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Modeling Drug
Efficacy: HIV and HCV
Alan S. Perelson, PhD
Theoretical Biology & Biophysics
Los Alamos National Laboratory
Los Alamos, NM
Model of HIV Infection
k
Infection Rate
p
Virions/d
T* T
Productively
Infected Target Cell
Cell
d c
Death Clearance
Model Used for Drug Perturbation Studies
dT * (t ) Drug efficacy
(1 RT )kVI T0 d T *
dt RT PI
dVI (t )
(1 PI ) Nd T cVI
*
Subscripts:
dt “I”: infectious
dVNI (t ) “NI”: non-infectious
PI Nd T cVNI
*
dt
From HIV-Dynamics in Vivo: …,
Perelson, et al, Science, 1996
Solution of Model Equations Assuming 100%
Efficacy of Protease Inhibitor Therapy (and
dT
Constant Level of Target d T ( 1 )
kVT Cells)
dt
dV
Nd T cV (2)
dt
V( t ) V 0 exp ( ct )
cV 0
c d
{cd
c
}
exp ( d t ) exp ( ct ) d t exp ( ct ) (6
HIV-1: First Phase Kinetics
Perelson et al.
Science 271, 1582
1996
Infectious virions decay
HIV-1: Two Phase Kinetics
Perelson et al. Nature 387, 186 (1997)
Mean Decrease in HCV RNA Levels Over
First 14 Days of QD IFN- Treatment
Days
0 7 14
0.5
Mean Decrease HCV RNA
0 HCV Genotype 1
(Log10 Copies/mL)
-0.5
-1
-1.5
-2
5MU
-2.5 10MU
15MU
-3
Lam N. DDW. 1998 (abstract L0346).
Model of HCV Infection
b
Infection Rate
p
Virions/d
I T
Infected
Cell
Target Cell
d c
Loss Clearance
First Phase: IFN
Partially Blocks Production
k
IFN p
Virions/d
I T
Infected
Cell Effectiveness Target Cell
d c
Death/Loss Clearance
Model of HCV Kinetics
T = number of cells susceptible to infection
I = number of cells infected with HCV
V = virus (HCV RNA)
dI/dt = kVT – dI
dV/dt = pI – cV
IFN Effectiveness in
Blocking Production
Let = effectiveness of IFN in
blocking production of virus
• = 1 is 100% effectiveness
• = 0 is 0% effectiveness
dV/dt = (1 – )pI – cV
Early Kinetic Analysis
Model predicts that after therapy is
initiated, the viral load will initially
change according to:
V(t) = V0[1 – + exp(-ct)]
This equation can be fit to data and c
and estimated.
Thus drug effectiveness can be
determined within the first few days!
Log10 HCV RNA/mL
6
7
8
5
0
10MU
1
Days
Log10 HCV RNA/mL
4
5
6
7
0
1
Days
15MU
2
2
Viral Kinetics of HCV Genotype 1
Viral Half-life Production
Clearance of & Clearance
Drug Constant Virions Rates
Efficacy (1/d) (Hours) (1012 Virions/d)
5MU 81 ± 4% 6.2 ± 0.8 2.7 0.4 ± 0.2
10MU 95 ± 4% 6.3 ± 2.4 2.6 2.3 ± 4
15MU 96 ± 4% 6.1 ± 1.9 2.7 0.6 ± 0.8
10MU 7
15MU
Log10 HCV RNA/mL
6
8 5
4
Log10 HCV RNA/mL
7 3
0 7 14
Days
6
5
4
0 7 14
Days
Viral Kinetics of HCV Genotype 1
Second
Phase Decay Half-life of
Drug Constant, d Infected Cells
Efficacy (1/d) (Days)
5MU 81 ± 4% 0.09 ± 0.14 2.2–69.3
10MU 95 ± 4% 0.10 ± 0.05 4.3–17.3
15MU 96 ± 4% 0.24 ± 0.15 1.7–6.3
HCV Viral Kinetics : Summary
Biphasic clearance of serum HCV RNA
1st phase rapid; depends on IFN- dose
– This appears to be due to dose-dependent
efficacy in blocking HCV production
– Possible to estimate efficacy from
measurements of HCV RNA decline over
first few days of therapy!
2nd phase slower. Slope appears to be a
measure of rate of infected cell loss
Current Therapy:
Peg-IFN 2b + RBV
Major Point: Peg-IFN given once weekly
Drug Pharmacokinetics Matters!
Pegylated Interferon (Peg-IFN)
21 HIV HCV Co-Infected Patients (A. Talal)
Dosing
–1.5 μg/kg Peg-IFN α-2b (12 kDa) weekly
–13 mg/kg ribavirin daily
Serum HCV RNA measurements at*:
–0, 6, 12, 24, 48, 72 hrs and 5, 6 days after
first dose
–0, 6, 12, 24, 48 hrs after second dose
–0, 1, 2, 14 days after third dose
*Measurements taken at all of these times in patients 1, 2, 6, 19, and 505 only.
HCV RNA and PEG-IFN α-2b
PEG
HCV
HCV RNA and PEG-IFN α-2b
(poor responders)
Absorption & Elimination
PK Model
ka ke
Absorption Site Blood
absorption elimination
dA
X FDe ka t
k a X ke A
dt
Amount of drug in blood (A), Concentration = A/Vd
X = amount of drug remaining at absorption site
F = bioavailability; Vd = Vol. distribution
D = dose
ka = absorption rate constant
ke = elimination rate constant
PK Model
Decline in drug concentration between
doses, described by:
ka FD e ket (e Nke 1) Nke ka
C (t ) ( ka )[1 e( ke ka )t (1 e( N 1) ka ) (eke eka ) ke e e ]
(ke ka )Vd e 1 (e 1)
τ= dosing interval and N = # of doses
Vd = volume of distribution
PD Model
Changing drug concentration
affects efficacy
C (t ) n
(t )
EC50 C (t )
n n
n = Hill coefficient, EC50 = 50% effective conc.
= delay
PK Model
Drug Concentrations
Drug Concentration Profile
1400
1200
Drug Concentration (pg/ml)
1000
800
600
400
200
0
0 5 10 15 20 25 30
Days
Drug Efficacy Profile
Efficacy Profile
0.9
0.8
0.7
0.6
Efficacy
0.5
0.4
0.3
0.2
0.1
0
0 5 10 15 20 25 30
Days
Data Analysis
Fit the plasma drug concentration data
to the PK model; estimate rate
absorption and elimination rate
constants, and FD/Vd
Use estimated C(t) in efficacy function
and then fit viral load data to the
infection model. Estimate parameters in
the PD model: Hill coefficient, EC50,
delay and viral dynamic parameters
Usually need to fix Hill coefficient and
delay
Fit of Model to PEG-IFN α-2b
Conc. and HCV RNA Data
Difference between responders
and nonresponders
Average drug conc. - Not different
Average efficacy – higher in responders
0.84 vs 0.55 (P=0.005)
Average drug conc./EC50 – higher in
responders 13.0 vs 2.0 (P=0.01)
Twice-Weekly Dosing
(Speculations)
Would twice weekly dosing improve
response?
We tested this as a hypothesis by
simulating the response of patients to twice-
weekly dosing using the PK/PD and viral
dynamics parameters for each patient
Responses fell into 3 groups
Once vs Twice-Weekly Dosing
P 001 P 004
1.E+08 1.E+08
1.E+07 1.E+07
HCV RNA (IU/ml)
HCV RNA (IU/ml)
1.E+06 1.E+06
1.E+05 1.E+05
1.E+04 1.E+04
1.E+03 1.E+03
1.E+02 1.E+02
0 28 56 84 112 140 168 0 14 28 42 56 70 84 98 112 126 140 154 168 182
Days Days
P 017 P 505
1.E+08 1.E+08
1.E+07 1.E+07
HCV RNA (IU/ml)
1.E+06
HCV RNA (IU/ml)
1.E+06
1.E+05
1.E+05
1.E+04
1.E+04
1.E+03
1.E+03
1.E+02
1.E+02 0 14 28 42 56 70 84 98 112 126 140 154 168 182
0 14 28 42 56 70 84 98 112 126 140 154 168 182 Days
Days
P 026 P 026
1.E+08 1.E+08
1.E+07 1.E+07
HCV RNA (IU/ml)
HCV RNA (IU/ml)
1.E+06 1.E+06
1.E+05 1.E+05
1.E+04
1.E+04
1.E+03
1.E+03
1.E+02
1.E+02
0 14 28 42 56 70 84 98 112 126 140 154 168 182
0 14 28 42 56 70 84 98 112 126 140 154 168 182
Days
Days
HIV
A similar approach of merging PK and
PD with viral dynamic models can be
used to model drug efficacy effects
Since antiretroviral act intracellularly we
include both plasma and intracellular
compartments and assume efficacy
depends on intracellular drug levels.
Drug transport
Cc = concentration within cell
Cb = concentration in blood
At equilibrium, Cceq = (1-fb)HCbeq
where fb = fraction of drug bound to plasma proteins
and unable to be transported across the membrane;
H= partition coefficient – takes into consideration
differences between intra and extracellular environment
dCc
kacell Cx kecell Cc
dt
We assume driving force for transport is difference
between these concentrations, i.e., (1- fb)HCb – Cc
and rate of absorption and elimination from the cell is
dCc
kacell Cx kecell Cc
dt
(1 f b ) HCb Cc if (1 f b ) HCb Cc 0
Cx
0 otherwise
Cc ( t )
(t )
IC50 Cc (t )
Protease Inhibitor - Ritonavir
D = 600 mg (dose)
Id = 0.5 days (dosing interval)
F~1 (bioavailability)
Vd = 400 ml/kg (vol distribution)
ka = 14.6 day-1 (absorption rate constant)
ke = 6.86 day-1 (elimination rate constant)
fb = 0.99 (fraction bound)
H = 0.052 (partition coefficient)
intracellular IC50 ~ 9 x 10-7 mg/ml
Dixit & Perelson, J Theoret Biol. 226: 95-109 (2004)
10-1 1
10-2 Cb
Drug concentration (mg/ml)
0.8
-3
10
Efficacy, PI
0.6
10-4
C
PI
0.4
10-5 C
c
0.2
10-6
-7
10 0
0 1 2 3 4
t (day)
---- indicates critical efficacy
106
HIV-1 RNA (copies/ml)
105
104
3
10
0 1 2 3 4 5 6 7
t (day)
Viral load decay in pt 104 (Perelson et al Science 96)
and best fit of model to data
NRTIs
Nucleoside reverse transcriptase inhibitors are
transported into and out of cells like PIs but
must be phosphorylated within cells to become
k1 f k2 f
C k1b
CP k2 b
active.
CPP
We consider tenofovir DF, which is
monophosphorylated and requires 2 additional
phosphorylation steps.
k1 f k2 f
C k1b
CP k2 b
CPP
dCc
kacell Cx kecell Cc k1 f Cc k1bCcp
dt
dCcp
kecell Ccp k1 f Cc k1bCcp k2 f Ccp k2bCcpp
dt
dCcpp
kecell Ccpp k2 f Ccp k2bCcpp
dt
Efficacy determined by Ccpp(t)
2
Ccpp
Drug concentration (mM)
1.5
1
0.5 Ccp
0
0 0.2 0.4 0.6 0.8 1
t (day)
Fit of PK model to data of Robbins et al (1998)
1
100
10-1
Drug concentration (mg/ml)
0.8
RTI
10-2 Cb Cc Ccp C
cpp
Efficacy, RTI
-3 C 0.6
10
10-4 0.4
10-5
0.2
-6
10
-7
10 0
0 1 2 3 4
t (day)
Plasma and intracellular conc of tenofovir DF
Efficacy lower than critical efficacy – predict
virus will ultimately rebound with monotherapy
105
HIV-1 RNA (copies/ml)
104
104
103
0 1 2 3 4 5 6 7
t (day)
Fit of VL data from 2 pts in Louie
et al. AIDS 17, 1151-1156 (2003)
Conclusions
Standard viral dynamic model assumes constant drug
effectiveness. The model when use for HCV summarizes
data on many patients given high dose daily IFN. Viral load
rebounds are not fit by the model
Viral loads of HIV/HCV patients given once-weekly PEG-
IFN α-2b tend to rise starting 3–4 days after dose
Combined pharmacokinetic and viral dynamic models can
be used to describe viral behavior during PEG-IFN
treatment
– In particular, can explain increase in viral load
between doses of PEG-IFN α-2b
– Notions such as effectiveness need to be revised,
effectiveness changes with time; min, max and
average effectiveness can be defined
Conclusions - II
Similar approach can be used for HIV;
instead of assuming an efficacy one can
use PK and IC50 data to estimate drug
efficacy; Dixit – Perelson, JTB 226:95
(2004), Antiviral Ther. 9:237 (2004)
Can allow IC50 to change as a reflection
of drug resistance; i.e. measure IC50 of
virus isolated from patients at different
times and use in a time-varying efficacy
model – captures viral load rebounds
(Hulin Wu - Perelson, JAIDS in press)
Ribavirin
Current therapy for HCV involves use of
both peg-IFN + ribavirin (RBV)
When used in combination with IFN
greatly increases ETR and SVR
Mechanism of action of RBV not known.
When used as monotherapy – very
weak antiviral; < 0.5 log decrease in
HCV RNA
Suggested to be IMPDH inhibitor,
polymerase inhibitor, Th2->Th1, lethal
mutagen
Ribavirin improves interferon
response rates in HCV infection
Summary of experimental results
ETR (%) SVR (%)
McHutchison, J. G. et al. N.
Eng. J. Med. 339, 1485-1492
Duration IFN + IFN +
IFN IFN (1998).
of therapy RBV RBV Reichard, O. et al. Lancet 351,
83-87 (1998)
Poynard, T. et al. Lancet 352,
24 weeks 37 – 59 64 – 77 8 – 21 39 – 53 1426-1432 (1998)
Fried, M. W. et al. N. Eng. J.
Med. 347, 975-982 (2002).
48 weeks 31 – 68 71 – 94 17 – 24 53 – 72
48 weeks
91 93 – 100 45 77
(pegIFN)
25-30% enhancement with ribavirin –
remains poorly understood
RBV and Lethal Mutagenesis
For polio, RBV shown to lead to
misincorporation of nucleotides and can
act via lethal mutagenesis.
Model for RBV acting in this way is
equivalent to HIV protease inhibitor
models, with production of a fraction r of
“non-infectious” virus.
Model of HCV dynamics
Mechanism of ribavirin action – mutagenesis –
renders a fraction of new virions noninfectious
dI
b TVI d I Infected cells
dt
dVI
1 r (1 ) pI cVI Infectious virions
dt
dVNI
r 1 pI cVNI Noninfectious virions
dt
RBV effectiveness IFN effectiveness
V=VI+VNI Viral load
Model calculations
rmax=0
rmax=0.5
rmax=1
r(t) =rmax(1-exp(-t/ta)), ta=5.6 days Glue, P. Sem. Liv. Dis. 19, 17-24 (1999).
RBV has no effect when IFN effectiveness high
rmax=0
rmax=0.5
rmax=1
RBV enhances second phase slope in a dose
dependent manner when IFN effectiveness low
Comparison with patient data
Representative fits
Model provides good fits to data
rmax unknown:
dmin=d (rmax=1) and dmax=d (rmax=0)
<d> =(dmin+dmax)/2
Caucasians vs African Americans
Median Effectiveness () of
10 MU IFN QD vs. IFN+ribavarin
IFN alone IFN+ P-value*
ribavarin
Caucasians 98.2% 98.2% NS
(n = 7) (n = 8)
African 87.0% 88.6% NS
Americans
(n = 10) (n = 9)
* NS = non-significant at the p=0.05 level by the Mann - Whitney U test
Median Viral Kinetic Parameters
by Treatment
Kinetic Parameter Caucasians African Americans
No RBV RBV P-value No RBV RBV P-value
- % effectiveness at 98.2% 98.2% 0.9 87.0% 88.6% 0.6
inhibiting viral prod.
d - loss rate of virus 0.2 0.17 0.8 0.06 0.21 0.4
producing cells / day
c - virus clearance 7.4 9.3 0.9 6.7 7.9 0.7
(/day)
delay (hours) 7.9 6.2 0.5 9.4 8.9 0.8
Median values reported, Mann-Whitney statistical test
Early Kinetic Parameters of
African Americans and Caucasians
Kinetic Parameter African Caucasians P-
Americans Value*
c - virus clearance/day 7.4 7.5
NS
(t1/2 hours) (2.3) (2.3)
delay (hours) 8.7 6.6 0.038
- % effectiveness at
88.6% 98.2% 0.005
inhibiting viral production
1st phase log drop
0.94 1.7 0.005
(first 24 hrs) log cp/ml
d - loss rate of virus
0.13 0.20 0.006
producing cells/day
Log drop 1st month of
1.2 3.6 0.001
therapy (log cp/ml)
Implications from data analysis
Patients with high IFN effectiveness:
<d> identical to d from previous models
Patients with low IFN effectiveness:
<d> lower than d from previous models
RBV enhances second phase slope -
ignored by current models
<<d>> similar for white and African Americans -
Death rate of infected cells race independent
RBV does not influence death rate of infected
cells, rather it lowers their formation rate
RBV not immune modulatory
Long term response
At the end of treatment:
Viral load below detection: ETR
Less than one virion in the body fluid: SVR
Given IFN and RBV effectiveness, patients
with d > dETR exhibit ETR and d > dSVR
exhibit SVR
d normally distributed with mean and variance
determined by viral load data analysis
Values of d needed for ETR, dETR, and SVR,dSVR
IFN V0 = 107
copies/ml
IFN+RBV
c = 9.5 day-1
= 0.3 day
rmax= 0.5
IFN effectiveness
Use measured distribution of d to predict fraction with
ETR and SVR
Long term response prediction
IFN +
IFN RBV
Improvement
of ~20-30%
due to RBV
when =0.5
IFN effectiveness
Comparison with experiments
Model predicts ETR and SVR for 24 weeks of
standard IFN therapy and 48 weeks of peg-IFN
therapy with and without RBV
Model over predicts response for 48 weeks of
standard therapy – patient compliance?
Conclusions
Model assuming RBV lowers HCV infectivity in
a dose dependent manner
Captures viral load decay patterns in HCV
infected individuals under combination therapy
Quantitatively predicts long term response
rates with and without RBV
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