AMBER Archive (2006)

Subject: Re: AMBER: modeling of ligand concentrations

From: Thomas Cheatham (tec3_at_utah.edu)
Date: Mon Oct 23 2006 - 17:51:28 CDT

> The term "standard state" in this context is referring to the concentration
> of binding ligand as defined in accordance with enzyme kinetic theory. In a
> multistep kinetic mechanism, as shown below.
>
> E + A --> EA --> EB --> E + B
>
> .the difference in energy between A and B translates in to Keq for the
> enzyme reaction in question. However, in simulating the kinetic constants
> of this reaction using first principles & thermodynamics, we need to treat
> each step sequentially. Hence, our first step would be to model E+ A -->
> EA, and so forth.

I understand that you want to see the first step, but you are confused
regarding what the definition of the standard state is. Plug it into
Google and a nice description appears at:
  
   http://www.nyu.edu/classes/tuckerman/honors.chem/lectures/lecture_15/node9.html

The issue is that you need a reference state to define the zero of
enthalpy, etc. since experimentally we measure changes in these values.

> Were I to model the E+A --> EA step using 1M concentrations, I know for a
> fact that these "standard state" concentrations will not reflect the system
> in equilibrium, which is what is needed in order to estaimte the kinetic
> constants for the system using rate coefficients and the methods of King &
> Altman. Hence, as described by Cleland, the problem is the choice of
> standard states.

Yes, you would not model at standard state, but at some different
concentration relative to standard state. [You do not redefine the
standard state, which for a solution is 1M, but simulate your reaction
network or systems biology rate expressions at the realistic
concentrations which for most "drugs" would be in the micromolar to
nanomolar range and +/- a few orders of magnitude in either direction for
metabolic reactions.]

> We have developed a protocol to allow convergence to equilibrium through
> adjustments in standard state concentration of reactant and product. It

You are not, I claim, adjusting "standard state"; perhaps concentrations
relative to standard state or more realistically, just changing the
concentrations to match what is observed.

> involves an advanced treatment of solvent using mm-pbsa to elucidate the dG
> of the "transition states" (here, binding intermediates). But to implement
> it, we need to be able to *choose* the concentration of binding ligand.

No problem, but you cannot choose the concentration with single molecule
simulation; here in our normal single molecule experiments, the
concentration is normally 1 molecule (i.e. 1 drug and 1 enzyme or 1 E and
1 A in the equation above) and from this we can estimate dG.

> David Case went over this previously. My big question for the day is, can
> we arbitrarily assign a concentration for A in the reaction E+A --> EA?

No this would not make sense as I mentioned when you try to estimate the
dG for the reaction. For example, to simulate a nM binder you would need
to simulate 1 billion E and 1 billion A in a simulation cell (which would
be way bigger than anything possible today) and observe that only 1 drug
was "free" on average. You can of course change concentrations anyway you
want if you are modeling the reaction network and rate expressions but
this is not the same as changing the standard state.

> Can we set the "standard state" from 1M to something else? That is all I
> need to know for now.

No, as this would not make sense.

I will respond further offline.

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