AMBER Archive (2006)

Subject: Re: AMBER: modeling of ligand concentrations

From: Thomas Cheatham (tec3_at_utah.edu)
Date: Mon Oct 23 2006 - 11:38:55 CDT

> In this regard, the term "standard state" refers to the concentration of
> binding ligand. Of course I am looking at larger sets of reactions (as in

That is not the definition of standard state.

> this clearer, we could look at a bimolecular reaction (E+A --> EA). The Keq
> will related to the difference in dG of the two species, and as such,
> equilibrium conditions need to be established. Hence, identification of the
> standard state for A needs to be evaluated. This is hard to explain in a
> chaper, let alone a paragraph.

No it is very easy to explain. Through molecular simulation, we may
obtain an estimate of the dG. This is done through an ensemble average
(over time). From dG you can obtain an estimate of the equilibrium
constant.

        dG = -RT ln K

A dG of ~-12 is approximately nM (10**-9) binding.

        K = [bound] / [free receptor][free drug]

We have an estimate of the binding without running a simulation with a
billion-fold less drug free than drug bound, i.e. running a concentration
with a billion drugs and a billion receptors seeing only 1 free drug and 1
free receptor per billion complexes.

> Perhaps a more appropriate question then would be: can an Amber user
> specify the concentration of the ligand that is interacting with a specific

Yes, although realistically this would require simulation of a true
solution with multiple receptors and ligands in a ratio appropriate to the
relative concentration and in a simulation system at the appropriate
density/concentration. Additionally, to simulate this, you would have to
simulate a length of time that is probably at least ten times longer than
the on/off rates to get proper statistics. This is unfeasible and likely
unnecessary.

Instead, we generally run simulations with 1 receptor and 1 ligand and
look at the free energy difference between the fully bound and fully empty
receptor state. This can give an estimate of the binding free energy
(subject to the approximations of free energy perturbation or MM-PBSA).
The binding free energy does not directly give us a measure of the on-off
rates; these would be tricky to measure in simulation (likely requiring
potential of mean force estimates of the barrier to binding and release
and then some estimate of the rates based on this barrier as the
time scales are likely longer than can be easily accessed in
simulation; i.e. forget about it unless you really know what you are
doing).

I would concentrate on dG = -RT ln K and realize that estimating dG is
still an active research question...

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