Maximum entropy principle for predicting response to multiple-drug exposure in bacteria and human cancer cells

Drugs are commonly used in combinations larger than two for treating infectious disease. However, it is generally impossible to infer the net effect of a multi-drug combination on cell growth directly from the effects of individual drugs. We combined experiments with maximum entropy methods to develop a mechanism-independent framework for calculating the response of both bacteria and human cancer cells to a large variety of drug combinations comprised of anti-microbial or anti-cancer drugs. We experimentally show that the cellular responses to drug pairs are sufficient to infer the effects of larger drug combinations in gram negative bacteria, \textit{Escherichia coli}, gram positive bacteria, \textit{Staphylococcus aureus}, and also human breast cancer and melanoma cell lines. Remarkably, the accurate predictions of this framework suggest that the multi-drug response obeys statistical rather than chemical laws for combinations larger than two. Consequently, these findings offer a new strategy for the rational design of therapies using large drug combinations.