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Virus life-history strategies and the
challenges theypose for T cell
vaccines
Andrew Yates
T cell vaccines
Vaccines aimed at eliciting protective antibody responses to
HIV and the Malaria parasite have been largely unsuccessful
to date
Much research effort & funding is currently directed
at generating vaccines that will generate
cytotoxic T lymphocytes (CTL)
CTL in action
Weidemann et al., PNAS (2006)
CTL survey cells for viral epitopes and kill infected cells
The numbers problem
e.g. CTL vaccines targeting the sporozoite stage of the Malariaparasite
~100 infected hepatocytes among 10 liver cells (humans) or 10 cells (mice)
How many CTL are needed to clear these cells before the release of theblood stage (approx day 7 in humans, day 2 in mice)?
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There’s little understanding of how many CTL a vaccine needs to generate to confer immunity in any
given tissue
Critical thresholds of CTL immunity - rough estimate
To achieve negative growth rate of infected cells requires specific CTL to be present above a critical spatial frequency C* = r/k
Assume CTL and infected cells are well-mixed and moving randomly, with a mass-action encounter rate
kC = total CTL-mediated mortality of infected cells1/k = mean time between CTL surveillance events
dI
dt= rI − kCI
Suppose infected cells are present in a tissue at spatial frequency I(t), growing at net per capita rate r in absence of CTL
CTL present at frequency C
Estimating surveillance rates of LCMV-specific CTL in vivo
One spleen CTL browses approximately 1-4 cells per minute
Regoes et al, PNAS (2006); Yates et al, PLoS One (2007)
Estimated ratek (per minute)
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Estim
ated
killi
ng ra
te, k
(min
-1)
CTLsurveillance
rate k(cells/min)
LCMV-immune mouse
Critical thresholds of CTL immunity - simplest calculation
So a preliminary ‘back-of-envelope’ estimate is that if the uncontrolled virus doubling time is T hours,
e.g. 12 hour doubling time means C* ~ 0.04%
C∗ =log 2
Tk� 5× 10−3
T
Problems with this rough estimate
1. Our estimate of the CTL surveillance rate k is specific to spleenIt is likely to be sensitive to the tissue architecture
Assumes CTL are already tissue-resident or influx is rapid
2. Ignores migration
This is likely only valid in a range of E:T ratiosMay need to consider CTL handling/recycling time at low CTL densities;
multiple CTL binding to one target at high densities
3. It relies on the assumption of ‘mass-action’ killing kinetics
4. Virus life-histories need to be considered
There may be restricted visibility of infected cells to CTL; e.g. lag between infection and expression of viral epitopes
on cell surface
Need to know the dynamics of virus production & epitope expression
Virus life-history strategies
Budding (envelope)
HIV (CD4)HSVSARS
Smallpox
Lytic (‘naked’)PoliovirusCoxsackieAdenovirus
Generation time
Modeling infected cell dynamics in the presence of CTL
x(a,t) is the density of infected cells of age a at time t
m(a) is the virus production schedule(rate of virion release at time a after virus entry)
k(a) is the age-dependent susceptibility to CTL killing
is the mortality of infected cells at age a (non-CTL)δ(a)
Half life of free virus is short; target cells are in abundance;CTL and targets are well-mixed with a mass-action killing rate
Assumptions
is the expected number of infected cells arising from one virion �
Age-structured model of infected cell dynamics
�
� ∞
0�(a)m(a)e−rada = 1
Growth rate r of infected cell numbers is obtained by solving
�(a) = exp�−
� a
0(δ(s) + k(s)C)ds
�
Survivorship(probability of an infected cell living for a time a)
Budding virus
Age sinceinfection
Age sinceinfection
Virion production rate, mVirion production
rate, m
Visibilityto CTL, k
Visibility to CTL, k
Virus-inducedmortality, d
maCTLa lysisaT
Lytic virus
da
Simple models of budding and lytic virus strategies
- Budding virus with no production lag time or CTL eclipse phase- Constant virus production rate and mortality
We’ll compare these to the ‘standard model’ of infected cell dynamics;
eclipse
phase
eclipse
phase
Modeling the effectiveness of CTL against different virus strategies
To calibrate our comparison of the three models,in the absence of CTL we set
Infected cell growth rates equal
Expected lifetimes of infected cells equal
We can then compare the levels of CTL needed to reducethe infected cell growth rate to zero
for different virus strategies
80%
0.000 0.001 0.002 0.003 0.004 0.005
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CTL frequency, C
Net
gro
wth
rate
(/ho
ur)
lyticbuddingbirth/death
0.000 0.001 0.002 0.003 0.004 0.005
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10
20
30
40
50
CTL frequency, CIn
fect
ed c
ell d
oubl
ing
time
(hou
rs)0.000 0.001 0.002 0.003 0.004 0.005
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0.1
0.2
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0.5
CTL frequency, C
Net
gro
wth
rate
(/ho
ur)
lyticbuddingbirth/death
0.000 0.001 0.002 0.003 0.004 0.005
0
10
20
30
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CTL frequency, C
Infe
cted
cel
l dou
blin
g tim
e (h
ours
)
T = 40% of generation time
Dependence of infected cell growth rate on CTL frequency
Standard Standard
T = 80% of generation time
Critical CTL frequencies required for clearance
Lytic Ly
tic
Budd
ing
Stand
ard
Budd
ing
Stand
ard
Compared to the standard virus dynamics model withexponentially-distributed lifetimes
and constant rates of virus shedding...
Comparing more realistic virus strategies with the standard model
1. The longer the CTL eclipse phase the more difficult it isto control viruses with lytic or budding strategies
2. There’s no general principle that makes one virus strategy(lytic, budding) more difficult for CTL to control than the other
This is perhaps counterintuitive for lytic viruses; we might expect they are easier to control because a CTL removing a cell infected with lytic virus
prevents the release of all viral progeny from that cell
Example - CTL control of acute HIV infection
HIV has a budding strategy
Early acute primary infection:Exponential growth of virus titres in blood
Can we use this data & our framework to estimate theadditional CTL numbers needed to control acute HIV infection?
- Early infected cell growth rate - Death rate of infected cells near the peak of viremia
Little et al (JEM 1999) measured:
Estimating HIV life-history parameters
Rate of productionof new infected cells by a
single productively infected cell
= lag before virus production in infected CD4 T cells, ~ 1dτ
= initial growth rate of virus titers and of infected cell numbers= 2 /d (range 1.4 - 3.5), or a doubling time of 5-12h
r0
e−r0τ =kC0 + d+ r0�m e−kC0T
Proportion ofinfected cells thatbegin to shed virus
= window of visibility of infected cells to CTL before virusshedding starts; range 6-18 hours
T
= total CTL-mediated death rate of infected cellskC0
= mean value of CTL surveillance rate x HIV-specific CTL density reflected in blood
Lotka-Euler eqn. for growth rate , when target cells are in excess, in
presence of CTL frequency
r0
C0
= = total infected cell death rate - in the range 0.3-0.5 /dkC0 + d δI
1 =δI + kCadd
(δI + r0)er0τ−kCaddT
Estimating the total additional killing rate needed for virus control
Assume an HIV vaccine can generate an additional population of HIV-specific CTL, , which reduces the virus growth
rate to zero
Eliminating the unknown parameters from the equationfor the growth rate,
Using the plausible ranges of parameters, we estimate the threshold killing rate required to control acute
HIV infection to be in the range 1.7 - 6/dayδI + kCadd
Cadd
What does this mean?
Interpreting this estimate
and if we use our estimates of k for LCMV in the spleen (1-10/min),
Estimated minimumadditional HIV-specific
CTL frequencies
kCadd =1.7
kCadd =6
0.01% - 0.1%
0.04% - 0.4%
If cell death early in infection is largely due to non CTL-mediated mechanisms(innate immunity, cytopathic effects of virus),
The normal CTL response to HIV needs to be boosted in numbers at least 6 - 20 fold by a vaccine
If infected cell death early in infection is largely due to CTL then
The upper bound is large -but a prime-boost vaccination regimen may generate large memory CD8 T cell
clones without significantly ablating immune memory to other pathogens
Vezys, Yates et al, Nature 2009
Potential problems - I
CTL-mediated selective pressure on the mutating virus during the growth phase of natural infection is expected to be low
But the vaccine-induced memory CTL will increase this pressure
To minimise this effect,we need broad coverage of HIV epitopes,
to both early and conserved proteins if possible.
1. CTL escape
Potential problems - II
2. Available data from acute HIV infection is limited
Virus titers in blood likely reflect infected cell growth rates in lymphoid tissue; but do they also mirror replication at other infection sites
(e.g. gut mucosa)?
This may not be the infected cell death rate in the acute phaseof virus growth
We need to quantify the relative contributions of virus cytopathicity and the CTL response to infected cell
death early in infection
Little et al obtained this using the decay of virus titers after initiation of antiretroviral therapy
This occurred over the 10 days following the approx. peak of viremia
3. These estimates hinge on measurements of the infectedcell death rate in acute infection
Summary
But ... control of virus with CTL is likely more difficultthan might be predicted with this model
When predicting CTL efficacy against different virus strategies,the details of the virus life history matter
By modeling the HIV life-history, we can improve our theoretical estimates of the minimum additional contribution to CTL
frequencies needed to control acute HIV infection
The standard model of virus dynamics has been very successful
e.g. demonstrating that HIV-infected cells turn over very rapidly (Perelson & Ho, Science 1996)
Thanks to collaborators
Rustom Antia(Emory U., Atlanta)
Minus van Baalen(U. Pierre et Marie Curie, Paris)
Basic reproductive number of budding strategy
R acute0 =
�m
kC0 + de−kC0T
r=0.5 /dayk=5 /minepsilon m = 0.25 (cells/hour)(budding: eps=0.05, m = 5)Budding starts after 6h (am)Visible to CTL after 2h (ac)Mortality d due to budding = 3/hour(half-life ~ 6 hours)Onset of virus induced mortality (ad) 4hExpected infected cell lifetime 4+ 1/d = 4.3hLytic: lifetime = a.lytic = 4.3hBurst size of virions ~ 240
Parameters for simulations