Concentration-dependent synergy and antagonism within a triple antifungal drug combination against Aspergillus species: analysis by a new response surface model

Abstract

Triple antifungal combinations are used against refractory invasive aspergillosis without an adequate understanding of their pharmacodynamic interactions. We initially studied the in vitro triple combination of voriconazole, amphotericin B, and caspofungin against Aspergillus fumigatus, A. flavus, and A. terreus by a spectrophotometric microdilution broth method after 48 h of incubation. We then analyzed these results with a recently described nonlinear mixture response surface E(max)-based model modified to assess pharmacodynamic interactions at various growth levels. The new model allows flexibility in all four parameters of the E(max) model and is able to describe complex pharmacodynamic interactions. Concentration-dependent pharmacodynamic interactions were found within the triple antifungal combination. At the 50% growth level, synergy (median interaction indices of 0.43 to 0.82) was observed at low concentrations of voriconazole (<0.03 mg/liter) and amphotericin B (</=0.20 mg/liter) and at intermediate concentrations of caspofungin (0.95 to 14.88 mg/liter), whereas antagonism (median interaction indices of 1.17 to 1.80) was found at higher concentrations of voriconazole and amphotericin B. Ternary plot and interaction surface analysis further revealed the complexity of these concentration-dependent interactions. With increasing concentrations of amphotericin B, the synergistic interactions of voriconazole-caspofungin double combination decreased while the antagonistic interactions increased. A similar effect was observed when voriconazole was added to the double combination of amphotericin B and caspofungin. In conclusion, the new nonlinear mixture-amount response surface modeling of the triple antifungal combination demonstrated a net antagonism or synergy against Aspergillus species depending upon drug concentrations and species.

FIG. 1.

Diagnostic plots used to assess the goodness of fit of the modified global model to the data. Plots of actual versus predicted data (left) and of residuals versus predicted data (right) for the A. fumigatus 4215 isolate are shown (R² = 0.91 for the modified global model).

FIG. 2.

Concentration-effect data (triangles) for voriconazole (VOR), caspofungin (CAS), and amphotericin B (AMB) alone and for voriconazole-caspofungin combinations at fixed U_VOR/U_CAS ratio of 0.9:0.1 in the presence of increasing amphotericin B concentrations for the A. fumigatus 4215 isolate. The regression curves obtained with the global model fitted to all data (solid lines) and with the E_max model fitted to each concentration-effect data individually (dashed lines) are shown.

FIG. 3.

Patterns of interaction for the double combinations voriconazole-caspofungin (left graphs), voriconazole-amphotericin B (middle graphs), and amphotericin B-caspofungin (right graphs) for 20% (top graphs), 50% (middle graphs), and 80% (bottom graphs) of growth of the A. fumigatus 4215 isolate. Regression curves (solid lines) and their 95% confidence bands (dashed lines) were derived from the modified global model, where diamonds represent individually determined interaction indices obtained using isobolographic analysis (26). Interaction indices of >1 indicate antagonistic interactions, whereas interaction indices of <1 indicate synergistic interactions. VOR, voriconazole; CAS, caspofungin; AMB, amphotericin B.

FIG. 4.

Ternary plots of the triple combination of voriconazole, caspofungin, and amphotericin B against the A. fumigatus 4215 isolate for 50% of growth, constructed based on the results of the model of White et al. (40) (left plot) and the modified (right plot) global response surface model used in the present study. The model of White et al. was modified in this study by eliminating the leading factor (1 − x)(1 − y)(1 − z). The ternary display is a triangle with sides scaled from 0 to 1. The labels on each side are the relative potency units of each drug. The color inside the triangles indicates the nature and the magnitude of interaction for mixtures with different relative potency units of the three drugs (gray dots). The relative potency units of each drug at a specific mixture can be found by extending the ticks on each side of the triangles towards the point inside the triangle. For example, the white dot in the right triangle represent the combination of 0.2 potency units of AMB (z), 0.5 potency units of CAS (y), and 0.3 potency units of VOR (x), which is synergistic since the interaction index is <0.5 (black area). The color at the x, y, and z sides of triangles represents interactions of the double combinations amphotericin B-voriconazole, voriconazole-caspofungin, and caspofungin-amphotericin B, respectively.

FIG. 5.

Interaction surfaces for the triple combination of voriconazole, caspofungin, and amphotericin B against the A. fumigatus 4215 isolate. The percentages of interaction (additive minus experimental percentage of growth obtained by the modified global model) are plotted for the voriconazole-caspofungin combination in the presence of increasing concentrations of amphotericin B. Volumes above the zero plane (dark gray) indicate synergistic interactions (less growth was observed than the theoretical additive), whereas volumes below the zero plane (light gray) indicate antagonistic interactions (more growth was observed than the theoretical additive). The height or depth of these volumes is proportionally related to the intensity of the synergistic and antagonistic interactions, respectively. The numbers above the synergistic volumes and below the antagonistic ones indicate the sum of all synergistic and antagonistic interactions, respectively, as a measure of both intensity and frequency of these interactions. The double combination of voriconazole plus caspofungin is synergistic at caspofungin concentrations of <32 mg/liter and antagonistic at higher caspofungin concentrations (A). The same holds for the double combination of caspofungin plus amphotericin B (see 0 mg/liter of voriconazole in panels B, C, D, E, and F). The double combination of amphotericin B plus voriconazole is antagonistic (see 0 mg/liter of caspofungin in panels B, C, D, E, and F graphs). Note that synergistic interactions decrease and antagonistic interactions increase with increasing concentrations of amphotericin B. Most of the synergistic interactions were located at low concentrations of amphotericin B (0.1 and 0.2 mg/liter) and voriconazole (0.016 to 0.125 mg/liter) and at 1 to 32 mg/liter of caspofungin. The additive and experimental response surfaces were calculated based on equations 2, 3, and 4 using the following estimates (± standard errors) obtained from the nonlinear regression analysis with the modified global model: B = −0.07 ± 0.02, E_max = 1.35 ± 0.03, a_D1 = −0.17 ± 0.04, a_D2 = −0.12 ± 0.05, a_D3 = −0.03 ± 0.01, b_D12 = −1.78 ± 0.31, b_D13 = 0.92 ± 0.10, b_D23 = −1.38 ± 0.22, g_D12 = −3.46 ± 0.54, g_D13 = 0.24 ± 0.11, g_D23 = 3.39 ± 0.31, d_D123 = −12.0 ± 1.87, a_m1 = −1.58 ± 0.19, a_m2 = −1.75 ± 0.30, a_m3 = −6.66 ± 0.50, b_m12 = 3.95 ± 0.86, b_m13 = 5.15 ± 1.23, b_m23 = 9.88 ± 1.47, g_m12 = 2.61 ± 1.15, g_m13 = −4.36 ± 1.83, g_m23 = −17.3 ± 2.73, and d_m123 = 15.3 ± 5.58. ADD, additivity.

FIG. 6.

Synergistic and antagonistic volumes (sum percentage of the interactions presented in Fig. 5) of the double combinations voriconazole-caspofungin (A), amphotericin B-caspofungin (B), and amphotericin B-voriconazole (C) with increasing concentrations of amphotericin B (AMB), voriconazole (VOR), and caspofungin (CAS), respectively. With increasing amphotericin B and voriconazole concentrations, respectively, the synergistic volumes of the voriconazole-caspofungin and amphotericin B-caspofungin double combinations decrease and the antagonistic volumes increase. With increasing caspofungin concentrations, the synergistic volumes of the amphotericin B-voriconazole double combination increase and the antagonistic volumes decrease. Points and error bars represent mean sum percentages and standard errors, respectively, among the three isolates. The squares and circles on the y axis of each graph represent the sum percentages of synergistic and antagonistic volumes, respectively, of only the double combinations voriconazole-caspofungin (A), amphotericin B-caspofungin (B), and amphotericin B-voriconazole (C) in the absence of the third drug.