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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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killi

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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

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CTL frequency, CIn

fect

ed c

ell d

oubl

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time

(hou

rs)0.000 0.001 0.002 0.003 0.004 0.005

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CTL frequency, C

Net

gro

wth

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(/ho

ur)

lyticbuddingbirth/death

0.000 0.001 0.002 0.003 0.004 0.005

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CTL frequency, C

Infe

cted

cel

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ours

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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