Transcript Mathematical modelling assessing the likely effectiveness

Mathematical modelling assessing
the likely effectiveness of anti-HIV
gene therapy
Associate Professor John M. Murray
School of Mathematics and Statistics, &
The Kirby Institute,
University of New South Wales, Sydney NSW 2052, Australia
[email protected]
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Outline
• A growing HIV epidemic despite antiretroviral
therapy.
• Gene therapy as a new treatment.
• Mathematical modelling of effect of ribozyme
gene therapy delivered to hematopoietic stem
cells – an ordinary differential equation
model.
• Different gene therapy classes.
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The HIV Pandemic
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Number of people living with HIV is
increasing
• At the end of 2009 there were 33
million people living with HIV in the
world.
• Each year this amount increases:
– In 2009 there were 2.6 million new
infections and 1.8 million AIDS
deaths.
– Over 6 million people in
low/middle income countries
receives antiretroviral therapy
(ART).
– However global funding is not
increasing.
Global HIV/AIDS Response, Progress Report 2011 UNAIDS
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The number of people living with HIV
in developed countries is increasing
• The size and average
age of the HIV-infected
population in
developed countries
are both increasing.
• The complications
associated with both
the disease and ART
will be compounded by
age-related factors.
Men and women living with
Diagnosed HIV in Australia
Melbourne Workshop February 2012Cysique et al., Sexual Health, 2011
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Treatment of HIV with antiretroviral
drugs
• Successful in reducing
HIV-related morbidity
and mortality.
• Does not eliminate
virus.
AIDS deaths in Australia
cART
becomes
available
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Palmer et al., PNAS, 2008
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Other treatment approaches are
needed
• ART requires daily use for the rest of a person’s life.
• The lengthening of an HIV-infected person’s life with ART
has been tremendously beneficial but this also results in
longer duration of ART.
• More HIV-infected people and longer duration of ART
results in increased direct cost – though this is outweighed
by the benefits.
• Ageing of the HIV-infected population and the resulting
need for drugs for age-related issues can lead to
complications with concurrent ART.
• Some individuals have resistant virus to many of the
available drug classes.
• A non-drug approach with a single application would be
beneficial.
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HIV infects CD4+ cells
• HIV virions bind to CD4 receptors
on the surface of immune cells
such as CD4+ T cells, monocytes,
macrophages.
• Also require attachment with a
co-receptor, initially CCR5 (later
CXCR4).
• After infection, the viral genome
HIV RNA, is reverse transcribed
into HIV DNA and inserted into
the host cell genome, to begin
production of new virus.
De Clerq, IJAA, 2008
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Gene therapy in other diseases
• Gene therapy involves the transfer of genetic
material into cells of an individual to treat an
underlying illness either through the
expression of advantageous genes or the
silencing of disadvantageous ones.
• Has been used to treat other illnesses such as
SCID-X1 (‘bubble babies’).
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Anti-HIV gene therapy
• Potentially a single
infusion of genetransduced cells will
provide life-long
protection from AIDS.
• Avoids toxicity issues
associated with ART.
• What cells should be
targeted?
Tutorvista.com
– CD4+ T cells or,
– Hematopoietic stem cells
(HSC, CD34+ cells).
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Rossi, Nat. Biotech, 2007
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What cells do you transduce with the
gene therapeutic – CD4+ T cells or
CD34+ hematopoietic stem cells (HSC)?
Ledger et al., Cell-delivered gene therapy for HIV, in Recent Translational
Research in HIV/AIDS, 2011.
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Recent HIV gene therapy trials
Cohen, Science, 2007
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Delivery of gene therapy only to CD4+
T cells will miss HIV reservoirs
• Collection of CD4+ T cells for transduction
with gene therapy occurs through apheresis
from peripheral blood.
• A large percentage of CD4+ T cells do not
traffic to peripheral blood.
• Macrophages in tissue are a source of HIV
infection that would not be affected by the
therapy.
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Output of new CD4+ T cells from
thymus decreases with age
• Introducing gene therapy into stem cells of an adult
will result in slow delivery of protected CD4+ T cells.
Murray et al., Imm. & Cell Biol., 2003.
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Mathematical modelling of HIV
• First mathematical modelling of
HIV that had a significant impact
described changes in virus levels
(HIV RNA/ml) after the start of
ART (Perelson et al., Science
1996, Wei et al., Nature 1995).
• Simple mathematical models
following changes in HIV RNA
after ART estimated for the first
time the turn-over of infected
cells I (t1/2 ~2 days) and virions V
(t1/2 6 hours).
• Strength of this modelling was
related to
dI
 kVT   I
dt
dV
 NI  cV
dt
– Experimental data
– The “right” (simplest) model to
incorporate data and biology
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Mathematical modelling of HIV gene
therapy
•
•
•
HIV researchers at Johnson &
Johnson Research Australia had
developed an anti-HIV gene therapy
and wanted to estimate its impact.
The therapy, a ribozyme that bound
to and cleaved part of HIV RNA, was
to be delivered to HSC.
How many HSC need to be
transduced with the gene therapy for
an observable effect in viral load after
1 year?
– HIV RNA assays are accurate to about
0.5 log10 so this was the minimum
change needed.
•
•
Delivery of gene therapy to HSC and
observations and changes estimated
from effects on viral production from
CD4+ T cells in peripheral blood.
Needed modelling of the
downstream effects of gene therapy
in HSC to impact throughout body.
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HIV sequence bound
and cleaved by ribozyme
Hammerhead
ribozyme
Amado et al., Human
Gene Therapy 2004
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Naive and Memory T cells
Naive T cells
Memory T cells
Antigen
Activated effector
cells against antigen
• Each T cell can target only a single antigen – Clonal Selection Theory. So need lots of
different T cell clones.
• Cells exported from the thymus are naive – they have not yet seen the antigen they
are specific for.
• When a T cell comes in contact with its antigen it becomes activated and proliferates
to produce many copies of itself. Most of these die once the antigen has been
cleared.
• At some stage in this process some of the activated cells become memory cells. If the
antigen re-occurs then there are now more memory cells specific for that antigen
(compared to the original number of naive cells) and these are faster to respond and
more efficient at clearing antigen.
• The purpose of vaccination is to produce memory cells that will eliminate the
infection before it has a chance
to takeWorkshop
off. February 2012
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Naive and Memory T cells
• If we want to get our gene therapy into all/most T cells then also
need them to develop into memory cells. So dependent on general
antigenic stimulation of naive cells via activated cells.
• Productive HIV infection preferentially occurs in activated cells
– HIV usually infects through the CCR5 co-receptor, so activated and
memory cells.
– Integration of HIV DNA into the host cell genome requires some
energy which is more likely in activated cells.
• Memory cells can have long lifespans. Memory to previous antigen
exposure can exceed 50 years.
• Describing how “protected” T cells expand in the periphery requires
description of the dynamical processes underlying generation of
memory cells.
• HIV infection is then overlaid on the normal system.
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•
Mathematical modelling of gene
therapy delivered to hematopoietic
stem
cells
(HSC)
Need to incorporate the homeostatic
processes regulating T cells to properly
model the effects of gene therapy in HSC
that produce protected T cells.
•
Deliver gene to HSC in bone marrow.
•
These produce T cell precursors that mature
in thymus.
•
New T cells exported from thymus are naive
to antigen (N).
•
Memory T cells (M) have arisen from
previous antigen contact.
•
Activated T cells (A) arise from antigen
stimulation. These cells are more
susceptible for productive infection by virus
(V) to give rise to infected cellsMelbourne
(I).
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Change in cell populations and virus
thymus
Production and
homeostasis of
CD4+ T cells
activation
death
– n(V)N – nN
reversion
+ mnM
dN/dt =
s(age)
dA/dt =
(n(V)N+m(V)M)(1 – A/A) – aA –
– aA – k(V)A
dM/dt =
aA + 2k(V)A – m(V)M – mnM – mM
dI/dt =
k(V)A – II
dV/dt =
NI – cV
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Standard HIV
infection model
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Infection predominantly occurs in
tissue and includes long-lived and
latently infected cells
• Infected macrophages are a source of infection.
Their longer lifespans than productively infected
CD4+ T cells (half-life of ~1 day) enables
continued transmission.
• As well as productively infected CD4+ T cells, HIV
establishes a reservoir of latently infected CD4+ T
cells (HIV integrated but not producing virus),
that with reactivation keeps infection going.
• Need to model the effect of gene therapy in HSC
leading to protected macrophages and impact on
replenishment of latent pool.
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Model of macrophage infection and
transmission
M infected macrophages
Ld CD4+ T cells with
defective unintegrated HIV
DNA
Lu with competent
unintegrated HIV DNA
Li with integrated HIV DNA
P productively infected
CD4+ T cells
V free virus
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Model of macrophage infection and
transmission
I  k vV  (1   )u Lu  i Li  I
V  NI  cV
Standard HIV model
with source from
latent infection
Ld  k d M  Ld
Lu  ku M  (   u ) Lu
Li  u Lu  (i   i ) Li
Generation of latent
infection and long-lived
infected cells
 k M  M
M
m
m
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The hard part of mathematical
modelling - parameter values
• Approximately 17 year half-life for total thymic output with age.
• death rates  = log(2)/(half-life)
• half-lives:
 naïve cells 10 years (McLean & Michie, PNAS, 1995)
 memory cells 10 years
 activated cells 8 days
 infected cells 2 days
 free virus 6 hours (Perelson et al., Science, 1996)
• reversion of 5% of activated to memory: a = 0.05a
• clonal expansion: on average 7 to 8 rounds of cell division, =200
• homeostatic level of activated cells: A=60
• virions produced per infected cell per day: N=320
• half-life of unintegrated HIV DNA 2.3 days
• other parameters chosen to duplicate HIV RNA and DNA levels in 5
untreated seroconverters, 4 with AZT, 9 with ART
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Effects of OZ1 gene therapy
• Modelled the effects of delivering the anti-HIV
ribozyme, termed OZ1, targeting and cleaving
a conserved region of HIV-1.
• CD34+ stem cells were assumed transduced
with OZ1 to P%.
• Assumed this delivered same percentage of
pre-thymocytes with this gene.
• Effects of these genes in CD4+ T cells and
macrophages based on in vitro experiments.
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OZ1 assumptions from in vitro
analyses
• OZ1+CD4+ T cells 1/10th as likely to be
infected.
• Infected OZ1+CD4+ T cells 1/20th as
productive.
• OZ1+ macrophages not infected.
• Sensitivity to these and other assumptions
performed.
• Simulations in Matlab.
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Simulated HIV progression without
gene therapy
Uninfected
HIV infected
Total CD4+ T cells
Memory cells
Naive cells
Murray et al., Journal of Gene Medicine, 2009.
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Estimated effects of gene therapy from
simulations
Log10 HIV RNA/ml
reduction:
After 6 months
After 1 year
After 2 years
Percentage OZ1+ HSC
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• Estimated transduction of
approximately 20% of HSC
to achieve observable
decrease in viral levels at 1
year.
• HIV RNA assays are
accurate to about 0.5 log10
so this was the minimum
change needed.
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Phase II trial of OZ1
Nature Medicine, 2009
• A randomized, doubleblinded trial of OZ1 was
conducted.
• Delivered in addition to ART
and evaluated during
structured treatment
interruptions.
• It was shown to be safe with
some effect.
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Current HIV gene therapy
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•
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•
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•
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The OZ1 trials was important as it established
that cell-delivered gene transfer is safe and
biologically active in the setting of HIV.
Most focus around HIV gene therapy now is on
reduction of CCR5 expression in cells.
CCR5 is a molecule on the surface of immune
cells involved in normal immune signalling.
It is also used as a coreceptor by HIV to infect a
cell.
Some individuals have a genetic mutation
(‘Delta 32’), that results in lower or no CCR5 on
their cells. They are less likely to be infected,
and if they are then they progress more slowly.
The “Berlin Patient” who had a bone marrow
transplant from an uninfected individual with
the Delta 32 mutation, is the only person to
have cleared HIV infection (Hutter et al., NEJM
2009).
The hope is an anti-CCR5 gene therapy will
perform similarly without the need to find a
matching bone marrow donor.
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Advantages of anti-CCR5 gene therapy
• Gene therapy against CCR5 expression
is targeting a cellular process. Normal
cellular mutation is very low so the
likelihood of an individual’s cells
changing back to CCR5+ is negligible.
• Targeting a viral process, as is done in
ART, does not have this advantage as
HIV mutates very quickly.
• Additionally gene therapy against CCR5
is a Class I therapy, as it stops infection,
rather that reducing viral production
once infected.
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Ledger et al., 2011
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Mathematical modelling of different
gene therapy classes
• Lund et al., (Bulletin of Math. Biol. 1997), von Laer et al., Applegate
et al (Retrovirology 2010) have mathematically demonstrated the
relative advantages of the different gene therapy classes.
• Class III genes provide no selection advantage.
• Evolutionary pressure from HIV infection and cell death allow Class
1 containing cells to multiply and protect.
Von Laer et al.,
Journal of Theoretical
Biology 2006
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Von Laer et al., Journal of Gene Medicine 2006
Summary
• HIV gene therapy is an expanding field with great promise.
• Mathematical modelling has an important role in the
development of gene therapy.
• Estimation of the effects of this therapy require analysis of
a complicated immune-virus dynamical system.
• Biomedical researchers appreciate the part mathematicians
can play. However they rarely communicate in the language
of mathematics.
• For there to be an effective interaction, mathematicians
must make themselves familiar with the biomedical
background, and speak to the researchers in their own
language.
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Acknowledgements
• Johnson & Johnson Research.
• Calimmune.
• Dr G. Symonds, JJR/Calimmune.
• Australian Research Council Linkage Grant
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