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.

交互作用和紧急过程对于研究包含许多组件的复杂系统至关重要。大多数研究仅关注成对相互作用，而忽略三个或更多组件之间的高阶相互作用。为了深入了解高级相互作用和复杂环境，我们研究了应用于致病性大肠杆菌的抗生素组合并获得前所未有的详细数据（251种两药组合，1512种三药组合，5670种四药组合和13608种五药组合）。与先前的假设和报告完全相反，我们发现随着细菌环境中药物数量的增加，高阶相互作用的频率也会增加。具体而言，随着添加更多药物，我们观察到净协同作用的频率升高（效果大于独立个体效应所预期的效果），而且出现的拮抗作用实例也有所增加（效果基于低级相互作用效应而低于预期）。这些发现对药物组合的潜在功效具有影响，对于更好地解决与多组分系统组合复杂性相关的问题至关重要。