A little bit of pharmacology: Dose-response relationships

Pharmacology is essentially the study of drugs, legal or otherwise.  It has a little sister, toxicology, which has a slightly wider scope, as it also deals with substances that we do not usually think of as drugs, like heavy metals for example.  Pharmacology is so much more, but for our purposes this will be enough for now.
You can understand better virtually any class of phenomenon (including pharmacological phenomena) if you are able to describe it in graphical form; we humans are after all, visual animals.
In these lines, dose-response curves are some of the most useful tools in pharmacology; not only they allow one to visualize a process but they make said process easily quantifiable (this means to express it in numerical form) and therefore amenable to mathematical analysis.  Furthermore, you can work with dose-response relationships in an intuitive, practical way.  For example, South American natives mastered the use of pharmacological agents as applied to hunting.  It is well-known that they used a variety of plants for these purposes, including the curare plant.  An extract of the plant applied to the tip of a dart makes it poisonous.  The extract contains a substance (curare, of which  there are various forms) that cause paralysis by blocking a neuromuscular receptor.  This makes for a very interesting story in itself and I may write a post just for that, but as usual, I digress.

Credit: http://www.motifake.com/tags/curare
The point that I am trying to make is that it is well-documented that South American Natives measured the potency of a particular curare extract by using an intuitive dose-response curve.  They actually counted how many trees a particular monkey was able to jump to after being hit by a curare-coated dart!  The fewer the trees jumped by the unlucky monkey, the more potent the extract.  A graph showing an imaginary preliminary test can be drawn as:

Incidentally, all these graphs are based on the concept of dependent- vs independent-variables, which we’ll not explain here but if you are curious about them, you may want to take a look here.
You can even compare different extracts for their potency to paralyze a monkey:

Here is immediately evident that extract #1 is the most potent one…
Al alternate way of expressing this information is to show how many trees a monkey can jump depending on the number curare-coated darts you shoot at it:

In this case, we state this as something like “…number of trees jumped as a function of the number of curare-numbered darts”.
Using curves like the one above, one can also compare the relative potency of more than one curare extract, in pretty much the way that we did before:

This type of curves is useful to compare the relative potencies of substances for a particular effect.  Let’s just say that a monkey hit with an uncoated dart is able to jump to ten trees before turning back and waving a fist against you.  That will be our starting point, our “control” if you will.  Now, if we ask ourselves the question:
How many curare-coated darts would it take to reduce the strength of a monkey in such a way that it is only able to jump 5 trees (50 % of the control strength)?
We can easily use the graph to see which curare extract is the most potent.

As you can see, the curare extract #3 is the most potent one because it takes only one dart to reduce the monkey’s strength halfwise, while it takes extracts 1 and 2 two and five darts respectively to do the same.
I like pharmacology…
This is only a sample of the many things we can do to understand drug responses.  Incidentally, congratulations!  You are now equipped with some tools to understand a little better my next post, which will be about a paper that we published in 2009 about the relationship of nicotine and an example of a very interesting type of compounds, the cembranoids.  Stay tuned!
Monkey face picture credit: uvumi.com.  All graphs created by Baldscientist.  These examples were done with hypothetical monkeys; no animals were harmed in the writing of this blogpost.
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