a| Perturbations in different simple architectures of metabolic networks. Synergy is formed between perturbations in two alternative pathways that produce the same product. Each perturbation alone has little effect, as the flux can continue through the alternative pathway33,65. Together, however, their effect is stronger, as their joint product can no longer be formed. Antagonism can occur in partial loss of function of two parallel pathways for building blocks of a single essential product. The most limiting pathway masks perturbation in the other pathway. A special type of antagonistic interaction, called co-equality, is formed when two perturbations completely inhibit two different targets within a linear pathway of an important but unessential metabolite. Each perturbation alone completely stops the flux through the pathway, neutralizing the effect of the other perturbation. b | Functional relatedness between two perturbed pathways can be inferred by the similarity of their interactions with other perturbations. The schematic on the left shows eight drugs (A–H) for which drug pairs interact synergistically (red lines), antagonistically (green lines) or additively (no lines). The middle schematic shows how drugs can be grouped into functional classes (dashed ovals) that interact with each other monochromatically (that is, with purely antagonistic or purely synergistic interactions between any two clusters). The schematic on the right shows a simplified network of a system-level view, showing the main groups and the interactions among them. c | This concept was used to generate a system-level view of antibiotic interactions based on data for all pair-wise combinations of 21 drugs. Figure modified, with permission, from Nature Genetics REF. 35 © (2006) Macmillan Publishers Ltd. All rights reserved.

a| In synergistic drug pairs, the effect of antibiotics is larger when combined together. Resistance mutations to either drug (for example, drug A) are favourable for the bacteria and allow a subsequent favourable resistance mutation to the other drug (for example, drug B). Development of multidrug resistance could occur by sequential single-drug resistance steps. φ represents no drug. b | Resistance is less likely to occur in reciprocally suppressive drug combinations, as each single-drug resistance step (dashed arrows) is unfavourable. c | Although the ideal case of reciprocal suppression has not been observed in antibiotics, unidirectional suppression (one drug suppresses the effect of the other) is not very rare. Here, drug B reverses selection for resistance to drug A, but drug A does not reverse selection for resistance to drug B. In such cases, the population is not fully locked in a sensitive state (as occurs in b), but this tactic could slow resistance. d,e | The same idea can be understood in a more refined model that accounts for drug dosages. As drug resistance means that the bacteria effectively see a reduced concentration of the drug, the growth region of resistant mutants could be approximated as a geometrical rescaling of the growth region of the wild type. This same rescaling leads to profoundly different outcomes in synergy versus antagonism. In the synergistic case (d), the growth region of the resistant mutant is completely inclusive of that of the wild type. In the antagonistic case (e), however, there is a region of drug concentrations (asterisk) where the wild-type strain can grow, but the resistant mutant cannot10. f,g | Direct competition of doxycycline-sensitive (dox^s) and doxycycline-resistant (dox^r) Escherichia coli strains revealed selection against resistance. Resistant and sensitive cells were differentially labelled, inoculated at 1:1 into an array of drug environments (black dots) and counted by flow cytometry after 24 hours. In the drug environment of the synergistic pair doxycycline–erythromycin, the resistant strain always wins (f), but in the antagonistic pair of doxycycline–ciprofloxacin, the sensitive strain outcompetes the resistant strain under certain drug ratios (g).

a| Schematic of the frequency of spontaneous resistance mutations as a function of drug concentrations for a single-drug environment46. The point at which the frequency drops to undetectable values is called the mutant prevention concentration (MPC). As evolution requires both mutations and selection, evolution is thought to proceed primarily below the MPC and above the minimum inhibitory concentration (MIC). This region is called the mutant selection window (MSW). b | The concept of the MSW can be extended to multidrug combinations, for which it becomes the area (red) between the MIC line (solid) and MPC line (dashed) in the drug–drug concentration space. A fixed drug ratio corresponds to a linear line with angle θ that extends from the origin and is associated with an effective MSW. c | Data for fusidic acid and erythromycin show that some drug ratios can decrease the MSW, compared with the MSW of single drugs. Recent experiments and modelling suggest that the best reduction in MSW can be achieved by greater antagonistic interactions and lower cross-resistance12.

Bacterial populations were grown in an automatic robotic system with daily dilutions in different drug pairs and concentration ranges (~200 different conditions). a | Growth rate of one typical population, showing adaptation time (T_1/2) and fitness gain (Δ). The inset shows the daily growth rates, which were measured by continuous optical density (OD) monitoring (first day, green; eighth day, red). b | The adaptation rate (Δ/T_1/2) is negatively correlated with drug interactions; synergistic drug pairs accelerate the rate of adaptation. Figure modified, with permission, from REF. 11 © (2008) National Academy of sciences.