Prediction of ultra-high-order antibiotic combinations based on pairwise interactions


Abstract

Drug combinations are a promising approach to achieve high efficacy at low doses and to overcome resistance. Drug combinations are especially useful when drugs cannot achieve effectiveness at tolerable doses, as occurs in cancer and tuberculosis (TB). However, discovery of effective drug combinations faces the challenge of combinatorial explosion, in which the number of possible combinations increases exponentially with the number of drugs and doses. A recent advance, called the dose model, uses a mathematical formula to overcome combinatorial explosion by reducing the problem to a feasible quadratic one: using data on drug pairs at a few doses, the dose model accurately predicts the effect of combinations of three and four drugs at all doses. The dose model has not yet been tested on higher-order combinations beyond four drugs. To address this, we measured the effect of combinations of up to ten antibiotics on E. coli growth, and of up to five tuberculosis (TB) drugs on the growth of M. tuberculosis. We find that the dose model accurately predicts the effect of these higher-order combinations, including cases of strong synergy and antagonism. This study supports the view that the interactions between drug pairs carries key information that largely determines higher-order interactions. Therefore, systematic study of pairwise drug interactions is a compelling strategy to prioritize drug regimens in high-dimensional spaces.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Effect of single and pairs of ten antibiotics on E coli growth was measured to determine the dose model parameters.
The panels on the diagonal shows the relative growth reduction of E. coli grown with individual antibiotics (Table 1) at 13 doses (dots). Doses for each drug were spaced linearly such that the halfway effect D50 is approximately at the middle dose. These dose-response curves are well described by Hill curves (solid line). The off-diagonal panels show the two-drug responses for all 45 pairs of the ten drugs, at 13 dose combinations (dots). For example, the panel located at the 4th row and 7th column shows the pair response of drug 4(CHL) and drug 7(MOX) (also shown in the inset figure). We mixed the drugs at the 13 doses used for the single-drug dose-response curves, thus diluting each drug by a factor of two. The pair response curves were used to determine the dose model parameters (aij). After fitting the parameters, the response curves of the pairs are well described by the dose model (solid lines). The pair interactions strength I = log(g12-g1g2+1), which indicates the mean deviation from the Bliss model (dashed line) is visualized by the color of each panel. The response curves presented here are the average of two (for combination 1–28) or three (for combination 29–115) biological replicates.
Fig 2
Fig 2. The dose model predicts well the effect of combinations of 2–10 antibiotics on E. coli growth.
(A) The response curves for all 115 combinations (dots) compared to the dose model predictions (solid lines) and the bliss model predictions (dashed lines). The Interactions strength I = log(g12-g1g2+1), which indicates the mean deviation from the Bliss model (dashed line) is visualized by the color of each panel. The black and white squares on the top-right corner of each panel indicated which drugs where included in the cocktail. For example, in the first panel drugs AMP(1), MER(6) and MOX(7) were included in the cocktail. (B) The normalized growth compared to the dose model (x) and the Bliss model (o) predictions for 2–10 antibiotics. (B) R2 and RMSE values for the Dose model (x) and the Bliss model (o). The combination legend is also in S1 Table. The response curves presented here are the average of two (for combination 1–28) or three (for combination 29–115) biological replicates.
Fig 3
Fig 3. The effect of single and pair of 9 TB drugs on M. tuberculosis growth was measured to determine the dose model parameters.
The panels on the diagonal shows the individual antibiotics (Table 2) response at 13 doses (dots). Doses for each drug were spaced linearly such that the halfway effect D50 is approximately at the middle dose. These dose-response curves were well described by Hill curves (solid line). The off-diagonal panels show the two-drug responses for all 36 pairs of the 9 drugs, at 13 dose combinations (dots). For example, the panel located at the 4th row and 6th column shows the pair response of drug 4 and drug 6 (also shown in the inset figure). We mixed the drugs at the 13 doses used for the single-drug dose-response curves, thus diluting each drug by a factor of two. The pair response curves were used to determine the dose model parameters (aij). After fitting the parameters, the response curves of the pairs are well described by the dose model (solid line). The pairs interactions strength I = log(g12-g1g2+1), which indicates the mean deviation from the Bliss model (dashed line) is visualized by the color of each panel. The response curves presented here are the average of two biological replicates.
Fig 4
Fig 4. The dose model predicts well the effect of combinations of 3–5 TB drugs on M. tuberculosis growth.
(A) The response curves for all 9 combinations (dots) compared to the dose model predictions (solid lines) and the bliss model predictions (dashed lines). The Interactions strength I = log(g12-g1g2+1), which indicates the mean deviation from the Bliss model (dashed line) is visualized by the color of each panel. (B) The normalized growth compared to the Dose model (x) and the Bliss model (o) predictions for 3–5 TB drugs. (C) R2 and RMSE values for the Dose model (x) and the Bliss model (o). The full names of the drugs are in Table 2. The response curves presented here are the average of two biological replicates.
See this image and copyright information in PMC

Similar articles