Here's a new paper from Michael Shultz of Novartis, who is trying to cut through the mass of metrics for new compounds. I cannot resist quoting his opening paragraph, but I do not have a spare two hours to add all the links:
Approximately 15 years ago Lipinski et al. published their seminal work linking molecular properties with oral absorption.1 Since this ‘Big Bang’ of physical property analysis, the universe of parameters, rules and optimization metrics has been expanding at an ever increasing rate (Figure 1).2 Relationships with molecular weight (MW), lipophilicity,3 and 4 ionization state,5 pKa, molecular volume and total polar surface area have been examined.6 Aromatic rings,7 and 8 oxygen atoms, nitrogen atoms, sp3 carbon atoms,9 chiral atoms,9 non-hydrogen atoms, aromatic versus non-hydrogen atoms,10 aromatic atoms minus sp3 carbon atoms,6 and 11 hydrogen bond donors, hydrogen bond acceptors and rotatable bonds12 have been counted and correlated.13 In addition to the rules of five came the rules of 4/40014 and 3/75.15 Medicinal chemists can choose from composite parameters (or efficiency indices) such as ligand efficiency (LE),16 group efficiency (GE), lipophilic efficiency/lipophilic ligand efficiency (LipE17/LLE),18 ligand lipophilicity index (LLEAT),19 ligand efficiency dependent lipophilicity (LELP), fit quality scaled ligand efficiency (LE_scale),20 percentage efficiency index (PEI),21 size independent ligand efficiency (SILE), binding efficiency index (BEI) or surface binding efficiency index (SEI)22 and composite parameters are even now being used in combination.23 Efficiency of binding kinetics has recently been introduced.24 A new trend of anthropomorphizing molecular optimization has occurred as molecular ‘addictions’ and ‘obesity’ have been identified.25 To help medicinal chemists there are guideposts,21 rules of thumb,14 and 26 a property forecast index,27 graphical representations of properties28 such as efficiency maps, atlases,29 ChemGPS,30 traffic lights,31 radar plots,32 Craig plots,33 flower plots,34 egg plots,35 time series plots,36 oral bioavailability graphs,37 face diagrams,28 spider diagrams,38 the golden triangle39 and the golden ratio.40
He must have enjoyed writing that one, if not tracking down all the references. This paper is valuable right from the start just for having gathered all this into one place! But as you read on, you find that he's not too happy with many of these metrics - and since there's no way that they can all be equally correct, or equally useful, he sets himself the task of figuring out which ones we can discard. The last reference in the quoted section below is to the famous "Can a biologist fix a radio?" paper:
While individual composite parameters have been developed to address specific relationships between properties and structural features (e.g. solubility and aromatic ring count) the benefit may be outweighed by the contradictions that arise from utilizing several indices at once or the complexity of adopting and abandoning various metrics depending on the stage of molecular optimization. The average medicinal chemist can be overwhelmed by the ‘analysis fatigue’ that this plethora of new and contradictory tools, rules and visualizations now provide, especially when combined with the increasing number of safety, off-target, physicochemical property and ADME data acquired during optimization efforts. Decision making is impeded when evaluating information that is wrong or excessive and thus should be limited to the absolute minimum and most relevant available.
As Lazebnik described, sometimes the more facts we learn, the less we understand.
And he discards quite a few. All the equations that involve taking the log of potency and dividing by the heavy atom count (HAC), etc., are playing rather loose with the math:
To be valid, LE must remain constant for each heavy atom that changes potency 10-fold. This is not the case as a 15 HAC compound with a pIC50 of 3 does not have the same LE as a 16 HAC compound with a pIC50 of 4 (ΔpIC50 = 1, ΔHAC = 1, ΔLE = 0.07). A 10-fold change in potency per heavy atom does not result in constant LE as defined by Hopkins, nor will it result in a constant SILE, FQ or LLEAT values. These metrics do not mathematically normalize size or potency because they violate the quotient rule of logarithms. To obey this rule and be a valid mathematical function HAC would subtracted from pIC50 and rendered independent of size and reference potency.
Note that he's not recommending that last operation as a guideline, either. Another conceptual problem with plain heavy atom counting is that it treats all atoms the same, but that's clearly an oversimplification. But dividing by some form of molecular weight is an oversimplification, too: a nitrogen differs from an oxygen by a lot more than that 1 mass unit. (This topic came up here a little while back). But oversimplified or not - heck, mathematically valid or not - the question is whether these things help out enough when used as metrics in the real world. And Shultz would argue that they don't. Keeping LE the same (or even raising it) is supposed to be the sign of a successful optimization, but in practice, LE usually degrades. His take on this is that "Since lower ligand efficiency is indicative of both higher and lower probabilities of success (two mutually exclusive states) LE can be invalidated by not correlating with successful optimization."
I think that's too much of a leap - because successful drug programs have had their LE go down during the process, that doesn't mean that this was a necessary condition, or that they should have been aiming for that. Perhaps things would have been even better if they hadn't gone down (although I realize that arguing from things that didn't happen doesn't have much logical force). Try looking at it this way: a large number of successful drug programs have had someone high up in management trying to kill them along the way, as have (obviously) most of the unsuccessful ones. That would mean that upper management decisions to kill a program are also indicative of both higher and lower probabilities of success, and can thus be invalidated, too. Actually, he might be on to something there.
Shultz, though, finds that he's not able to invalidate LipE (or LLE), variously known as ligand-lipophilicity efficiency or lipophilic ligand efficiency. That's p(IC50) - logP, which at least follows the way that logarithms of quotients are supposed to work. And it also has been shown to improve during known drug optimization campaigns. The paper has a thought experiment, on some hypothetical compounds, as well as some data from a tankyrase inhibitor series that seem to show the LipE behave more rationally than other metrics (which sometimes start pointing in opposite directions).
I found the chart below to be quite interesting. It uses the cLogP data from Paul Leeson and Brian Springthorpe's original LLE paper (linked in the above paragraph) to show what change in potency you would expect when you change a hydrogen in your molecule to one of the groups shown if you're going to maintain a constant LipE value. So while hydrophobic groups tend to make things more potent, this puts a number on it. A t-butyl, for example, should make things about 50-fold more potent if it's going to pull its weight as a ball of grease. (Note that we're not talking about effects on PK and tox here, just sheer potency - if you play this game, though, you'd better be prepared to keep an eye on things downstream).
On the other end of the scale, a methoxy should, in theory, cut your potency roughly in half. If it doesn't, that's a good sign. A morpholine should be three or four times worse, and if it isn't, then it's found something at least marginally useful to do in your compound's binding site. What we're measuring here is the partitioning between your compound wanting to be in solution, and wanting to be in the binding site. More specifically, since logP is in the equation, we're looking at the difference in the partitioning of your compound between octanol and water, versus its partitioning between the target protein and water. I think we can all agree that we'd rather have compounds that bind because they like something about the active site, rather than just fleeing the solution phase.
So in light of this paper, I'm rethinking my ligand-efficiency metrics. I'm still grappling with how LipE performs down at the fragment end of the molecular weight scale, and would be glad to hear thoughts on that. But Shultz's paper, if it can get us to toss out a lot of the proposed metrics already in the literature, will have done us all a service.