AMBER Archive (2009)

Subject: Re: [AMBER] Ki and G

From: Adrian Roitberg (roitberg_at_qtp.ufl.edu)
Date: Mon Sep 14 2009 - 09:28:57 CDT

I have personal and strange views on this issue, so please bear with me
here.

First, the deltaG listed below cannot really be computed as the log of
the binding equilibrium constant 'as-is'.

Experimentalists usually report their Kd and or Ki as nM, or microM.

Quite obviously, the log of an object with units would cause you major
problems !

The trick is that equilibrium constant are unitless, because of the
so-called standard concentration. If the standard concentration is 1M
(it usually is) then one can take the log of the Kd NUMBER, expressed in
MOLAR, and go on your way.
There is also the issue raised by Thomas S, where experimentalists
report IC50 and people go on their merry way treating it like an
equilibrium constant, which it is not.

For the computational point of view, most delta G people compute cannot
possibly be compared with the experimental delta G.

Most people will do a mix of FEP, TI, MMPBSA, etc etc to make the ligand
appear or disappear. This gets us back to the issue of standard
concentration. There is significant work associated with getting the
ligand and receptor in the neighbor of each other, and the
concentrations in molecular dynamics are rarely 1M (mostly because
people do not even try to compute it).

So, the free energy of making a ligand appear inside an active site it
is not the delta G of binding.

There are published corrections and ways to deal with this, you should
read some recent work my Mike Gilson and Benoit Roux on this (With
apologies to many others that wrote on this issue !).

Now, if you compute relative free energies of binding, for instance
changing ligand into another of the same family, adding a small group
here and there, all is much better.

The problems with standard concentration go away, and calculations and
experiment could at least be compared in a proper thermodynamics footing.

Cheers

Adrian

steinbrt_at_rci.rutgers.edu wrote:
> Hi Bill,
>
> the binding (association) constant Ka of a ligand is connected to its free
> enthalpy of binding via
>
> dG = -RT ln(Ka)
>
> Most often, its inverse, the dissociation constant Kd is given (just flip
> the sign in the equation above). If the Ki you have is just the binding
> constant of an inhibitor to a receptor:
>
> E + I <-> EI
>
> that is all you need. Be aware that in many ligand binding studies,
> competitive inhibition is what's actually measured and the given constants
> are IC50 values. In this case, you need to use the Cheng-Prussoff equation
> for the conversion:
>
> IC50 = Ki ( 1 + [L]/kD )
>
> and the IC50 value depends on the used ligand concentration as well. See
> Cheng et al. Biochem. Pharmacol. 22, 3099-3108 (1973). Also note that
> binding constants are often determined with respect to ph7 and
> physiological ion strength in biochemical systems, which makes a
> difference if the binding involves proton uptake/release.
>
> So you have to check the experimental data on what they actually measured
> for any comparison.
>
> Kind Regards,
>
> Dr. Thomas Steinbrecher
> BioMaps Institute
> Rutgers University
> 610 Taylor Rd.
> Piscataway, NJ 08854
>
> _______________________________________________
> AMBER mailing list
> AMBER_at_ambermd.org
> http://lists.ambermd.org/mailman/listinfo/amber
> 

-- 
                            Dr. Adrian E. Roitberg
                              Associate Professor
                             Quantum Theory Project
                            Department of Chemistry

                  Senior Editor. Journal of Physical Chemistry
                           American Chemical Society

University of Florida                         PHONE 352 392-6972
P.O. Box 118435                               FAX   352 392-8722
Gainesville, FL 32611-8435                    Email adrian_at_qtp.ufl.edu

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