Yseult F. Brun Cancer Prevention and Population Sciences, Roswell Park Cancer Institute

1. Modeling of the three antifungal agent combination (Amphotericin B + Micafungin + Nikkomycin Z) against Aspergillus fumigatusin vitro usinga novel response surface paradigm Yseult F. Brun Cancer Prevention and Population Sciences, Roswell Park Cancer Institute UB School of Pharmacy and Pharmaceutical Sciences / Novartis fellowship

2. Acknowledgements • Brahm H. Segal • Carly Dennis • William R. Greco • Donald B. White ISAP presentation – antifungals modeling

3. Experimental Methods • Aspergillus fumigatus, 3.9 103 per well • Amphotericin B, Nikkomycin Z and Micafungin. • Randomized 96 well plates • XTT assay after 24 hour exposure. ISAP presentation – antifungals modeling

4. Our Unique Dataset • 91 different fixed ratios at 11 log spaced increasing amounts • At least, quadruplicates • 5 separate experiments • Controls and drugs alone for each experiment • 5610 data points ISAP presentation – antifungals modeling

5. Hill Equation – Single Drug ISAP presentation – antifungals modeling

6. Model challenges • Model must take into account the following challenges: • Different slope parameters for each agent • Arbitrary patterns for slope, background parameters • Irregular isobols, local synergy, antagonism, additivity • More than 2 agents ISAP presentation – antifungals modeling

7. Example of hill model fitted to data from one fixed-ratio ISAP presentation – antifungals modeling

8. Scaled concentrations ISAP presentation – antifungals modeling

9. Example of isobol and Log CI50 ISAP presentation – antifungals modeling

10. Ternary Plot ISAP presentation – antifungals modeling

11. Three-drug Hierarchical Model Example Effect(V,A, q) = ISAP presentation – antifungals modeling

12. Conclusions • Effective modeling system • Complex response surface, projection of irregular isobols • The most synergistic region is at the center of the response surface, for approximately equal normalized amounts of the three agents, amphotericin B, nikkomycin Z and micafungin • Thank you! ISAP presentation – antifungals modeling

13. Extra slides

14. Randomization ISAP presentation – antifungals modeling

15. Weighting ISAP presentation – antifungals modeling

16. Example for B ISAP presentation – antifungals modeling

17. Using Scheffé’s PolynomialsExample With Slope B • Third Order model for B in three drug experiment: • B(V,qB) = ISAP presentation – antifungals modeling

18. Example for slope parameter for two drugs ISAP presentation – antifungals modeling

19. Example for m – three drugs ISAP presentation – antifungals modeling

20. Modifications for CI50 ModelsTo Account for Scaling • Model Log(CI50) in place of CI50 • Note the leading factor (1-x)(1-y)(1-z) - forces the polynomial to zero at the single drug vertices • LogCI50(V,qD) = ISAP presentation – antifungals modeling

21. Log CI50 fit for three drugs ISAP presentation – antifungals modeling