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Analytical Chemistry

The Entropic Term is Laughing At Us

There are plenty of things to optimize in a med-chem project other than binding affinity. But if you don’t have at least some level of binding, you may not have a med-chem project. And while from the outside, you might think that understanding how and why compound A binds to a given target while compound B doesn’t is the first thing that medicinal chemists must be able to tell you, that just isn’t the case. We would very, very much like to be able to tell you that – and tell you that before we go to the trouble of making and testing compound B at all – but we can’t quite do it.

Here’s a surprising new paper that shows some of the complexity. You can understand a lot about compound binding to a protein target – if not predict it – by breaking apart the two terms of the free energy equation. Favorable binding means that free energy (delta-G) has to go down, otherwise it ain’t favorable, and it is of course made up of delta-H (enthalpy) minus delta-S (entropy) terms (that second one multiplied by the temperature, which for drug molecules in the body is always pretty much the same and can be neglected). And that’s where things get spectacularly hairy, because there are a lot of things that can contribute to both terms, both positively and negatively, and they are both wildly variable and computationally difficult to address reliably.

For example: a classic med-chem trick is to take a ligand, one that you know has some binding affinity for your target, find flexible parts of its structure, and restrict their movement. You can do that by adding some bulk near rotatable bonds, or tying two parts of the structure together to form a ring, and so on. Ring formation can be a death-or-glory move: it tends to either make binding quite a bit better or quite a bit worse. If your new ring keeps the compound from achieving the shape it needs to be in to bind, your affinity might just disappear. But if you’ve locked the molecule from the start into the conformation that it needs, you’ve gotten rid of the need for it to do that itself. Other things being equal, then, that means a better entropic term: instead of the molecule going from loose, floppy, and rotating to a single conformation (loss of entropy, which makes the overall free energy change less favorable), you’ve preorganized it so it doesn’t really lose any entropy at all in the binding event. Everyone’s happy!

Maybe not. What I’ve just given is the classic med-chem explanation for conformational restriction, and to be fair, there are many examples of it working in just that way. But not always. In this new paper (from a multicenter team at Marburg, Frankfurt, and Florence), the authors have taken a known kinase inhibitor, fasudil, and varied part of its structure (a homopiperazine ring) in just the way that you’d imagine a project team doing: they go to six-membered rings instead of seven, or break the homopiperazine ring open in different ways. They have X-ray crystallographic data on all of these variations, and they all have the same binding mode of the quinoline/sulfone part of their structures, which interacts with the hinge region of the kinase. They all have similar affinity as well.

But when you break down the thermodynamic profile of the compounds (via calorimetry) you find that they’re all over the place enthalpically and entropically, taking many different routes to roughly the same overall free energy change. That’s not so uncommon, although we don’t always take the trouble to see it. Weirdly, though the most flexible ligand of the bunch (compound 5 above) is actually the most entropically favorable, which is not what rule-of-thumb med-chem would predict at all. It’s actually the least enthalpically favorable as well, but that’s offset completely by the entropic term.

Bearing down on the problem with NMR relaxation measurements and calculations, it appears that it comes down to water molecules. If you’re looking for something to blame for an odd thermodynamic result in compound binding, that’s actually a good all-purpose answer, because they really are (1) crucial and (2) capable of all sorts of behavior. Releasing a bound water from a protein active site can, for example, be entropically good. Or entropically bad. Enthalpically bad. Or enthalpically good. It all depends, sadly, and it depends on things like the structure and motion of the rest of the protein, how it interacts with itself, the ligand, and the other water molecules in play, as well as the water molecules that were formerly around the ligand molecule and have to get out of the way for it to get into the binding site.

It’s a mess, and this paper is a pretty clear example of the reasons. It appears that ligand 5 has a conformation in solution that folds back and tends to partly trap some of its associated water molecules. Its hydration pattern is different than any of the others, and when it sheds those more-bound-than-usual waters, there’s a larger-than-usual gain in entropy as they leave. And this totally cancels out the mental picture that most of us med-chem types have, which depends on the entropy of the ligand structure and not of the water molecules around it.

So once again, there’s nothing simple about the thermodynamics of compound binding, and there are no details of it that cannot be important under one condition or another. Even quite similar compounds can display very different behavior, and depending on how closely you look, you may not even realize that they’re doing so. So if you’d like to know why we can’t just look at a big list of compounds and predict which ones will be the winners in a binding assay: this is why. And as I mentioned at the start of all this, binding affinity is just the beginning of what it takes to make a drug.

Some years ago, I asked a former med-chem colleague of mine who’d gone off to work as an analyst on Wall Street why, if each of us was supposed to be so smart and all, we’d picked professions where intelligence was necessary but nowhere near sufficient for success. Good question!

Update, via the comments: for more on this topic, see this earlier paper from Steve Martin’s group, and this review (free access) from the Chodera lab.

20 comments on “The Entropic Term is Laughing At Us”

  1. Tim Duignan says:

    I really don’t understand why any one tries to gain insight into binding affinity from entropy entropy partitioning. Karplus showed there are large water-water interaction contributions to enthalpy and entropy that rigorously cancel out in the free energy. your just introducing a bunch of irrelevant noise into.

  2. Tourettes of Chemistry says:

    Salvation by Solvation!

    Not just for Sundays anymore.

    Have been too occupied to respond with discipline to the earlier post on water in the context of the topic sentence.

    Way down there it is an entropy attenuator and is the most weakly appreciated aspect of ligand transfer from bulk bio milieu to a site of action. It often appears as a binary tribal type of thing.

    Great information.

  3. Imaging guy says:

    What can you say about QSAR based on this paper? What about peoples who are claiming that machine learning will predict whether a compound will bind to a protein?

    1. John says:

      This is what my team does…in excrutiating detail. I can basically say that the more you abstract things (ie move away from explicit water and quantum mechanical modelling) the rapidly worse everything gets. Machine learning is great and all, but the data going in…you know what they say. I think this will still be lots of brains and eyes on the problem for a while yet.

    2. secret sauce says:

      If you have enough data, especially within a homologous or among closely related chemical series, you can be quite predictive. That’s nothing new (i.e. Free-Wilson J. Med. Chem. 1964) and it’s still of course a prerequisite for newer QSAR models/machine learning/AI/yada-yada-yada.

      To Derek’s point and Wienen-Schmidt et al., it’s the physical causes of variation in binding affinity that’s of interest – why is this more potent, but not that? Or, equipotency may be due to non-obvious, compensating free-energy terms. “AI” doesn’t give a $%^& about the “why”. And co-crystal structures are just average snap-shots that lack insight into entropy – by it’s nature, entropy is difficult to physically visualize. So it’s important to understand the physics to improve first-principle modeling or gut-level synthetic design, especially if you don’t have enough data to build decent knowledge-based models.

  4. luysii says:

    Pop quiz. How would you make an enzyme in a cold dwelling organism (0 Centrigrade) as catalytically competent as its brothers living in us at 37 C?

    We know that reactions go faster the hotter it is, because there is more kinetic energy of the reactants to play with. So how do you make an enzyme move more when it’s cold and there is less kinetic energy to play with.

    They use entropy (and glycines on their surface) — for how see —

  5. Peter S. Shenkin says:

    @tim_duignan Well, this is an example of water-water interactions participating in a surprising way: the water-water interactions change when the solvation shell of the ligand is released to the bulk upon binding.

    So the question for med chemists is whether the knowledge thus gained can be used in ligand design to propose new drug candidates. Could a med chemist, in other words, design modifications of a lead candidate that would improve affinity using exactly this effect?

    The question for comp chemists is whether this effect can be predicted easily, given a virtual drug candidate — or a million of them.

    Ligand-based computational methods, such as pharmacophore, qsar and some forms of AI attempt to predict affinity based on ligand structure alone. An effect like this, though subtle and perhaps even rare, might be susceptible to these methods, given an appropriate training set.

    However, a complicating factor in this particular case is the large conformational change in the protein that occurs when binding only to this ligand, of those studied (Figure 2B of the paper) – also involving a “GLY loop”, @luysii. So it sounds like a tough one…

  6. Chrispy says:

    “What about the water?” is always a turd-in-the-punchbowl question when someone presents their new docking program. We are so far from being able to model this important part of binding that it really is embarrassing. That’s why I have always thought the most of the utility of in silico screening was to maintain interest in a program rather than to actually generate out-of-the-gate useful leads.

  7. Uncle Al says:

    professions where intelligence was necessary but nowhere near sufficient for success.
    Excess wealth creates polities wherein everything is gamed and documentation is written by Quill. We are privileged to engage a profession in which – if it isn’t in Pyrex, polystyrene, or steel – it cannot be net gamed.

  8. STIM says:

    This topic reminded me of a paper from Steve Martin’s lab:

  9. Barry says:

    not incidentally, the price for making this the entropically most favored binder of the cohort is making it the enthalpically least favored binder. It takes energy to desolvate.

    1. secret sauce says:

      Thanks for providing a pdf – looks like a great review by you and DM of the topic!

    2. Derek Lowe says:

      Thanks very much – I’ll put this up into the post as well.

  10. RET says:

    Well done, STIM.
    Steve Martin was the first I recall calling out the fact that classic med chem examples of restricted rotation analogues typically had additional atoms that affected enthalpy AND that when you corrected for this with actual isomeric analogue, entropy reared its head and not in a predicted way. This is another good example and this blog post needs to be read by many.

  11. Wavefunction says:

    There’s also the work from the Whitesides lab demonstrating such counterintuitive effects, in that case resulting (presumably) from changes in water networks around the ligand.

    1. Christophe Verlinde says:

      Except that the crystal structures that are supposed to back up the claims exhibit nearly non-existing electron density for some of the ligands.

  12. old man says:

    So is anybody looking at thermodynamics of binding as you progressively replace water with deuterium oxide? Sorry if this is a stupid question. Not a med-chemist.

    1. Anonymous says:

      I don’t know about your D2O Q. Instead of H20 to H2O, some of the experiments can be modified to look at partitioning from non-H2O solvents to the H20 systems. E.g., DMSO or MeCN (or more complex systems). In theory, all the water rearrangement terms thus only occur on the system side.

  13. compchem says:

    I always assumed the real world would be like this. Don’t understand why people would be surprised!

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