Discrepancy in `E_norm` Calculation Between GISTTOOLS and GIST Tutorial

[gkxiao]

Description:

I’ve noticed a significant difference in how the normalized total energy E_norm is computed between GISTTOOLS and the official GIST Tutorial.

1. In GISTTOOLS (gist.py line 1071):

• The _recipe_A_norm method defines:

    def _recipe_A_norm(self, index):
        """Create A_norm."""
        return (
            self.loc[index, "Eww_norm"]
            + self.loc[index, "Esw_norm"]
            - self.loc[index, 'dTSsix_norm']
        )

It means:

A_norm = Eww_norm + Esw_norm - dTSsix_norm      (1)

and:

E_norm = Eww_norm + Esw_norm         (2)

2. In the GIST Tutorial (Python example for figure 5.):

import gisttools as gt
# Load the GIST data, make sure to set the correct reference energy
gist = gt.gist.load_gist_file('gist.dat',
struct='solute-centered.pdb', eww_ref=-9.5398)
# Calculate the total energy without double counting
gist['E_norm'] = gist['Eww_norm'] * 2 + gist['Esw_norm']
# Set the energy to zero for all voxels with no population
gist.loc[gist['population'] == 0, 'E_norm'] = 0
# Save the new energy to a dx file
gist.save_dx('E_norm', 'gist-E-per-mol-norm.dx')

Where, the comment claims double counting is avoided, but the code includes a factor of 2 for Eww_norm,

E_norm = 2 * Eww_norm + Esw_norm       (3)

which may imply double counting rather than avoidance. The intention behind this should be clarified.

Eqation 3 effectively doubles the water-water interaction term.

This discrepancy raises concerns about consistency and physical interpretation:

• Multiplying by 2 implies a correction for double counting, but it’s unclear whether this factor is already embedded in the Eww_norm values provided by GIST.
• If Eww_norm is already computed per interaction (not per molecule), then multiplying by 2 would be incorrect.
• Conversely, if Eww_norm is defined per molecule, then doubling would be appropriate for the total.

Question: Could you please clarify the definition of Eww_norm in the GIST output and confirm which version of the E_norm formula is correct for standard GIST analysis?

This is important for ensuring consistency when using GISTTOOLS for visualization, scoring, or comparison with literature results.

Thank you!
— Gaokeng Xiao

[vhoer]

Hi, this is indeed an important question and something that we tried to clarify in section 7.3 of the tutorial.

In short: both formulas are wrong or right depending on the context. Since GIST treats solvation on a per-voxel basis, each voxel counts the interactions with the solvent of all other voxels. As such, one would double-count the solvent-solvent interaction when integrating over more then one voxel - therefore the GIST code itself outputs 1/2 Eww for each voxel. This is then also used in Gisttools to calculate A.
However, when looking at small regions encompassing only a single water site, this is problematic. In the extreme of a single voxels or a group of voxels sharing a single water, there is only interaction to the outside, and no double counting within the region. Therefore, one must correct the default behaviour by doubling Eww - like we did in the tutorial for the isosurfaces of the binding site.
In practice, I'd recommend to be aware of this issue and handle it according to the problem at hand. For looking at single water sites (usually with the _norm values per water) I prefer 2xEww wheras for integrating over a large region 1xEww is the way to go (e.g. figure 6 of the tutorial).

I'll keep this issue open and will clarify the code in the future.

[gkxiao]

Thank you so much for the detailed and insightful explanation — this clears up the confusion perfectly. I really appreciate the careful clarification, especially the distinction between small regions (like binding sites) and larger integration volumes. Your explanation of why Eww needs to be doubled in certain contexts, and the reasoning behind GIST's default 1/2 Eww output, is very helpful and well-articulated.

It's great to know that this issue will be addressed further in the code documentation — I’ll keep an eye out for the updates. Thanks again for your time and for maintaining such a high-quality tool and community support.

Gaokeng Xiao