Transcript Modeling HCV Antivirals Steven S. Carroll, David B. Olsen, Jeffrey S. Saltzman, Robert B.

Modeling HCV Antivirals
Steven S. Carroll, David B. Olsen, Jeffrey S.
Saltzman, Robert B. Nachbar
IMA – 26 October 2007 - 2007-ms-1374
Outline
• Introduction and Background
• Modeling & Simulation
–
–
–
–
Perelson model
Merck model
Viral load time course
Polymerase Inhibitor data fitting
• Clinical Trial Design
– Model parameter sensitivity
– Stochastic model
– Phase I design
• Resistance mutants
Challenges of Drug Discovery
• *Paracelsus (1493-1541) Known as 'The Father
of Medicine' said "All that man needs for
health and healing has been provided by God
in nature, the challenge of science is to find
it." Also known as 'The Father of Toxicology,
he said, "All things are poison and nothing is
without poison, only the dose permits
something not to be poisonous."
• Little and much have changed …
*http://en.wikipedia.org/wiki/Paracelsus#Biography
Of 10,000 compounds in basic
research, on average only five will
enter clinical testing and just one
will make it to the market. (Source:
PhRMA, March 2005)
Preclinical
and Safety
Discovery
Discovery
Preclinical
and Safety
Clincal and
Postmarketing
Clincal and
Postmarketing
Drug Development Process
By the year 2000 R&D costs for a
single drug had exceeded
$800M. Only 3 of 10 drugs
recouped their R&D investment.
Applied Mathematics, Computing and Modeling
• Understanding
– Moving from Qualitative to Quantitative
– More compact representation of knowledge that is easier to
disseminate.
• Efficiency
– Can reduce cycle time or increase productivity via elimination of
empirical work or redundant testing.
• Towards the Elimination of Animal Testing
– Imaging and image processing enables longitudinal studies of animal
reducing N (for humans and nonhumans).
– Some mathematical models are better predictors then corresponding
“animal models”.
• Many Contributors
–
–
–
–
–
–
–
Applied Computer Science and Mathematics (ACSM)
Biometrics Research
Clinical Statistics
Epidemiology
Metabolism
Molecular Profiling
Pharmacology and many others…
Background*
•
Hepatitis C virus (HCV) is currently the major cause of parenterallytransmitted non-A,non-B hepatitis (NANB-H).
•
In the majority of cases, infection by HCV results in a chronic disease
characterized by liver inflammation and in some cases, slow progression to
cirrhosis, liver failure and/or hepatocellular carcinoma.
•
There is no vaccine available for HCV and current therapy with interferon
alpha (IFNα) and the nucleoside analog ribavirin produces complete
response in less than half of treated persons infected with genotype 1, the
predominant genotype in the US and many other countries.
•
It is estimated that 3% (> 170 million) of the world’s population and 2% ( > 4
million) of the US population is affected by the disease.
•
HCV is transmitted primarily through direct percutaneous exposure to blood
and is the most common chronic blood-borne infection in the US.
* World Health Organization, http://www.who.int/mediacentre/factsheets/fs164/en/.
HCV Replication Cycle
(2)
(1)
(3)
(4)
(5)
(6)
(1) virus binding and internalization
(2) cytoplasmic release and uncoating
(3) internal ribosomal entry site (IRES)mediated translation and polyprotein
processing
(4) RNA replication
(5) packaging and assembly
(6) viron maturation and release.
A cartoon of the HCV cell structural. HCV RNA replication occurs in a specific, selfconstructed membrane, the membranous web (MW). Positive and negative strand RNA are
each
Modeling & Simulation
•
•
•
•
How can this system be modeled?
What parts of the system are observable?
What are the important variables?
How much detail is necessary?
Perelson Model
• Basic Continuum Assumptions
–
–
–
–
Uniform infection of the liver hepatocytes.
Significant viron count.
Significant infected cell count.
Constant kinetics rates (production and clearance).
• Simplifying assumptions
– T is constant
• Some Implied Limitations
– Early infection
– Sustained viral clearance to cure
Perelson Model
Compartmental Representation
(1-η) β V T
s
Uninfected
Cells (T)
δI
Infected
Cells (I)
(1-ε) p I
dT
Virons (V)
cV
•Neumann, A. U.; Lam, N. P.; Dahari, H.; Gretch, D. R.; Wiley, T. E.; Layden, T. J.;
Perelson, A. S. Science. 1998, 282, 103-107.
Perelson Model
ODE Representation
dT
 s  d T  (1   ) VT
dt
dI
 (1   ) VT  I
dt
dV
 (1   ) pI  cV
dt
where T is the number of uninfected cells, I is the number of infected cells,
and V is the number of virons; new hepatocytes are produced at rate s, and
die at rate d, and are infected at rate β; infected hepatocytes are cleared at
rate δ, and produce new virons at rate p; virons are cleared at rate c.
Perelson Model - Conclusions
• Biphasic decline in viral load implies blocking of
viron production, not infection of hepatocytes
• Major initial effect of interferon-α is to block
virion production or release
• Estimated mean virion half-life 2.7 hours
• Pretreatment production and clearance of 1012
virions per day
• Estimated infected cell death rate exhibited large
interpatient variation (corresponding t1/2 51.7 to
70 days), was inversely correlated with baseline
viral load
Modifications to Perelson Model
• Liver size (sum of healthy + infected cells)
is constant
• Explicit account for viron loss during
infection
• Rate constants refit to our data for
nucleoside polymerase inhibitor in chimps
Constrained Total Hepatocyte Model
Compartmental Representation
T + I = T0
(1-η)
β Vβ TV T
s
Uninfected
Cells (T)
δI
Infected
Cells (I)
(1-ε) p I
dT
ρT
Virons (V)
cV
Constrained Total Hepatocyte Model
ODE Representation
t
t
t
2
1
t
t
t
t
t
1
f t
p
t
t
c
t
t
t
f t p
T0
t
t
t
t
t
t
t
c
t
t
t
t
t
t
t
T0
p 1
t
f t
t
t
c
t
t
T0
t
t
Steady State Analysis
Steady State
Jacobian
0
Uninfected
T0
p 1
0
c
Infected
p1
p1
c
p1
c
f
T0
f
p1
f
c
f
T0
c
p1
c
f
p1
T0
f
c
T0
T0
cp 1
p1
c
f
f
f
Eigenvalues
1
2
Uninfected
c
T0
c
Infected
c2 p 1
f
4 c2
2
2
p1
f
f
2
p 1
c2 p 1
Discriminant
f
T02
2
2
c
2p1
f
T0
T0
c
p 1
?
p 1
f
f
2
T0
T0
2
2c
p 1
f
Steady State Analysis
Stability
Numerical Eigenvalues
without treatment
Uninfected
,
Infected
?
Numerical Eigenvalues
0
8.97598, 0.0559827
8.27301,
0.0607397
with treatment
8.67016,
0.9995
0.249841
1.41155, 1.5346
• Results Differ from HIV as:
– Without treatment the uninfected steady state is unstable and will
evolve to the stable infected steady state
• Therefore, initial infection will not spontaneously clear.
– With treatment the infected steady state is unstable.
• Therefore, infected steady state must be driven to the stable uninfected
steady state with continuous treatment.
Viral Time Course Under Therapy
0.999
10 8
10 8
viral
clearance
10 6
reinfection
10 6
infected
IU mL 1
clearance
10 4
10 4
rebound
100
100
LOQ
1
0
10
20
time
30
d
40
50
1
Infected Cell Ratio and Cure
Boundary
T heinfectedcell ratio
I
i
T0
is derived from thedifferential equationsas
i
1
dV
(
 cV ).
(1   ) pT0 dt
T hecure boundary is thesteady stat e value of theinfected
cell ratio.
ib  1 
c
 (1   ) pT0
If theratiois positivethen theinfectedcells are nevercleared. Otherwise
if ib is zero or negativethenall theinfectedhepatocytseare cleared- a cure.
Viral Time Course Under Therapy
Above and below the cure boundary
36 weeks of therapy
10 8
0.25
new set point
10 6
IU mL
1
0.40
10 4
100
LOQ
1
0
50
100
150
time d
200
250
300
Data Fitting
Nucleoside Polymerase Inhibitor in Chimps
1.
10 8
1.
10
X115 , 0.2 mpk , IV, Bayer
6
1.
10
X115 , 2. mpk , IV, Bayer
6
1.
10 8
1.
10
10000
100
100
100
1.
10 8
1.
10 6
0
10
20
30
10
0
10
20
X115 , 2. mpk , IV, Cenetron
6
10000
1
IU mL
10 8
10000
10
viral load
1.
30
10
0
10
20
30
X120 , 1. mpk , PO, Cenetron
10000
100
0
1.
10 8
1.
10 6
20
40
60
X160 , 0.2 mpk , IV, Bayer
1.
10 8
1.
10 6
X160 , 2. mpk , IV, Bayer
1.
10 8
1.
10 6
10000
10000
10000
100
100
100
10
0
10
20
30
10
0
time
10
d
20
30
X160 , 2. mpk , IV, Cenetron
10
0
10
20
30
Clinical Trial Design
• Can we use our model and its simulation to
predict the outcome from a clinical trial?
• Can we estimate
– the confidence interval about the mean time to cure,
i.e., duration of therapy to achieve SVR?
– probability of break through?
– the confidence interval about the mean time to
rebound for a given duration of therapy?
• Can we help minimize the cost and/or the cycle
time of a trial?
Stochastic Parameter Sensitivity
All parameters varied under normal distribution with standard deviation of 10% of
parameter value; 1000 simulations.
Discrete Modeling
• Need
– ODE model gives the mean time, but says nothing about distribution
– When few virons remain, random fluctuations in behavior significant
– Want to determine the variance of treatment times to complete cure
• Implementation
– Use parameters from Neumann et al. 1998 for human, our fitted values
for a polymerase inhibitor in chimps
– Stochastic Simulation Algorithm (Gillespie et al.)
– Convert ODEs into discrete events with exponential probability
distributions
– Use continuous model until hourly stochastic variation > 1%
• Continuous model starts with ~1011 virons, ~1011 infected hepatocytes
• Stochastic model begins at ~104 virons, ~106 infected hepatocytes
Stochastic Modeling
Gillespie Algorithm
• Individual events vs. statistical ensemble
• Rate constants define propensity of events
• Sum of propensities define time between
events
A Stochastic Process in Action
Healthy
Hepatocytes
Choose an
event at
random
Infected
Hepatocytes
Virons
infect (β)
Distribution of Simulated Time to Cure
Continuous Interferon α in humans
Virons
10 8
det . time to
10 6
10 8
1
2
Infected Hepatocytes
10 8
det . time to
1
2
10 8
10 6
10 6
10 4
10 4
10 4
10 4
100
100
100
100
1
1
100
1
1
stochastic
det .
150
200
time
250
0.01
300
0.01
stochastic
100
150
d
200
time
time to cure for
0.99, n 500
0.05
L95CI
median
U95CI
0.04
frequency
det .
0.01
0.03
N 234.325,11.9505
0.02
P o 234.325
0.01
0.00
200
220
10 6
240
260
time d
280
300
d
250
0.01
300
Distribution of Simulated Time to Cure
36 week Interferon α in humans
0.99, n
•
•
92% of the runs cured during
treatment
3.8% cured after treatment
3.2% remained infected
60
frequency
•
500
cured
cured
during
after
treatment
treatment
40
20
•
36 weeks not enough time to
clear all the infected cells
0
25
30
35
40
cure time
Virons
10 8
45
50
w
Infected Hepatocytes
10 8
10 8
10 6
10 6
10 6
10 4
10 4
10 4
10 4
100
100
100
100
10 6
LOQ
1
1
det.
100
1
stochastic
1
det.
0.01
150
200
time d
250
0.01
300
10 8
stochastic
0.01
100
150
200
time d
250
0.01
300
Phase I Trial Design
• When should blood samples be taken for
PK and viral load determination?
• Can we use a 5-day per week study center
instead of a 7-day per week center?
Stochastic Parameter Sensitivity
Effect of Patient Variability
10 4
10 4
100
LOQ
100
1
1
2.50.02.5 5.07.510.012.5
time
d
10 6
10 6
10 4
10 4
100
LOQ
100
1
1
2.50.02.5 5.07.510.0
12.5
time
d
0.9999
10 8
1
10 6
10 8
IU mL
10 6
0.99
10 8
1
1
IU mL
10 8
IU mL
0.9
10 8
10 8
10 6
10 6
10 4
10 4
100
LOQ
100
1
1
2.50.02.5 5.07.510.012.5
time
d
Parameters varied with normal distribution about nominal values with
a 20% standard deviation.
Analytic Parameter Sensitivity
Viral load and parameter sensitivity for 3 doses
0.9999,
0.999,
0.99
infection
1.7
10 4
LOQ
0.4
1.6
IU mL 1
IU mL 1
10 6
100
production p
p
IU mL 1
10 8
1.5
1.4
1.3
0
5
0.2
1.0
10
0
0
10
0.6
2
4
c
0.8
1.0
10
0.0
IU mL 1
IU mL 1
0.4
5
efficacy
0
0.0
IU mL 1
5
viron clearance c
hepatocyte clearance
0.2
0.0
1.2
1.1
1
0.2
0.2
0.4
0.6
0.8
6
1.0
1.2
0
5
10
0
5
time d
10
0
5
10
Phase I Trial Design
Effect of Enrollment Day on Data Fitting
10
IU mL 1
10
8
6
4
2
8
•
6
4
2
LOQ
0
LOQ
0
Sa
S M
T
W Th
F Sa
S
M
T
W Th
F Sa
S
M
T W Th
F Sa
S M
T
W Th
F Sa
Sa
S
M T
W Th
F Sa
S
M T
W Th
time d
10
IU mL 1
10
8
6
4
LOQ
F Sa
S
M T
W Th
F Sa
•
6
•
4
LOQ
0
Sa
S M
T
W Th
F Sa
S
M
T
W Th
F Sa
S
M
T W Th
F Sa
S M
T
W Th
F Sa
Sa
S
M T
W Th
F Sa
S
M T
W Th
time d
F Sa
S
M T W Th
F Sa
S
M T
W Th
F Sa
time d
enroll on Tuesday
enroll on Friday
12
10
10
IU mL 1
12
8
6
log10
IU mL 1
M T W Th
8
2
0
log10
S
enroll on Thursday
12
log10
log10
IU mL 1
enroll on Monday
4
2
F Sa
time d
12
2
•
enroll on Wednesday
12
log10
log10
IU mL 1
7day week study site
12
6
4
2
LOQ
0
•
8
LOQ
0
Sa
S M
T
W Th
F Sa
S
M
T
W Th
F Sa
S
time d
M
T W Th
F Sa
S M
T
W Th
F Sa
Sa
S
M T
W Th
F Sa
S
M T
W Th
F Sa
S
time d
M T W Th
F Sa
S
M T
W Th
F Sa
First panel shows
model for 7-day per
week study site
Other panels show
results for 5-day per
week study site on
given enrollment day
Enrollment on
Monday-Thursday is
quite acceptable
Enrollment on Friday
leads to data loss and
much less confident
data fitting
Ability to use 5-day
site saves approx.
$2500 per patient
Business Impact of the HCV
Infection Modeling
• We have a better understanding of the disease
process under therapy, especially when
traditional biomarkers fail to show the presence
of disease, and we can design better treatment
regimens.
• Modeling has shown that a less expensive
clinical trial design can yield data of the same
quality and utility as that from a more
comprehensive and more expensive design.
Acknowledgements
• Antiviral Research
– Steve Ludmerer
• ACSM
–
–
–
–
• Clinical Research
– Erin Quirk
– Jackie Gress
• HCV Antiviral EDT
Ansu Bagchi
Arthur Fridman
Thomas Mildorf*
Andrew Spann*
• Clinical Drug
Metabolism
– Jack Valentine
* Summer intern