Sample-efficient identification of high-dimensional antibiotic synergy with a normalized diagonal sampling design

Abstract

Antibiotic resistance is an important public health problem. One potential solution is the development of synergistic antibiotic combinations, in which the combination is more effective than the component drugs. However, experimental progress in this direction is severely limited by the number of samples required to exhaustively test for synergy, which grows exponentially with the number of drugs combined. We introduce a new metric for antibiotic synergy, motivated by the popular Fractional Inhibitory Concentration Index and the Highest Single Agent model. We also propose a new experimental design that samples along all appropriately normalized diagonals in concentration space, and prove that this design identifies all synergies among a set of drugs while only sampling a small fraction of the possible combinations. We applied our method to screen two- through eight-way combinations of eight antibiotics at 10 concentrations each, which requires sampling only 2,560 unique combinations of antibiotic concentrations.

Fig 1. Calculation of the MECI, TSS, and ESS for a three-drug experiment.

(A) Testing three drugs at four concentrations each could be performed exhaustively using a three-dimensional checkerboard assay, as depicted here. When the effectiveness measure is taken to be the absence of visible growth, the MEC can be calculated for each effective measurement in the checkerboard assay. (B) Computation of select MEC values from the checkerboard assay. The MECI of a drug combination is the minimum MEC among tested combinations. The MECI, TSS, and ESS of all subsets are computed according to their definitions, with normalization N_i = 1 μg/mL for all drugs. The well in the upper-left corner of each combination’s calculated values witnesses the MECI of that combination; we see that the wells tested by the NDS design (shown with bold edges) are sufficient to identify the MECI. (C) If the behavior of the antibiotics satisfies Definition 3.1, we prove that the NDS design always identifies the MECI for every combination tested. We illustrate some examples of allowed and disallowed behavior of the measured response as a function of increasing some antibiotic (combination) A as the concentration of antibiotic (combination) B remains fixed.

Fig 2. Results from the breakpoint-normalized experiment.

(a) Distribution of TSS and ESS scores across all 2⁸ different breakpoint-normalized combinations of the eight antibiotics in Table 1, separated by the number of drugs in the combination. (b) Representations of the 17 drug combinations exhibiting weak synergy. Each row represents one combination; dark shades (black and blue) indicate presence of the drug, while light gray indicates absence. Black represents combinations that are weakly synergistic according to the breakpoint normalization but not the MIC normalization (next section), while blue shows the five combinations that exhibited weak synergy according to both normalizations.

Fig 3. Results of the MIC-normalized experiment.

(a) Distribution of TSS and ESS scores across all 2⁸ different MIC-normalized combinations of the eight antibiotics in Table 1, separated by the number of drugs in the combination. (b) Representations of the 44 drug combinations exhibiting weak synergy; combinations that were also weakly synergistic under the breakpoint normalization are shown in blue. Each row represents one combination; black/blue indicates presence of the drug, while gray indicates absence.