yseult f. brun cancer prevention and population sciences, roswell park cancer institute
DESCRIPTION
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. Brun Cancer Prevention and Population Sciences, Roswell Park Cancer Institute - PowerPoint PPT PresentationTRANSCRIPT
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