What is a distribution coefficient?

An explanatory video by Prof. Simon Gaisford – Pharma Drama

Welcome to Pharma Drama, the channel where we look at the science of healthcare and healthcare products. In this video I’m going to explain distribution coefficients – what they are and how they differ from partition coefficients. So distribute your time between the kitchen, so you can get a drink, and your computer and let’s make a start.

Distribution coefficients are very similar in principle to partition coefficients, so it should come as no surprise that I’m going to suggest very strongly that you watch the video on partition coefficients before watching this one. The link is here so if you haven’t watched it yet then… what are you still doing watching this? Go and watch it and then come back!

OK, assuming you’re up to speed, I will remind you that the basis of partitioning is that any compound, whether it is a drug or not, is likely to have some affinity for polar solvents, such as water, and some affinity for non-polar solvents, such as oils and organic phases. Water and organic solvents do not usually mix – we say they are immiscible – so when added together in a container the organic solvent will float on top of the water. When a material is added to this mixture of solvents, the molecules will naturally distribute between the liquids, with a greater proportion dissolving in the organic phase if the compound is lipophilic and a greater proportion dissolving in water if the compound is hydrophilic. The ratio of the concentrations in the two phases is called the partition coefficient.

So far so good. But why do we also have a distribution coefficient and what is it I hear you ask? Good questions. It’s because some compounds, such as acids, bases and salts, can ionise in water and this has a big impact on partitioning because ionised drugs are completely insoluble in organic solvents. It might not be immediately obvious why this is a problem, so let me show you some examples to help explain.

On the screen is a schematic of a mixture of oil and water – we will assume there are fifty millilitres of each phase and we have added one hundred milligrams of a compound. The final amounts of compound in each phase at equilibrium are sixty six point seven milligrams in oil and thirty three point three milligrams in water. This means the concentration in oil is one point three three milligrams per mL and in water is nought point six seven milligrams per mL. The ratio of these, two, is the partition coefficient.

Imagine, however, that the compound was able to ionise in water. We might end up with different amounts of compound in the two phases, as shown on the screen. Now we have forty milligrams of compound in the oil phase and sixty milligrams of compound in water (of which twenty milligrams is un-ionised and forty milligrams is ionised). When we measure the concentrations (say with UV spectroscopy) we cannot distinguish between ionised and un-ionised solute, so we will calculate the concentrations as nought point eight milligrams per mL in oil and one point two milligrams per mL in water. The ratio is now nought point six seven, not two. The compound appears to be more hydrophilic because the ratio is less than one, but in reality its affinity for the two phases is the same as before, but we have calculated a different ratio because some of the compound has ionised in the water phase and so can no longer distribute into the oil phase. To account for this difference, we say that the experimentally determined ratio for compounds that ionise is a distribution coefficient, NOT a partition coefficient.

You might notice, incidentally, that in the example I am using, if we were to calculate the concentrations in the oil and water phases using only the un-ionised fraction, we could have concentrations of nought point eight milligrams per mL in oil (it’s the same as before as nothing has changed) and naught point four milligrams per mL in water. The ratio is 2 and this is the partition coefficient, as it reflects the true relative affinities for the compound between the phases.

Phew! That’s complicated, so let me summarise; A partition coefficient represents the relative affinities for a compound between oil and water phases. A distribution coefficient represents the experimentally measured ratios of concentrations for a compound between oil and water phases, but does not necessarily reflect the true ratio of affinities, because it includes a portion of the sample that cannot partition. If a compound cannot ionise then the partition coefficient and the distribution coefficient will become equal.

One final point to note is that the distribution coefficient is equal to the partition coefficient multiplied by the fraction of drug that is un-ionised.

Right, that’s all we need to know. A partition coefficient represents the true relative affinities for a compound between oil and water phases, while a distribution coefficient takes account of ionisation and where there is no ionisation partition coefficients and distribution coefficients are the same. I hope you found that description useful. If you did, please hit the ‘like’ button and consider subscribing – it really helps the channel. Otherwise, thank you so much for watching, and I’ll see you again soon.