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

Modeling of the three antifungal agent combination (Amphotericin B + Micafungin + Nikkomycin Z) against Aspergillus fumigatus

in vitro using

a novel response surface paradigm

Yseult F. BrunCancer Prevention and Population Sciences,

Roswell Park Cancer InstituteUB School of Pharmacy and Pharmaceutical

Sciences / Novartis fellowship

December 19th 2005 ISAP presentation – antifungals modeling

Acknowledgements

Brahm H. Segal Carly Dennis William R. Greco Donald B. White

December 19th 2005 ISAP presentation – antifungals modeling

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.

December 19th 2005 ISAP presentation – antifungals modeling

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

December 19th 2005 ISAP presentation – antifungals modeling

Hill Equation – Single Drug

slope m

Emax/2 + b

b

CONCENTRATION(Log scale)

0.001 0.01 0.1 1 10 100 1000

EFFECT(% control)

0

50

100

Econ

IC50

Emax =Econ - b

bICC

ICCbEconE

m

m

)/(1

)/(*)(

50

50

December 19th 2005 ISAP presentation – antifungals modeling

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

December 19th 2005 ISAP presentation – antifungals modeling

Example of hill model fitted to data from one

fixed-ratio

[FK ]+ [Nikk]+[ampho] (g/mL)

1e-5 1e-4 1e-3 0.01 0.1 1 10 100 1000

Res

po

nse

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8FK:nikk:ampho 8:2:1

December 19th 2005 ISAP presentation – antifungals modeling

Scaled concentrations

2,50

2

1,50

1

50

50

)/(1

)/)((

ICC

ICCA

BCIA

CIABEconE

m

m

December 19th 2005 ISAP presentation – antifungals modeling

Example of isobol and Log CI50

Nikkomycin Z + FK463

[FK]/IC50,FK

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

[Nik

k]/I

C50

,nik

k

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

% IC50 equivalents of FK

0.0 0.2 0.4 0.6 0.8 1.0

CI5

0 (l

og

sca

le)

0.1

1

10

)]()[1)(1()50( 21 yxyxyxyxyxCILOG

December 19th 2005 ISAP presentation – antifungals modeling

Ternary Plot

December 19th 2005 ISAP presentation – antifungals modeling

Three-drug Hierarchical Model Example

Effect(V,A, ) =

100)),(/(1

)),(/100

),(50

),(50

EconB%(V,θ

CIA

CIAEconB%(V,θ

EconB

mD

mD

B

m

m

V

V

V

V

December 19th 2005 ISAP presentation – antifungals modeling

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!

Extra slides

December 19th 2005 ISAP presentation – antifungals modeling

Randomization

December 19th 2005 ISAP presentation – antifungals modeling

Weighting

December 19th 2005 ISAP presentation – antifungals modeling

Example for B

2210 ** xBxBBB

December 19th 2005 ISAP presentation – antifungals modeling

Using Scheffé’s Polynomials

Example With Slope B Third Order model for B in three drug

experiment: B(V,B) =

xyzzyyzzxxzyxxy

yzxzxyzyx

BBBB

BBBBBB

123231312

231312321

)()()(

December 19th 2005 ISAP presentation – antifungals modeling

Example for slope parameter for two drugs

2210 ** xmxmmm

December 19th 2005 ISAP presentation – antifungals modeling

Example for m – three drugs

m observed

-5 -4 -3 -2 -1 0

m p

red

icte

d

-5

-4

-3

-2

-1

0

Expt AExpt BExpt CExpt DExpt Ered one drug, purple two, blue three

December 19th 2005 ISAP presentation – antifungals modeling

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,D) =

])()()(

)[1)(1)(1(

123231312

231312321

xyzzyyzzxxzyxxy

yzxzxyzyxzyx

DDDD

DDDDDD

December 19th 2005 ISAP presentation – antifungals modeling

Log CI50 fit for three drugs

Log CI50 observed

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Log

CI5

0 es

timat

ed

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0