. I am about to simulate in solution the molecular dynamics of A, B and AB complex separately and calculate the free energy of each system using g_lie. Then, I suppose, deltaG = G(AB) - (G(A) + G(B)).
> Is it a correct algorithm? Or maybe it's better to use "slow-growth" method (whith lambda = 1 for the absence of ligand in the binding pocket) to calculate the difference between G(AB) and G(A)?

I would suggest digging in to the literature on this. There are two
basic classes of methods for estimating free energies, each of which
has several sub-classes, and you need to decide what level of accuracy
you want and what computational price you're willing to pay. Here's

Class 1: Approximate "free energy" methods: Methods which include some
protein/ligand flexibility and strain energies, and sometimes some
entropic effects, but make significant approximations to the
statistical mechanics and thus do *not* give true free energies.
Members of this class include:
(a) LIE
(b) MM-PBSA/MM-GBSA
>From what I know about LIE, it usually has two (?) adjustable
parameters which need to be tuned in order to give reasonable results
for your particular system of interest. These parameters tend not to
be transferrable from one system to another.

Class 2: Asymptotically "exact" free energy methods (in that in the
limit of sufficient sampling, they give the correct free energy, for
the particular force field used):
(a) Alchemical free energy methods (i.e. TI, and various forms of free
energy perturbation). These have most commonly been used for computing
only relative binding free energies, but more recently are being used
for absolute binding free energies.
(b) Umbrella sampling methods (calculating a potential of mean force,
or free energy landscape, for removing the ligand from the binding
site).

There are a few other variants in this second class as well.

So, if you're asking about LIE, "Is it a correct algorithm," well,
it's hard to say. It's probably correct in the sense that it does what
it's supposed to. But in terms of giving "true" binding free energies,
no: It's an approximate method.

Personally, I use methods out of the second class (usually alchemical
free energy methods) because I think the additional accuracy is worth
the (extra?) computational cost, but you should probably dig in to the
literature and decide for yourself. Everybody has a favorite method,
so asking people how you should calculate binding free energies is a
bit like asking who you should vote for in the next election: You'll
get a lot of different answers, and YOU have to be the one to pick
what's best for you.

To get you started, there are a number of recent review papers on free
energy methods, including some from around 2003 by Rodinger and Pomes,
and by David Kofke. Michael Shirts and John Chodera and I have another
review in press (Annual Reports in Computational Chemistry) and you
can find quite a few references in my latest paper:
http://dx.doi.org/10.1016/j.jmb.2007.06.002. There is also a recent
book edited by Chipot and Pohorille:
http://www.springer.com/west/home/chemistry?SGWID=4-135-22-173675111-0.

Best wishes,
David Mobley
UCSF

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