Transcript Perelson_Utrecht 2005

Cytotoxic T Lymphocytes
CTLs can kill virus-infected cells. Here, a CTL (arrow) is attacking
and killing a much larger influenza virus-infected target cell.
http://www.cellsalive.com/
Models of CTL Response
dT/dt = l – dT – kVT
dT*/dt = kVT – dVT* - dEET*
dV/dt = pT* - cV
dE/dt = kEET* - mE
CTL Effectors
Nowak and Bangham, Science 272, 74 1996
LCMV Infection
LCMV Armstrong into BALB/c mice, Ahmed 1998
Simple Model of CD8 Response
DeBoer … Perelson, J Virol. 75,10663 (2001),
On-Off Model
Activation function
Ton = recruitment time
A(0) = cells recruited
Model Predictions
Continuous Model
Parameter Estimates
Simulating CTL Response
Low affinity
clones
sometimes
dominate 10
response
V
Total
CTL
V
□, ∆,◊ are
3 highest
affinity
clones
Modeling the Kinetics of
Hepatitis B and C Infections
Alan S. Perelson, PhD
Theoretical Biology & Biophysics
Los Alamos National Laboratory
Los Alamos, NM
Viral Hepatitis - Overview
Type of Hepatitis
A
Source of
virus
Route of
transmission
Chronic
infection
Prevention
feces
fecal-oral
no
B
C
D
blood/
blood/
blood/
blood-derivedblood-derived blood-derived
body fluids body fluids body fluids
E
feces
percutaneouspercutaneous percutaneous fecal-oral
permucosal permucosal permucosal
yes
yes
yes
no
pre/postpre/post- blood donor
pre/post- ensure safe
exposure
exposure
screening;
exposure
drinking
immunization immunization risk behavior immunization;
water
modification risk behavior
modification
Estimates of Acute and Chronic Disease
Burden for Viral Hepatitis, United States
Acute infections
(x 1000)/year*
Fulminant
deaths/year
Chronic
infections
Chronic liver disease
deaths/year
HAV
HBV
HCV
HDV
125-200
140-320
35-180
6-13
100
150
?
35
0
1-1.25
million
3.5
million
70,000
5,000
8-10,000
1,000
0
* Range based on estimated annual incidence, 1984-1994.
Hepatitis B and C Virus


HBV is a DNA virus
– Genome is very small, ~ 3.2kb,
– Takes the form of a partially closed
circle
– Vaccine; therapy to control not cure
HCV is a positive strand RNA virus
– Genome is about 9.3kb,
approximately the same size as HIV
– No vaccine; therapy successful in
50% of people treated
Mean Decrease in HCV RNA Levels Over
First 14 Days of QD IFN- Treatment
Days
Mean Decrease HCV RNA
(Log10 Copies/mL)
0
7
0.5
0
HCV Genotype 1
-0.5
-1
-1.5
-2
-2.5
5MU
10MU
15MU
-3
Lam N. DDW. 1998 (abstract L0346).
14
Model of HCV Infection
b
Infection Rate
p
Virions/d
I
Infected
Cell
T
Target Cell
d
Loss
c
Clearance
What if IFN blocks infection?
IFN
p
virions/d
I
Infected
Cell
b
d
death
T
Target cell
c
clearance
What if IFN
Blocks Production?
b
IFN
I
Infected
Cell
p
Virions/d
e
Target Cell
Effectiveness
d
Death/Loss
T
c
Clearance
What if IFN blocks
production?



If IFN treatment totally blocks virus
production, then
-ct
dV/dt = - cV => V(t)=V0 e
Viral load should fall exponentially with
slope c. However, data shows an acute
exponential fall followed by slower fall.
IFN Effectiveness in
Blocking Production

Let e = effectiveness of IFN in
blocking production of virus
• e = 1 is 100% effectiveness
• e = 0 is 0% effectiveness

dV/dt = (1 – e)pI – cV
Early Kinetic Analysis

Before therapy, assume steady state so that
pI0 =cV0. Also, assume at short times,
I=constant=I0, so that dV/dt= (1-e)cV0 - cV

Model predicts that after therapy is initiated,
the viral load will initially change according
to:
V(t) = V0[1 – e + e exp(-ct)]

This equation can be fit to data and c
and e estimated.

Thus drug effectiveness can be determined
within the first few days!
8
Log10 HCV RNA/mL
Log10 HCV RNA/mL
10MU
0
15MU
7
7
1
Days
6
5
4
0
1
2
Days
6
5
2
Viral Kinetics of HCV Genotype 1
Viral
Clearance
Drug
Constant
Efficacy
(1/d)
Half-life
of
Virions
(Hours)
Production
& Clearance
Rates
(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
Standard Model of HCV Dynamics
Equations
Parameters
dT
 l  dT  bVT
dt
dI
 bVT  d I
dt
dV
 (1  e ) pI  cV
dt
l Supply of target cells
d Net loss rate of target cells
Variables
T Target Cell Density
I Infected Cell Density
V Virus Concentration
Initial Conditions
T(0) = T0
V(0) = V0
I (0) = I0
β
d
Infectivity rate constant
Infected cell death rate
e Drug efficacy
p Virion production rate
c Virion clearance rate constant
Solution: Change in Viral Load

Assuming T = constant,
1
c  d  2e c  l1 (t t0 )
c  d  2e c  l2 (t t0 )
V (t )  V0 [(1 
)e
 (1 
)e
]
2


where
1
l1  (c  d   )
2
1
2
l2  (c  d   )
  (c  d ) 2  4(1  e )cd
t0 = delay between treatment commencement and onset of effect

When c>>δ, λ1 ≈ c and λ2 ≈ εδ
10MU
7
Log10 HCV RNA/mL
8
Log10 HCV RNA/mL
15MU
7
6
5
4
3
0
7
14
Days
6
5
4
0
7
Days
14
Current Therapy:
Peg-IFN 2b + RBV
Peg-IFN given once a week
Major Point: Drug Pharmacokinetics Matters!
Pegylated Interferon (Peg-IFN)
21
HIV HCV Co-Infected Patients (A. Talal)
Dosing
–1.5 μg/kg Peg-IFN a-2b (12 kDa) weekly
–1000 or 1200 mg ribavirin daily
Talal et al., Hepatology (2006)
HCV RNA and PEG-IFN α-2b
Talal et al., Hepatol. (2006)
PEG
HCV
Pharmacodynamics
Emax Model
Drug concentration, C(t),
affects efficacy
e max C (t   )
e (t ) 
n
n
EC50  C (t   )
n
n = Hill coefficient, EC50 = 50% effective conc.
 = delay between receptor binding and effect
PK Model for Absorption &
Elimination of Peg-IFN
ka
Absorption Site
Blood
absorption
X  FDe
 Amount
 ka t
ke
elimination
dA
 ka X  ke A
dt
of drug in blood (A), Concentration = A/Vd
 X = amount of drug remaining at absorption site
 F = bioavailability
 D = dose
 ka = absorption rate constant
 ke = elimination rate constant
Following a single dose
FD ka
 ka t
 ket
e  e 
C (t ) 
Vd ke  ka
PK Model
Following
multiple doses,
Nke
ka FD
e ket
(
e
 1) Nke ka
( ke ka )t
( N 1) ka
ke
ka
C (t ) 
( ka )[1  e
(1  e
)  (e  e ) ke
e e ]
(ke  ka )Vd e 1
(e 1)

= dosing interval and N = # of doses
Vd = volume of distribution
PK Model
Drug Concentrations
Drug Concentration Profile
1400
Drug Concentration (pg/ml)
1200
1000
800
600
400
200
0
0
5
10
15
Days
20
25
30
Drug Efficacy Profile
Efficacy Profile
0.9
0.8
0.7
Efficacy
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
Days
20
25
30
Fit of Model to PEG-IFN α-2b
Conc. and HCV RNA Data
Difference between responders
and nonresponders
Talal et al., Hepatol. (2006)




Average drug conc. - Not different
Median EC50 10-fold lower in SVR
(0.04 mg/L) than NR (0.45 mg/L), P=0.014
Median efficacy – higher in responders
0.92 vs 0.45 (P=0.02)
Median drug conc./EC50 – higher in
responders 10.1 vs 1.0 (P=0.012)
Conclusions



HCV kinetic models can be used to
quantitatively estimate the effectiveness
of different drug regimes, and help
establish appropriating dosing.
They can give quantitative insights into
biology of viral infection – rates of virion
production, clearance, cell loss, etc.
When using peg-IFN 2b drug
effectiveness can change during the
dosing interval and models need to be
modified to take this into consideration.
Viral dynamics and immune
responses in acute hepatitis
B infection
Stanca M. Ciupe, Ruy M. Ribeiro,
Patrick W. Nelson, Alan S. Perelson
Patient data
(Webster, Lancet 2000; Whalley, Hepatol. 2000)

HBV outbreak was
identified in the UK in
1998 due to
autohemotherapy

Serological exposure to
the same HBV variant in
57 patients.

7 identified in the
preclinical phase and
studied here.
Biphasic decay of viral load
•First phase - span 56 days;
- half life 3.4 days;
•Second phase - span 148 days;
- half life 23 days;
Models
A number of models of HBV infection exist:
Nowak & Thomas, PNAS 1996; Tsiang et
al Hepatol., 1999; Levin et al Hepatol.
2001; Murray & Chisari, PNAS 2005.
With exception of Murray & Chisari (2005)
they were developed to analyze drug
therapy and are missing a number of
key features of HBV infection that are
important during acute infection.
Viral Lifecycle
•


Model continued
Here we will consider that almost 100% of
hepatocytes are thought be infected at the
peak of the infection. Due to this both cytolytic
and non-cytolytic mechanisms may be
needed to clear the infection.
Further, a large amount of hepatocyte
proliferation accompanies viral and cccDNA
clearance in animal models (woodchuck, duck
and chimpanzee) and presumably in human
infection.
Key Question: As virus is cleared and
uninfected hepatocytes replace infected ones,
what prevents infection of these newly
generated hepatocytes?
Model
Cytolytic death
p1
*
1
T
k
infection
1 cccDNA
cccDNA dilution
T
cccDNA

R
1 E
*
2
T
2 E
refractory
Cytolytic death

p2
V
virus
c
clearance
activation

mE
Cytolytic death

Virus production
z
≥2 cccDNA
R
mE
s
E
effectors
dE
45
Model equations
dT
T
 ( rT  rT1* )(1  tot )  kVT   R R
dt
Tmax
dT1*
 kVT  ( 1 E  z )T1*  mT1* E
dt
dT2*
T
 rT2* (1  tot )  zT1*   2T2* E  mT2* E
dt
Tmax
dV
 p1T1*  p2T2*  cV
dt
dE
 s   (T1* (t   )  T2* (t   )) E (t   )  d E E
dt
dR
T
 1T1* E   2T2* E  rR (1  tot )   R R  m1 RE
dt
Tmax
Ttot  T  T1*  T2*  R
46
Parameter fitting
• Assumptions: some parameter values
fixed based on literature
x  [ r , Tmax , c, s, d E ]

(McDonald, Tsiang, Hep.
1999, Lau, Hep. 2000,
Lewin, Hep. 2001, Ahmed, Science 1996)
- initial conditions (Whalley JEM 2001);
- incubation time:80-140 days (Bertoletti, Hep.
2003);
47
Others we estimate by Monte Carlo
search
x  [ p1 , p2 , r2 , , m , m1 , z , , 1 ,  2 ,  R ]
•Fitness function:
f ( x)   (log( ViralTitert )  log( Vt ))
2
data
•Search within a predefined range for parameters;
•Once a good fit is found, search locally.
48
Model gives biphasic decay of
viral load
Best fit of model to data
Patient 7 is the only patient not to clear HBV
ALT and Effector cells
hepatocytes
E
ALT
ALT=alanine aminotransferase
ALT
ALT and Effector cells
E
Cytolytic and Noncytolytic
Immune Responses
cytolytic
cytolytic
Non-cytolytic
Non-cytolytic
• Noncytolytic response occurs early followed by the cytolytic
one 3-4 weeks later
• Weak CTL response in patient7 who does not clear infection.
Cytolytic vs non-cytolytic
Model Results


99% hepatocytes are infected cells at the peak
Viral production by T1* is estimated to be
approximately half the production by T2* .This
suggests that all cccDNAs may not be good
replicative templates. Needs to be examined
experimentally.
Refractory cells
refractory
R
infected
• Prevent the rekindling of the viral infection
• Slow transition back into the target population,
although when virus is cleared and cytokine milieu
changes this rate may increase.
Are all model assumptions
needed?

This model is very complicated and involves four
features not present in the drug therapy models
used so far to fit HBV DNA data:
– Proliferation of infected and uninfected
hepatocytes
– with no proliferation hepatocyte mass
decreases substantially during the course of
infection if a cytolytic response occurs. Also,
proliferation contributes to loss of cccDNA by
dilution and allows uninfected cells to
repopulate the liver as infected ones are
killed.

Model includes a cytolytic response
– This is required to obtain the two
phase HBV DNA decay seen in the
data
– However, model suggests a strong
enough noncytolytic response could
do the job of clearing infection. Thus,
whether a cytolytic response is truly
required to clear infection in not
certain.
With CTL response model gives
biphasic decay of viral load
Best fit of model to data
Patient 7 is the only patient not to clear HBV
No CTL response
No CTL response
Is non-cytolytic response
needed?

Model has a non-cytolytic response that
converts infected cells into cells refractory to
infection. In the absence of a non-cytolytic
response, the system must rely on a cytolytic
response to clear infection. This requires
massive loss of hepatocytes. Further,
proliferation of uninfected cells to replace
cells that are killed, generates new targets
and rekindles the infection.
No non-cytolytic response
hepatocyte loss
infection rekindles
No non-cytolytic response
Assumption about R cells

If the noncytolytic response simply
“cures” cells, then again new targets are
generated that rekindle the infection
No R cells; direct transition of
infected cells into uninfected cells
No R, direct transition into target
population
Can antibodies replace R cells and prevent
re-establishment of infection?

If an anti-HbsAg response occurs, then
these antibodies may neutralize
remaining virus and prevent reestablishment of infection as infected
cells are replaced by uninfected ones.
Antibodies

Anti-HBs antibodies are detectable, but after
the resolution of acute infection.
Acute Hepatitis B Virus Infection with Recovery
Typical Serologic Course
Symptoms
HBeAg
anti-HBe
Total anti-HBc
Titer
HBsAg
0
4
8
anti-HBs
IgM anti-HBc
12 16 20 24 28 32 36
52
Weeks after Exposure
100
Hepatitis B Virus
Model of Ab response

We consider:
-the production of free antibodies by plasma
cells.
-attachment of antibody to both subgenomic
and infectious viral particles.
-allow antibodies to neutralize the virus, i.e.
reduce the infectivity rate k depending on
the amount of antibody bound.
Effect of anti HBV Ab



Model can not generate
a high enough
concentration of Ab to
fully block infection
HbsAg positive
subgenomic particles
bind the majority of Ab
Model predicts viral
rebound in most
patients at the end of
the second phase
10  7
Antibody
Summary





Have developed a model of acute HBV infection that
reproduces the observed HBV DNA and ALT kinetic patterns
Model suggests that both cytolytic and noncytolytic responses
play a role in viral clearance.
The model also reveals that as infected cells are cleared and
replaced by uninfected ones a mechanism is needed to
prevent the infection of these cells.
We have postulated that these newly generated cells are
temporarily refractory to new infection. This could be due to a
sustained “antiviral” state established by a noncytolytic
response or due to selection of cells that have reduced levels
of the cell surface receptors HBV uses to enter cells.
Anti-HbsAg antibodies could play a similar role, but ongoing
modeling suggests that the great excess of subgenomic
particles prevents effective antibody neutralization of the virus.