Download Modeling the antibody response to HIV

What controls the initial dynamics of
influenza and HIV
Alan S. Perelson
Theoretical Biology and Biophysics
Los Alamos National Laboratory
Los Alamos, NM
[email protected]
Acute HIV Infection: Target Cell
Limited?
78 of 102 pts had single founder virus
Keele et al
PNAS 105:
7552 (2008)
Salazar-Gonzalez
J Exp Med 206:
1273 (2009)
Keele et al
J Exp Med 206:
1117 (2009)
Viral stock diverse
Acute HIV-1 Infection
Onset cytokines
apoptosis, Day 7
Virus Concentration in Extracellular Fluid
or
Plasma (Copies/ml)
Acute Phase Reactants
Days -5 to-7
Free IgM anti-gp41 Ab, Day 13 (non-neutralizing)
Ab-virus Immune
Complexes
Day 9
108
Autologous
Neutralizing Antibody
107
106
105
?
104
Reservoir
eclipse
103
102
101
0
10-1
10-2
Transit
10-3
CTL Escape
CD8 T Cell
Virus
Responses
dissemination
Autologous
Neutralizing
Antibody
Escape
T0
10-4
10-5
0
Transmission
5
10
15
20
25
30
35
40
Time Post Exposure (days)
45
50
55
60
65
70
Model of HIV Infection
k
Infection Rate
p
Virions/d
I
+
Infected
Cell
T
Target Cell
d
Death
c
Clearance
Model of Viral Infection
Basic Target Cell-Limited Model
dT
   dT  kVT
dt
dI
 kVT  dI
dt
dV
 pI  cV
dt
T, target CD4 cells
I, infected Cells
V, virus
λ,
d,
k,
p,
c,
d,
T cell production
normal T cell death
infectivity constant
viral production
viral clearance
infected cell death
λ = 10,000 cells/μL/day
d = 0.01/day
c = 23/day
δ, k, and p are fit.
HIV Primary
Infection
Target cell limited
model can fit HIV RNA
data during early AHI
Stafford et al. JTB
203: 285 (2000)
At loner times the target
cell limited model may
show oscillations that are
not in the data and may
overestimate the HIV RNA
level if immune responses
are playing a role
Stafford et al. JTB
203: 285 (2000)
Anti-HIV Antibodies
• Plasma samples obtained by CHAVI from blood
bank donors have been analyzed for the
presence of HIV RNA as well IgG, IgM and IgA
antibody levels. G. Tomaras et al. JVI 82: 12449
(2008) has shown that the earliest antibodies
are anti-gp41 and that immune complexes form
between these antibodies and HIV.
• The question we want to address is whether the
presence of anti-env antibodies impacts viral
dynamics.
We Study Three Effects of Antibody
• Opsonize viral particles and increase their
rate of clearance.
• Neutralize HIV and decrease rate of
infection of cells.
• Bind to infected cells and hasten their
destruction either through complement
mediated lysis or antibody-dependent
cellular cytotoxicity (ADCC).
Results: Fits to the Target Cell
Limited Model (First 40 days
after virus detected - T100)
Target Cell Limited Model
Model of Antibody Enhanced Virion Clearance
The viral clearance term, c, in the target cell-limited model
is assumed to be increased proportional to the Ab conc.
dT
   dT  kVT
dt
dI
 kVT  dI
dt
dV
 pI  c(1  IgG (t ))V
dt
T, target CD4 cells
I, infected Cells
V, virus
λ,
δ,
k,
p,
c,
T cell production
normal T cell death
infectivity constant
viral production
viral clearance
λ = 10,000 cells/μL/day
d = 0.01/day
c = 23/day
δ, k, p, and α are fit.
Anti-gp41 IgG antibody term added to c
Model of Antibody Mediated Viral Neutralization
The infectivity term, k, of the target cell-limited model
is reduced by Ab
dT
k
   dT 
VT
dt
1   IgG (t )
dI
k

VT  d I
dt 1   IgG (t )
dV
 pI  cV
dt
No improvement in fit is seen except for 9032
T, target CD4 cells
I, infected Cells
V, virus
λ,
d,
k,
p,
c,
T cell production
normal T cell death
infectivity constant
viral production
viral clearance
Anti-gp41 IgG antibody term added to k
SSR increases
as β increases,
with k, p, and δ
set to the best-fit
parameters of
the target celllimited model.
Model of Antibody Enhanced Infected Cell Death
The infected cell death rate, d, in the target cell-limited
model is assumed to be increased proportional to the
anti-gp41 concentration.
dT
   dT  kVT
dt
dI
 kVT  d (1   IgG (t )) I
dt
dV
 pI  cV
dt
Again no improvement in fit is seen
T, target CD4 cells
I, infected Cells
V, virus
λ,
δ,
k,
p,
c,
T cell production
normal T cell death
infectivity constant
viral production
viral clearance
λ = 10,000 cells/μL/day
d = 0.01/day
c = 23/day
δ, k, p, and α are fit.
Patient
Clearance
Enhanced,
IgG
Clearance
Enhanced,
IgM
Clearance
Infectivity
Infectivity
Infectivity Cell death Cell death
Enhanced, Diminished, Diminished, Diminished, enhanced, enhanced,
IgG+IgM
IgG
IgM
IgG+IgM
IgG
IgM
Cell death
enhanced,
IgG+IgM
6240
0.320
0.326
0.266
0.975
0.977
0.975
0.975
0.975
1.000
6246
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
9032
0.004
0.006
0.001
0.005
0.006
0.006
0.89
0.011
0.923
9077
0.567
0.998
0.687
0.604
0.998
0.623
0.722
0.998
0.991
9079
0.992
0.994
0.960
0.998
0.649
0.992
0.964
0.070
0.598
12008
0.566
0.607
0.590
0.648
0.546
0.657
1.000
1.000
1.000
9077
0.567
0.998
0.687
0.604
0.998
0.623
0.722
0.998
0.991
9079
0.992
0.994
0.960
0.998
0.649
0.992
0.964
0.070
0.598
P-values from F-test comparison of target-cell limited model with antibody-including models for all
patients, fitting through day 40. The value in bold indicates the lowest p-value for patient 9032, the only
patient better fit by an antibody-including model.
Limitations
• One possible limitation of our approach is
that the antibody data we used is the
concentration of free anti-gp41 antibody.
• Antibody in immune complexes is being
ignored as well as antibodies with other
specificities.
• Only looked at first 40 days after virus is
detectable.
Viral infectivity may vary with time
May be due to host or virus; Ma et al J Virol. 83: 3288 2009
SIV Infection
CTL Escape
• Gertrude Elion – “An antiviral is a drug that
selects for resistance”.
• Similarly, one can assess the potency of a
CTL response by asking if it selects for
escape mutations.
Escape from CTL pressure
Idea: By examining rate of escape one can estimate the CTL pressure on the virus
Asquith et al., PLoS Biol 2006
Goonetilleke et al. J Exp Med. 2009
Escape from CTL pressure
CTL killing
dw
 aw  dw  kw
dt
dm
 a ' m  dm
dt
Replication rate
a’=a(1-c)
Wildtype virus (infected cells)
Escape mutant (infected cells)
For WT, d =d+k = total rate of killing
Note, k/d is fraction of killing attributed to CTL
Fitness cost, c=0 no cost, c=1 maximal cost
Time course of escape variants
Proportion of mutant virus over time
m(t )
p(t ) 

w(t )  m(t )
1
w (0)  rt
1
m (0) e
We can use this equation to fit McMichael’s data and
estimate the rate of escape r.
Model Fits to Kinetics of HIV-1 Escape from CTL Responses in Acute
Infection
TW10
TW10
Escape rates and epitopes
Mutations
Patient
CH40
CH77
CH58
SUMA0874
Median
Escape rate
(day-1)
(days)
CD8 T
cell
epitope
t50%
Confirmed T cell
response (HXB2
position)
Nef S188R/N, R196Q
0.22
15
yes
Yes, (Nef185-202)
Gag A120D
0.17
31
no
no
Gag I401L, R403K
0.17
31
yes
Yes (Gag389-406)
Vpr S84R
0.16
31
yes
no
Vif T167I
0.37
38
yes
no
Pol K76R
0.015
119
yes
Yes, (Pol73-90)
Env R355K/S/N,T358A
0.36
9
yes
Yes, (Env350-368)
Nef R21K/G, R22K/G/,TD23E/N, P25S
0.30
19
yes
Yes, (Nef17-34)
Nef K82Q/T/P, A83G, L85H, L87I
0.29
24
yes
Yes, (Nef81-98)
Gag I147L
0.035
101
yes
Yes, (Gag140-157) IW9
Gag T242N,V247I, G248E/S
0.063
124
yes
Yes, (Gag236-253) TW10
Env Y586H
0.10
21
yes
Yes, (Env576-596)
Env F829V/S/L, I830M/L/F, A832T, V833I
0.12
27
no
no
Gag T248N, G254E
0.085
60
yes
Yes, (Gag236-253) TW10
Gag I147L
0.007
430
yes
Yes , (Gag140-157) IW9
Rev R48K, Q51H, Q53R, S54L, L55I
0.32
30
yes
Yes, (Rev47-55)
0.17
30
Results: Median rate of CTL escape = 0.17/d; Maximum rate of CTL escape = 0.37/d
Avg death rate of productively-infected cells on HAART = 1/d.
Elispot / IFN g staining
Conclusions
• Escapes measured here are faster than previously seen:
– Median r =0.17 day-1, max r =0.37 day-1
– Asquith et al. (2006), median r = 0.04 day-1
• Comparing rate of escape with the death rate of infected cells, d= 1
day-1 (HAART data) one sees CTL pressure to one epitope is high and
accounts for as much as 37% of the killing rate and on average 17%.
However, virus rapidly escapes this pressure.
• Multiple simultaneous responses could account for even more of the
loss rate of infected cells (new modeling work is examining this).
Influenza
• Unlike HIV, influenza is generally rapidly
cleared.
• Clearance can be due to target-cell
limitation as long as target cells do not
replenish before the virus is eliminated.
– If targets replenish, virus can resurge and an
immune response is needed to ultimately
clear virus.
Data: Infection in Humans
Murphy, B. R et al., Evaluation of influenza
A/Hong Kong/123/77 (H1N1) ts-1A2 and coldadapted recombinant viruses in seronegative
adult volunteers. Infect. Immun. 29:348-55
1980.
• Exponential growth of virus, peaks day 2-3,
then declines and is cleared.
Data
MODEL
dT
TI
   VT  rT (1 
)
dt
T0

Targets
Infected
p
c
Virus
d
dI
  VT  d I
dt
dV
 pI  cV
dt
Model with Infection Delay
dT
dt
dI1
dt
dI 2
dt
dV
dt
   TV
  TV  kI1
 kI1  d I 2
 pI 2  cV
Baccam et al. JVI 2006
DELAY is dashed
Double Peaks
Interferon Response
dF
 sI 2 (t   )   F
dt
ˆ
 
1  1 F
p
pˆ
1 2F
Conclusions
• Target cell limited models work well in
explaining viral load data obtained early in
HIV and influenza infection. As infection
progresses immune responses are seen
and contribute to the late dynamics.
Quantifying the precise contribution of
both innate and adaptive responses is
ongoing.