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.

Flatland: still a nice place to be

In 2009 we highlighted a paper reporting that approved drugs have a higher fraction of sp³-hybridized carbon atoms than discovery-phase compounds. Perhaps focusing on molecules with a high Fsp³, the ratio of sp³-hybridzed carbons to total carbons, would lead to greater success. Or not: a new analysis in Nat. Rev. Chem. by Ian Churcher (Janus Drug Discovery), Stuart Newbold, and Christopher Murray (both at Astex) finds that the relationship has not held up.

 

The 2009 “Escape from Flatland” paper was widely discussed at conferences and has been cited more than 3000 times. But according to the authors of the new study, most of these citations are from papers describing new synthetic methodologies rather than from papers discussing medicinal chemistry.

 

And not all the attention has been positive. As we noted in 2013, Pete Kenny and Carlos Montanari reanalyzed the data and found that an apparent correlation between Fsp³ and solubility disappeared when plotting all discrete data points instead of binned data.

 

More recently, we highlighted a paper that found no significant difference between the shapeliness of drugs, as assessed by their principal moment of inertia (PMI), and the shapeliness of small molecules in the ZINC database.

 

The new paper looks at Fsp³ values for drugs approved during various time periods. Among 980 drugs approved up to 2009, the average Fsp³ was 0.458. However, of the 431 drugs approved after 2009, the average Fsp³ has dropped to 0.392. The researchers speculate that this (statistically significant) decrease may be due to an increase in the number of kinase inhibitors, which are usually highly aromatic, as well as an increase in the use of metal-catalyzed cross coupling reactions.

 

In my analysis of the 2009 paper, I asked whether higher Fsp³ ratios would lead to lower hit rates, and indeed this seems to be the case, as shown in a paper we discussed in 2020. Thus, if you pursue difficult targets, you may increase your chances of finding hits by screening molecules with lower Fsp³ ratios. Also, multiple studies, including one published just last month, have found no correlation between the shapeliness of a fragment (as defined by deviation from planarity, or DFP) and the shapeliness of the resulting lead, so there appears to be no penalty to starting with a flattish fragment. 

 

The researchers conclude that their “analysis of drug development trends over the last 15 years suggests that Fsp³ may not have been a useful metric to optimize.” Importantly, the supplementary information includes a list of >1400 approved drugs and >1500 investigational drugs along with associated properties, so you can do your own analyses.

 

In the end, generalizations will only get you so far, and may even lead you astray. At least for now, there are few shortcuts in the long slog of experimental studies necessary to discover a drug.

Flatland: a nice place to be

The ideal shape of compounds used for biological screens is a subject of vigorous debate, with some arguing that shapely molecules may be superior in various ways to the “flatter” aromatic compounds that tend to dominate libraries. This view was expressed more than a decade ago in the paper, “Escape from Flatland: Increasing Saturation as an Approach to Improving Clinical Success.” However, those conclusions have been challenged. Since many of us are trying to discover drugs, it is worth asking what actual drugs look like. This is the subject of a new ACS Med. Chem. Lett. paper by Seth Cohen and colleagues at University of California, San Diego.

Assessing shapeliness is itself contentious. Here the researchers chose the intuitive metric, principal moment of inertia (PMI), which uses a simple triangle plot to assess whether a molecule is more rod-like, disk-like, or sphere-like. The degree of shapeliness (3D Score) can be calculated by summing the x- and y-coordinates to give values between 1 (rod- or disk-like) and 2 (sphere-like).

The researchers first extracted more than 8500 drugs and nutraceuticals from DrugBank, all of which had associated three-dimensional structures and MW >100. PMI calculations revealed that nearly 80% were linear or planar, with 3D Scores < 1.2. Another 17.5% had 3D Scores up to 1.4, while only 0.5% were greater than 1.6. Interestingly, this distribution is similar to that of the ZINC database of small molecules. You might expect a correlation between size and shapeliness, with larger molecules being more three-dimensional, but this was not the case. Perhaps related, a separate analysis found no correlation between shapeliness of fragments and resulting leads.

The 3D structures of compounds in DrugBank are calculated for energy-minimized conformations, which are not necessarily the biologically relevant conformations. So the researchers next went to the protein data bank (PDB) and its crystal structures of 502 unique DrugBank molecules bound to various proteins. Some molecules were represented multiple times (1036 structures of sapropterin!), and for these the PMIs were averaged. The results of this analysis were similar, with 83.5% of molecules having a 3D Score < 1.2 and just three molecules with a 3D Score > 1.6. As with the DrugBank data, there was no correlation between 3D Score and molecular weight.

Further analyses of compounds with multiple crystallographic structures was interesting. For diclofenac, with 51 PDB entries, 3D Scores ranged from 1.03 to 1.52, with the minimized score being 1.22. However, some of these structures are likely low affinity with questionable biological relevance. In contrast, for five approved HIV drugs, the PMIs remained very similar for molecules bound in the active sites.

Getting out of flatland is surprisingly difficult: the researchers examined the PMIs for several fragments from libraries designed to have shapely members and found that none had 3D Scores > 1.4. They suggest clever ways of increasing three dimensionality, such as building organometallic molecules. While this is likely to increase novelty and patentability, it also introduces unknown biological risks. One analysis that would be interesting is whether natural-product-derived drugs are significantly shapelier than their purely synthetic counterparts.

The researchers conclude:

The true need for topological diversity in feedstocks and final drug molecules remains unclear given the overwhelming number of linear and planar drugs. The question remains as to whether more 3D compounds represent attractive and untapped therapeutic space, or if more linear/planar molecules are indeed the best topologies for bioactive molecules.

This is indeed an interesting question, and I hope that chemists – particularly those in academia – continue to make and test ever more exotic molecules. But since the first word of this blog is “Practical,” I would not discount the more planar molecules that make up most of our pharmacopoeia.

Measuring 3D Fragments

3D fragments is still a topic up for discussion/debate.  Of course, determining what is a 3D fragment is also open to debate.  As presented last year, nPMI seems to be the current "best" method.  FOB Chris Swain has done some neat analyses around nPMI and included it in his overview of commercial libraries.  Last year at the NovAliX Biophysics conference, Glyn Williams from Astex presented the "plane of best fit" (PBF) as a superior way to analyze 3D-arity.  At the recent Zing FBDD conference, Chris Murray presented the "plane of best fit" and argued again that it was superior.  So, of course, I asked Chris Swain if he had compared them, and he said, but wait a minute.  

Well, Chris was able to compile it with the help of his son, Matt (obviously the apple does not fall from the tree).  So, go check out his comparison of nPMI with PBF.  He ran 1000 fragments through both and concluded this: 

Whilst both descriptors are intended to provide information on the 3D structure of the molecule it looks like the PBF provides more granularity which may be particularly useful when looking at small fragments.

 So, I present this as a "go get 'em, folks!".  I am particularly interested to know if people are currently using PBF and if their results jibe with Matt's. 

3D Fragments...An Analysis

[**Programming Note**  Sorry about two posts in one day, but I thought this was too cool to wait.]

 

The 3D-arity of fragments is a common topic of discussion in this field.  ICYMI, Chris recently did an analysis of PPI interactions and the compounds that target them.  However, even more recently, Chris just put up his analysis of the 3DFrag consortium's fragment collection.  The 3DFrag collection does not look any more 3D than commercially available collections.  Justin Bower from the Beatson points out that this is because their fragment collection is largely due to culling from commercial collections.  

Now, no one will argue that nPMI is the best metric for assessing 3D-arity.  But it is the best we have so far.  So, Chris has tried to improve on the visualization of nPMI for very large libraries.  Chris has divided the PMI plot into regions that are disc, rod-like, or spheres (he details how he classifies them at his page).  The upshot of this is that he can then generate very simple plots like this:

 

I think this is a great leap forward.  Obviously, because of the nature of the chemistry performed over the past umpteen years, this would be totally expected.  As Peter Kenny has pointed out previously, rods have volume, but I think that is not what the 3D-eers are aiming at.  What's really nice is that 3DFrag has chemists to make fragments.  In May, they reported that they had added 221 synthesized fragments.  I would like to see how these 221 fragment differ from the commercially available ones.  The proof is always in the pudding after all. 

What you are Missing.

The nice part about blogging is you can post anything you want.  Mostly, we post on interesting (to us at least) papers, news about fragments, conferences, and so on.  We have assiduously avoided being a commercial outfit; what we post is what we believe in and we don't post for cash or barter.  So, we tend to not promote people/companies.  I am so totally breaking that rule right now.  

Many of you probably know Chris Swain, the principal of Cambridge MedChem Consulting.  [Full Disclosure: Chris and I have worked and published together.  I hope that does not diminish your feelings about him.  :-)] If not, this post will introduce you to him and the many wonderful resources he curates, particularly in the FBHG world.  There is so much there, sometimes I forget what he has; in fact, Chris's site goes by the rule, "Why make them buy the milk, give it to them, and the cow too!"  

One of the great resources Chris has is a graphical snapshots of a metric pile of fragment collections.  On Monday, Chris added nPMI (Principal Moment of Inertia) to these snapshots.  As has been discussed some, I (and Justin Bower from the Beatson) think this is the best way to evaluate "3D-arity".  It is interesting to just browse through the snapshots.  Some of the collections that are VERY large do seem to have a good to excellent amount of 3D-arity.  Does this correlate with increased hit rates for certain target classes?  

Well, Chris has thought of that.  He has been collecting the compounds from the literature that are reported as fragment hits.  He has just updated that snapshot with nPMI also.  What do the reported fragment hits tell us?  I would say that the vast majority of the reported fragments are Voldemort Rule compliant.  No surprising.  What I would like to see is a breakdown of fragment property against target type.  This may the part of the cow Chris isn't giving away.  There may be other slices/dices too.  

Trust me, go and spend some time on Chris site.   I won't call it a time waster, but it will suck you in.