[gmx-developers] Reaction field questions (David van der Spoel)

David van der Spoel spoel at xray.bmc.uu.se
Wed Mar 4 20:47:51 CET 2015

On 2015-03-04 20:12, Shirts, Michael R. (mrs5pt) wrote:
>> I wouldn't agree with this. The Hamiltonian is well defined and you do
>> sample a Boltzmann distribution. But the Hamiltonian and distribution
>> might be very different from the "correct" Hamiltonian. GB and RF are
>> effective free-energies, as averaged over certain conditions. If the
>> conditions you use them in are different from the conditions used to
>> derive the potential (free-energy), than your results might differ (be
>> wrong) a bit or a lot.
> I'll agree with Berk as well.  I think the key is if you are averaging out
> components, then you have lost some entropy, in which case the temperature
> dependence will necessarily become nonequivalent to the original
> temperature dependence.

In fact, the hamiltonian contains potential energy V(r) and a PMF like 
term G(r) which by definition includes the entropy and is an average 
over time and/or coordinates. In other words we get a new potential energy
V'(r) = V(r) + G(r)
note that G(r) is now at fixed temperature. dV'(r)/dr is now rather 
different from dV(r)/dr, since it contains dH/dr - TdS/dr due to e.g. 
the solvent. I would say this is a non-physical energy function which 
may have some limited use for scoring functions, but not for dynamics or 
cases where the objective is to compute reliable free energies. For sure 
one loses the entropy due to correlated motions between e.g. protein and 
solvent (for an implicit solvent).

As a result, I think, all thermodynamic quantities including the 
temperature dependence (heat capacity) will be systematically wrong. 
This even goes for united atom models (or indeed when using constraints).

Now the question is, HOW bad is this?
That I'm not completely sure off (but working on it). For entropy of 
liquids the effect of using constraints on the entropy is an entropy 
loss of a few %. I suspect that the effect of a reaction field may be 
measurable as well.

Given that some people are rather strict when it comes to accuracy of 
integrators and thermostats (thinking of you Michael ;)) the subject of 
simplifying the potential should not be disregarded completely.

> In systems w/o long range order (gases, fluids w/o interfaces, or
> proteins) then very little entropy is being is being lost.  When there is
> long range order (interfaces, crystals), you are losing something by going
> to anything approach that uses averages.
> Note that Ewald also loses something by averaging over unit cells, but
> it's not as much as by averaging outside a 1 nm or so cutoff.
> Best,
> ~~~~~~~~~~~~
> Michael Shirts
> Associate Professor
> Department of Chemical Engineering
> University of Virginia
> michael.shirts at virginia.edu
> (434) 243-1821

David van der Spoel, Ph.D., Professor of Biology
Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205.
spoel at xray.bmc.uu.se    http://folding.bmc.uu.se

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