# Drug Toxicity, Interaction and Complexity

In our past blog on the subject, we suggest that molecule complexity may be a proxy of its toxicity. In other words, a highly complex molecule can be more toxic because, on a molecular (atomic) dynamics level, it exhibits a more intricate and more articulate behaviour. We know from experience that high complexity is nearly always a source of vulnerability precisely because highly complex systems possess very many modes of behaviour, some of which may be non-intuitive and even risky. In effect, if you can get things done adopting a simpler solution, go for the simpler solution. It will cause less headaches. Even Ockham knew that.

“Anytime you take more than one medication, or even mix it with certain foods, beverages, or over-the-counter medicines, you are at risk of a drug interaction. Most drug interactions are not serious, but because a few are, it is important to understand the possible outcome before you take your medications.” Read more.

Suppose that you take two drugs, drug A and drug B. Suppose that their respective complexities are Ca and Cb. When the two drugs interact, what will the resulting complexity be? Drug interaction doesn’t of course mean that the two molecules will merge, forming a larger molecule, corresponding to some “new drug”. That is not what happens. What happens is information exchange at atomic level. The question is, therefore, what is the complexity (potential increase in toxicity) of the combined action of the two molecules, i.e. C(a+b)?

We have recently demonstrated a theorem which states that C(a+b) >= Ca + Cb. In other words, combining two systems will always lead to complexity that is higher than the sum of the complexities of the components. The magnitude of C(a+b) with respect to that of Ca + Cb depends, evidently, on the degree of coupling, i.e.e on matrices X and Y. Let’s see two examples. Suppose you have two molecules of 20 and 10 atoms respectively. When you “combine” them, here is what a case of weak coupling (weak drug-drug interaction) could look like. The nomenclature is that of the mentioned theorem.

while this case corresponds to a higher degree of drug-drug interaction (information exchange between the two drugs):

The difference in overall complexity between the two cases is over 70%.

The potential combined toxicity effects of drug-drug interaction using QCM technology can be performed easily using Molecular Dynamics codes. It is sufficient to simulate each molecule separately – which is what pharma companies do during drug discovery – and then let QCM figure out what the combination will lead to.