# Theory¶

EON uses a field-based measure of Tanimoto to compare the electrostatic potential of two small molecules. This electrostatic potential is calculated internally using Zap, OpenEye’s Poisson-Boltzmann (PB) electrostatics toolkit.

The basic equation for a field Tanimoto is:

$Tanimoto_{A,B} = \frac{\int A(\vec{r})*B(\vec{r})}{\int A(\vec{r})*A(\vec{r}) + \int B(\vec{r})*B(\vec{r}) - \int A(\vec{r})*B(\vec{r})}$

The two boundary cases for Electrostatic Tanimoto occur when B = A:

$\begin{split}Tanimoto & = \frac{\int A(\vec{r})*A(\vec{r})}{\int A(\vec{r})*A(\vec{r}) + \int A(\vec{r})*A(\vec{r}) - \int A(\vec{r})*A(\vec{r})} \\ & = 1\end{split}$

and the opposite case, when B = -A:

$\begin{split}Tanimoto & = \frac{\int A(\vec{r})*-A(\vec{r})}{\int A(\vec{r})*A(\vec{r}) + \int -A(\vec{r})*-A(\vec{r}) - \int A(\vec{r})*-A(\vec{r})} \\ Tanimoto & = \frac{- \int A(\vec{r})*A(\vec{r})}{\int A(\vec{r})*A(\vec{r}) + \int A(\vec{r})*A(\vec{r}) + \int A(\vec{r})*A(\vec{r})} \\ & = -\frac{1}{3}\end{split}$

In EON, we report two different Electrostatic Tanimoto(ET) measures, based on the outer dielectric used in the PB calculation. ET_pb uses an outer dielectric of 80, while ET_coul uses a value of 2.0. The rationale for using a PB electrostatic field is that the external potential is dampened by orientation of the aqueous solvent. It is a common observation that proteins essentially act to reproduce the aqueous desolvation of well-bound ligands. As a result a PB electrostatic field is more likely to correctly capture the essential elements of binding than that from the Coulombic field. However, this would still seem to be a point to be proven. As such we provide both Tanimotos. They typically track each other very closely.

For hit list ranking, we also report a score (ET_combo) that is the sum of the Shape Tanimoto (ST) and the PB Electrostatic Tanimoto (ET_pb).