Rule of Three considered harmful?

I should start this post by saying that I’ve never actually used the Rule of Three for fragment selection. Part of the reason for this is simply a matter of timing since I’d been designing fragment libraries before the Rule of Three came along. However, I believe that there are reasons that you need to take a very close look at the Rule of Three if you’re planning to build a fragment library strategy around it. The rule was introduced in late 2003:

“We carried out an analysis of a diverse set of fragment hits that were identified against a range of targets. The study indicated that such hits seem to obey, on average, a ‘Rule of Three’, in which molecular weight is < 300, the number of hydrogen bond donors is ≤3, the number of hydrogen bond acceptors is ≤3 and ClogP is ≤3. In addition, the results suggested NROT (≤3) and PSA (≤60) might also be useful criteria for fragment selection. These data imply that a ‘Rule of Three’ could be useful when constructing fragment libraries for efficient lead discovery.”

My first criticism of the Rule of Three is that the authors do not say how they define hydrogen bond acceptors. I’ll illustrate this point with reference to the phenylhydantoin below which along with the accompanying properties was retrieved from eMolecules. As far as I’m concerned, this compound would have been perfectly acceptable for inclusion in a fragment library before the Rule of Three was published and the publication of the rule would not make change my mind. If, however, you asked me whether the compound complied with the Rule of Three, I’d have to admit that I simply don’t know. The number of hydrogen bond donors is not an issue because there is only one of these in the molecule. The number of acceptors is more problematic. I would only count the oxygen atoms in this molecule as acceptors and, since there are two of these, the molecule would be compliant with the Rule of Three. However the well-known Rule of Five treats all nitrogen and oxygen atoms as acceptors so if you use those criteria you’ll count a total of four acceptors and conclude that the compound is not compliant with the Rule of Three. This is not a problem for me because I don't use the Rule of Three but spare a thought for the person assembling a commercial fragment library.

My second criticism of the Rule of Three concerns how it was actually derived. The authors describe performing “an analysis of a diverse set of fragment hits” without actually saying anything about what this analysis entailed. If they were analysing hits from their own fragment screens then the characteristics of the hits will reflect the criteria by which compounds were selected for fragment screening. If they were sampling from a more extensive database of screening hits, I’d still want to know how the fragment hits were distinguished from the other hits.

My third criticism is as much about how cut offs get used as it is of the Rule of Three. There’s a diagram of a funnel that you often see in virtual screening reviews. We also use funnels (or filters as we prefer to call them) in screening library design and in fact this activity is not a whole lot different from working up a virtual screen. Typically we apply filters and sample (e.g. using molecular diversity criteria) from what makes it through. Note that I say ‘filters’ rather than ‘a filter’. The Core and Layer (CaL) approach to library design has been described both in this blog and in a journal article. In CaL the filters used prioritise compounds get less restrictive as more compounds are added to the library. The reason for doing this is that it gives better control of chemical space coverage since it forces the selection of the smallest and least complex molecules first. A molecular diversity maximiser such as BigPicker, will tend to pick larger, more complex molecules because these tend to be more dissimilar to each other.

I am also prepared to accept compounds that have measured/calculated logP values in excess of 3 provided that the appropriate precautions (select ionisable compounds and/or use measured solubility values) have been taken to minimise the risk of poor solubility. You don’t want a whole library of compounds with logP values in excess of 4 but having some will increase the range of targets that you can nail. I am more concerned about the distribution of logP and molecular size in a library than I am with their maximum values and believe using multiple cut offs allows better control of these distributions.

You'll find plenty of material on the internet that deals with the Rule of Three although inconsistencies can be observed. It is not clear whether or not the Rule of Three includes the restrictions on NROT and PSA. As I read it in the original article, I don't think it does but I'm not sure and think it could have been made clearer. This webpage (accessed 11-Jan-2011) appears to suggest that Maybridge FBDD team think that the NROT and PSA criteria are included in the Rule of Three. However, another webpage (accessed 11-Jan-2011) seems to suggest that the FBDD team at Chembridge think otherwise. Cambridge Medchem Consulting (accessed 11-Jan-2011; I expect that this page will get updated once the error is discovered) appear to share the Chembridge view that the NROT and PSA criteria are not included in the Rule of Three although they use < instead of ≤ when stating the Rule which makes a big difference when the number in question is 3. Yet another variation on the Rule of Three can be found in the BioScreening.net glossary (accessed 12-Jan-2011) in which the hydrogen bond criteria are stated as "number of H-bond donors and acceptors less than, or equal to 3", which could be taken to imply that the sum of donors and acceptors cannot exceed 3.

I should of course let you know where the title of this post comes from since I borrowed most of it from a computer science paper that is over forty years old. I can’t even claim originality for adapting the title of the earlier paper because my friends at OpenEye have beaten me to that as well.

I hope that this post will at least make people ask a few questions when presented with rules like these in the future. I'll also set up a discussion in the LinkedIn Medicinal Chemistry group which will facilitate posting of comments.

Literature cited

Congreve, Carr, Murray & Jhoti, A ‘Rule of Three’ for fragment-based lead discovery? Drug Discov. Today 2003, 8, 876-877 | DOI

Lipinski, Lombardo, Dominy &Feeney, Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Adv. Drug Deliv. Rev. 1997, 23, 3-25 | DOI

Blomberg, Cosgrove, Kenny & Kolmodin, Design of compound libraries for fragment screening. JCAMD, 2009, 23, 513-525 | DOI

Dijkstra, go to statement considered harmful. Communications of the ACM, 1968, 11, 147-148 | DOI