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Mel reviewed an important article on maximal affinity of ligands to kick off our sequence of posts on ligand efficiency. There are a number of reasons that this upper limit for potency might be observed and it's worth having a bit of think about them.
One interpretation of the upper limit is that it represents a validation of the molecular complexity concept. If a ligand makes many interactions with the protein they are less likely to be of ideal geometry. Hydrogen bonds between the binding partners and water are more likely to be of near-ideal geometry. Another factor that can impose limits on affinity is the finite size of a binding site. Once the site has been filled, increasing the size of the ligand does not lead to further increases in affinity because all the binding potential of the protein has already been exploited.
However, there is another reason that an upper limit for affinity might be observed and it has nothing to do with molecular complexity or fully exploited binding sites. Measuring very strong binding is not as easy as you might think it would be. In a conventional enzyme assay, you normally assume that the concentration of the ligand is much greater than that of the enzyme. This works well if you’ve got 10nM enzyme in the asaay and a micromolar ligand. However, things will get trickier if you’re trying to characterise a 10pM inhibitor since you’ll observe 50% inhibition of the enzyme for a 5nM concentration of the inhibitor. And you’ll see something very similar for a 1pM inhibitor…
This behaviour is well known and is called tight-binding inhibition. If you want to characterise very potent inhibitors you need reduce the concentration of the enzyme and be a bit more careful with the math. However, not everybody does this and I suspect that this may be one reason there appears to be an upper limit for affinity.
Literature cited
Kuntz et al, The maximal affinity of ligands. PNAS 1999, 96, 9997-10002. Link to free article.
Williams & Morrison, The kinetics of reversible tight-binding inhibition. Methods Enyzmol. 1979, 63, 437-467 DOI
Tuesday, 14 April 2009
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
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
Physicochemical properties
Fragments typically have to be screened at high concentration because they normally only bind weakly to their targets and the physicochemical property most relevant to FBDD is aqueous solubility. Both charge state and lipophilicity influence solubility in aqueous media.
General
Avdeef, Physicochemical profiling (solubility, permeability, and charge state). Curr. Top. Med. Chem. 2001, 1, 277-351 Link
Hydrogen bonding
Kenny, Hydrogen bonding, electrostatic potential, and molecular design. J. Chem. Inf. Model. 2009, 49, 1234-1244 DOI
Laurence & Berthelot, Observations on the strength of hydrogen bonding. Perspect. Drug Discov. Des. 2000, 18, 39-60 DOI
Kenny, Prediction of hydrogen bond basicity from computed molecular electrostatic properties: implications for comparative molecular field analysis. J. Chem. Soc., Perkin Trans. 2, 1994, 199-202 DOI
Abraham et al, Hydrogen bonding. Part 9. Solute proton donor and proton acceptor scales for use in drug design. J. Chem. Soc., Perkin Trans. 2, 1989, 1355-1375 DOI
Partition coefficients
Toulmin et al, Toward Prediction of Alkane/Water Partition Coefficients. J. Med. Chem. 2008, 51, 3720-3730 DOI
Leahy et al, Model solvent systems for QSAR. Part 2. Fragment values (f-values) for the critical quartet. J. Chem. Soc., Perkin Trans. 2, 1992, 723-731 DOI
Solubility
Colclough et al, High throughput solubility determination with application to selection of compounds for fragment screening. Bioorg. Med. Chem. 2008, 16, 6611-6616 DOI
General
Avdeef, Physicochemical profiling (solubility, permeability, and charge state). Curr. Top. Med. Chem. 2001, 1, 277-351 Link
Hydrogen bonding
Kenny, Hydrogen bonding, electrostatic potential, and molecular design. J. Chem. Inf. Model. 2009, 49, 1234-1244 DOI
Laurence & Berthelot, Observations on the strength of hydrogen bonding. Perspect. Drug Discov. Des. 2000, 18, 39-60 DOI
Kenny, Prediction of hydrogen bond basicity from computed molecular electrostatic properties: implications for comparative molecular field analysis. J. Chem. Soc., Perkin Trans. 2, 1994, 199-202 DOI
Abraham et al, Hydrogen bonding. Part 9. Solute proton donor and proton acceptor scales for use in drug design. J. Chem. Soc., Perkin Trans. 2, 1989, 1355-1375 DOI
Partition coefficients
Toulmin et al, Toward Prediction of Alkane/Water Partition Coefficients. J. Med. Chem. 2008, 51, 3720-3730 DOI
Leahy et al, Model solvent systems for QSAR. Part 2. Fragment values (f-values) for the critical quartet. J. Chem. Soc., Perkin Trans. 2, 1992, 723-731 DOI
Solubility
Colclough et al, High throughput solubility determination with application to selection of compounds for fragment screening. Bioorg. Med. Chem. 2008, 16, 6611-6616 DOI
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