The structures were handled using the same partial charges treatment and the same charge-tier scheme for the case-testing above.
The higher order charge-tiering schemes (i.e. where k > 3) has indeed proven beneficial in discriminating between complex and large structures (e.g. globular protein domains) by resolving the degeneracy through assigning less atoms per charge-tier (data not shown).
This is because partitioning provides simpler sub-shapes with less dense distance distributions that still span the whole charge-tier spatial coordinates, resulting in more canonical distributions with lesser probability of approaching normality.
The former indeed physically account for the average distance and spatial dispersion of the corresponding charge-tier atoms, rendering the method more sensitive to the size and extendedness in space, which is a desirable effect, as significant distortions in such parameters (either due to conformational changes or chemical modification) would severely affect the binding capacity of the ligand.
As shown in the "Methods" section, the selected distribution descriptors encode distinct features pertaining to the distribution, for c 1 through c 5 would give an account on atomic spatial dispersion; average interatomic distance, statistical dispersion, distribution skewness, and distribution kurtosis, respectively, within each charge-tier.
Therefore, partitioning the atoms into separate charge groups can be described as a form of coarse-grained encoding of the electrostatic field, whereas the charge-tier comprising the non-polar charges interval could implicitly account for the distribution of the hydrophobically interacting molecules, and collectively, they still encode the net steric field.
These intervals lead to a reasonably symmetrical population of the charge-tiers (to avoid charge bias).
Averting the inclusion of the scaled partial charges as a fourth dimension was done by partitioning atom groups into separate charge-tiers.
In the first step, after inspecting the full propensity distribution of atomic charges of all the ligand atoms, tripartite partitioning was performed among three charge-tiers.
This approach effectively decreases the computation cost of the distribution sampling from roughly O(n 2) to (Oleft( {frac{{n^{2} }}{k}} right)), where n is the number of atoms, and k is the number of charge-tiers.
This should be considered inline with the expectation that better enrichment at a particular molecular size is achieved when the query structure atoms are best dispersed between the different charge-tiers; the situation where the intramolecular atomic charge diversity is greatest.
