A primer on lipophilicity

Well it has been a while since we last posted and it is not too far into 2012 for us to wish you a very happy new year that is free of categorical sin. In the next post, we’re going to take a look at relationships between aqueous solubility and lipophilicity so we thought that a lipophilicity primer would represent a noble public service. The most important quantity when discussing lipophilicity is the partition coefficient, P, which for a compound that lacks ionisable groups can be measured by shaking the compound with water and an organic solvent (usually 1-octanol ) that does not mix with it and we’ll only be discussing measurements in the octanol/water system in this post. When you’ve shaken everything long enough for compound to equilibrate properly between the solvents, you can stop shaking and wait for the octanol and water to separate into two layers. Once this has happened, we just need to measure the concentration of the compound in each solvent and calculate logP (we generally use the logarithm of P rather than P itself) using equation 1. The measurement of partition coefficients is pretty routine these days and there is even a piece of kit called a shake flask which means that you can go for well-earned coffee rather than having to shake a separation funnel. However, please remember that you can only use equation 1 to calculate logP for compounds that are predominantly neutral at the pH of the experiment.



When the compound has ionisable groups, the situation gets a bit more complicated. But only a bit, so please don’t worry because we’ve been through situations like these before together. First thing to remember is that when we measure lipophilicity of a compound we’re actually measuring something called the distribution coefficient, D. This quantity D is just like P except that we use the total concentration of both neutral and ionised forms of the compound in each solvent to determine D and the general situation can get rather messy. When we measure lipophilicity using octanol/water partitioning, we normally assume that only the neutral form of the compound goes into the octanol and that ionised forms of the compound will stay in the water. This assumption can break down but we’re not going to worry about that right now because it probably (hopefully?) doesn’t happen too much. The situation that we most frequently encounter when thinking about logD values is one in which the compound has a single ionisable group. In this case, we can calculate logD from measured concentrations using equation 2 which we’ve re-arranged to equation 3.



Let’s take a look at what equation 3 tells us. Firstly, when there is no ionisation, the fraction of compound in its neutral from is 1 so logP and logD are identical. Secondly, the fraction of compound in its neutral form cannot exceed 1 so its logarithm cannot exceed zero and logD cannot exceed logP. Thirdly, equation 3 tells us how to obtain logP from measured logD values. One approach is to measure logD at a pH at which the proportion of the compound in the ionised form is insignificant. For example, we could measure logD for a carboxylic acid at low pH (you’ll know if that it’s low enough if logD stops increasing as you lower pH). The alternative is to use pK_a to calculate the fraction of compound in the neutral form and use equation 3 to calculate logP. Suppose we measure a logD value of 2.0 at a pH of 7.4 for an amine with a pK_a of 10.4. In the buffer, the amine is 99.9% ionised and 0.1% neutral so the logP for this amine is 5.0.

An obvious question is which of logP and logD is more relevant to Drug Discovery and to be quite honest we’re not sure. The snap answer is that it depends on context. Both logP and logD are measures of how strongly the molecules of a compound interact with water and high values reflect weak interactions with water and a tendency for those molecules to head elsewhere should they find themselves in water. 'Elsewhere' can be any of a number of places including the hydrophobic core of a lipid bilayer membrane, inside a crystal lattice or bound to a protein. As a very rough rule of thumb, logD will be more relevant if the molecules have to 'de-ionise' to go ‘elsewhere’ while logP will be more relevant if the molecules go ‘elsewhere’ in their ionised states. This all sounds like pseudo-mystical psychobabble, we hear you cry and so we’ll try to make it a bit clearer with something a bit more specific. Let’s start with aqueous solubility and many of you will remember extracting carboxylic acids from organic solvents by shaking them some aqueous sodium hydroxide. This works because aqueous solubility of ionisable compounds tends to be limited by the solubility of the neutral form. Suppose a carboxylic acid with a pK_a of 4.4 has a solubility of 1000µM at a pH of 7.4. The concentration of neutral acid under these conditions will only be 1µM and we can infer that the solubility of the neutral form of the acid is only 1µM. Let’s magically increase the pK_a of the acid to 5.4 (which the observant amongst you will have observed may be a bit high for a typical carboxylic acid), leaving the solubility of the neutral form unchanged and see what happens. Our new acid is now only 99% ionised under assay conditions instead of 99.9% ionised which means that the neutral form will start precipitating (supersaturation permitting) once the total concentration of acid gets to 100µM. Increasing pK_a which makes the acid less acidic results in a decrease in the measured solubility .

So we hope that this will give you a better idea of what ‘elsewhere’ means in this context. The next question is how should we use logP and logD as descriptors for analysing data. What you do depends a bit on what you have available and what sorts of compounds you’re dealing with. If you have measured logD values and the compounds lack ionisable groups then logD and logP are identical and these measured values will be more relevant than predicted values (provided of course you have a clear idea of the dynamic range of the logD measurement and quantification/detection limits). Life gets more complicated if you have to handle compounds with ionisable groups because you’re unlikely to have measured pK_a values available for all the compounds that you’re interested in and access to logP will involve a predictive element if logD has only been measured at a single pH. You might decide that logD is more relevant than logP to your situation in which case you can use logD. However, when you use logD measured at a pH of 7.4 to model data you need to remember (equation 3) that you’ll be treating an amine with a pK_a of 11.4 and a logP of 6.0 as equivalent to an amine with a pK_a of 8.4 and a logP of 3.0.

The situation most frequently encountered when using lipophilicity as a descriptor is the one where both logP and logD are themselves predicted. Usually logD will be predicted from logP using an estimate for the pK_a and, if this is the case, you really need to be asking yourself whether it really makes sense to bundle logP and f_N together when they two quantities describe such different phenomena. If you use logD in a predictive model then that model will respond identically to the same change in logP and logf_N and, if you’re really thinking about what you’re doing, you’ll be asking yourself if you really want your model to be doing this.

It’s getting to the point at which we should be wrapping up. We’ll leave you with links to a wikipedia page and an article that present some of the material we’ve discussed from a different angle and in more depth and we hope that you find them useful. In next Crapshoot we’ll returning to the critical review of literature that you’ve come to expect of us and you can expect some getting physical in drug discovery.