Rotatable Bonds 2: A Sacred Cow Culled?

We are now in a position to review the first of our featured articles. This heavily cited study of molecular properties that influence oral bioavailability claims that and polar surface area and the number of rotatable bonds (NROT) are both good predictors of bioavailability, independent of molecular weight (MW). Now as we pointed out in the previous post, NROT in a molecule tends to correlate with molecular weight. So we were extremely curious as to how bioavailability could be shown to be more dependent on the flexibility of molecules than their size.

A good place to start is Table 2 which shows the correlation coefficients of bioavailability (%F) with MW and NROT of -0.35 and -0.39 respectively for the full data set of 1117 compounds. The dataset is then sliced into 3 categories ( MW<400, >500, everything else) and correlation coefficients are also quoted for these groups. It is no surprise that the correlation coefficient of %F with MW is lower for each of the groups. However the authors note clear relationships (correlation coefficients of -0.40 and -0.34) between %F and NROT for the two highest molecular weight categories.

It is easy enough to calculate correlation coefficients. These statistics tend to be most meaningful when the relevant variables are normally distributed. The data points furthest from the average have the greatest influence on this quantity so it is not surprising that lower correlation coefficients for %F and MW are observed for each of the 3 MW categories than for the entire dataset. Now NROT is not perfectly correlated with MW and so its distribution doesn’t get chopped as drastically by the categorisation process and correlations with %F don’t drop as much. We think an interesting control would have been to split into 3 groups by NROT and then look at correlations of %F with MW and NROT. We expect that it would now be the correlations with NROT that weakened while the correlations with MW were less affected less affected by the categorisation of the data. The essence of this analysis is that it is asymmetric with respect to how it treats these two potential descriptors of bioavailability. So when the descriptors behave differently, does that reflect something meaningful or is it just a result of the asymmetric treatment of the descriptors?

So the correlation coefficients were not overly convincing so let’s take a look at the other stuff. The data was also categorised by bioavailability into two groups of %F < 20 and %F≥20. Now just remember when you categorise like this, a bioavailability of 19% is treated the same as a bioavailability of 1% and different to a bioavailability of 21%. Categorisation distorts relationships. Anyway with that health warning, let’s just accept that the categorisation of %F is OK and take a look at Figure 1.

Figure 1 claims to show that the effect of molecular rigidity is independent of molecular weight. The data set is now split by MW into two (MW≥500, MW<500) groups and by NROT into three groups (NROT≤7, 710). The proportions of compounds in each of the NROT categories with %F of at least 20 are compared for the two MW categories. The proportions appear in each case to be the same for the two MW categories and this is presented as evidence that the effect of molecular rigidity is independent of molecular weight.

We are just simple folk and really don’t know what to make of all this slicing and dicing of the data. To be honest, we got a bit lost once we went from three MW categories to two. Why couldn’t we just have a plot of %F against MW and another plot of %F against NROT instead of all the categorical gymnastics? Also that would treat the descriptors in a symmetric manner which one might argue is essential if you’re going to come to conclusions about which is the more important determinant of bioavailability.

Now let’s go back and take another look at Figure 1. The distributions for each of the NROT categories do indeed look very similar for the two MW categories but that doesn’t mean that there is there is no dependence of %F on MW. It also doesn’t mean that the correlation between MW and NROT has miraculously disappeared either. You just need to know where to look.

And where to look is the bottom of Figure 1 where it says “n =”. Using these figures you can work out the fraction of compounds in each NROT category with MW≥500. We find that only 14% of the compounds in the NROT≤7 category have MW≥500 but this figure rises to 72% for the NROT>10 category.

A penetrating insight into the complex world of oral bioavailability or categorical sin? Is the effect real or an illusion created by the asymmetric manner in which the descriptors have been treated? It is not for us to say and we leave it to you the reader to decide. This article did generate some commentary in the literature and in the next post we will take a closer look at some of that.

If you got this far in a long and particularly turgid literature review, we salute your stamina while respectfully suggesting that you get a life. Nevertheless, we hope that you’ll drop by again sometime soon.