Drug cocktails – both antibiotic and anti-cancer – are increasingly used, among other reasons, because simultaneously attacking pathogenic cells with several different methods can reduce the risk of drug resistance. Drug combinations are especially useful when drugs cannot achieve effectiveness at tolerable doses. Moreover, both doctors and pharmaceutical companies are interested in the advance of drug “mixology” because it can help create novel applications for existing drugs, since new ones are costly to develop and slow to reach the market.
But adding drugs together does not generally result just in the sum of their effects. For instance, one drug can alert mechanisms in a cell that pump the other drugs out of the cell, thus changing the dose at which the other drugs will be effective. Conversely, side effects can add up, so researchers often want to identify the lowest possible dose of any given drug. With typically four or more drugs added together in chemotherapy cocktails, the number of possible combinations and doses is astronomical: It would be impossible to test them all to arrive at the optimal mix. This hurdle is known as the combinatorial explosion problem.
We recently approached this problem by a mathematical formula that reduces the problem to a feasible quadratic one. This formula termed the dose model uses measurements of drug pairs at a few doses, and can accurately predict the effect of combinations of three and four drugs at all doses. During the course of this grant we also tested the model validity at higher order drug cocktails. We measured the effect of combinations of up to ten antibiotics on E. coli Growth yield, and of up to five tuberculosis (TB) drugs on the yield of M. tuberculosis. We found that the dose model accurately predicts the effect of these higher-order combinations, including cases of strong synergy and antagonism. This study supports the view that the interactions between drug pairs carries key information that determine higher order interactions, and can therefore be the basis of drug cocktails design.
The dose model is not always applicable since it requires source material which is sufficient for several measurements on each drugs pair. To overcome this problem we developed an additional model termed the pair model which requires pair measurements at a single concentration. We found that also in this case the model can predict much of the variation for the high order cocktails, outperforming the commonly used approaches
