Re: [AMBER] Inconsistent Internal energy from monomer to dimer

From: Jason Swails <>
Date: Wed, 04 Apr 2012 10:33:40 -0400

On Wed, 2012-04-04 at 05:37 -0400, Carlos Simmerling wrote:
> i'm not sure i understand your statements here, and I want to make sure its
> clear.
> you calculated 3 trajectory energies- the dimer trajectory (AB), and then
> each of the 2 monomers from the same trajectory (A+B). You're saying that
> A+B still isn't equal to AB. I'm asking because below you only quote 2
> energies, and I'm not sure if you mean to say that the split monomers had
> identical energies (possible, but seems unlikely).
> If this is the case, then something is clearly wrong with the energy
> calculations (or perhaps in the inputs).
> Can you confirm, and provide all 3 energy values?

I think what he's saying is that A + B _does_ equal AB, but that A + B
taken from AB has 22 kcal/mol more internal energy than twice A alone.

The thing that I think is important to look at is the non-bonded
interactions between the two monomers in AB. My guess is that the
charge and VDW terms add up to far more than 22 kcal/mol. The key is,
if you do not allow the monomers to adjust their conformations upon
binding with one another, is the _reduction_ in the non-bonded
interactions more than 22 kcal/mol (because they won't 'fit together' as
well)? If so, then the added stabilization of the non-bonded
interactions favors a more strained conformation for each monomer
(something like the induced fit argument).

Bonds are also much stiffer than angles and dihedrals, so it's not
surprising that the differences arise in those terms. Binding events
between 2 monomers into a dimer will almost always cause internal
energies of the monomer to increase, since you're providing additional
incentive (via non-bonded interactions with the other monomer) to adopt
an alternative conformation. Furthermore, I would expect this increase
to vary linearly (maybe more, quadratically?) with system size
(specifically, the number of bonds, angles, and dihedrals), since the
numbers you're dealing with continue to increase.

Also, if you look at the relative magnitudes of your nonbonded energies
(EEL, EGB, and VDW) vs. your internal energies (bond/angle/dihed/1-4's),
your nonbonded interactions are much stronger for biological
systems--you only have a negative total potential energy because of
nonbonded interactions.

I would expect that the change in internal energy upon dimer formation
would be directly related to the number of available degrees of freedom
(number of angles and dihedrals, specifically). The more degrees of
freedom you have, the more angles/dihedrals that can be slightly
perturbed to accommodate binding, and all of these perturbations are
additive given the fact that they will be positive energy contributions.

I think an interesting thing to observe would be 'how does this monomer
internal energy vary with system size?' -- specifically, as you get to
smaller and smaller monomers, how does this internal energy difference
upon binding decrease? This would be a difficult question to answer,
I'd imagine, since you can't control _just_ system size...


Jason M. Swails
Quantum Theory Project,
University of Florida
Ph.D. Candidate
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Received on Wed Apr 04 2012 - 08:00:03 PDT
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