AMBER Archive (2006)

Subject: Re: RE: AMBER: potential energy

From: Thomas Cheatham (
Date: Tue Sep 19 2006 - 11:57:47 CDT

> But how about MM-PBSA? For the protein, ligand and the
> protein-ligand comples should have something in common
> and comparable on energy. So what will be their 0
> point for each component of the energy?

MM-PBSA is a simple energy post-processing that calculates the gas-phase
molecular mechanical energy and an estimate of the solvation free energy
(and optionally the solute entropy). If run correctly (i.e. the prmtop's
match the coordinates), when comparing a protein-ligand complex to the
free protein and free ligand (either in a single trajectory or multiple
trajectories), the molecular mechanical energies are comparable as the
zero point energies cancel (as pointed out by Ross Walker). As such, the
calculation will approximate the absolute free energy of binding.

Towards this end, it is expected that negative values mean favorable
binding, consistent with a binding constant change of ~1.4 kcal/mol per
order of magnitude (at room temperature) increase in binding, i.e. from

        dG = -RTlnK.

changing the value of K.

-9 kcal/mol = ~6.4 x 1.4 kcal/mol or micromolar binding affinity.
-12 kcal/mol = ~8.6 x 1.4 or ~nanomolar binding affinity.

In an ideal world, positive MM-PBSA energies would mean unfavorable
interaction and negative would be favorable. However, a wrinkle is that
(a) this is an approximation, (b) there are sampling limitations, and (c)
entropic effects are poorly estimated, most notably the rotational and
translational entropy loss upon binding. The rot/trans component is nearly
30 kcal/mol for a bimolecular association using the standard rigid
rotor/ideal gas formulas at 300K. Estimates from the literature span a
range from 3-30 kcal/mol. Consensus is that values in the range of 10-15
kcal/mol are reasonable (from both theory/experiment). Excellent
discussion of the finer points is in papers by MK Gilson.

In practice, what I do first is turn off the NMODE calculation (since it
is outrageously expensive) and look at the raw MM-PBSA values calculated
both with PB and GB (noting that there is often considerable difference
between the two numbers in practice, both in relative and absolute values
across a series of drugs/receptors, but normally this difference is in the
range of 10 kcal/mol or less, relative difference). If the raw numbers
show values > +/- 30 kcal/mol for the delta (complex - (receptor +
ligand)), I go back and make sure that everything was run correctly, that
the appropriate charges were used in Delphi, appropriate radii, that the
movies look good, etc, etc.). Numbers +/- 50 or greater usually signify
something wrong or absent from the picture; unfortunately the
script as written does not provide much info to determine the cause for
error. Moreover, specific ion interaction or hydration can alter the
numbers; see for example the Stefl et al. Biopolymers 2001 paper on
G-quadruplexes comparing energies with and without explicit inclusion of
the bound counterions.


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