Research ArticleDRUG INTERACTIONS

Efficient measurement and factorization of high-order drug interactions in Mycobacterium tuberculosis

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Science Advances  11 Oct 2017:
Vol. 3, no. 10, e1701881
DOI: 10.1126/sciadv.1701881
  • Fig. 1 DiaMOND for measuring pairwise drug interactions.

    (A) Simulated 2D checkerboard assay as demonstration of additive (left), synergistic (middle), and antagonistic (right) pairwise drug combinations. In each assay, one drug is linearly increased on each axis, and growth inhibition (white to blue color bar) is recorded for each concentration combination. A combination of a drug with itself will yield linear isophenotypic contours (isoboles). Drug combinations with linear, concave, or convex isoboles are classified as additive, synergistic, or antagonistic, respectively. To efficiently approximate the isoboles, DiaMOND samples the most information-rich dose responses of the checkerboard: the single-drug dose responses (white rectangles) and the 1:1 two-drug combination dose response (yellow rectangle; along the diagonal of the checkerboard). The dashed blue line connecting the observed single-drug dose responses approximates the additivity isobole for a given phenotype (for example, IC50), and the intersection of this line with the two-drug dose response is the expected dose in the null model (e1; blue diamond). The circles indicate the drug doses that result in the particular phenotype for each dose response. In this setting, the blue diamond (e1) will be the same distance as, closer to, or further from the origin in additive, synergistic, or antagonistic combinations. The circles are colored by drug interaction type throughout the manuscript: white, additivity; green, synergy, red, antagonism. (B) DiaMOND experimental setup to measure pairwise drug interactions requires three dose-response experiments, where drug dose is linearly increased. Two dose responses are single-drug dose responses. In the third dose-response experiment (yellow rectangle), a 1:1 mixture of drug X and drug Y is linearly increased. This mixture has half the concentration of both drug X and drug Y, and its dose response is the dose response of the diagonal sampling shown in (A). The expected dose (e1), shown by a blue diamond, is calculated using the geometric argument described in (A). When the observed dose is the same as, less than, or more than the expected dose, additivity, synergy, or antagonism is concluded, respectively. The brackets illustrate the expected (e1) and observed (o2) doses for the two-drug dose response (see also fig. S1). (C) All pairwise interactions among nine antibiotics tested in Mtb. The dose response of nine antibiotics and all 36 pairwise combinations is shown. Circles or blue diamonds mark the observed or expected IC50, respectively. Circles smaller or larger than expectation are marked by green or red, indicating synergy or antagonism. FIC2 scores obtained by dividing observed with expected IC50 are shown on the right of each two-drug dose response. (D) Hierarchical clustering of the pairwise interactions among nine antibiotics. The geometric mean of two biological replicates is represented. (E) Validation of two synergies and one antagonism via the traditional checkerboard method in Mtb. Simulated dose-response data are shown in blue gradient, and experimentally determined dose-response data are shown in grayscale gradient throughout.

  • Fig. 2 DiaMOND for measuring high-order drug interactions.

    (A) Top: The blue surface connecting the IC50 of three single drugs is used to define the additive expectation. As in the 2D case, the expected dose based on additivity is determined by finding the intersection of the three-drug combination dose response and the blue surface. If the observed IC50 of the equipotent mixture of three drugs is smaller than, equal to, or larger than the additive expectation, synergy, additivity, or antagonism is concluded, respectively. Bottom: DiaMOND experimental setup to measure three-way drug interactions requires four dose-response experiments where drug dose is linearly increased. Three dose responses are single-drug dose responses. In the fourth dose-response experiment, a 1:1:1 mixture of drug A, drug B, and drug C is linearly increased. Expected dose, shown by a blue triangle, is geometrically calculated (method S1). When the observed dose is less than, identical to, or more than the expected dose, synergy, additivity, or antagonism is concluded, respectively. (B) Experimental measurement of all pairwise, three-way, four-way, and five-way interactions among five antibiotics in Mtb. Dose response of five antibiotics and all possible combinations are shown in duplicate. Circles or blue triangles mark the observed or expected IC50, respectively. Circles smaller or larger than expectation are marked by green or red, indicating synergy or antagonism. FICn scores obtained by dividing observed with expected IC50 in this replicate are shown on the right of each n-drug dose response. Simulated dose-response data are shown in blue gradient, and experimentally determined dose-response data are shown in grayscale.

  • Fig. 3 DiaMOND for measuring emergent high-order drug interactions.

    (A) Each circle indicates an observed IC50 in either single-drug or two-drug dose responses for a three-drug combination. The expected surfaces obtained by connecting the IC50 values observed in two-drug combinations are shown in magenta. For clarity, only one two-drug axis [X + Y]/2 is shown as a magenta line. If the observed IC50 of the equipotent mixture of three drugs is smaller than, equal to, or larger than the pairwise expectation, emergent synergy, additivity, or antagonism is concluded, respectively. The blue triangle represents the expected surface given single-drug IC50 values. When pairwise interactions are additive, synergistic, or antagonistic, the expectation given pairs (magenta triangle) will be equal to, smaller than, or larger than the expectation given singles, respectively (blue triangles). (B) Simulated dose responses are given for single drugs, pairwise drugs, and possible outcomes for three-drug dose responses. The blue and magenta triangles mark the additive expectation given single drugs or pairwise combinations, respectively. The top and bottom of the circles representing the observed IC50 values are colored according to the interaction given singles (FICn) and emergent interaction (εFICn) that would be concluded. While two interaction types are the same when drug pairs are additive, a three-drug pair may have opposite interaction types when pairs are synergistic or antagonistic (indicated by “*”). Simulated dose-response data are shown in blue gradient. (C) All interaction scores for two-, three-, four-, and five-way combinations among five antibiotics are shown as a network representation. Nodes are specific combinations, whose contents are indicated by the barcode. The color of a combination shows the FICn or εFICn (geometric mean of two replicates) of a combination, whereas the size corresponds to deviation from additivity (FICn = 1). Edges are drawn between each combination that differs by one drug.

  • Fig. 4 The relationship between high-order interactions and their components.

    Three-, four-, and five-way interactions are denoted by triangles, squares, and stars, respectively. Each data point is obtained by factorization of one high-order interaction experiment. In each comparison, FICn is shown on the y axis. (A) Emergent interactions significantly correlate with FICn (Spearman’s r = 0.45, P = 9.6 × 10−3). (B) The product of emergent interaction and the geometric mean of all FICn−1 scores strongly correlates with FICn (Spearman’s r = 0.97, P = 3.1 × 10−20). (C) The geometric mean of all pairwise interactions among the drugs in a high-order combination is not significantly correlated with FICn (Spearman’s r = 0.33, P = 0.06). However, Embedded Image significantly correlates with FIC3, which is observed by the trend of triangles (Spearman’s r = 0.55, P = 1.2 × 10−2). (D) The multiplication of the geometric mean of the emergent interaction scores for all orders strongly correlated with FICn (Spearman’s r = 0.90, P = 1.6 × 10−12).

  • Table 1 The drugs used in this study, their abbreviations, target processes, and the minimum inhibitory concentrations (MICs).
    DrugAbbreviationTarget processMIC (μg/ml)
    BedaquilineBDQATP synthase0.6
    ClofazimineCLZDNA replication2.8
    EthionamideETAMycolic acid3
    EthambutolETHMycolic acid1.5
    IsoniazidINHMycolic acid0.18
    LinezolidLINProtein synthesis3
    MoxifloxacinMOXDNA gyrase0.35
    PretomanidPREProtein synthesis0.8
    RifampicinRIFRNA polymerase0.06

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/10/e1701881/DC1

    fig. S1. Data analysis pipeline to calculate FIC2 scores from dose-response growth data.

    fig. S2. Scatterplot of replicate interaction scores (FIC2) for all pairwise drug combinations shown in Fig. 1 (C and D).

    fig. S3. Correlation among FIC2 scores calculated at different levels of growth inhibition (IC30, IC40, IC50, IC60, and IC70) from the pairwise interaction data set described in Fig. 1 (C and D).

    fig. S4. Scatterplot of replicate interaction scores (FICn) obtained for all two-way (FIC2), three-way (FIC3), four-way (FIC4), and five-way (FIC5) drug combinations in two replicates for the experiment shown in Fig. 2B.

    fig. S5. Dose responses of isoniazid in combination with itself in one-way, two-way, three-way, four-way, and five-way combinations.

    fig. S6. 3D isobole of the checkerboard assay for the isoniazid + clofazimine + bedaquiline interaction.

    fig. S7. DiaMOND factorization model schematic.

    fig. S8. Scatterplot of the calculated lower-order (λFICn−1) interaction scores and the geometric mean of FICn−1 scores (Formula) from the high-order measurements described in Figs. 2 and 3.

    method S1. Derivation and formulas to calculate expectation doses.

    method S2. DiaMOND equation for four-drug combination derived from Eq. 5, approximation, and recursion.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Data analysis pipeline to calculate FIC2 scores from dose-response growth data.
    • fig. S2. Scatterplot of replicate interaction scores (FIC2) for all pairwise drug combinations shown in Fig. 1 (C and D).
    • fig. S3. Correlation among FIC2 scores calculated at different levels of growth inhibition (IC30, IC40, IC50, IC60, and IC70) from the pairwise interaction data set described in Fig. 1 (C and D).
    • fig. S4. Scatterplot of replicate interaction scores (FICn) obtained for all two-way (FIC2), three-way (FIC3), four-way (FIC4), and five-way (FIC5) drug combinations in two replicates for the experiment shown in Fig. 2B.
    • fig. S5. Dose responses of isoniazid in combination with itself in one-way, two-way, three-way, four-way, and five-way combinations.
    • fig. S6. 3D isobole of the checkerboard assay for the isoniazid + clofazimine + bedaquiline interaction.
    • fig. S7. DiaMOND factorization model schematic.
    • fig. S8. Scatterplot of the calculated lower-order (λFICn−1) interaction scores and the geometric mean of FICn−1 scores ( FICn−1 ) from the high-order measurements described in Figs. 2 and 3.
    • method S1. Derivation and formulas to calculate expectation doses.
    • method S2. DiaMOND equation for four-drug combination derived from Eq. 5, approximation, and recursion.

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