Re: Question on restraint behavior when part of system decouples

From: Jérôme Hénin (jerome.henin_at_ibpc.fr)
Date: Mon Jan 29 2018 - 09:53:51 CST

Hi Randy,

On 29 January 2018 at 16:19, Randy J. Zauhar <r.zauhar_at_usciences.edu> wrote:

> Hi, I have always been troubled by the following aspect of the way
> constraints are applied in the typical ‘alchemical’ transformation when
> evaluating free energy of binding of ligand to protein.
>
> 1) If ligand is in complex with protein with restraints, and some
> restraints involve both ligand and protein atoms (say dihedral angle
> involving protein and ligand) and others only ligand atoms (say ligand
> RMSD), and the ligand is decoupled from the complex - do all restraint
> energy contributions ‘disappear’ during decoupling, or only the
> protein-ligand part, or do NONE of the contributions disappear? In the end,
> is the ligand effectively unrestrained in vacuum, or are the restraints
> still in place?
>

If the restraints are implemented within the Colvars module, then they are
unaffected by the alchemical lambda and will persist in the decoupled
system. If they are implemented as extraBonds, I am not entirely sure,
depending on the options that allow for perturbing bonded terms.

> 2) Similarly, when the ligand is decoupled from bulk solvent, why does the
> recommended protocol only restraint the conformation, why not position and
> and orientation as well, to mimic the loss of positional and rotational
> freedom that occurs upon complex formation?

I'm not sure which recommended protocol you have in mind, but translational
and rotational restraints when decoupling from isotropic bulk solution
would have zero effect: they do not change the excess free energy that is
being calculated. Restraint in the bulk calculation will not mimic the
entropic effects of binding. More typically, restraints in the "protein"
leg of the alchemical transformation are there to improve numerical
convergence by increasing the overlap between the end-states. And then the
free energy of those restraints needs to be calculated to account for those
rotational and translational degrees of freedom.

And again, if ligand in bulk decouples from solvent, is the end result a
> small molecule in vacuum, or a small molecule in vacuum with restraints?
> Those are very different situations!
>

They are, but the effect of those restraints in vacuum is exactly the same
as in bulk solution, so their impact on the deltaG of decoupling is zero.

I had assumed that the decoupling ONLY involved the nonbonded interactions
> between parts of the system,

Typically, yes.

> and that you needed to handle everything involving restraints via
> integration;

Or analytically if possible.

> but if that is so, my mental picture of how the thermodynamic cycle works
> is really off.
>

There is more than one way to design a thermodynamic cycle for double
decoupling, but I think the statements I've made above are general.

Jerome

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