Thursday, 31 December 2015

The homeopathic limit of ligand efficiency

With the thermodynamic proxies staked, I can get back to salting the ligand efficiency (LE) soucouyant. In the previous post on this topic, I responded to a 'sound and fury' article which appeared to express the opinion that we should be using the metrics and not asking rude questions about their validity. One observation that one might make about an article like this is that the journal in question could be seen as trying to suppress legitimate scientific debate and I put this to their editorial staff. The response was that an article like this represents the opinion of the author and that I should consider a letter to editor if there was a grievance. I reassured them that there was no grievance whatsoever and that it actually takes a lot of the effort out of providing critical commentary on the drug discovery literature when journals serve up cannon-fodder like this. In the spirit of providing helpful and constructive feedback to the the editorial team, I did suggest that they might discuss the matter among themselves because a medicinal chemistry journal that is genuinely looking to the future needs to be seen as catalyzing rather than inhibiting debate. Now there is something else about this article that it took me a while to spot which is that it is freely available while 24 hours of access to the other editorial article in the same issue will cost you $20 in the absence of a subscription. If the author really coughed up for an APC so we don't have to pay to watch the toys getting hurled out of the pram then fair enough. If, however, the journal has waived the APC then claims that it is not attempting to stifle debate become a lot less convincing. Should we be talking about the Pravda of medicinal chemistry? Too early to say but I'll be keeping an eye open for more of this sort of thing.

Recalling complaints that our criticism of the thermodynamic basis of LE was 'complex', I'm going to try to make things even simpler than in the previous post.  They say a picture is worth a thousand words so I'm going to use a graphical method to show how LE can be assessed.  To make things really simple, we'll dispense with the pretentious energy units by using -log10(IC50/Cref ) as the measure of activity and I'll also point you towards an article that explains why you need that reference concentration (Cref) if you want to calculate a logarithm for IC50. I'll plot activity for two hypothetical compounds, one of which is a fragment with 10 heavy atoms ad the other is a more potent hit from high-throughput screening (HTS) that has 20 heavy atoms. I won't actually to say what units IC50 values are expressed in and you can think of the heavy atom axis as sliding up or down the activity axis in response to changes in the concentration unit Cref. I've done things this way to emphasize the arbitrary nature of the concentration unit in the LE context.

Take a look at the plot in the left of the figure which I've labeled as 'A'.  Can you tell which of the compounds is more ligand-efficient just by looking at this plot?  Don't worry because I can't either. 

It's actually very easy to use a plot like this to determine whether one compound is more ligand-efficient than another one. First locate the point on the vertical axis corresponding to an IC50 of 1 M. Then draw a line through this point and the point representing the activity of one of the compounds. If the point representing the activity of the other compound lies below the line then it is less ligand-efficient and vice versa. Like they say in Stuttgart, vorsprung durch metrik!

Now take a look at the plot on the right of the figure which I've labelled 'B'. I've plotted two different lines that pass through the point corresponding to the fragment hit. The red line suggests that the fragment hit is more ligand efficient than the HTS hit but the green line suggests otherwise. Unfortunately there's no way of knowing which of these lines is the 'official' LE line (with intercept corresponding to IC50 = 1 M) because I've not told you what units IC50 is expressed in. Presenting the IC50 values in this manner is not particularly helpful if you need to decide which of the two hits is 'better' but it does highlight the arbitrary manner in which the intercept is selected in order to calculate LE. It also highlights how our choice of intercept influences our perception of efficiency.  

You can also think of the intercept as a zero molecular size limit for activity. One reason for doing so is that if the correlation between activity and molecular size is sufficiently strong, you may be able to extrapolate the trend in the data to the activity axis. Would it be a good idea to be make assumptions about the intercept if the data can't tell you where it is? LE is based on an assumption that the 1 M concentration is somehow 'privileged' but, in real life, molecules don't actually give a toss about IUPAC.  You can almost hear the protein saying "IUPAC... schmupack" when the wannabe ligand announces its arrival outside the binding pocket armed with the blessing of a renowned thought-leader.  The best choice of a zero molecular size limit for activity would appear to be an interesting topic for debate. Imagine different experts each arguing noisily for his or her recommended activity level to be adopted as the One True Zero Molecular Size Limit For Activity. With apologies to Prof Tolkien and his pointy-eared friends,

One Unit to rule them all, One Unit to find them,
One Unit to bring them all and in the darkness bind them, 

If this all sounds strangely familiar, it might be because you can create an absence of a solute just as effectively by making its molecules infinitely small as you can by making the solution infinitely dilute. Put another way, LE may be a lot closer to homeopathy than many 'experts' and 'thought-leaders' would like you to believe.

So that's the end of blogging for the year at Molecular Design.  I wish all readers a happy, successful and metric-free 2016.


Dan Erlanson said...

Of course, these arguments also apply to binding free energy, which people nonetheless find useful.

And the Tolkien allusion was made previously in this post, and extended poetically by Brandon Findlay in one of the comments. Happy 2016!

Peter Kenny said...

Hi Dan, All the best for the 2016.

As a point of clarification, I have never suggested that free energy (or IC50 values) are not useful. When we use these quantities to compare activity/affinity, we can usually assume that the same standard/reference concentration applies to all measurements and so meaningful (and useful) comparisons can be made. If you do sensible things with free energies (like subtract them from each other) things will go smoothly but things will unravel quickly should you break the rules. If your view of a system changes when you change a unit of a quantity that specifies the system then it’s a clear sign that you’ve broken the rules and playing the ‘useful card’ will not (in a Monopoly sense) get you out of jail.

One needs to be very careful about invoking ‘useful’ in defense of metrics (and scientific concepts in general) because it’s a subjective term that some may even equate with the last refuge of the scoundrel. Is it possible to say whether LE defined using 1 M standard state is more useful than LE defined with a 100 mM standard state? Is LELP useful? Are the thermodynamic proxies that were skewered in an earlier post useful? The problem with ‘useful’ is that anyone can claim that a metric is useful.