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Ligand Efficiency Rethought

Peter Kenny has a paper out on ligand efficiency that’s required reading for medicinal chemists using (or thinking about) that concept as a design tool. I’d recommend reading it with this recent paper – between the two of them, you’re going to have references to a huge swath of the literature on how to measure drug optimization, and you’ll emerge with a strong background on just how hard that is to do.

Broadly put, LE is (or is supposed to be) a way to think about binding of a molecule to its target, adjusted for the size of the molecule. At that level, things aren’t really controversial: there are ligands that do a better job of binding to their targets because they involve more of their own structures in various interactions. Imagine some compound with a molecular weight of 230 (or the equivalent number of heavy atoms, etc.) that has a binding constant of 1 micromolar versus its protein target. Now imagine another molecule, also with 1 micromolar binding, with a molecular weight of 600. It seems clear that the smaller molecule is using its structure more thoroughly, whereas the larger one would seem to have a good deal of its structure not involved very productively at all. If there aren’t other good reasons to keep all that stuff, why should you? Don’t add things to your compound’s structure unless you’re getting some sort of return on them. This we can agree on.

The problem, as Kenny shows, is the way that most of us define LE. He says that it’s “a good concept that is poorly served by a bad metric”. The problem is that most of those definitions have a log function of some sort in them that causes trouble (as pointed out several years ago, responses to that here and here) and this makes some of the LE definitions either play rather loose with the math and/or causes the ligand efficiency numbers themselves to depend hugely on how you define the drug concentrations. The standard ligand efficiency metric, indeed, assumes an arbitrary concentration as a starting point to make the numbers come out “right”, and there’s just no thermodynamic basis for this. As Kenny observes, acidly but appropriately, “In thermodynamic analysis, a change in perception resulting from a change in a standard state definition would generally be regarded as a serious error rather than a penetrating insight.” Later on in the paper, after showing through example how LE varies with the units chosen for concentration, he puts it this way: “A physical quantity that is expressed in different units is still the same quantity. If perception changes when a quantity is expressed using a different unit then neither the change in perception nor the quantity itself can be regarded as physically meaningful“.

And here’s where we look under the hood of property-based drug design. You can see some of its assumptions in my paragraph above – the idea (to quote Kenny) is “balancing the risk associated with poor physicochemical characteristics against the risk of not being able to achieve the necessary level of affinity”. Both of these risks are necessarily rather hard to get a handle on, but that hasn’t stopped people from trying (see that 2013 blog in the paragraph above). And the whole situation has been muddied thoroughly by the “if it can be measured it will be managed” phenomenon, a problem that’s found in more places than just the drug industry. Over the years, too many people have seized on the idea of measuring and calculating their way to drug-discovery success – crudely, “Just fix X and you’ll be OK”, where X is any number of physical properties or structural characteristics. By this time, it should be clear that there is no X that fits a “Just fix X” mentality. One hates to fall back on saying “It’s too complicated for that”, but you know, it really is too complicated for that.

Drug design guidelines are typically based on trends observed in data and the strengths of these trends indicate how rigidly guidelines should be adhered to. While excessive molecular size and lipophilicity are widely accepted as primary risk factors in design, it is unclear how directly predictive they are of more tangible risks such as poor oral absorption, inadequate intracellular exposure and rapid turnover by metabolic enzymes. This is an important consideration because the strength of the rationale for using LE depends on the degree to which molecular size is predictive of risk.

That’s very sensibly put. Sometimes the trends we can measure are useful predictors, and other times they aren’t. And even the things that we tend to think are useful a greater part of the time (such as molecular weight and lipophilicity) have real problems as predictive tools. But if these things aren’t predictive on some given project, why use ligand efficiency as a tool at all? And why do we think that those properties are useful in general? Kenny lays down the challenge: “Drug designers should not automatically assume that conclusions drawn from analysis of large, structurally-diverse data sets are necessarily relevant to the specific drug design projects on which they are working.”

I’m getting mildly infamous for a talk that I give which compares the workings of drug discovery to those of Wall Street, but in this case it’s impossible not to be reminded of the investing classic “Where are the Customer’s Yachts”, a book that is a rich concentration of good sense. In it, Fred Schwed reviews a few of the classic ideas about stock market prices and concludes that “All of these theories are true part of the time; none of them true all of the time. They are, therefore, dangerous, though sometimes useful.” This applies word-for-word to the use of compound metrics for drug discovery. And the provocative line above is powerfully reminiscent of one from the 1930s fund manager John W. Pope, whom Schwed quotes: “It is the belief of the management of this corporation that a diversified list of carefully selected securities, held over a period of time, will not increase in value“.

Both sound like heresy, but they should be given a careful hearing. One of Kenny’s points is that drug discovery is too various to make broad averages of behavior broadly useful. There are too many special considerations in this business that can override the rules of thumb – a situation that is not improved by the way that this always sounds like special pleading when it’s invoked.

There’s also a solidly argued section in the paper that goes into the problems of using LE to try to break down the contributions of individual parts of a molecule to its overall affinity. Read the paper, but what you’ll find is that this dream – and it is a dream, breaking everything down into independent pieces this way – is generally unworkable. Problems of stoichiometry and non-local effects (one end of the molecule affecting another in indirect ways) confound this approach. Not that it keeps people from trying it, under many guises – it’s just too appealing.

What about all the papers that talk about using ligand efficiency metrics for guiding a project along? Here’s Kenny’s take on that, and anyone familiar with the med-chem literature from the inside may well cringe in recognition:

. . .a depiction of an optimization path for a project that has achieved a satisfactory endpoint is not direct evidence that consideration of molecular size or lipophilicity made a significant contribution toward achieving that endpoint. Furthermore, explicit consideration of lipophilicity and molecular size in design does not mean that efficiency metrics were actually used for this purpose.

By the time a project is written in in J. Med. Chem. or wherever, the story you’re reading is likely not quite the story as it happened. The delays in industrial publication are one factor – people have left, and even without that, it can be hard to reconstruct the order that things happened in, which ideas came from where, why certain things lasted as long as they did or why others weren’t realized earlier. Every project looks that way on close inspection, when such inspection is possible. (Amateur astronomy analogy: every reflecting telescope’s mirror looks filthy if you shine a flashlight across it at a low angle, even if it’s perfectly serviceable). So while you should be able to believe the data, believing the rationales advanced along with those data is a riskier move. This goes (as the paper demonstrates) for many fragment-based drug discovery papers that use LE to tell their story. Kenny’s fine with the idea behind using fragments as starting points (as am I!) and he’s find with the idea of trying to make additions to a fragment’s structure prove their worth along the way. He’s just saying that LE is not the way to do it.

Well, my overall advice is “read the paper”! You’ll find some provocative (but difficult to refute) statements, a thorough review of the literature, and plenty of food for thought. It looks like a thorough re-evaluation of the whole idea of measured compound metrics is underway, now with years of evidence behind it, and we need to decide if we’re getting enough utility out of these things or not. The answer at this point, frankly, looks like “not”.

31 comments on “Ligand Efficiency Rethought”

  1. jim says:

    Do you have example Derek where someone uses a different unit for LE calculation?

    1. Derek Lowe says:

      Check out the paper (it’s open access on Chemxiv) – Kenny has some figures and tables showing the effect.

    2. Peter Kenny says:

      Although it is certainly uncommon to use a concentration unit other than 1 M, antibacterial efficiency is defined using a concentration unity of 1 mg/ml (I have linked the doi for the article as the URL for this comment).

  2. As you note (cf. earlier In the Pipeline posts, etc.), Pete has been cogently making this fundamentally sound point for many years. Ligand efficiency, as currently defined and widely used, is thermodynamically indefensible.

    That said, the more general concept of “Let’s get a handle on how big and/or greasy our molecules are, relative to how well they engage the target productively” is absolutely valid and useful. Separates the junk from the gems, and helps to guide useful v. useless chemical modifications.

    To me, the Moral of the Story is this: Don’t slavishly pursue some numerical metric thinking that’s where the Pot of Gold lies hidden.

    1. Hap says:

      “If I can’t measure it, I can’t manage it.” is probably why it persists – people don’t like being held responsible for making the wrong guesses (with big money on the line), and so they’d rather have something to devolve blame (even if it works worse than a judgment-based method) than to run the risk of being nailed for a judgment. Also related to the persistence of impact factors and citation counts – judgments are difficult and slippery, while numbers don’t lie (even if they don’t tell the truth, or all of it).

  3. Kudos to Peter Kenny (and other “heretics”) for trying to keep Ro5 evangelists, Ro5-wannabes, and bean-counting management honest, or at least in check over the years. How many project teams have had to deal with numbskull application of Ro5 (et al) as doctrine, and still do? Fortunately, Michael Shultz’s analysis suggests that not everyone drank the koolaid, or least the discovery chemistry scientists were clever enough to work around it.

  4. TJ says:

    David – now we are all dying to see your infamous drug discovery = Wall Street talk. Are the slides somewhere?

  5. Leo says:

    Increasing ligand efficiency might not be great for ligand specificity – if the “extra bulk” of the molecule is more compatible with a specific binding site.

  6. anon3 says:

    Sorta a long drawn out argument about something that, regardless of the outcome, will have no meaningful impact on actual drug discovery.

  7. Wavefunction says:

    I think the problem is that human minds are not trained to grasp and use semi-qualitative notions, so they have to quantify these to the point of flawed utility.

  8. ChemGod says:

    Any word on Relay Therapeutics? Last time I checked, there were great promises made but things seem wishy washy there at the moment…

  9. I’ve read the paper, and while I agree with the broad point that drug discovery is complex and that no metric should be treated as a commandment, I disagree strongly with the assertion that ligand efficiency is “thermodynamically indefensible.”

    Pete has been complaining about the standard state for years (click my name for a 2016 exchange, with links to earlier discussions). If we throw out standard state, we also throw out our definitions as to whether ligand binding to a protein is favorable or not. The old cliche about babies and bathwater is relevant.

    1. Peter Kenny says:

      Hi Dan, if you disagree with Derek’s statement (which I fully agree with) that LE is “thermodynamically indefensible” then you do need to offer a defense. Contrary to what you say, I have not been complaining about the standard state for years. What I have complained about is analyses that fail to recognize that the choice of standard state is arbitrary and I’d suggest that you take a look at the articles by Mike Gilson that I cited. If your analysis requires that a particular concentration unit be used to define the standard state then you are no longer doing thermodynamics.

      I would strongly challenge your statement “If we throw out standard state, we also throw out our definitions as to whether ligand binding to a protein is favorable or not.” First recognizing that the standard state is arbitrary is not throwing it out. Second, whether or not ligand binding to protein is favorable depends on the ratio of ligand concentration to Kd and is independent of the standard state definition. The difficulty of measuring Kd values greater than 1 M pretty much guarantees that standard free energy of binding (for 1 M standard state) will be negative. When arguing the case for 1 M as the one true standard concentration, it can be instructive to consider what a 1 M solution of a protein might look like.

      1. anon says:

        @ Kenny….I am not a physical organic chemist and am still trying to make some sense out of it all, after what we have been taught about LE. How does nature devise endogenous ligands for a given receptor and in your estimate, at what concentrations? We are talking talking about evolution over millions of years? Just curious.

    2. Dan, I believe Pete is correct, here.

      To me, the key is this: “[W]hether or not ligand binding to protein is favorable depends on the *ratio* of ligand concentration to Kd and is independent of the standard state definition.”

      Once one has defined ones (arbitrary) “standard state”—e.g., 1 mole/liter = an arbitrary number of molecules, in an arbitrary volume—then all is good, because deltaG depends on the *ratio* of two numbers referenced to that (arbitrary) “standard state.” Thankfully, then, all that arbitrariness goes flying out the window (“arbitrary/arbitrary” = 1).

      For those who are thinking that Avogadro’s number is “special,” recall that it is (roughly) defined the number of carbon-12 atoms in 12 grams of carbon (or is it oxygen-16 atoms? definitions change…).

      Well, what is 12 grams? Imprecisely, the mass of 12 cubic centimeters of *water*.
      What’s so special about water? (Ask Phillip Ball)
      What’s a centimeter? Imprecisely, but originally [1793], one-hundredth of “one ten-millionth of the distance from the equator to the North Pole.”
      What’s so special about Terra (other than that it’s our very comfortable and beautiful spaceship)?

      Doesn’t get more arbitrary than that.

      All this is to suggest that our Friends elsewhere in the Universe are unlikely to think in terms of our very anthropomorphic and geomorphic units…and yet thermodynamics works for them as well (at least, I presume it does).

      1. Peter Kenny says:

        Hi David, I believe that water featured (a litre of water weighs a kilogram) in the establishment of the metric system and the 1 M standard state has its origins in developments in France at the end of the 18th century. In general, the molarity of a solute has a weak dependence on both temperature and pressure.

      2. Hi David and Pete,
        Sure, the definition of standard state is arbitrary, as is the definition of the mole. Where I think we disagree is over whether this makes metrics that use standard state or moles “thermodynamically indefensible.”

        The following 2015 exchange (link in my name) illustrates the rather absurd “relativism” that results if you fiddle with standard state definitions.

        Dan: Kd = [P][L]/[PL], where [P] = concentration of protein, [L] = concentration of ligand, and [PL] = concentration of complex at equilibrium

        Pete: Agree

        Dan: ΔG˚ = −RT ln Kd/C°

        Pete: Agree although on the understanding that the ΔG˚ in the equation is for the dissociation process. Normally we write this equation without the minus sign because we conventionally use a dissociation constant with an association free energy.

        Dan: Let’s take your example of a protein-ligand complex with Kd = 10 nM. Under standard state conditions where C° = 1 M and T = 298 K, ΔG˚ = + 10.9 kcal/mol

        Pete: Agree with the math (on the understanding that ΔG˚ is for the dissociation process) but disagree with inclusion of temperature in the definition of the standard state. Temperature is very important but is a very different to C° in the context of this discussion. If you change temperature, you really do change the system and you need to know about changes in enthalpy (and, in some cases, heat capacity) in order to use Kd measured at 298 K to calculate Kd at 310 K. It generally makes things clearer to write energies as RTln(ratio) in discussions like these although it’s not a big deal for what we’re talking about.

        Dan: If we define C° = 1 nM, ΔG˚’ = – 1.36 kcal/mol

        Pete: Agree for T = 298 K and on the understanding that that ΔG˚ is for the dissociation process.

        Dan: Thus, changing the definition of the standard state can change the sign of ΔG˚

        Pete: Agree

        1. Peter Kenny says:

          Hi Dan, the standard state definition is arbitrary and it is necessarily arbitrary since thermodynamics requires that that you come to the same conclusion regardless of how you define the standard state. The short answer is that to require C° to take a particular value of C° is “thermodynamically indefensible” (although I wouldn’t word it exactly as Derek has done, I am in full agreement with his statement). In science, you are allowed to express quantities in any dimensionally correct units that you want (I’m not claiming that all units are equally convenient and I still remember having to use poundals in high school math class while we were using newtons in physics class). A change perception when you change unit is, as I was forced to point out to one of the reviewers assigned by J Med Chem to my manuscript, a very serious error in the ‘not even wrong category’.

          It can be helpful to think of ΔG° as a function of C°. In thermodynamic terms, ΔG° (of binding) is simply the difference in chemical potential (a state function ) between the complex and the unassociated protein + ligand with all three species at C°. The stochiometry is important because dilution by a factor of 10 reduces the chemical potential of each species by 1.36 kcal/mol. This means that dilution always stabilizes the unassociated protein + ligand more than it stabilizes the complex. This is basis of the law of mass action which tells us that all reversibly formed protein-ligand complexes will dissociate if you dilute them enough. Tautomeric equilibria involve no net change in the number of species and cannot be driven by changing concentration (this is one reason that that equilibrium constants for tautomerism are typically difficult to determine).

          One of the points that I made in the article is the stoichiometry is a ‘hidden dimension’ of a free energy change. The problems associated with LE become much clearer if you do the math with equilbrium constants rather than free energy differences. The above reviewer stated that equation (9) was “nonsensical” . I pointed out that the equation was dimensionally and algebraically correct and if the reviewer found it nonsensical then it was perhaps because LE was nonsensical.

          Although you talk of “rather absurd ‘relativism’”, you do need to remember that all free energy changes are are relative. The folk doing free energy calculations talk of absolute and relative free energy. However, the ‘absolute’ free energies are still free energy differences (that depend on C°) and the ‘relative’ free energies are actually ΔΔG values (that are independent of C°). While there may a degree of novelty in the way that I treat stoichiometry as a dimension, the thermodynamics section of the article is standard physical chemistry (even though it got two of the reviewers spitting feathers). If you’re still uncomfortable with the idea of an arbitrary standard state then why not take a look at the articles by Mike Gilson that I cited? Also take a look at what Jencks was saying in 1981 about units and fragment linking.

  10. ML says:

    LE as a metric is flawed for a different reason rather than the maths underlying it…

    It is extremely unlikely that if you take a ligand efficient fragment you can maintain its ligand efficiency through development. The reason being is that fragments can fit a binding pocket and deliver interactions with the right bond angles/lengths and therefore be very efficient. As we grow a fragment into a drug we build up further interactions to increase binding affinity. Unfortunately, drug designers are limited by the range of bond angles/lengths they can use. It is therefore unlikely they can deliver all the additional interactions for a larger compound perfectly, resulting in a drop to ligand efficiency. For this reason, it is difficult to compare large and small compounds using LE!

    I only use LE to rank compounds during the analysis of say an HTS screen. After picking some of the most potent hits from a screen I then rank the remaining hits by LE. This allows me to select some really efficient small compounds that I would have otherwise ignored. I think this helps to balance the range of scaffolds selected for further optimisation.

    1. Markus Kossner says:

      If I understood the literature correctly, then LE is not even usefull for ranking a HTS outcome (for exactly the effect you menitoned in your post as well: larger molecules get inapropriately penalized!)

      1. Bozo says:

        So if you must choose between 2 HTS hits with a potency of 1 microMolar, and one has a MolWt of 250 and the other 500, which one would you prioritize for hit expansion (assuming that they otherwise look reasonable from a medchem perspective)?

        1. Evangelist says:

          Well, if it’s that clear, then the discussion has nothing to do with a need for a mteric

          1. Peter Kenny says:

            Evangelist, this is a good point and, for compounds with equal activity, favoring the one with lower molecular weight is a rational decision. The situation that LE is intended for is more like when you are trying to decide whether to go for the 1 mM fragment hit with 10 non-hydrogen atoms or the 3 µM HTS with 20 non-hydrogen atoms. In practise there are many other factors that need to be taken account of when deciding which screening hits to take forward.

        2. Markus Kossner says:

          I’d rank by activity first, then by heavy atoms. I’d pick the ligther one (all other things being equal)
          But that has nothing to do with Peter Kenny’s criticism of a proposed normalization formula that is at least dubious.

  11. Greg says:

    I think the paper misses the point of numbers and metrics. Their point is not to “solve” medicinal chemistry but provide guidance to enable systematic decision making. I don’t think there is anyone arguing the straw man position here of blindly following any metric. Its adoption is driven by people finding it useful not treating it as gospel

    The solution to the flaws in Ligand Efficiency is to make an even better metric to enable better decision making. Anyone can be a critic, few can do something about it

    1. Markus Kossner says:

      Hi Greg, I guess I dissagree:
      I still find Peter Kenny’s arguments for using the residuals of a fit to your data at hand more convincing.
      In other words, why use a hairy metric if basic data analysis (regression; residuals) is actually more acurate?

      1. Peter Kenny says:

        Markus, I’m glad that you found the arguments for using residuals convincing. One point worth making is that the residuals are not generated in isolation but come from analysis that arguably should be done anyway.

    2. Peter Kenny says:

      Greg, I would argue that LE is unfit for the purpose of providing guidance for systematic decision making. The reason for this is that perception of efficiency varies with the concentration unit used to express affinity and LE should not even be considered to be a metric. At very least, those who advocate that LE be used in decision making either need to demonstrate that their choice of concentration unit is appropriate or that the dependence of perception on concentration unit is not an issue. I do not believe that it is possible to define a compound-based ligand efficiency in an objective manner although I would be happy to be proven wrong on this point.

      Contrary to what you appear to be suggesting, I do make some recommendations and the need to directly observe relationships between affinity and molecular size is a recurring theme in the study. In particular, I do discuss what normalization means and suggest that residuals can be used to quantify the extent to which the activity of a compound beats (or is beaten by) the trend in the data.

  12. Medchemist says:

    Pretty much everything Kenny said, I have said the same when I was in big pharma, and was persecuted for it. Why did it take so long to see a paper like this? It shouldn’t have taken a genius like Kenny to figure this out.

    1. Dr CNS says:

      Well… the manuscript was rejected by J Med Chem.
      That alone is telling you something about the current state of Medicinal Chemiatry, perhaps? Or maybe a few reviewers…

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