# Re: [AMBER] Per-residue decomposition energy MMGBSA.py

From: Jason Swails <jason.swails.gmail.com>
Date: Mon, 16 Mar 2015 10:26:57 -0400

On Mon, 2015-03-16 at 21:49 +0800, maryam azimzadehirani wrote:
> Dear all,
> Can anyone simply explains to me how MMGBSA.py calculates per-residue
> decomposition energy?
> I assume it is similar to binding energy calculation where it calculates
> the free energy of ligand (solvated and in vacuum), free energy of receptor
> (solvated and in vacuum) and ligand-receptor free energy (solvated and in
> vacuum). Then calculate Gibbs free energy of binding, as they mentioned in
> advance tutorial 3:

Loosely speaking, this is almost equivalent to what happens.

> If we don't talk about entropy at all, which makes everything confusing...
> In a simple way, the same method is used for each residue in per-residue
> decomposition calculation, where the whole ligand is replaced by each
> residue that we chose in the mask?

No, this is not what happens. This would be more "correct" than what is
currently done (I enclose in quotes since you would need to
appropriately handle the dangling valences caused by cutting residues
out of the polymer chain and then account for the extra atoms you needed
to add to cap that valence... it would be challenging, not to mention
expensive, to do that "correctly").

What's done in reality for MM/GBSA pairwise decomposition is much
simpler: the formula for GB free energies is a pairwise sum (see
equation 4.2 in the Amber 14 manual on page 57, along with Equation
4.3). The sum is actually a double-sum (and the 1/2 accounts for
including both i->j and j->i in the sum).

You can imagine based on this formula calculating the "contribution" to
the total energy for each atom (or for pairwise decomposition, for each
atom pair). Then, all you do is add up the energies for each atom in a
particular residue to get the "per-residue" decomposed energy.

This is rigorously correct if you have a truly pairwise potential energy
function. While Eq. 4.2 looks that way at first glance, the term R (see
Eq. 4.5) is itself a sum over all atom pairs as well... which means that
the GB energy function is *not* pairwise decomposable. But the
resulting decomposition can be qualitatively useful.

HTH,
Jason

```--
Jason M. Swails
BioMaPS,
Rutgers University
Postdoctoral Researcher
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Received on Mon Mar 16 2015 - 07:30:03 PDT
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