I'm using APBS to calculate electric fields within proteins.  I am doing this is using a two-stage focusing strategy with the multigrid solver.  I create dummy atoms along the vector which I want to know the electric field on and use the 'write atompot' keyword to return the potentials at those dummy atoms.  I then take the negative of the change in potential to find the field.  There are a couple interesting behaviors I have observed and I was wondering if this has been addressed/observed before and quantitatively explained. It should be noted that, although my end-goal is the electric field, I am talking about the potential values here.  I do not see a systematic change in the potentials in such a way as, although the potentials are different, their rate of change are the same.  I am seeing different potentials which is leading to different fields.

My first observation regards the boundary condition.  For the same protein structure with a fixed grid spacing, increasing the box size incrementally, I sometimes see relatively large changes in the potential (from ~7 kbT/e to ~5 kbT/e, so about a 30% change) while other times I see essentially no changes in the potential at my dummy atoms.  Situations in which I see large changes seem to be correlated to a number of large partially charged atoms (typically oxygen) going from outside the second-stage calculation box to inside the second-stage calculation box.  For snapshots I have done this test one, once the second-stage box exceeds ~20 angstroms, I stop seeing these large changes in potential.  This leads me to believe that within some r-distance, the boundary condition inadequately describes the surrounding system.  Is this an artifact of using a very coarse grid spacing for the first stage calculation, (first-stage calculation is is 240x240x240 angstrom box with 97 grid points in each dimension, so a grid spacing of 2.5 angstroms) or does the boundary condition simply not adequately account for large charges outside the box while the box is small enough for 1/r to be significant?  

The second observation regards the interpolation of charge at the grid points to atoms (specifically my dummy atoms).  In my system, the dummy atoms are along a nitrile bond vector.  In the previously described observation, I zeroed out the charge on the nitrile atoms to better observe the contribution of the field due to everything else (since the potentials due to the nitrile part of the system dominate due to the small 1/r term).  Here I am zeroing out the charge on everything that is NOT the nitrile so that I can better observe just the nitrile contribution (although, again, the nitrile contributions dominate so zeroing nothing out gives essentially the same results).  What I've seen here are, for a fixed second-stage box size (using a 19 angstrom box), large changes in the potential near the nitrile atoms (changes of ~40%, 20-400 kbT/e within ~.2 angstroms of an atom) and smaller changes ( <0-3 kbT/e when > .2 angstroms from the bond vector).  I do not see this behavior when the charges on the nitrile are zeroed out, meaning this is only present when there are charged atoms near the dummy atoms.  The solution to this seems to be to cluster the dummy atoms closer to the bond mid point, although I've been unable to find the algorithm which maps the potential on the grid back to atoms, so I'm not sure what the resolution limit (if any) relative to the grid spacing is.

Thanks for the assistance,
Andrew Ritchie
Department of Chemistry and Biochemistry
The University of Texas at Austin
The Webb Group