Hidden suppressive interactions are common in higher-order drug combinations

Abstract

The rapid increase of multi-drug resistant bacteria has led to a greater emphasis on multi-drug combination treatments. However, some combinations can be suppressive-that is, bacteria grow faster in some drug combinations than when treated with a single drug. Typically, when studying interactions, the overall effect of the combination is only compared with the single-drug effects. However, doing so could miss "hidden" cases of suppression, which occur when the highest order is suppressive compared with a lower-order combination but not to a single drug. We examined an extensive dataset of 5-drug combinations and all lower-order-single, 2-, 3-, and 4-drug-combinations. We found that a majority of all combinations-54%-contain hidden suppression. Examining hidden interactions is critical to understanding the architecture of higher-order interactions and can substantially affect our understanding and predictions of the evolution of antibiotic resistance under multi-drug treatments.

Keywords: Microbiology; Systems Biology.

Graphical abstract

Figure 1

Antibiotic interactions in 2-drug and 3-drug combinations Hatched bars represent growth in a no-drug environment; black bars represent the fitness of bacteria treated with a single antibiotic. Light gray bars represent the fitness of additive drug interactions, synergistic interactions are in red, antagonistic interactions are in green, and suppressive interactions are in teal. Note that the 2-drug combinations do not need to have the same net interaction type for a 3-drug combination to have a particular net interaction. Suppressive interactions are an extreme form of antagonism: notice that the bacteria treated with the suppressive drug combination has a higher fitness than the single drugs. Importantly, suppressive interactions can be hidden: this occurs when the highest-order combination has higher fitness than a lower-order combination but it does not have higher fitness than any of the single drugs. Thus, hidden suppression can only occur in a combination of 3 or more drugs. Also, note that bacteria treated with the 3-drug combination with hidden suppression has a higher fitness compared with any of the 2-drug combinations but not one of the single drugs.

Figure 2

An illustration of the fitness landscapes and the importance of ruggedness in evolutionary trajectories (A) A smooth landscape only has one peak. As a population evolves to an environment there is always a path that leads to the optimum set of traits resulting in the highest possible fitness. (B) In a rugged landscape, multiple peaks and valleys make evolving to the highest fitness not as straightforward as in a smooth landscape. Populations may have to cross a valley, which means (1) a loss of fitness must first occur before a net increase in fitness, (2) the population can become stuck at a local peak rather than evolve and ascend to the global peak, or (3) the population must make a jump from one peak to the next. Without the lower-order interactions, we may miss key details of intermediate peaks and valleys in the fitness landscape.

Figure 3

The paths for a 4-drug and a 5-drug combination consisting of drugs A, B, C, D, and E (A) All 24 possible paths are shown for a 4-drug combination. (B) All 120 possible paths are shown for a 5-drug combination. For both the 4-drug (A) and 5-drug (B) combinations, a single path is shown in a bold line with the highest-order combination and each lower-order combination highlighted in gray. This single path represents a unique set of drugs, one at each level of combinations (4-drug, 3-drug, 2-drug, and a single drug), allowing for an assessment of any nesting. For this example, nested hidden suppression occurs when the 5-drug combination is suppressive to the 4-drug, the 4-drug combination is suppressive to a 3-drug combination, and the 3-drug combination is then suppressive to a 2-drug combination. And, if appropriate, the 2-drug combination is suppressive to the single-drug effects (this is only considered if the combination is net suppressive). If this is true for all paths the combination is considered to be fully nested. If this is only observed in some paths the combination is considered to be partially nested.

Figure 4

Hidden suppression is present in a majority of higher-order combinations Hidden suppression was found in all levels examined—3-drug, 4-drug, and 5-drug combinations. The amount of hidden suppression increases as the number of drug increases.

Figure 5

The distributions and relative proportion of hidden suppression for each interaction type for net (A) and emergent (B) interactions for 3-, 4-, and 5- drug combinations. The proportion of combinations with hidden suppression (HS) of suppressive interactions (teal) decreases as the number of drugs in a combination increases. The percentage written inside the darker shades of the bars represents the proportion of combinations with hidden suppression present in that specific interaction type. The y axis is the percentage of each interaction type within the designated level of the drug combination, showing the overall distribution of net or emergent interactions. For example, in (A) the net suppressive 4-drug combinations, 92% of the combinations have hidden suppression within them. As the number of drugs increases, the amount of hidden suppression within additive, synergistic, and antagonistic combinations also increase.

Figure 6

Hidden suppressive interactions occur more frequently within net suppressive combinations rather than within non-net suppressive combinations The amounts of hidden suppression are shown out of the total number of lower-ordered combinations within a single higher-order combination that is either net suppressive (teal) or has some instances of hidden suppression (gray).

Figure 7

Fitness graphs show the importance of considering hidden interactions Fitness graphs show similar information as a fitness landscape; they both help to visualize the relationships between stressors or genetic mutations and their effects on fitness. However, fitness graphs can be more appropriate for discrete data. Here we show fitness graphs of two synergistic 5-drug combinations (for abbreviations see Table 1). Drug combination 1 has no hidden suppression (top), and drug combination 2 has hidden suppression (bottom). The left-hand side shows the fitness graphs not considering the hidden suppression; notice how similar these two appear to be. Although the figures on the right-hand side show the fitness graphs including the lower-order combinations, notice the increase in ruggedness is due to the hidden suppressive interactions (the decrease in fitness at one of the 4-drug combinations) in the bottom right. The edges in red highlight the paths involved in hidden suppression. For more detailed information about these paths please see Figure S4.