Subject: Re: Force Field Nonbon Param

From: [email-masked] (Bill Ross )
Date: Sun, 1 May 1994 14:06:34 -0700

Frank Jensen wrote:

> 	Another question along the same lines: why do people
> insist that the non-bonded energy parameters _must_ be broken
> down to atomic parameters? The non-bonded energy depends on 
> two atoms, just as the strecth energy. Why then assign atomic
> non-bonded parameters but stretch parameters which depends
> on both atoms? Maybe one could get much better non-bonded 
> energies if accepting the parameters as two atom dependent,
> and thereby also avoiding the sometimes rather complicated rules
> for combining the atomic non-bonded parameters to the actual
> energy expression. Yes, that would give more parameters to fit, but
> it would be no worse than the stretch energy, and still much
> less than the torsional parameters.

The "complicated" combining rules allow for a net simplification,
since although all atom type pairs are not necessarily bonded, they 
all must have nonbonded parameters, i.e. instead of vdw terms for 
on the order of N atom types, one would need terms for N + N(N-1)/2 
type pairs. For example, the current release of Amber has 75 atom 
types, which can be grouped into 19 unique vdw types.  Without the 
combining rule, those 19 vdw types would require 190 pairwise 
parameters.

In my opinion, the real complication is in working with the different 
combining rules used by different force fields, not each rule per se. 
However:

One reason for taking at least a partial step in the direction of
per-pair vdw potentials is that water force fields such as TIP and 
SPC use inflated oxygen radii to encompass the hydrogens. Such force 
fields were developed to reproduce the behavior of pure water; they 
capture O-O and O-H radial distribution functions reasonably well 
for the computer time required. Now consider the parameterization 
of a cation in such a situation, where the radial distribution ion-O 
first peak is made to fit experimental data (e.g. Aqvist, J Phys 
Chem '90, 94, 8021-8024). The ion nonbonded parameters will allow 
for the larger oxygen radius, so generally will result in a smaller 
ion in relation to atoms parameterized in a more general force field 
such as Amber. The potential minimum for O-O interactions is at 2 * 
1.77 A for TIP3 water, while for an Amber oxygen it is 2 * 1.60 A.  
For example, Cs+ was parameterized to have an ion-O first peak at 
3.10 Angstroms in TIP3 water, but in a complex with Amber oxygens, 
the first peak was at 2.95 A.

Thus, even though one may find the use of per-atom nonbonded 
parameters with combining rules acceptable for a relatively 
self-consistent force field such as Amber, the consequences of 
mixing force fields should be considered in the light of the 
purpose of each simulation attempted. While I have shown how ion 
parameterization affects relative free energies in water and DNA 
complex (paper with C.C. Hardin, accepted by JACS), one may wonder
if the disparity of force fields affects solute conformations in 
subtle ways as well.

I believe Frank Jensen's proposal for vdw parameterization would 
minimize the chances for errors on the part of relatively naive 
users, and is the only way to achieve consistent interatomic 
distances.  GROMOS is one program / force field that has taken this 
approach (van Gunsteren & Mark, Euro J Biochem '92, 204, 947-961). 
However, it may be sufficient and preferable to use different combining 
rules for inter- and intra-force field interactions, to avoid the 
profusion of parameters from order N to order N^2.

Bill Ross