Monday, 6 April 2009

The upper limits of binding: Part 1

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I originally intended to discuss some of the factors that impose the upper limits on binding that are observed. Unfortunately the introduction got a bit out of hand so this is going to have to be a two-parter.

It’s been a while since I said anything about ligand efficiency although its hard core enthusiasts appear to have worked the concept into something that approaches discipline status. My view is that molecules interact with their environments by presenting their molecular surfaces to those environments. Dividing the standard free energy change for an interaction by the area of the molecular surface is effectively a statement of how effectively the molecule makes use of its surface in making the interaction. I believe that this is the most fundamental measure of ligand efficiency.

Assays are not normally set up to measure standard free energy changes for binding. Ligand efficiency is frequently calculated from an IC50 rather than dissociation constant for the ligand protein complex. The IC50 that you’ll measure for competitive inhibitors depends on the concentration of whatever you’re trying to compete with. This can make comparing IC50 values for different assays risky. For example, you might run inhibition assays for two different kinases at their respective Km values with respect to ATP despite both kinases being exposed to the same intracellular concentration of ATP. If you’re using ligand efficiency to compare hits from the same assay, the distinction between IC50 and dissociation constant is not too much of an issue as long as you remember the two quantities are not the same.

Molecular surface area is not the easiest quantity to deal with if you’re looking for a quick metric with which to compare hits from a screen. You’ll need a 3D model of the molecule in order to calculate this quantity properly and that means that you’ll need to deal with multiple conformations. If you’re going to deal with multiple conformations, you need to be thinking about energy cutoffs and how many conformations you want to use to sample the conformational space of your molecule. You also need to be thinking about how to deal with surface area that is inaccessible even though it is on the molecular surface. All very messy!

A while ago, some folk at Novartis showed that it is possible to calculate molecular surface area directly from the molecular connection table which is more commonly called the 2D structure because that’s what you get when you write it on a piece of paper. It turns out that surface area is roughly proportional to the number of non-hydrogen (often termed heavy) atoms in the molecule. Counting heavy atoms involves nice, predictable integer math and is much better suited for defining ligand efficiency than all the horrid floating point math demanded by 3D structures.

My preferred measure of ligand efficiency is to divide minus the log of whatever potency measure the assay generates by the number of non-hydrogen atoms in the molecule. Because you can’t take a log of a concentration the potency measure should be divided by the appropriate units of concentration. This means that if you use different units of concentration, you’ll get different ligand efficiencies. This isn’t a problem if you’re aware of it and using ligand efficiency to compare hits from a single assay. However, it’s probably pushing it a bit to use a different concentration unit and claim that you’ve found a new ligand efficiency metric. Put another way, you can make the standard free energy of binding for a 10nM compound positive simply by using 1nM as your standard state. If you think this is a crazy idea, imagine what a molar solution of your favourite protein might look like!

Another reason that I prefer to define ligand efficiency in terms of pIC50 or pKd is that these measures of potency/affinity are unitless so that the ligand efficiency has units of reciprocal number of heavy atoms. Once you convert your potency into a free energy you need to state your energy units when you use ligand efficiency. People often don’t bother although it is unlikely that the authors of anything that I have reviewed for a journal will be presenting ligand efficiencies without having defined the appropriate units. The other reason I don’t like converting IC50 of Kd values to energies is that I believe this conveys an impression of thermodymamic rigour which is normally unjustified.

This is is a natural break point. Some what is discussed above is also presented in the AstraZeneca fragment based lead generation paper from a couple of years ago. In the next post I’ll be taking a look at some of the factors which may place upper limits on ligand efficiency.

Literature cited

Albert et al, An Integrated Approach to Fragment Based Lead Generation: Philosophy, Strategy and Case Studies from AstraZeneca's Drug Discovery Programs Curr. Top. Med. Chem. 2007, 7, 1600-1629 link

Ertl et al, Fast calculation of molecular polar surface area as a sum of fragment-based contributions and its application to the prediction of drug transport properties. J. Med. Chem. 2000, 43, 3714-3717 DOI

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