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Drug Assays

Unraveling An Off-Rate

Medicinal chemists talk a lot more about residence time and off rate than they used to. It’s become clear that (at least in some cases) a key part of a drug’s action is its kinetic behavior, specifically how quickly it leaves its binding site. You’d think that this would correlate well with its potency, but that’s not necessarily so. Binding constants are a mix of on- and off-rates, and you can get to the same number by a variety of different means. Only if you’re looking at very similar compounds with the same binding modes can you expect the correlation your intuition is telling you about, and even then you don’t always get it.
There’s a new paper in J. Med. Chem. from a team at Boehringer Ingelheim that takes a detailed look at this effect. The authors are working out the binding to the muscarinic receptor ligand tiotropium, which has been around a long time. (Boehringer’s efforts in the muscarinic field have been around a long time, too, come to think of it). Tiotropium binds to the m2 subtype with a Ki of 0.2 nM, and to the m3 subtype with a Ki of 0.1 nM. But the compound has a much slower off rate on the m3 subtype, enough to make it physiologically distinct as an m3 ligand. Tiotropium is better known by its brand name Spiriva, and if its functional selectivity at the m3 receptors in the lungs wasn’t pretty tight, it wouldn’t be a drug. By carefully modifying its structure and introducing mutations into the receptor, this group hoped to figure out just why it’s able to work the way it does.
The static details of tiotropium binding are well worked out – in fact, there’s a recent X-ray structure, adding to the list of GPCRs that have been investigated by X-ray crystallography. There are plenty of interactions, as those binding constants would suggest:

The orthosteric binding sites of hM3R and hM2R are virtually identical. The positively charged headgroup of the antimuscarinic agent binds to (in the class of amine receptors highly conserved) Asp3.32 (D1483.32) and is surrounded by an aromatic cage consisting of Y1493.33, W5046.48, Y5076.51, Y5307.39, and Y5347.43. In addition to that, the aromatic substructures of the ligands dig into a hydrophobic region close to W2004.57 and the hydroxy groups, together with the ester groups, are bidentally interacting with N5086.52, forming close to optimal double hydrogen bonds. . .

The similarity of these binding sites was brought home to me personally when I was working on making selective antagonists of these myself. (If you want a real challenge, try differentiating m2 and m4). The authors point out, though, and crucially, that if you want to understand how different compounds bind to these receptors, the static pictures you get from X-ray structures are not enough. Homology modeling helps a good deal, but only if you take its results as indicators of dynamic processes, and not just swapping out residues in a framework.
Doing point-by-point single changes in both the tiotropium structure and the the receptor residues lets you use the kinetic data to your advantage. Such similar compounds should have similar modes of dissociation from the binding site. You can then compare off-rates to the binding constants, looking for the ones that deviate from the expected linear relationship. What they find is that the first event when tiotropium leaves the binding site is the opening of the aromatic cage mentioned above. Mutating any of these residues led to a big effect on the off-rate compared to the effect on the binding constant. Mutations further up along the tunnel leading to the binding site behaved in the same way: pretty much identical Ki values, but enhanced off-rates.
These observations, the paper says with commendable honesty, don’t help the medicinal chemists all that much in designing compounds with better kinetics. You can imagine finding a compound that takes better advantage of this binding (maybe), but you can also imagine spending a lot of time trying to do that. The interaction with the asapragine at residue 508 is more useful from a drug design standpoint:

Our data provide evidence that the double hydrogen interaction of N5086.52 with tiotropium has a crucial influence on the off-rates beyond its influence on Ki. Mutation of N5086.52 to alanine accelerates the dissociation of tiotropium more than 1 order of magnitude than suggested by the Ki. Consequently, tiotropium derivatives devoid of the interacting hydroxy group show overproportionally short half-lives. Microsecond MD simulations show that this double hydrogen bonded interaction hinders tiotropium from moving into the exit channel by reducing the frequency of tyrosine-lid opening movements. Taken together, our data show that the interaction with N5086.52 is indeed an essential prerequisite for the development of slowly dissociating muscarinic receptor inverse agonists. This hypothesis is corroborated by the a posteriori observation that the only highly conserved substructure of all long-acting antimuscarinic agents currently in clinical development or already on the market is the hydroxy group.

But the extracellular loops also get into the act. The m2 subtype’s nearby loop seems to be more flexible than the one in m3, and there’s a lysine in the m3 that probably contributes some electrostatic repulsion to the charged tiotropium as it tries to back out of the protein. That’s another effect that’s hard to take advantage of, since the charged region of the molecule is a key for binding down in the active site, and messing with it would probably not pay dividends.
But there are some good take-aways from this paper. The authors note that the X-ray structure, while valuable, seems to have large confirmed the data generated by mutagenesis (as well it should). So if you’re willing to do lots of point mutations, on both your ligand and your protein, you can (in theory) work some of these fine details out. Molecular dynamics simulations would seem to be of help here, too, also in theory. I’d be interested to hear if people can corroborate that with real-world experience.

20 comments on “Unraveling An Off-Rate”

  1. Teddy Z says:

    This was a hot subject at the recent Biophysics in DD conference in Strasbourg (I blogged my thoughts just this morning, link above). The question for kinetic (and thermodynamic) data is can it be a prospective tool, or is it fated to be only a retrospective tool?

  2. I am glad that long residence times are slowly but surely appearing on medicinal chemists’ radar. It’s about time. Robert Copeland has been emphasizing this concept and its applications for a long time, and in his excellent book “Evaluation of Enzyme Inhibitors in Drug Discovery” there is a whole chapter dedicated to case studies where long residence times rather than potency correlated with the effects of a drug. My favorite was a case where residence time correlated with the ultimate phenotypic endpoint – death.

  3. watcher says:

    On/Off rates are not a new concept in drug design. I was involved in trying to use them 25+ years ago. But so far, it has been impossible to design a slow binding or tight binding (not covalent) inhibitor de novo. And I really don’t see that this paper or others have made much progress in helping design de novo new active site binders that have such properties.

  4. Curious Wavefunction says:

    I forgot to mention that except in exceptional cases, you would probably have to run MD simulations for a prohibitively long time to actually simulate such long residence times. However you could certainly get qualitative hints from short simulations, for instance regarding certain specific interactions (like the hydroxyl-arg tryst in this case) which would point to potential determinants of long off rates.

  5. anon says:

    To #2: A concept that has been well known for years. See All the examples in Bob’s book are retrospectively analyzed. None were done by proactive design. Look at the very detailed kinetic papers by John Morrison, and examples/applications from Steve Benkovich.

  6. SAR Screener says:

    @1 I don’t know, but how many people have ever tried using it as a prospective tool? I’ve sat through plenty of target residence time talks now and never seen one that wasn’t post rationalisation of the data.

  7. Hap says:

    Why does k(off) determine so much on its own? Since Ki = k(on)/k(off), doesn’t a low k(off) but a similar Ki mean that k(on) has to be low, also? That would mean that you’d either have to get a higher concentration around to get it into receptors so it can stay or you would have to have it stay around the compartment with the receptors for longer so that it can bind.

  8. Teddy Z says:

    Also remember that prolongation only helps you when koff

  9. Pete says:

    Slow binding is pharmacokinetically equivalent to slow distribution and one question that one might want to consider is whether one would want to design slow distribution into a drug. As free drug levels start to fall, a drug that binds slowly will have engaged its target to a lesser extent than a faster binder with the same Kd.

  10. #6: Since we are only now starting to get a handle on understanding slow dissociation rates, I am hopeful that we will be able to use them as a prospective tool soon. For instance we are increasingly recognizing that displacing water molecules can lead to long k(off)s (Jonathan Mason from Heptares had a paper on this recently) so targeting water molecules could be a viable strategy in the future. Success would of course still be target-dependent but that’s the case for pretty much every tool in drug design.

  11. weirdo says:

    To Hap’s and Pete’s points:
    There’s a good paper out there going through the math of this — the title is something like “Binding Kinetics Don’t Matter Pharmacologically”. OK, maybe I’m paraphrasing.
    Bottom line is kinetics won’t help you if you don’t fix clearance issues.

  12. SAR Screener says:

    @9 Goran Dahl has published a paper modelling pharmacokinetics and residence time. The gist of it seems to be that PK is more important than residence time. Not sure how that squares with the observation that most drugs do display unusual kinetics though.

  13. annonie says:

    #6: In concept that sounds good, but in pracctice has major flaws. What PK parameter would/could be evaluated to know if you have a slow tight binder? Also, PK parameters are macro parameters, while koff is a micro parameter. In addition, #11’s practical concern, the number (eg concentration) of binding sites systemically for a typical target are very small relative to the concentrations and levels of drug measured in in vivo PK studies. So, slow release rates would be missed. Certainly, it might be possible to identify longer retention in tissues with high levels of the target receptor or enzyme using radiolabel. But that is not a routine experiment, and not one that can be conducted in humans.

  14. Mutatis Mutandis says:

    GSK is experimenting with “albudabs”, albumin-binding antibody fragments that are linked to peptide drugs. (They bought the firm, but are willing to share the technology with academics.) The idea is that this would give the peptide the much longer in vivo half-life of albumin. It is an interesting idea, but of course it requires that the albumin binding doesn’t prevent a drug from getting efficiently to its real target. And the concept is not so easily transferred to small molecules, although you could imagine a molecule designed to bind to two different binding sites (as if it is not hard enough…)
    It does raise a side question. “Long residence time” means in effect longer than the half-life of the protein to which the drug is bound. And how many people even know that of a new target?

  15. Anthony Nicholls says:

    Since I am the residence skeptic on MD, I should point out three things are hypothesized and none are confirmed by MD here:
    1) An hypothesis that certain tyrosines form a ‘cage’, locking the ligand in place, such that any mutation in them has a disproportionate change in the off-rate. This is not examined by the simulations, and seems expected from the x-ray static structure. Similarly for the effect of a Valine to Isoleucine along the path the ligand probably takes- again not examined by dynamics. (2) That mutations in the loop region that allows flexibility of the “lid” could be understood by MD- yet essentially they aren’t, it’s all hand-waving of the worst sort. (3) An unexpected experimental finding that the change of a key binding residue (N508) leads to a larger than expected change in off-rate. Observed is a change in interaction with N508, as expected for a change in affinity, plus a change in the mobility of the lid. But that this accounts for a delta in off-rate is just speculation. Furthermore, any interaction of the ligand with the flap can also be associated with a change in affinity, hence off-rate. Without actually simulating dissociation, MD is merely providing a posteriori rationalizations- the way docking programs do but with one more degree of freedom. See you tomorrow, CW!

  16. watcher says:

    14: That is true about half-life of protein vs residence time, but many examples exist showing that a protein’s half-life is lengthened when associated to a tight binding ligand. Perfect example is HMGcoA reductase and statins. The protein concetration builds up when inhibited in tight complex with a statin, so that when the statin treatment is abruptly removed there has been expressed the possibility of concern about an excess of enzyme activity in making a gush of cholesterol.

  17. Pete says:

    Ensuring adequate sampling is a key issue with any simulation and this becomes particularly critical when looking at rare events like crossing energy barriers. One of my pet gripes is when people talk about dynamic effects on binding when affinity is an ensemble averaged property.

  18. SAR Screener says:

    @13 I was more thinking of right at the start of a drug discovery project.
    Can you find cpds at HTS that show different off rates and follow that through the project / can we follow the changes in structure that turn a fast off cpd into a slow off one? I’m not aware that this is something we routinely track through a drug discovery project and I wonder if it would be useful if we did start do this and build hopefully up an understanding of SKR.

  19. Skeptic says:

    Undoubtedly this is a very interesting topic. Yet I’m still not convinced that this so-called “residence time” or “on/off rate” is a purely kinetic phenomenon. If we think of Ki as the ratio of k1 to k-1 (by definition), where k1 is the rate of binding and k-1 that of dissociation, what is the true “nature” of such “rates”? They should simply describe the bimolecular event of the ligand binding onto a prefixed conformation of the protein, without considering all other events that happen before (diffusion in the solvent, conformational changes of the protein, desolvation), as if ligand and protein were rigid balls interacting in the vacuum. In other words, strictly speaking there isn’t a good way to measure such “rate”. The residence time, or off rate, would then be the result of a sequence of event in time (that can be minutes long!), whereby the protein wiggles around the ligand, until it finally finds the reactive conformation that can expel such ligand, winning over an activation energy barrier. In other words, this would be better seen as thermodynamic event, which is the result of a series of complex motions invisible to an X-ray structure and hard to simulate by modeling, I guess. So, no wonder that trying to utilize such experimentally determined values of “off-rates” to design more potent and selective ligands is so challenging. It would be like trying to edit a movie to perfection having only a few snapshots here and there, instead of the entire shooting on film…

  20. Julien says:

    #6: There is this recent paper in JMC that is kind of prospective, but doesn’t go beyond in vitro assays:

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