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Interactions and emergent processes are essential for research on complex systems involving many components. Most studies focus solely on pairwise interactions and ignore higher-order interactions among three or more components. To gain deeper insights into higher-order interactions and complex environments, we study antibiotic combinations applied to pathogenic Escherichia coli and obtain unprecedented amounts of detailed data (251 two-drug combinations, 1512 three-drug combinations, 5670 four-drug combinations, and 13608 five-drug combinations). Directly opposite to previous assumptions and reports, we find higher-order interactions increase in frequency with the number of drugs in the bacteria’s environment. Specifically, as more drugs are added, we observe an elevated frequency of net synergy (effect greater than expected based on independent individual effects) and also increased instances of emergent antagonism (effect less than expected based on lower-order interaction effects). These findings have implications for the potential efficacy of drug combinations and are crucial for better navigating problems associated with the combinatorial complexity of multi-component systems.

Interactions among drugs play a critical role in the killing efficacy of multidrug treatments. Recent advances in theory and experiment for three-drug interactions enable the search for emergent interactions-ones not predictable from pairwise interactions. Previous work has shown it is easier to detect synergies and antagonisms among pairwise interactions when a rescaling method is applied to the interaction metric. However, no study has carefully examined whether new types of normalization might be needed for emergence. Here, we propose several rescaling methods for enhancing the classification of the higher order drug interactions based on our conceptual framework. To choose the rescaling that best separates synergism, antagonism and additivity, we conducted bacterial growth experiments in the presence of single, pairwise and triple-drug combinations among 14 antibiotics. We found one of our rescaling methods is far better at distinguishing synergistic and antagonistic emergent interactions than any of the other methods. Using our new method, we find around 50% of emergent interactions are additive, much less than previous reports of greater than 90% additivity. We conclude that higher order emergent interactions are much more common than previously believed, and we argue these findings for drugs suggest that appropriate rescaling is crucial to infer higher order interactions.

Understanding how multiple stressors interact is needed to predict the dynamical outcomes of diverse biological systems, ranging from drug-resistant pathogens that are combated and treated with combination drug therapies to ecosystems impacted by environmental toxicants or disturbances. Nevertheless, extensive studies of higher-order (more than two component) interactions have been lacking. Here, we conduct experiments using 20 threedrug combinations and their effects on the bacterial growth of Escherichia coli. We report our measurements of growth rates in single, pairwise and tripledrug combinations. To uncover emergent interactions, we derive a simple framework to calculate expectations for three-way interactions based on the measured impact of each individual stressor and of each pairwise interaction. Using our framework, we find that (i) emergent antagonisms are more common than emergent synergies and (ii) emergent antagonisms are more common and emergent synergies are more rare than would be inferred from measures of net effects that do not disentangle pairwise interactions from three-way interactions.

BackgroundIn drug-drug interactions, there are surprising cases in which the growth inhibition of bacteria by a single antibiotic decreases when a second antibiotic is added. These interactions are termed suppressive and have been argued to have the potential to limit the evolution of resistance. Nevertheless, little attention has been given to suppressive interactions because clinical studies typically search for increases in killing efficiency and because suppressive interactions are believed to be rare based on pairwise studies.ResultsHere, we quantify the effects of single-, double-, and triple-drug combinations from a set of 14 antibiotics and 3 bacteria strains, totaling 364 unique three-drug combinations per bacteria strain. We find that increasing the number of drugs can increase the prevalence of suppressive interactions: 17% of three-drug combinations are suppressive compared to 5% of two-drug combinations in this study. Most cases of suppression we find (97%) are “hidden” cases for which the triple-drug bacterial growth is less than the single-drug treatments but exceeds that of a pairwise combination.ConclusionsWe find a surprising number of suppressive interactions in higher-order drug combinations. Without examining lower-order (pairwise) bacterial growth, emergent suppressive effects would be missed, potentially affecting our understanding of evolution of resistance and treatment strategies for resistant pathogens. These findings suggest that careful examination of the full factorial of drug combinations is needed to uncover suppressive interactions in higher-order combinations.Electronic supplementary materialThe online version of this article (doi:10.1186/s12866-017-1017-3) contains supplementary material, which is available to authorized users.

Interactions and emergent processes are essential for research on complex systems involving many components. Most studies focus solely on pairwise interactions and ignore higher-order interactions among three or more components. To gain deeper insights into higher-order interactions and complex environments, we study antibiotic combinations applied to pathogenic Escherichia coli and obtain unprecedented amounts of detailed data (251 two-drug combinations, 1512 three-drug combinations, 5670 four-drug combinations, and 13608 five-drug combinations). Directly opposite to previous assumptions and reports, we find higher-order interactions increase in frequency with the number of drugs in the bacteria's environment.Furthermore, we observe a shift towards net synergy (effect greater than expected based on independent individual effects) and towards emergent antagonism (effect less than expected based on lower-order interaction effects). These findings have implications for the potential efficacy of drug combinations and are crucial for better navigating problems associated with the combinatorial complexity of multi-component systems.

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