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.

Environmental factors like temperature, pressure, and pH partly shaped the evolution of life. As life progressed, new stressors (e.g., poisons and antibiotics) arose as part of an arms race among organisms. Here we ask if cells co-opted existing mechanisms to respond to new stressors, or whether new responses evolved de novo. We use a network-clustering approach based purely on phenotypic growth measurements and interactions among the effects of stressors on population growth. We apply this method to two types of stressors-temperature and antibiotics-to discover the extent to which their cellular responses overlap in Escherichia coli. Our clustering reveals that responses to low and high temperatures are clearly separated, and each is grouped with responses to antibiotics that have similar effects to cold or heat, respectively. As further support, we use a library of transcriptional fluorescent reporters to confirm heat-shock and cold-shock genes are induced by antibiotics. We also show strains evolved at high temperatures are more sensitive to antibiotics that mimic the effects of cold. Taken together, our results strongly suggest that temperature stress responses have been co-opted to deal with antibiotic stress.

Understanding how stressors combine to affect population abundances and trajectories is a fundamental ecological problem with increasingly important implications worldwide. Generalisations about interactions among stressors are challenging due to different categorisation methods and how stressors vary across species and systems. Here, we propose using a newly introduced framework to analyse data from the last 25 years on ecological stressor interactions, for example combined effects of temperature, salinity and nutrients on population survival and growth. We contrast our results with the most commonly used existing methodanalysis of variance (ANOVA)and show that ANOVA assumptions are often violated and have inherent limitations for detecting interactions. Moreover, we argue that rescalingexamining relative rather than absolute responsesis critical for ensuring that any interaction measure is independent of the strength of single-stressor effects. In contrast, non-rescaled measureslike ANOVAfind fewer interactions when single-stressor effects are weak. After reexamining 840 two-stressor combinations, we conclude that antagonism and additivity are the most frequent interaction types, in strong contrast to previous reports that synergy dominates yet supportive of more recent studies that find more antagonism. Consequently, measuring and reassessing the frequency of stressor interaction types is imperative for a better understanding of how stressors affect populations.

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.

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.

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