I’d like to throw a few more logs on the ligand efficiency fire. Chuck Reynolds of J&J (author of several papers on the subject, as aficionados know) left a comment to an earlier post that I think needs some wider exposure. I’ve added links to the references:
An article by Shultz was highlighted earlier in this blog and is mentioned again in this post on a recent review of Ligand Efficiency. Shultz’s criticism of LE, and indeed drug discovery “metrics” in general hinges on: (1) a discussion about the psychology of various metrics on scientists’ thinking, (2) an assertion that the original definition of ligand efficiency, DeltaG/HA, is somehow flawed mathematically, and (3) counter examples where large ligands have been successfully brought to the clinic.
I will abstain from addressing the first point. With regard to the second, the argument that there is some mathematical rule that precludes dividing a logarithmic quantity by an integer is wrong. LE is simply a ratio of potency per atom. The fact that a log is involved in computing DeltaG, pKi, etc. is immaterial. He makes a more credible point that LE itself is on average non-linear with respect to large differences in HA count. But this is hardly a new observation, since exactly this trend has been discussed in detail by previous published studies (here, here, here, and here). It is, of course, true that if one goes to very low numbers of heavy atoms the classical definition of LE gets large, but as a practical matter medicinal chemists have little interest in extremely small fragments, and the mathematical catastrophe he warns us against only occurs when the number of heavy atoms goes to zero (with a zero in the denominator it makes no difference if there is a log in the numerator). Why would HA=0 ever be relevant to a med. chem. program? In any case a figure essentially equivalent to the prominently featured Figure 1a in the Shultz manuscript appears in all of the four papers listed above. You just need to know they exist.
With regard to the third argument, yes of course there are examples of drugs that defy one or more of the common guidelines (e.g MW). This seems to be a general problem of the community taking metrics and somehow turning them into “rules.” They are just helpful, hopefully, guideposts to be used as the situation and an organization’s appetite for risk dictate. One can only throw the concept of ligand efficiency out the window completely if you disagree with the general principle that it is better to design ligands where the atoms all, as much as possible, contribute to that molecule being a drug (e.g. potency, solubility, transport, tox, etc.). The fact that there are multiple LE schemes in the literature is just a natural consequence of ongoing efforts to refine, improve, and better apply a concept that most would agree is fundamental to successful drug discovery.
Well, as far as the math goes, dividing a log by an integer is not any sort of invalid operation. I believe that [log(x)]/y is the same as saying log(x to the one over y). That is, log(16) divided by 2 is the same as the log of 16 to the one-half power, or log(4). They both come out to about 0.602. Taking a BEI calculation as real chemistry example, a one-micromolar compound that weighs 250 would, by the usual definition, -log(Ki)/(MW/1000), have a BEI of 6/0.25, or 24. By the above rule, if you want to keep everything inside the log function, then say -log(0.0000001) divided by 0.25, that one-micromolar figure should be raised to the fourth power, then you take the log of the result (and flip the sign). One-millionth to the fourth power is one times ten to the minus twenty-fourth, so that gives you. . .24. No problem.
Shultz’s objection that LE is not linear per heavy atom, though, is certainly valid, as Reynolds notes above as well. You have to realize this and bear it in mind while you’re thinking about the topic. I think that one of the biggest problems with these metrics – and here’s a point that both Reynolds and Shultz can agree on, I’ll bet – is that they’re tossed around too freely by people who would like to use them as a substitute for thought in the first place.