How best to assess molecular shapeliness?

The shape of a molecule influences its properties. While this is true on a per-compound level, things get a little more controversial when discussing molecules in general. Back in 2009 researchers argued that “three dimensional” molecules have better drug-like properties, though this assertion has been challenged, repeatedly. But how do you assess the shape of a molecule in the first place? In a recent (open-access) Drug Discov. Today paper, Iwan de Esch and collaborators at Vrije Universiteit Amsterdam compare the main metrics.

 

The researchers focus on three metrics: fraction of sp³-hybridized carbons (F_Csp³), which we wrote about here; plane of best fit (PBF), which we wrote about here; and principal moment of inertia (PMI), which we wrote about here. F_Csp³, which ranges from 0 to 1, is simple to calculate based on the chemical structure alone, while the other two metrics rely on the three-dimensional shape of the molecule, requiring calculations and indeed choices since many molecules can assume multiple conformations. PBF is measured in angstroms with a minimum of 0 Å and no maximum; a protein, for example, could easily have a PBF above 10 Å. PMI is represented by two normalized PMI ratios, and these are often added to give a number (3D Score or ΣNPR) between 1 and 2.

 

The researchers calculated F_Csp³, PBF, and ΣNPR for a set of nearly half a million commercially available fragments which we discussed here; PBF and ΣNPR were calculated based on the single lowest energy conformation for each molecule. As noted above, PBF is somewhat size-dependent. For example, adamantane and buckminsterfullerene have PBF scores of 0.79 and 1.76 Å but identical ΣNPR scores. Nonetheless, the researchers found a correlation between these two metrics, and this correlation increased when PBF was divided by the root of the molecular volume to attempt to normalize for size.

 

In contrast, no correlation was found between F_Csp³ and PMI, making the former “a poor descriptor for predicting 3D molecular shape.” Is there a simple alternative? F_Csp³ only considers carbon atoms, so the researchers proposed F_HAsp³, which includes nitrogen, oxygen, and sulfur atoms. Perhaps not surprisingly, this didn’t improve the correlation.

 

Three years ago we wrote about “spacial scores,” which were developed to assess molecular complexity. The researchers calculated normalized spacial scores (nSPS) for their set of compounds, but these also showed no correlation to PMI.

 

The researchers conclude that, “once corrected for size, PBF captures three-dimensionality similarly to ΣNPR values. However, unlike a PMI analysis, it is not capable of further distinguishing between rod- and disc-shaped molecules, giving PMI a higher resolution in capturing shape diversity.” Interestingly, this is the opposite conclusion of an analysis Teddy wrote about in 2014. My take is that, if you want to assess shapeliness, steer clear of F_Csp³, but both PBF and PMI are fine.