Pairwise interactions and the battle against combinatorics in multidrug therapies

Drugs are often used in combination to treat bacterial infections, viruses, and cancer. Drug combinations may exhibit increased potency, decreased dosage-related side effects, and even the capacity to slow the emergence of resistance. The increased efficacy imparted by combining drugs—so-called drug “synergy”—has been a topic of fervent interest for decades (1), while recent studies have also highlighted the evolutionary impacts of counteracting (“antagonistic”) combinations (2⇓–4). The spectrum of potential drug–drug interactions is rich and multifaceted, offering the promise of optimized combination therapies tailored to specific treatment objectives (5). Unfortunately, the inherent flexibility of combination therapy also presents a considerable practical hurdle: the number of possible drug combinations grows exponentially with the number of drugs, making exhaustive screening with even a modest number of drugs intractable. In PNAS, Zimmer et al. (6) develop a robust method for predicting the effects of multidrug combinations for microbial infections and cancer, potentially sidestepping the combinatorial explosion that limits systematic design of combination therapies. Comprehensively testing the efficacy of N drugs at D doses requires D N measurements, and this number grows unwieldy for even a modest number of drugs. For example, evaluating a 10-drug combination at 10 doses requires 10 billion measurements (Fig. 1). To put this in perspective, consider that a high-throughput screen capable of evaluating 105 drug combinations per day—a rate on par with some large-scale research facilities—would require more than 270 y to fully characterize all possible drug dosages. In addition to the overwhelming time cost, brute-force approaches are practically limited by the cost of … [↵][1]1Email: kbwood{at}umich.edu. [1]: #xref-corresp-1-1