Spacial Scores: new metrics for measuring molecular complexity

Molecular complexity is one of the theoretical underpinnings for fragment-based drug discovery. Mike Hann and colleagues proposed two decades ago that very simple molecules may not have enough features to bind tightly to any proteins, whereas highly functionalized molecules may have extraneous spinach that keeps them from binding to any proteins. Fragments, being small and thus less complex, are in a sweet spot: just complex enough.

 

But what does it mean for one molecule to be more complex than another? Most chemists would agree that pyridine is more complex than methane, but is it more complex than benzene? To decide, you need a numerical metric, and there are plenty to choose from. The problem, as we discussed in 2017, is that they don’t correlate with one another, so it is not clear which one(s) to choose. In a new (open access) J. Med. Chem. paper, Adrian Krzyzanowski, Herbert Waldmann and colleagues at the Max Planck Institute Dortmund have provided another. (Derek Lowe also recently covered this paper.)

 

The researchers propose the Spacial Score, or SPS. This is calculated based on four molecular parameters for each atom in a given molecule. The term h is dependent on atom hybridization: 1 for sp-, 2 for sp²-, 3 for sp³-hybrized atoms, and 4 for all others. Stereogenic centers are assigned an s value of 2, while all other atoms are assigned a value of 1. Atoms that are part of non-aromatic rings are also assigned an r value of 2; those that are part of an aromatic ring or linear chain are set to 1. Finally, the n score is set to the number of heavy-atom neighbors.

 

For each atom in a molecule, h is multiplied by s, r, and n². The SPS is calculated by summing the individual scores for all the atoms in a molecule. Because there is no upper limit, and because it is nice to be able to compare molecules of the same size, the researchers also define the nSPS, or normalized SPS, which is simply the SPS divided by the number of non-hydrogen atoms in the molecule. Although SPS can be calculated manually, the process is tedious and the researchers have kindly provided code to automate the process. Having defined SPS, the researchers compare it to other molecular complexity metrics, including the simple fraction  of sp³ carbons in a molecule, Fsp³, which we wrote about in 2009. 

 

The researchers next calculated nSPS for four sets of molecules including drugs, a screening library from Enamine, natural products, and so-called “dark chemical matter,” library compounds that have not hit in numerous screens. The results are equivocal. For example, the nSPS for dark chemical matter is very similar to that for drugs. On the other hand, natural products tend to have higher nSPS scores than drugs, as expected. Interestingly, the average nSPS score for compounds in the GDB-17 database, consisting of theoretical molecules having up to 17 atoms, is also quite high.

 

The researchers assessed whether nSPS correlated with biological properties, and found that compounds with lower nSPS tended to have lower potencies against fewer proteins, as predicted by theory. That said, this analysis was based on binning compounds into a small number of categories, and as Pete Kenny has repeatedly warned, this can lead to spurious trends.

 

The same issue of J. Med. Chem. carries an analysis of the paper by Tudor Oprea and Cristian Bologa, both at University of New Mexico. This contextualizes the work and confirms that drugs do not seem to be getting more complex over time, as measured by nSPS. This may seem odd, though Oprea and Cristian note that by “normalizing” for size, nSPS misses the increasing molecular weight of drugs.

 

This observation also raises other questions, such as the fact that SPS explicitly excludes element identity. Coming back to benzene and pyridine, both have identical SPS and nSPS, which does not seem chemically intuitive. One could quibble more: why square the value of n in the calculation of SPS? Why allow s to be only 1 and 2, as opposed to 1 and 5?

 

In the end I did enjoy reading this paper, and I do think having some metric of molecular complexity might be valuable. I’m just not sure where SPS will fit in with all the existing and conflicting metrics, and how such metrics can lead to practical applications.