*Not mitochondrial, but very cool
Cocktail therapies are common to treatments of a diverse array of diseases, in order to combat effects such as: antibiotic resistance in bacterial infections; persister cells in tuberculosis; and chemotheraputic resistance in cancer. It is, however, incredibly difficult to optimize the dose of multiple theraputic agents because of combinatorial explosions. For instance, if we have 10 possible doses for 3 different drugs, then we must test 10x10x10 = 1000 different dose combinations to find the optimal treatment. This becomes 10,000 if we wish to use 4 drugs. What makes this problem even more difficult is that drugs often show antagonism: it is not simply the case that using higher and higher doses of each drug is more effective, the optimum is often found at intermediate doses.
Here, the authors use mathematics to try and approximate the optimal dose of a cocktail of three or more drugs (N in general) whilst avoiding the problem of combinatorial explosion. They model the survival of cells (g) versus drug concentration (Di), for each drug (i), using Hill curves. They approximate g(D1, ... ,DN) using information only from single-drug dose response curves g(Di) and two-drug data g(Di, Dj) for all pairs of drugs. Their computation therefore only scales quadratically with the number of drugs N, rather than exponentially if we were to brute-force compute the global optimum. The authors show that their method is able to well-describe dose-response curves for a case study of six triplet and two quadruplet combination therapies, with 0.85 < R^2 < 0.93 for all of the examples tested.
These methods not only allow us to find the most effective doses, but also has the potential to minimize side effects by optimizing with the assumption that side-effects increase with higher dose. More realistic predictions could be made with more accurate models for side-effects.