Masaya Orita and colleagues from Astellas Pharmaceuticals have published a thought-provoking paper in Drug Discovery Today (in press). In it, they describe two new measurements based on the golden ratio.

As mathematicians, art historians, and readers of The Da Vinci Code know, the golden ratio, or phi, is an irrational number whose first ten digits are 1.618033988. Phi describes the relationship between two numbers, such as 6765 and 4181, in which the ratio of the sum of the numbers to the larger number is equal to the ratio of the larger number to the smaller number. It pops up in many unexpected places, though, like Elvis, many of these sightings are disputed. Now it may have made (two!) appearances in the world of fragment-based drug discovery.

The authors examined 30 examples of fragment-based ligand discovery in which the final compound had an affinity better than 100 nM and a MW less than 600 while the starting fragment had an affinity greater than 1 micromolar. They found that the average number of heavy (non-hydrogen) atoms of the final compound was 28.933, the average number of non-hydrogen atoms of the fragment was 17.833, and thus 11.1 heavy atoms were grown or added to the fragment during optimization. 28.933 / 17.833 is approximately equal to 17.833 / 11.1, which is approximately equal to phi, the golden ratio.

The authors suggest that, if a protein target has known inhibitors with N heavy atoms, a fragment library might be more likely to produce hits if it contains compounds that have N/phi heavy atoms. I’m not sure this is the best strategy. It seems that, regardless of the target, one will want to keep the final molecular weight low, and thus a “Rule of 3” approach is probably the best bet (which, as the authors note, is related by phi to the “Rule of 5”). That said, perhaps it is worth screening larger fragments for particularly intractable targets such as protein-protein interactions, which seem to require larger ligands.

The second observation of phi is based on a reanalysis of Kuntz’s seminal “Maximal affinity of ligands”, which includes binding data for more than 150 ligand-receptor interactions. After removing heavy metals and other non-drug like ligands, and plotting ligand efficiency vs heavy atoms for the strongest-binding ligands, Orita and colleagues found that, as the number of heavy atoms doubled, the maximal ligand efficiency decreased by a factor of phi. From this they derived a new measurement:

%LE = (LE / maxLE)*100

Where maxLE = phi^log2(10/HA)

This measurement is intended to give a sense of how closely any ligand with a certain number of heavy atoms approaches the maximum ligand efficiency achievable for a ligand with the same number of heavy atoms.

The paper is a fun read (don’t be put off by the equations!), but will the observations of phi hold up to further scrutiny? And will the new indices be useful? The authors are appropriately circumspect:

Why does the Golden Ratio appear in FBDD? This might be an artefact caused by human minds (medicinal chemists), to whom such a ratio is attractive. It is expected that arguments about the existence and usefulness of the Golden Ratio in the field of drug discovery will be advanced in future.

What do you think? Are these demonstrations of patterns in medicinal chemistry, or of pattern-finding instincts in medicinal chemists?

## 7 comments:

I must confess this article did little to ease my ‘efficiency metric fatigue’. Half the circumference to diameter ratio (1.57079633) of a circle may also work well for this sort of analysis. For those with an interest in astrology, it may prove possible to find a planet, comet or asteroid for which the ratio of the principal axes of the orbital ellipse is in alignment with the data.

The authors of the article suggest that for enzymes using ATP as a co-factor a screening library with HA ~ 19 (divide HA for ATP by golden ratio) should be used. The average HA for an NMR or crystallographic screening library is typically lower than this and the figure of 19 will be close to the upper limit for molecular size. NAD (HA = 44) and NADP (HA = 48) are significantly larger molecules than ATP so it’s not clear what size fragments the authors would recommend for enzymes that use the former two as cofactors. A number of the entries in Table 1 are proteases for which the natural substrates tend to be extremely large on the fragment size scale.

If you are looking for other amazing coincidences in the fragments literature then refer to our complexity paper (JCICS 2001, 41, 856). The average MW increase for the set derived from Sneader's set of prototypes and drugs was 42, which for followers of the Hitchhiker's Guide to the Galaxy will be known to be the answer to the ultimate question. I bet there is also a planet out there with a dimension of 42 somethings!

I don't know, the only thought this paper provoked in me was "How the heck did this get published?"

Seriously. Relating the Fibonacci sequence to drug discovery? Both numbers are about 1.6, proving the importance of the relationship?

If this had been published on April 1, I would have felt better.

Really fantastic your post. I look forward to future posts.

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I guess it's only a matter of time before someone comes up with a LE metric that yields the magic number 666. :-P

Usually i don't believe in nemerology!! But this post makes me reconsider my belief!! Great!

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