Prediction of ultra-high-order antibiotic combinations based on pairwise interactions

Drug combinations are a promising approach to achieve high efficacy at low doses and to overcome resistance. Drug combinations are especially useful when drugs cannot achieve effectiveness at tolerable doses, as occurs in cancer and tuberculosis (TB). However, discovery of effective drug combinations faces the challenge of combinatorial explosion, in which the number of possible combinations increases exponentially with the number of drugs and doses. A recent advance, called the dose model, uses a mathematical formula to overcome combinatorial explosion by reducing the problem to a feasible quadratic one: using data on drug pairs at a few doses, the dose model accurately predicts the effect of combinations of three and four drugs at all doses. The dose model has not yet been tested on higher-order combinations beyond four drugs. To address this, we measured the effect of combinations of up to ten antibiotics on E. coli growth, and of up to five tuberculosis (TB) drugs on the growth of M. tuberculosis. We find 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 largely determines higher-order interactions. Therefore, systematic study of pairwise drug interactions is a compelling strategy to prioritize drug regimens in high-dimensional spaces.Author summary: Drug combinations are important to increase efficacy and reduce resistance of treatment for infection and cancer. The major challenge is the vast number of experiments needed to scan the space of combination in order to find rare synergistic drugs and their optimal doses. In the past few years there has been an advance in the ability to predict the effects of drug cocktails, using a small number of experiments on drug pairs. These approaches have not been tested on combinations of more than a few drugs. Thus, it remains unclear whether there are useful combinations of 5–10 drugs that work at low doses. Here we show that a mathematical model can use data for drug pairs to predict ultra-high-order cocktails for E. coli and an important pathogen, M. tuberculosis. (1) We measured the effect of 124 new combinations of 3–10 antibiotic drugs, each at 13 doses. (2) We show that our model accurately predicts the effect of these cocktails using pair measurements alone. (3) We predict and verify new high-order combinations for TB that provide high efficacy at low doses, overcoming the well-known problem in TB that each drug alone has low efficacy.