Download The Role of CD8 immune responses in HIV infection

1
The Role of CD8 immune responses in HIV
infection
Tendai Mugwagwa
Supervisor:
Dr. Gareth Witten.
(University of Cape Town)
An essay submitted in partial fulfilment of the requirements for AIMS Diploma in
Mathematical Sciences.
May 2004.
1
2
Acknowledgements
I would like to thank the following for their contribution in the success of this essay : Dr
Gareth Witten (My supervisor), Dr Mike Pickles, Carl Scheffler and Prof Wesley Kotze. I
am grateful to Prof Neil Turok, Prof Fritz Hahne and all my lecturers at AIMS in 2003-2004
for helping me through an exciting mathematical journey and the discovery of my passion for
epidemiology. I would also like to thank the sponsors of AIMS and all its collaborators for
making all this possible. Lastly I dedicate this essay to my family for their unconditional love
and encouragement. Thank you Mom.
2
Abstract
Mathematical models and experiments have shown the importance of CD8 responses in control
of HIV infection. In this paper we review the theoretical and empirical evidence and how the
two compliment each other as they shed more light on the progression of HIV infection. This
paper also highlights the controversies pertaining the subject. We present some models that
investigate the role of a CTL response and a CTL memory in control of HIV. These models
show that a strong CTL response can control the viral load, however, in some cases the virus
has been known to persist regardless of the immune response. We extend the basic immune
response model to account for the escape of HIV from CTL responses via epitope mutations.
We find that a broad and long lived CTL response efficiently controls the virus even in the event
of mutations. On the other hand, a gradual switch from a slow replicating HIV strain to a faster
replication kinetics, has also been suggested as a mechanism for disease progression. To explore
the factors influencing this switch, we extend the CTL memory model to include macrophage
cells, non-lytic CD8 responses and the evolution of HIV from a slow replicating strain(R5)
towards a faster replicating strain (X4). We find that macrophages act as a reservoir for the virus
hence promote viral persistence. However in the course of the infection, the success of a switch
from the R5 strain to the X4 strain dependson the cytopathicity of the individual strains. The
cytopathicity, evolution rate, infection rate and the strength of the immune response determine
the time lapse before a switch occurs. We conlude that these factors determine the length of the
asymptomatic period of HIV infection.
Contents
Abstract
2
1 Cellular immune response and disease progression
2
1.1
The stages of HIV infection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
Dynamics of HIV infection and the role of CD8 cells. . . . . . . . . . . . . . .
4
1.3
The role of CTLs in HIV infection . . . . . . . . . . . . . . . . . . . . . . . .
6
1.4
Lytic and non-lytic CD8 responses . . . . . . . . . . . . . . . . . . . . . . . .
13
2 Examples of mathematical models for the interaction between CD8 cells and HIV 18
2.1
The Basic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.2
The effect of Immune response on viral dynamics . . . . . . . . . . . . . . . .
20
2.3
CTL memory and viral dynamics . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.4
Multiple epitopes and viral dynamics . . . . . . . . . . . . . . . . . . . . . . .
27
3 Gradual evolution of HIV as a mechanism for disease progression
32
3.1
Developments of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.2
Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4 Conclusions
43
Bibliography
44
1
Chapter 1
Cellular immune response and disease
progression
HIV is a retrovirus which means that its genome is RNA and is translated into DNA during its
life cycle. HIV attaches itself to target cell using a coreceptor (CCR5 or CXCR4). It then gains
entry into the target cell and uses its machinery to complete its life cycle however destroys
them in the process. Target cells include macrophages and T cells. A healthy human adult
has about 1000 CD4 cells per micro litre of blood, but in an infected patient, the CD4 count
can drop to lower levels. Currently, if a patient has a CD4 count of below 200 CD4 cells per
micro litre, he or she is said to have AIDS. Like any other pathogen, invasion of the body by
HIV stimulates an immune response. Although there is a wide range of immune responses, we
will focus on T helper cells and CD8 cells, also known as cytotoxic T lymphocytes (CTLs).
CD8 cells control the virus by either lysing the infected cell or inhibiting HIV replication and
entry into target cells. It is unfortunate that the main target cell of HIV are CD4 cells because
these play a major role in fighting viral infections [49]. In this chapter we review models and
experimental evidence that has been presented to explain the relationship between CD8 cells
and disease progression.
2
1.1 The stages of HIV infection
3
1.1 The stages of HIV infection
To understand the development of AIDS from HIV infection, it is important to analyse the
dynamics of HIV CD4 cells and CD8 cells throughout the period of infection. The pattern of
disease progression is divided into three stages summarised in fig(1).
Plasma concetration levels
Primary phase
Asymptomatic phase
AIDS
CD8+ cells
CD4+ cells
Virus load
2−10 weeks
up to 15 years
Figure 1.1: A qualitative diagram to show the time course of HIV infection in a typical infected
adult.[36]
• Primary Phase: During the first few weeks after infection with HIV, patients experience
a period of increasing viral load and a decline in CD4 cells numbers. Flu like symptoms
have been associated with this phase[49]. The end of this period coincides with the first
signs of a CD8 immune response against HIV.[26, 37, 7]
• Asymptomatic Phase: Although there are no visible symptoms present, the replication
kinetics of the virus are extremely fast [20, 59, 38, 7]. However, there is little change in
the viral load. The CD8 responses are thought to control the virus to low levels but the
3
1.2 Dynamics of HIV infection and the role of CD8 cells.
4
CD4 cell numbers continue to decline. The length of this phase may range from a few
months to 15 or more years.[49, 7]
• AIDS: This is the final stage of the disease. CD4 cells falls below 200 micro litres and is
an overall weakness in the immune system allows opportunistic infections to frequently
occur.[17, 7, 49]. Diseases from these infections eventually lead to death.
1.2 Dynamics of HIV infection and the role of CD8 cells.
Mathematical models have provided insight into the dynamics of HIV during the different stages
of infection. The models have been used to estimate how rapidly HIV replicates, the number of
virus particles produced and cleared daily, and the lifespan of productively infected CD4 cells
[49]. The basic model (discussed in greater detail in chapter 2) and a variant containing latently
infected cells have been used to model the rise, fall and subsequent establishment of a viral load
set point. However a combination of parameters may result in the variation of this set point.
Muller et al[30] showed that small variations from patient to patient for several parameters
resulted in large variations in the observed viral load set point.
Although the basic model shows a fall in the viral load it does not include an explicit immune
response. One then asks : Do CD8 cell control the virus in the primary phase of infection?.
Phillips [40] showed that the fall of the viral load was due to a decline in the target cells(CD4
cells), a process called target cell limitation. There has been considerable controversy about
the role of CD8 cell in viral control, in particular whether CD8 cells reduce the viral load.
Simian immunodeficiency virus (SIV), infects monkeys (Macaques) in a way similar to HIV in
human beings. Jin et al [22] used an antibody OKT8F to delete CD8 cells in 6 SIV infected
macaques and 1 uninfected macaque. They observed a drastic CD8 level drop in all infected
macaques and a subsequent increase in viral load. This seemed to support the idea that CD8
cells play a role in viral control. The infected macaques showed a subsequent drop in CD4
levels, however unexpectedly, the level also dropped in the uninfected macaque. This implies
that SIV infection cannot solely account for the drop in CD4 cells. This was attributed this to
4
1.2 Dynamics of HIV infection and the role of CD8 cells.
5
the increase in viral load and activation induced apoptosis [22]. To investigate whether this drop
was due to the deletion of CD8 cells, Jin et al [22] introduced a control antibody, P1.17, into
uninfected macaques that did not delete the CD8 cells. CD4s dropped by 51%. This implied
that antibodies could induce T cell activation hence increasing the target cells for the virus. The
increase in viral load could thus have been due to an increase in target cells and not the absence
of a CD8 response.
Although some authors have doubted the role of CD8 cells in viral control([6, 14, 37]), there
is strong evidence to show that HIV specific CD8 responses are generated and are inversely
related to viral load [7, 2, 22, 44, 26, 37]. However there is no direct evidence that this immune
response can modulate the natural history of HIV infection [37].
PLASMA CONCETRATION
CTL RESPONSE
VIRAL LOAD
TIME
Figure 1.2: A qualitative diagram to show the inverse relation between CTLs and viral load
[29]
CD8 responses can be divided into (i) The lytic response (Cytotoxic T Lymphocytes,CTLs)
which make use of proteins in their cytoplasm such as peforin and granzymes for cell lysis.
5
1.3 The role of CTLs in HIV infection
6
This is also known as a direct killing response. (ii) Non-lytic responses (Chemokines) are soluble substances secreted by CD8 cells, for example is cytokines. These work by either inhibiting
HIV replication or inhibiting viral entry into target cells. As we mentioned earlier, CD8 responses can change the viral set point, however it is not clear which of the two responses are
involved. This marks the branching point in research on the role of CD8 responses in HIV infection. In the following subsections we will first examine key experiments and mathematical
models developed for CD8 lytic responses (CTLs) and then those that include CD8 non-lytic
responses.
1.3 The role of CTLs in HIV infection
CD8 lytic responses are also known as CTLs (Cytotoxic T lymphocytes). The basic model for
HIV infection was extended to include an explicit immune response [32, 56, 54, 50, 51]. These
models have the typical form of an ecological food chain model [30]. CD4 cells are the prey,
productively infected cells being their predators and the immune response as the top predator
[32, 13, 30]. Nowak and Bangham [32] used such a model to hypothesise that viral control depended on CTL responsiveness and viral diversity. They suggested that a strong CTL response
would decrease the viral set point however imposed a selection pressure on the virus resulting
in increased viral diversity and escape from the immune response. A diverse virus resulted
in an increase in viral load and thus disease progression. HIV has been shown to establish
such persistence and escape from the immune responses over time [29]. The removal of CTLs
has been shown to increase the lifespan of productively infected cells and thus increasing viral
production[22], hence, CTL persistence is essential in viral control. On the other hand, Wodarz
and Nowak [56] used a mathematical model to illustrated that apart from a high responsiveness,
a long lived CTL response was efficient in viral control(fig 3).
6
1.3 The role of CTLs in HIV infection
7
2000
Viral load
1500
1000
500
0
0
0.005
0.01
0.015
0.02
r: CTL responsiveness
Figure 1.3: A bifurcation diagram showing the effect of CTL responsiveness on the steady state
viral load [32]
They hypothesised that a long asymptomatic period was due to a long lived CTL response.
This was supported by an observation that HIV infected individuals with an asymptomatic infection for 15 years had persistently low viral loads, a stable CD4 count and a strong proliferative
response to HIV [23]. This result suggests that the quality of the immune response crucial in
determining the course of disease progression. Although these models have demonstrated the
key processes during the primary and asymptomatic phase of infection, they fail to represent
the final stage, i.e the development of AIDS. After the primary phase of infection, these models
reach a steady state where the CD4 cells, CTLs and viral loads are constant, but this has been
shown not to be so[17, 7, 49]. We pose the question: should the rate of production of CD4 cells
be a constant function as assumed in the models? It seems likely that the production of the cell
may depend on other factors such as presence of antigen to stimulate thier production. Having
established that a persistent CTL response is necessary to keep the viral set point low, we now
look at factors affecting CTL persistence.
7
1.3 The role of CTLs in HIV infection
8
1.3.1 CTL exhaustion
Before we look at factors that promote CTL persistence we will first look at why it fails. Wodarz
et al [58] developed a mathematical model in which they found that for a lymphocyte infecting
virus such as HIV, the ability to infect CD4s and a fast replication rate were the main factors
causing of the decline in CD8 cells. They referred to this process as ‘CTL exhaustion’. A
low initial CD4 count also led to the same result. They defined a threshold value depending
on viral replication rate. The higher the replication rate, the more likely the CD8 count drop.
They used this to describe the mechanism for disease progression as the gradual evolution of
HIV towards higher replication rates. This was in agreement with the findings of Connor and Ho
[10] that long-term non-progressors harbour only relatively slowly replicating HIV variants[58].
Van Den Boek et al[47] also showed that rapid replicating LCMV resulted in CTL exhaustion in
mice. However, if there are variations is viral replication rate during disease progression, should
β the replication rate in the models be a constant? Experimental evidence[47] which supports
model by Wodarz et al[58] involved a non-cytopathic virus LCMV. HIV has been shown to have
different viral strains at different infection stage. These viral strains have different cytopathicity
levels [45, 48, 12]. Therefore should the death rate for infected cells in the models be also a
constant? A lasting CTL response was suggested to depend on CD4 help [52]. If consider the
latter question, a cytopathic HIV strain would impair CD4 help leading to a decrease in CTL
response, a case not accounted for by Wodarz et al [58].
1.3.2 CTL memory
Now having established the causes of CTL exhaustion, we look at factors that promote CTL
persistence, which is also know as CTL memory. Traditionally CTL memory had been associated with protection against re-infection. A persistent CTL response has been shown to be
important for viral control. CTL memory was redefined to include the role it plays in clearance
of primary infections [57]. CTLs were divided into two groups:
• CTL precursors (CTLp): these are CTLs that have never seen the antigen and do not take
part in the killing of target cells. They are also called the CTL memory cells.
8
1.3 The role of CTLs in HIV infection
9
• CTL effectors (CTLe): these differentiate from CTLps on an encounter with an antigen.
These carry out the killing of target cells.
Elevated numbers of CTLps have been observed long after viral clearance [21, 35, 19, 57]. This
CTL memory is thought to protect the host form secondary infections. There are disagreements
on the nature and protectiveness of CTL memory, in particular, the role of a persistent antigen
or CD4 cells in maintaining memory. An experiment showed that initially CD4 deficient mice
and wild type mice infected with LCMV, both had viral loads at undetectable levels. However,
the virus reappears to high levels in the CD4 deficient mice. This observation was attributed
to the failure in establishment of CTL memory. CD4 help was suggest to interfere with the
generation and/or maintainance of CTL memory in primary infection [57]. Mathematical models were developed to test the hypothesis that CTL memory depended on CD4 help[57]. The
models demonstrated that the impairment of CD4 help during primary infection resulted in CTL
exhaustion. Although a CTL response would be produced, it would not last long. As mentioned
earlier, CTL memory is favoured by a slow replicating virus and also requires a high initial
value of CD4 count and a low viral load[58].
Long term non-progressors of HIV infection have been characterised by a relatively high
level of CTL response despite low viral loads[18, 52]. Such patients have also shown strong
CD4 proliferative responses[42, 52].However Wodarz et al[52] showed that specific CTL precursors (CTLp) in chronically HIV infected patients decayed rapidly after therapy[23]. With
this result it is not clear whether the loss of CTLps was due to an impaired CD4 help or a
reduction in antigen level by anti-viral therapy. Some researchers believe that CTL memory depends on CD4 help while others are in favour of an antigen-dependent CTL memory, however
mathematical models have suggested that the two might work together[57].
CTL memory dependence on antigen and/or CD4 help
The role of an antigen in CTL memory persistence was drawn from the traditional definition
of CTL memory in which we required a persistent antigen. Kundig et al[28] showed that for
an efficient immunisation, a large antigen dose was require to maintain CTL memory. However
Wodarz et al[57] used a mathematical model to show that antigen-dependent CTL memory was
not sufficient for successful viral control. During the asymptomatic period of HIV, the viral load
9
1.3 The role of CTLs in HIV infection
10
is low hence it may not fail to stimulate a CTL response. More recent studies insist on CD4
help as being nessecesary in the initial development of CTL memory however, the interactions
between CD4 and CD8 remain unclear. McMicheal and Rowland-Jones [29] identified three
functions of T help in relation to CD8 memory have.
Function (i): Initiation of CD8 responses
CD4 cells were said to initiate production of CD8 cells. Two pathways by which this occurs
were defined. Traditionally, the role of CD4 cells was to produce a cytokine, interleukin(IL12). This cytokine trigger dentritic cells to produce CD8 cells. This is called the classical pathway [50]. On the other hand, some viruses can directly stimulate the dentritic cells. Whether
HIV also does this remains to be clarified. Alternatively CD4 cells activate antigen-presenting
cells APC which then trigger the production of CD8 cells. This is called the CD4-APC-CD8
pathway[50]. Wodarz and Jansen [50] used a mathematical model to investigate the role of
each of these pathways in CD8 production. The model predicted that the ’classical pathway’
would be efficient at inducing CD8 cell expansion at high viral level in early infection stages.
However, at lower viral levels the ’CD4-APC-CD8 pathway’ would be efficient in ensuring viral clearance. This result meant that the two pathways would work together for successful viral
control throughout the infection period. The results also showed that CD4 help plays a role in
the development of CTL memory but on the other hand suggesting that in the absence of CD4
help APCs alone can also establish a CTL memory. Experiments to distinguish the importance
of the two pathways in view of different viral levels are still to be done.
Function (ii): CD8 maturation
Another function of CD4 is facilitating CD8 maturation. Animal models were used to show
that the absence of T help leads to CD8 cell ’immaturity’[29]. Maturity here implying failure
of CD8 cells to fully differentiate and carry out their functions. Kalams[23] showed that in the
absence of CD8 help, CTL can be persistent but in a non-functional state. Low levels of peforin
(a substance used by CTLs in cell lysis) were observed in HIV infected patients with a low CD4
count[29]. These results show that HIV specific CD8 cells may be less efficient in their lysing
property than expected. We then pose the question: should the rate of CTL killing in model
[54, 32, 58, 50] be a constant function? What could it be a function of?
10
1.3 The role of CTLs in HIV infection
11
Function (iii): Maintainance of CD8 memory
The last function of CD4 cells was identified as the ability to maintain CTL memory. Kalams
[23] presented data to show a positive correlation between T help and CD8 memory. However
the relation was questioned when McMicheal and Rowland-jones [29] showing the long survival
of CD8 memory in chronically infected patients despite the impaired CD4 help. This implied
that naturally activated CD8 cells may survive better in the absence of CD4 help.
Wodarz et al [52] use mathematical models to compare the role of CD4 help dependent and
CD4 independent CTL responses. They found that a cooperation between the two responses
was essential for viral control. During initial infection stages, viral load in high and this compromises the CD4 pool. The CD4-independent response dominates the immune responses. As it
reduces the viral load, the CD4 cell pool recovers. On the other hand, as the availability of CD4
cells improves, the CD4 dependent response brings the viral load to lower levels. These low
viral load levels cannot sufficiently stimulate a CD4 independent response. Wodarz et al[52]
point out that help dependent CTL memory is broad hence viral escape would be difficult. They
use this to accounts for the long asymptomatic period in HIV infected patients saying that CD4
help dependent CTL memory dominated this stage of HIV infection. However another mathematical model by Wodarz et al[56] showed that broad response can lead to immunodominance
depending on the CTL lifespan and CTL responsiveness to various epitopes. Knowing the high
mutation rate within epitopes, immunodominance could easily lead to loss of viral control. It
would therefore be important to investigate these properties in HIV before concluding that a
broad response would successfully control the virus. The mathematical model on CTL memory
and multiple epitopes will be discussed in greater detail the chapter 2. From discussion thus far,
we found that;
• Progression of HIV infection is equivalent to progression towards the threshold for CTL
exhaustion.
• Impairment of CD4 help results in an inefficient CTL memory.
• HIV can escape the immune responses via mutations.
11
1.3 The role of CTLs in HIV infection
12
In all three cases CTLs function to the benefit of the host. It has however been shown that CTL
activity can be detrimental to the host [54]. This process is called CTL induced pathology.
1.3.3 CTL induced pathology
A CTL response can cause severe immunopathology through destruction of the host cells. A
classic example is an experiment in which a mouse infected with LCMV remains healthy in the
absence of a CTL response [58, 31]. This result is due to the non-cytopathicity of LCMV . The
presence of an efficient CTL response can successfully control the infection, however a less efficient CTL response can lead to severe immunopathological effect characterised by wasting of
the mouse [31, 61, 57]. Such CTL mediated immunopathology has been suggested as a possible reason for the eventual development of AIDS. As mentioned earlier, the viral charectaristics
differ depending on the host cell[53]. Since HIV infects a number of different cells such as
macrophages and T cells, it becomes difficult to investigate the conditions for immunopathology in HIV experimentally. A mathematical model was used to examine the properties of CTL
induced pathology an its implication for HIV infection [57]. The degree of CTL mediated
pathology was defined as the total number of T cells found in the presence of a virus and CTL
repsonse( the sum total of the infected and uninfected T cell). The model predicted that the
degree of pathology was determined by the rate of viral replication relative to the CTL responsiveness. The faster the replication rate of the virus, the stronger the CTL response needed to
be in order to be beneficial to the host and avoid pathology. Wodarz and Krakuer [54] then
introduced the need for non-lytic CD8 responses in the model. They suggested that cytokines
would reduce the replication rate by inhibiting viral replication. A reduced rate of replication
can in-turn prevent cytopathology in an individual with an intermediate CTL response. In mice
infected with a slow replicating Armstrong strain, the absence of a non-lytic response did not
compromise viral control and no CTL induced pathology was observed. On the other hand,
mice infected with a faster replicating Traub strain, the absence of a non-lytic response resulted
in severe tissue damage and wasting of the host [46].
12
1.4 Lytic and non-lytic CD8 responses
13
1.4 Lytic and non-lytic CD8 responses
In the following section, we now look at the role of both lytic and non-lytic CD8 responses in
viral control. Initially Researchers thought that non-lytic CD8 responses worked independently
in control of viruses of different cytopathologies. Kagi et al[24] hypothesised that lytic CD8
responses were essential for the control of non cytopathic viruses whereas the no lytic CD8
responses were sufficient to deal with cytopathic viruses. However recent experiments have
shown that non-lytic CD8 responses may also contribute to resolving non-Cytopathic viruses
while lytic cell independently resolving some cytopathic infections. The importance of nonlytic responses was also discussed by Wodarz et al [58], who pointed out that HIV progression
towards the CTL exhaustion threshold may not only be achieved by the virus evolving towards
higher replication kinetics, but also by a loss of efficiency of those branches of the immune
system that limit the overall replication kinetics of the virus. This branch being the non-lytic
CD8 responses. A decrease in cytokine production may lead to increased viral kinetics driving
the system towards CTL exhaustion. This view was supported by experiments in which some
mice lacking inteferons (a kind of chemokines), where infected with a cytopathic virus, Vaccinia while others with a non-cytopathic virus LCMV [47]. In both cases no CTL activity was
detected. This result was explained as follows, the absence of non-lytic responses to control
the replication rate of the virus led to a failed CTL response possibly due to CTL exhaustion.
Wodarz et al[53] then discarded the simple rule that lytic responses are required to deal with
non-cytopathic viruses where as non-lytic responses were sufficient to deal with cytopathic
viruses. They suggested that the relevance of the two responses in resolving viruses depended
on the viral cytopathicity relative to its replication rate. They presented two cases;
• Case 1) if viral cytopathicity lies below a certain threshold, a combination of lytic and
non-lytic CD8 response is likely to resolve the infection. The non-lytic response would
reduce the viral replication rate hence minimising immunopathology and enabling the
lytic response to clear the infection.
• Case 2) If cytopathicity lies above the threshold, both the lytic and non-lytic response can
in principle, resolve the infection independently.
13
1.4 Lytic and non-lytic CD8 responses
14
The cytopathicity of HIV is not well understood. The virus has been characterised by different
replication rates and levels of cytopathicity in different cell types for example in macrophages
and T cells [53]. Experiments have been done with LCMV, a non cytopathic virus and VSV, a
cytopathic virus to support Wodarz et al’s [53] hypothesis. In the experiments, peforin deficient
mice infected with LCMV developed severe cytokine mediated aplastic anaemia and succumbed
to the infection [4]. The lack of peforin meant the lack of a CTL response. It was also shown that
with Human T cell leukaemia virus, a chronic state of activation of the immune system resulted
in overproduction of cytokines and damage the host[4]. This showed that CTLs alone could not
resolve the infection despite the non cytopathic nature of the virus. For VSV infected mice, they
showed that animals lacking a CD4 and CTL response could not control the infection by use of
non-lytic responses alone[4]. However it has been shown that in hepatitis B virus (HBV), viral
control was achieved by an intricate balance between a lytic and non-lytic CD8 response [16].
Wodarz et al [53] then used mathematical models of lytic and non-lytic CD8 responses to
conclude that reduction of replication rate the virus by non-lytic responses was always beneficial
to the host. On the other hand, increasing the death rate of the virus by lytic responses could
be both detrimental and beneficial to the host. Lytic responses were likely to be detrimental
when the virus replicated at a fast rate. In the model, the relevance of a lytic and non-lytic CD8
response in viral control depended on viral cytopathicity. Since HIV has been characterised by
different replication rates and levels of cytopathicity in different cell types[53], we therefore ask:
is not important to include other target cells in the model such as macrophages. Macrophages
are believed to form a harbour for the virus in which it can escape the CTL response [25].
1.4.1 The role of latently infected cells
An introduction of macrophages into the model also brings with it the issue of HIV tropisms as
HIV entry into cells differs with different target cells. However, let us first look back at the models discussed thus far. Although they all provide insight into the events during primary infection
and part of the asymptomatic period, none of these models shows the eventual development of
AIDS. In addition, they do not explain variation of the length of the asymptomatic period which
14
1.4 Lytic and non-lytic CD8 responses
15
ranges between a few months and up to 15 years. Wodarz and Krakuer [54] explained that at
the beginning of the asymptomatic period, the slow replicating HIV strain dominates the viral
population while the replication kinetics of the virus increase during disease progression until
the development of AIDS. In section (1.3.2) it was argued that impairment of T help cell in the
primary stages of infection may lead to an inefficient CTL memory response. A weak CTL response and a fast replicating virus according their model, would lead to CTL induced pathology
and contribute to the development of AIDS [54]. In this section we look at this change in viral
strain bringing us back to HIV tropisms.
HIV tropisms
HIV can exhibit distinct cellular tropisms that have important implications for the viral
pathogenesis and disease progression [12]. There two main tropisms named depending on the
type of coreceptor they use and their target cells. The M-tropic HIV strain has been shown
to dominate the primary and initial stages of the asymptomatic period of infection [12, 45,
60].Virus isolates in this period tend to use the CCR5 coreceptor hence it is also known as the
R5 strain [5].It is characterised by :
• a slow replication rate [45]
• a relative acytopathicity
• shows the non-synctium inducing(NSI) phenotype
• infects macrophages and primary T cells [12, 11]
• it can be inhibited by cytokines[51].
• associated with slow disease progression[9].
Later in the course of infection, HIV has been shown to evolve to the T-tropic strain which
uses the CXCR4 coreceptor [12]. This viral strain is called the X4 strain [5]. Some individuals
may retain thier use of the CCR5 coreceptor hence they show a dual tropism [12, 8]. Such
individuals are said to have the R5X4 strain. However the X4 strain is characterised by :
• a fast replication rate
15
1.4 Lytic and non-lytic CD8 responses
16
• a high degree of cell killing
• shows the synctium inducing phenotype
• infects T cells [51, 11]
• associated with an accelerated disease progression [9].
Switching tropisms during the asymptomatic period
The evolution of HIV towards a faster replicating strain has been hypothesised as the major
driving force underlying the progression to AIDS [54, 45]. This is equivalent to a switch from
the R5 strain to the X4 strain that marks the onset of AIDS. Wodarz et al [51] use mathematical
models to show that at the beginning of HIV infection when the immune response is strong,
a slow replicating virus such as the R5 strain can successfully infect macrophages. However,
since lytic CTL responses are less effective in killing macrophages compared to T cells [54],
macrophages create a buffer or refuge for the virus [25, 45]. This is thought to be the major contributor to viral persistence [45]. During the course of the infection the virus evolves towards to
the faster replicating rates, at the same time escaping the immune system through epitope mutation [32, 7, 57]. This creates a condition favourable for the emergence of the X4 strain. During
the primary infection stage, a slow replicating virus like the R5 strain allows for establishment
of a persistent virus by infecting macrophages. This explains why individuals with defective
CCR5 coreceptors,∆ CCR5 deletion, are said to be immune to HIV infection [50, 3].
1.4.2
Why is the asymptomatic period long in slow disease progressors
We know that HIV has a rapid viral turnover and hence mutation frequency is high. Surprisingly
the asymptomatic period can be long in slow disease progressors[7]. This question has been a
major challenge for researchers. Wodarz and Krakuer [54] proposed an explanation for the long
time span in the asymptomatic phase. They found that increasing the replication rate of HIV
results in evolution towards CCR5 tropism to escape CTL responses. However, the virus is then
inhibited by non-lytic CD8 responses and pathology is prevented for longer periods of time.
The X4 strain is also limited by lack of active T cell. However, opportunistic infections may
16
1.4 Lytic and non-lytic CD8 responses
17
cause high rate of T cell activation promoting the fast replicating virus to evolve towards the
CXCR4 tropism. This proposal was supported by Giorgi et al[15] who found that short survival
in HIV patients was associated with an increase in level of T cell lymphocyte activation. The
non-lytic responses in a way slow down disease progression until there is enough activated T
cells. Transition of the virus from R5 to X4 would mean that the virus becomes insensitive to
inhibition by chemokines released by CD8 cells (see review by [29]). They also point out that
efficient HIV escape from CTL killing would be via epitope mutations hence a change to X4
will actually be in favour of an escape from CTLs. Escape of HIV from CTLs through epitope
mutation will be discussed in the Chapter (2).
To summarise, during primary infection, increased viral loads cause an impairment of CD4
cells. This compromises the longetivity of CD8 memory and suppresses expansion of the X4
strain due to lack of targets. However a CTL response is stimulated by the high antigen levels,
this brings the viral load to very low levels in the asymptomatic phase. The virus slowly evolves
towards the fast replicating virus, conditions which favour the R5 strain. This does not mean
the X4 strain is absent. A slow progressor is characterised by a low number of activated CD4
cells [15] and a strong CTL response. These two maintain a low viral load. However the
low viral load cannot sustain an immune response due to reduced stimulation. Depending on
the lifespan of CTLps at low antigen and CD4 levels the immune system gradually weakens.
Eventually opportunistic infections invade the system causing an increase in activated CD4
cells, a condition suitable for the X4 strain. Since X4 has a higher replication rate it quickly
dominates the system and escape the immune system via epitope mutations. The increased viral
load or CTL induced pathology then leads to the development of AIDS [15, 54]. Alternatively,
when the virus switches from R5 to X4, this is equivalent to an escape from chemokines the
reduce the viral replication kinetics. A combination of the ability to infect CD4 cells and a fast
replication rate will lead to CTL exhaustion and hence to the development of AIDS.
17
Chapter 2
Examples of mathematical models for the
interaction between CD8 cells and HIV
In a bid to understand the relationship between CD8 responses and HIV, mathematical model
have been used to compliment experimental evidence. In this section discuss in greater detail
some mathematical models mentioned in chapter (1). We restrict ourselves to models were
developed to test the following hypothesis:(i) CTLs control the viral load steady state value,(ii)
CD4 help determines CTL memory establishment, and (iii) HIV can escape a CTL response by
way of mutations in epitopes. We start by looking at how the basic model is developed. We
then look at its extensions and how they are used to explore the different hypothesis.
2.1 The Basic model
HIV requires a host cell to reproduce itself. The basic model of viral dynamics has three variables; uninfected CD4 cells T , infected CD4 cells T ∗ and the free virus particles v. We assume
that uninfected CD4 cells are supplied from precursor cells at a constant rate λ and the die at
a rate dT T . Uninfected cells are infected by free virus particles at a rate βT V . Infected cell
in turn die at a rate dT ∗ V . Considering that viruses can be cytopathic, we assume that infected
CD4 cells have a high death rate compared uninfected CD4 cells hence dT ∗ > dT . Free virus
particles are produced from infected CD4 cells at a rate kT ∗ and decline at a rate dv hence
18
2.1 The Basic model
19
the average lifespan of a viral particle is
1
.These
dv
assumptions lead to the following system of
differential equations.
The basic HIV model
Ṫ = λ − dT T − βT V
T˙∗ = βT V − dT ∗ T ∗
V̇
= kT ∗ − dv V
(2.1)
[32]
The basic reproductive ratio for (2.1) is given by
R0 =
βλk
dT ∗ dT dv
(2.1) has two equilibrium points whose stability depends on R0 .
If R0 < 1 the virus will not spread hence
λ
dT
= 0
T1 =
T∗1
(2.2)
V1 = 0
If R0 > 1 the virus will spread and an infection is established
T2 =
λ
dT R0
dT dv
βk
dT
= (R0 − 1)
β
T∗2 = (R0 − 1)
V2
(2.3)
The value of R0 depends on the replication rate of the virus,β, and its cytopathicity dT ∗ . If
the β >
dT dT ∗ dv
λk
then infection succeeds and the virus persists. However the viral load may
be controlled by unavailability of CD4 cells. This is known as target cell limitation. On the
other hand if β <
dT dT ∗ dv
,
λk
the virus will die out and (2.1) converges to (2.2). Here the basic
reproductive number is below unitary hence infection fails to establish. HIV depends on CD4
cells for reproduction. If the virus is highly cytopathic, it will deplete the CD4 cell pool before
an infection can be established. If a <
βkλ
,
dT dv
there are enough CD4 cells to allow for a successful
infection hence the (2.1) converges to (2.3).
19
2.2 The effect of Immune response on viral dynamics
20
2.2 The effect of Immune response on viral dynamics
The introduction of an immune response into the basic model(2.1) affects the equilibrium
points. We introduce a new variable C which is the magnitude of the CTL response. We
assume that a CTL response proliferates in response to an antigen at a rate rCT ∗ . The parameter r denotes the CTL responsiveness, which is the growth rate of of CTLs after encountering
an infected cell. In the absence of an antigen CTLs decay at a rate dc C. CTLs kill infected CD4
cells at a rate pCT ∗ . These assumptions lead to the following extension of the basic model:
The basic immune response model
Ṫ = λ − dT T − βT V
T˙∗ = βT V − dT ∗ T ∗ − pT ∗ C
V̇
= kT ∗ − dv V
Ċ = rT ∗ C − dc C
(2.4)
[32] (2.4) has three equilibrium points given by (2.2), (2.3) and
λrdv
rdT dv + βdc k
dc
=
r
βk
=
rdv
λβrk
1
(
− dT ∗ )
=
p rdT dv + βdc k
T3 =
T∗3
V3
C3
(2.5)
The equilibrium to which (2.4) will converge to depends on CTL responsiveness r.However the
new reproductive ratio is given by
R1 = 1 +
βdc k
rdv dv
R1 is always greater than unitary hence elimination of the virus is not possible. If r >
dc
T2∗
the
immune response is strong enough to control the infection hence the system (2.4) converges to
(2.5). Comparing (2.3) and (2.5) we find; T3 > T2 , T3∗ < T2∗ and V3 < V2 . This shows that the
activity of an immune response reduces the viral load and increases the equilibrium abundance
of uninfected CD4 cells. The stronger the CTL responsiveness, the higher the equilibrium
20
2.2 The effect of Immune response on viral dynamics
abundance of CD4 cells and the lower the viral load. If r <
21
dc
T2∗
(2.4) converges to (2.3) assuming
R0 > 1. The diagram below(fig 2.1) shows the changes in the CTL responsiveness affects the
steady state value of the uninfected CD4 cells and the virus. It shows a positive correlation
between CTL responsiveness and uninfected CD4 cells while there is a negative correlation
between CTL responsiveness and the viral load.
uninfected CD4 cells
50
40
30
20
10
0
0
0.005
0.01
0.005 0.015
0.02
0.01
0.015
0.02
0.015
0.015
0.015
0.02
0.02
uninfected
Viral
Viralload
CD4
loadcells
50
2000
40
1500
1500
30
1000
1000
20
500
500
10
0
0 0 0
0 0
0.005
0.005
0.005
0.01
0.01
0.01
r: CTL responsiveness
Figure 2.1: Bifurcation diagrams showing the effect of CTL responsiveness on uninfected CD4
cells and viral load
The model predicts that a strong CTL response is required for viral control [32]. Studies
have shown an inverse association between the frequency of HIV-specific CTLs and plasma viral RNA load [24, 43]. It was also shown that HIV specific CTL responses in slowly progressing
individuals was more vigorous[34]. From this we can conclude that CTL responsiveness plays
an major role in viral control.
21
2.3 CTL memory and viral dynamics
22
2.3 CTL memory and viral dynamics
As discussed in chapter(1), there is substantial evidence that successful viral control requires
a persistent CTL response [52]. Patients who do not progress to AIDS after 15 years or
longer have been observed to have significantly higher levels of CTLs compared to typical
HIV-infected patients [52]. However it remains unclear how this persistence is established. A
favourable hypothesis has been that CTL memory depends on CD4 help [58]. Altfeld et al[2]
found that maintainance of effective CTLs required virus specific T helper cells. Putting this
into consideration, we split CTL response into two, CTL precursors (memory), W , and CTL
effectors, C. We then assume the following:
(i) CTL precursors proliferation depends on both infected and uninfected CD4 cells at a rate
rT W T ∗.
(ii) CTL precursors differentiate into CTL effectors in response to infected cells at a rate
fWT∗
(iii) CTL precursors decay at a rate dw
(iv) CTL precursors do not take part in killing infected cells
(v) CTL effectors decay at a rate dc
These assumption result in the mathematical model:
Ṫ = λ − dT T − βT V
T˙∗ = βT V − dT ∗ T ∗ − pT ∗ C
V̇
= kT ∗ − dv V
Ẇ = rT ∗ W T − f W T ∗ − dw W
Ċ = f W T ∗ − dc C
(2.6)
[57]
This system of differential equations has three stationary points given by (2.2), (2.3) and
22
2.3 CTL memory and viral dynamics
T4 =
where X =
T∗4 =
V4 =
W4 =
C4 =
23
p
X 2 − 4dT rf λ
2dT r
dw βk
λr + f dT −
dv
dw
rT4 − f
kdw
dv (rT4 − f )
dc (rT4 − f )( βk
T − dT ∗ )
dv 4
X+
dw pf
βk
T
dv 4
− dT ∗
p
(2.7)
Assuming that R0 > 1, stability of the equilibrium points to (2.6) depend on a number of
factor including CTL responsiveness, CTL lifespan and viral replication rate. Equilibrium (2.3)
describes a case where the CTL response goes to extinction a condition called CTL exhaustion.
Equilibrium (2.7) on the other hand represent successful establishment of CTL memory. To
determine which equilibrium (2.6) will converge to depends on on the following inequalities:
X 2 < 4dT rf λ
dT ∗ dv
T4 <
βk
f
T4 <
r
(2.8)
(2.9)
(2.10)
If any of the inequalities is satisfied equilibrium (2.7) is unstable. However (2.3) is stable if
β >
dT dT ∗ dv
.
λk
This implies that CTL exhaustion will allow viral persistence however target
cells limitation comes into play. On the other hand, if all the inequalities are not satisfied, and
β<
dT dT ∗ dv
,
λk
then equilibrium (2.3) becomes unstable and (2.6) converges to (2.7). This implies
CTL memory is established because the virus has a relatively low infection rate which does not
compromise the CD4 help. A CTL memory then reduces the viral load to lower levels. A strong
CTL response can drive the virus to extinction.
If the inequalities, (2.8),(2.9) and (2.10) are satisfied, and if β <
dT dT ∗ dv
,
λk
the outcome of
infection depends on the initial conditions. If initially we have a high viral load and a low
23
2.3 CTL memory and viral dynamics
24
CD4 count, impairment of CD4 help will result in CTL exhaustion. However, if we initially
have a low viral load and a high CD4 count, the CD4 help can contribute to the establishment
of CTL memory and viral control. In summary, there are two threshold values β1 and β2 . If
β < β1 , CD4 help impairment is minimal during the primary infection hence CTL memory is
established. If β > β2 , the fast replicating virus impairs the CD4 help during primary infection
and CTL memory cannot be established. If however β1 < β < β2 the establishment of a CTL
memory depends on initial conditions. These findings are summarised in the table.
CTL memory
CTL exhaustion
CTL exhaustion
(CTL memory generation)
-high initial virus load
(CTL memory fails)
-low initial CD4+ cell count
-naive state of host
CTL memory
-low initial virus load
-high initial CD4+ cell count
-high initial CTLp numbers
↑
↑
βT1
βT2
direction increasing rate of viral replication β
→
[58]
The following diagrams (fig(2.2) and fig(2.3)) are results of computer simulations showing
the outcome of a the system at different replication rates.
24
2.3 CTL memory and viral dynamics
100
25
16000
uninfected CD4 cells
98
virus
14000
96
12000
94
10000
92
8000
90
6000
88
4000
86
2000
84
0
0
100
200
300
400
200
180
160
140
120
100
80
60
40
20
0
500
600
700
0
100
200
300
400
500
600
700
600
700
4
CTLp
CTLe
3.5
3
2.5
2
1.5
1
0.5
0
0
100
200
300
400
500
600
700
0
100
200
300
400
500
Figure 2.2: A simulation showing development of CTL memory at a low replication rate of
Parameter values: β = 2.4 ∗ 10−6 dT = 0.01; dT ∗ = 0.24; dv = 2.4; k = 15000; dw = 0.05; p =
1; r = 0.005; λ = 1; f = 0.01; dc = 0.1. The low viral replication rate does not cause much
damage to CD4 help, hence a CTL memory is successfully developed. This CTL memory implies
a persistent CTL response which keeps the viral load at low values for a long time.
25
2.3 CTL memory and viral dynamics
100
90
80
70
60
50
40
30
20
10
0
26
90000
uninfected CD4 cells
virus
80000
70000
60000
50000
40000
30000
20000
10000
0
0
100
200
300
400
500
600
700
600
0
100
200
300
400
500
600
700
600
700
25
CTLp
CTLe
500
20
400
15
300
10
200
5
100
0
0
-100
-5
0
100
200
300
400
500
600
700
0
100
200
300
400
500
Figure 2.3: A simulation showing development of CTL exhaustion at a higher replication rate.
Parameter values: β = 2.4∗10−5 ; dT = 0.01; dT ∗ = 0.24; dv = 2.4; k = 15000; dw = 0.05; p =
1; r = 0.005; λ = 1; f = 0.01; dc = 0.1. The high replications rate of the virus impairs CD4
help hence hampering the development of a CTL memory. In the absence of a CTL memory, the
virus load increases but will then be limited by the availability of target cells(CD4s).
26
2.4 Multiple epitopes and viral dynamics
27
These findings are supported by studies that have shown that HIV-specific CTLs are hardly
detectable at low CD4 T cell count [25]. During primary HIV infection, CTLs disappearances
were observed, but these could not be attributed to escape mutants. This model suggest that
this may have been a result of CTL exhaustion. In other experiments, the depletion of CTLs by
antibodies, was shown to result in a rapid increase of the viral load in SIV-infected macaques
[22, 43]. This also showed the role of CTLs in viral control.
2.4 Multiple epitopes and viral dynamics
Despite the presence of CTLs, HIV has been known to persist. This has been attributed to the
emergence of escape mutants. In this section we look at how escape mutants can arise and how
they lead to loss of viral control even in the presents of a strong CTL response. We explain
how the steady state during the asymptomatic phase is shifted in favour of the virus. Altfeld
[2] observed that despite a strong antiviral response, most HIV infected individuals had poorly
controlled viral loads and progress to AIDS quickly. The generation of viral escape mutants and
development of high viral diversity over time was pointed out as the factor contributing. These
mutations would occur within the viral epitopes. An epitope is a site on the viral surface. Immune response cells attach themselves onto these sites during infection. T cells have receptors
which can recognises these epitopes. However these receptors are epitope specific. In the basic
model we assume that the virus has one epitope which is recognised by the CTL response. It is
however possible that a virus can have several of epitopes. If a virus has multiple epitopes, this
implies that we also require a broader CTL responses for viral control. Therefore if we have 3
epitopes it means we also 3 different CTL responses for each of them. We modified the model
[32] for viral dynamics by assuming:
(i) The virus has 10 epitopes and 10 corresponding CTL responses Ci .
(ii) Each CTL response Ci has a different responsiveness ri such that r1 < r2 < ... < r10
(iii) The CTL proliferation rates ri are positively correlated to their killing rate pi p1 < p2 <
... < p10 .
(iv) The CTL responses decay at the same rate dc
27
2.4 Multiple epitopes and viral dynamics
28
The above assumptions gave rise to the followings system of differential equations.
Ṫ = λ − dT T − βT V
T˙∗ = βT V − dT ∗ T ∗ − T ∗
10
X
C i pi
i=1
V̇
= kT ∗ − dv V
Ċi = T ∗ ri Ci − dc Ci
(2.11)
From computer based simulations of the model, we found that the outcome of a infection
depended on the lifespan of the CTL response
1
.
dc
If
1
dc
was small, the less responsive CTL
responses would be driven to extinction while the most responsive response remained. The
competitively superior CTL clone reduces the viral load to levels too low to stimulate the weaker
CTL clones [56]. This is known as immunodominance. On the other hand, if
1
dc
was large or
the CTL has a long lifespan, then the different CTL responses can coexisted and successfully
controlled the virus. In this case the competitively superior CTL clone did not reduce the virus
to low levels[56] and the weaker responses could persist . We also found that a long lived CTL
response would more efficient in the overall control of the viral load as shown in fig(2.6).
28
2.4 Multiple epitopes and viral dynamics
29
-8
-8.5
log(CTL response)
-9
-9.5
-10
-10.5
-11
-11.5
-12
0
50
100
150
200
250
300
time
Figure 2.4: When the lifespan of the CTL response is small (dc = 0.01)the less responsive CTLs
are driven to extinction while the strongest become dominant. The most responsive CTL clone
is represented by the top curve. The rest are in descending order with the least responsive at the
bottom. Parameter values dT = 0.01; dT = 0.24; β = 2.4 ∗ 10−5 ; dv = 2.4; k = 15000; λ = 1
-6
-6.5
log(CTL response)
-7
-7.5
-8
-8.5
-9
-9.5
0
50
100
150
200
250
300
time
Figure 2.5: When the lifespan of the CTL response is large (dc = 0.001)the CTLs coexist hence
there is no immunodominance.The most responsive CTL clone is represented by the curve at the
top. The rest are in descending order with the least responsive at the bottom. Parameter values
the same as in fig(2.4)
29
2.4 Multiple epitopes and viral dynamics
30
35000
long lived CTL
short lived CTL
30000
log(viral load)
25000
20000
15000
10000
5000
0
0
50
100
150
200
250
300
time
Figure 2.6: A long lived CTL broad response controls the virus better than a short lived CTL
response. Parameter values the same as in fig(2.4) except short lived CTL response: dc = 0.1
and k=1500,long lived CTL response: dc = 0.001 and k=1500
What is the effect of variations in epitopes
Considering the fast replication rate of HIV, mutation are bound to frequently occur. CTLs
provide a selection pressure for generation of escape mutants[2]. Studies have shown the positive selection of CTL escape variants within Nef during primary infection. This explains the
disappearance of the inverse correlation between the viral load and CTL response just after primary infection. This model can explain this loss of control of the virus by CTLs as follows: if
a mutation occurs in immunodominant epitope, the following can happen
(i) a new CTL response may be induced together with the old ones.
In this case immunodominance is maintained.
(ii) a partial shift of immunodominance to the next epitope.
(iii) the mutant may induce a new specific CTL response that is stronger than
the original and also induce a partial shift to the next epitope.
(iv) a total shift of immunodominance to the a weaker epitope[33]
If a mutation does not induce a new CTL response, the virus is said to have escaped the
immune response. The mutant epitope can then increase the viral load. The model predicts that
if there is immunodominance, a variation if the most dominant CTL clone results in an increase
30
2.4 Multiple epitopes and viral dynamics
31
in the viral load. However if the CTL responses coexist a mutation in the same epitope will
lead to a slight increase in the virus load but the virus can still be controlled. From this model
we conclude that although CTLs reduce the viral load they also provides a selection pressure
for emergence of viral mutants. Such mutation result in escape mutants. These mutants then
create a window through which the virus can escape CTL responses leading to an increase in
viral load. In general CTLs and target cell availability controls the viral load. A persistent CTL
response depends on the availability of CD4 help. However at times the virus can persist in
the presences of a strong immune response. This would have been a result of mutations within
epitopes such that the immune system fails to recognise the virus.
31
Chapter 3
Gradual evolution of HIV as a mechanism
for disease progression
The gradually switching of HIV from a slow replicating strain to a faster one, has been suggested
as a determinant of disease progression. We hypothesis that HIV makes use of different strains
in adapting to its environment. Wodarz et al [51] developed a model which includes the different
viral strains. However they did not include the effect of the non-lytic CD8 responses on the
infected macrophages and the gradual evolution of the R5 strain towards the X4 strain during the
disease progression. In this chapter we develop a model that seeks to investigate the parameters
that affects the this gradual switch from one strain to the other. In so doing we also gain
insight to the conditions affect the switching from one viral strain to the other. Our model
was developed on the following assumptions
1). CTLs can reduce viral load [32, 43, 24]
2). CTL memory is required for successful viral control[50]
3). A lasting CTL memory depends on CD4 help[50]
4). Non-lytic CD8 responses also play a role in viral control [54]
5). HIV can infect macrophages and CD4 cells [51]
6). There are two main viral strains of HIV, R5 and X4.[5, 45]
32
3.1 Developments of the model
33
3.1 Developments of the model
It has been shown that can have several coreceptors can be found on a single virus particle
[12, 11, 5]. In our model we assume a single viral population with two coreceptors CCR5 and
CXCR4. However the each virus particle can only use one coreceptor at a time. We therefore
split the viral population into a population of the R5 strain ’R5 ’ and the X4 strain ’X4 ’. We
also introduce two target cell populations, macrophages ’M’ and CD4 cells ’T’ [5, 45]. For
simplicity we assume that the R5 strain infects macrophages while the X4 strain infects the CD4
cells [12, 11]. Since we assumed a single virus population, the infection rates for the two strains
are assumed to be the same. Macrophages are produced at a constant rate µ, decay naturally at
a rate dm∗ M and are infected by the R5 strain at a rate βMR5 . HIV can only replicate in active
and dividing cells. However this is not a requirement for macrophage infection [51]. On the
other hand CD4 cells are split into resting CD4 cells ’S’ and active CD4 cells ’T’ [51]. HIV has
been shown to complete its life cycle in active cells [51]. We assume that the virus only infects
active cell. Resting CD4 cells are produced at a constant rate λ. They are activated as a result
of an interaction with antigens at a rate gS[T ∗ + M ∗ + N] where N is the background activation
by other infections. This background activation is neseccary to keep the active CD4 population
present at low virus levels, a condition required for the onset of AIDS [7]. Resting CD4 cells
decay at a rate S and active CD4 cells decay at a rate dT T where ds < dT .
Infected cells produce free virus particles into the plasma. In the model the R5 strain is
produce at a rate KR5 M ∗ and the X4 strain at a rate KX4 T ∗ . Both viral strains decay at the
same rate dv , however R5 evolves to X4 during the course of the disease [45, 12] at a constant
rate ev R5 . Chemokines are believed to inhibit the replication and entry of the R5 strain [11].
We therefore modify the R5 strain infection term to
βR5 M
HC+1
where H is the efficiency of the the
non-lytic response in inhibiting the viral replication and entry into macrophages. However, the
CTL response has been shown to be inefficient towards the macrophages as compared to the
CD4 cells. We do not include a CTL response for the infected macrophages but infected CD4
cells are killed by CTLs at a rate pT ∗ C. From the previous chapter we established that CTL
memory dependented on CD4 help, we include a CTL memory term and CTL response term
33
3.1 Developments of the model
34
similar to that in (6). Both infected macrophages and infected CD4 cells activate CTLps at a
rate rW T (T ∗ + M ∗ ).
Going back to the characteristics of HIV tropisms [51] we came up with the following
condition for our parameters;
• KX4 > KR5 ; The replication rate of the X4 strain has been shown to be fast faster than
the R5 strain. [51, 45, 48, 5]
• dT ∗ > dm∗ ; The cytopathicity of the X4 strain has also been shown to be higher.[51, 45,
48, 5]
• X4 = 0 and R5 6= 0 at time=0; The R5 strain has been shown to dominate the primary
and part of the asymptomatic period of infection. On the other hand the X4 strain has
been shown the appear in the later stages of infection [7, 12, 5]. We therefore had only a
population of the R5 strain at the beginning of the simulations.
The above assumption lead us to a system of 9 nonlinear differential equations given by:
Ṡ = λ − ds S − gS(T ∗ + M ∗ + N)
Ṫ = gS(T ∗ + M ∗ + N) − dT T − βT X4
T˙∗ = βT X4 − dT ∗ T ∗ − pT ∗ C
βMR5
Ṁ = µ − dm M −
HC + 1
βMR
5
Ṁ ∗ =
− dm∗ M ∗
HC + 1
Ṙ5 = KR5 M ∗ − dv R5 − ev R5
Ẋ4 = KX4 T ∗ − dv X4 + ev R5
Ẇ = r(T ∗ + M ∗ )W T − f W (T ∗ + M ∗ ) − dw W
Ċ = f W (T ∗ + M ∗ ) − dc C
34
(3.1)
3.2 Results and analysis
35
3.2 Results and analysis
In this section we seek to investigate the factors the that affect the switching of the the two
strains. These results are based on computer simulations. The general results of the simulations
depended on the initial conditions. The first case is when T > f /r. In this case there are enough
CD4 cells to establish a CTL memory. Here persistence of the viral population depends on the
efficiency of the CTL response. For a weaker CTL response, the viral load persists but at low
levels. However if the CTL response is strong then both viral strains are driven to extinction.
The second case is when T < f /r. In this case there are a number of factors affect the
dynamics of the simulation. The following observations were based on the assumption that this
in equality was true.
• CTL responsiveness
Since T < f /r CTL memory fails to persist. However the CTL response can still be
stimulated but does not persist for the entire period of infection. However this short lived
presents has an effect on the out come of the system. Increasing the CTL responsiveness,
r while maintaining the inequality T < f /c, the viral load is kept at a low level before
the immune response fades. An increases in CTL responsiveness therefore increases the
time taken for the X4 strain to appear and for a switch from the R5 strain to the X4 strain
to occur. The rate at which the CTLps differentiate to CTLes f has an same effect as r.
• Cytopathicity
There was a negative correlation between the cytopathicity of both viral strains (dT ∗ and
dm∗ ) and the steady state value their corresponding viral loads. However this was the case
provided dm∗ <
βλKR5
.
dm (dv +ev )
The effect of each individual cytopathicity was independent
of the other, for instance an increase in the cytopathicity of the R5 strain only decreased
the the viral load of the R5 strain and not the X4 strain. There was a threshold for both
dT ∗ and dm∗ which determined whether X4 < R5 or R5 < X4. Therefore if dT is above
this threshold or dm∗ is below it, no switch would occur. If however dm∗ ≈ dm then the
presence of a switch depends on the cytopathicity of the X4 strain(dT ∗ ). On the other
35
3.2 Results and analysis
hand if dm∗ >
βλKR5
,
dm (dv +ev )
36
then always R5 goes to extinction as the basic reproduction
number is below unitary. In this case the R5 strain fails to establish an infection. In the
absence of the R5 strain, the X4 strain also fails to emerge as it has to evolve for the R5
strain. In general increasing the cytopathicity reduced the number of infected cells hence
the overall viral production. This then resulted in a reduced viral load. We also found that
the cytopathicity of the R5 strain dm∗ , had a negative correlation with the time taken for
a switch to occur. However the cytopathicity of the X4 strain had a positive correlation
with this time. Results shown in Fig(3.1) and (3.2)
(b)
(a)
7e+08
R5
X4
6e+08
virions
5e+08
4e+08
3e+08
2e+08
1e+08
0
0
1000
2000
3000
4000
5000
Time(days)
(b)
(b)
7e+08
7e+08
R5
X4
virions
6e+08
6e+08
5e+08
5e+08
5e+08
4e+08
4e+08
4e+08
3e+08
3e+08
3e+08
2e+08
2e+08
2e+08
1e+08
1e+08
1e+08
0 0
0 0 0
0
1000
1000
1000
2000
2000
2000
Time(days)
Time(days)
3000
3000
3000
4000
4000
4000
5000
5000
Figure 3.1: The effect of a variation in the cytopathicity of the X4 strain on the presence or
absence of a switch. (a). dT ∗ = 0.01; Low cytopathicity of X4 maintains a high number of
infected CD4 cells which can sustain the X4 population until a switch occurs. (b)dT ∗ = 0.1 the
high cytopathicity of X4 reduces the number of infected CD4 cells present for viral production.
This keeps the X4 viral load is kept at a low level and hence a switch fails.
36
3.2 Results and analysis
37
(a)
7e+08
6e+08
5e+08
4e+08
3e+08
2e+08
1e+08
0
R5
X4
0
1000
2000
3000
4000
5000
(a)
(b)
7e+08
6e+08
6e+08
5e+08
5e+08
4e+08
4e+08
3e+08
3e+08
2e+08
2e+08
1e+08
0
R5
X4
0
1000
2000
3000
4000
5000
(b)
(c)
(c)
6e+08
3.5e+08
5e+08
4.5e+08
3e+08
5e+08
4e+08
3.5e+08
2.5e+08
3.5e+08
4e+08
3e+08
3e+08
2.5e+08
2e+08
3e+08
2.5e+08
2e+08
1.5e+08
2e+08
2e+08
1e+08
1.5e+08
5e+07
1e+08
1e+08
5e+07
0
5e+07
0 0 0
0 0
R5
X4
1000
1000
1000
2000
3000
2000
2000 Time(days) 3000
3000
4000
4000
4000
Figure 3.2: The effect of a variation in the cytopathicity of R5 on the time lapse for a switch
to occur. (a). dm∗ = 0.005 (b). dm∗ = 0.01 and (c).dm∗ = 0.08. A lower cytopathicity
of R5 increases the availability of infected macrophages for viral production. However since
this does not affect the X4 viral load it therefore takes more time for the switch to occur as
compared to when the cytopathicity is much high. Note that in (a) dm∗ < dT ∗ , (b).dm∗ = dT ∗
and (c)dm∗ > dT ∗ .
37
5000
5000
3.2 Results and analysis
38
• evolution rate
The evolution rate determines the time taken for the X4 strain to emerge. If rate at which
the R5 strain evolves to the X4 strain ev > dv then X4 > R5 throughout the simulation
period. This implies that the X4 strain appears soon after initial infection and dominates
the population throughout the period of infection. If ev < dv then the population is
initially dominated by the R5 strain however there is a negative correlation between ev
and the time taken for the X4 strain to emerge. There is also a similar relation with the
time it takes for dominant population to switch from R5 to X4. The lower the value of
ev the more time it takes for the switch to occur. On the other hand, ev had a positive
correlation with the viral load of X4 while having a negative correlation with the R5
population. These findings are illustrated in fig(3.3).
7e+08
(1) R5
(1) X4
(2) R5
(2) X4
6e+08
5e+08
virions
4e+08
3e+08
2e+08
1e+08
0
0
1000
2000
3000
4000
5000
Time(days)
Figure 3.3: An increase in the evolution rate from R5 to X4 reduces the time lapse for the
emergence of the X4 strain and the time lapse for a switch to occur. However this increase also
results in an increase of the X4 viral load and a subsequent decrease in the R5 viral load. (1).
ev = 1 and (2).ev = 10−5 . note that in all cases ev < dv .
38
3.2 Results and analysis
39
• Infection rate
There are two threshold value of β which affect the out come of the simulation. First if
β <
dm∗ dm (a+ev )
λKR5
then the the replication kinetics are too slow for an infection to occur.
Despite the condition T < f /c, if β is low enough , a CTL memory can be established
and drive the viral population to extinction. If the virus manages to persist, only the
R5 strain is presence. The X4 strain fails to appear at all or weakly appears but is the
driven to extinction. On the other hand if β >
dm∗ dm (a+ev )
λKR5
but is lower than a second
threshold β2 , persistence of the virus depends on the cytopathicity of the different strain
relative to the efficiency of the CTL response. If cytopathicity is high for both strains, a
weak CTL response may result in CTL induced pathology [54]. This pathology reduces
the availability of target cells hence the viral strains are driven to extinction. However
for a lower cytopathicity, both viral strains can coexist. In this case there is a negative
correlation between the infection rate and the time it takes for the dominant strain to
switch from R5 to X4. An increase in infectiousness reduces the time taken for the switch
to occur. If the infection rate goes beyond β2 the system becomes limited by availability
of target cells as CTL exhaustion and pathology come into play. In this case both viral
strains are again driven to extinction.
• Background activation
Surprisingly the background activation term did not have an effect on the outcome of the
simulation. One would have expected that in the absence of background activation, it
would take more time for the switching to occur. Maybe this was because it was introduced right from the beginning of the simulation. On the other hand the activation term
could be of a form other than the one we used. In similar models, background activation
has been shown to affect the dynamics of the system [7]. Experiments have also shown
that disease progression is associated with an increased T cell activation by infections
other than HIV[15].
39
3.3 Discussion
40
3.3 Discussion
On the contrary to the model by Callaway et al [7], the outcome of our model depended on
the initial conditions. If at the beginning the is a large pool of active CD4 cells (T > f /c),
this is sufficient to stimulate and establish a strong and lasting immune response. The
presents of such a strong immune response is enough to drive the R5 strain to extinction
and the prevent the X4 strain from emerging. However, if the initial CD4 cell population
is not large enough (T < f /c), then the virus can establish an infection but its outcome
now depends on a number of other parameters.
We restricted our analysis to the case when infection is established. As the virus persists,
the CD4 cells gradually decline and so does the strength of the immune response (CD8
cells). When the CD8 cells go below a critical threshold the immune response becomes
too weak to suppress the the R5 and X4 viral strains. At this point the X4 strain emerges
and due to it fast replication rate [9, 27], its population grows exponentially. Depending
on other parameters such as the cytopathicity of the X4 strain, there maybe a switch in the
dominant viral strain from the R5 to the X4 strain. When the X4 strain first emerges there
was a significant decline in the CD4 cell count. This has also been shown in experiments
[27, 7]. However from the time when the X4 strain emerges the two strains coexist and
this has also been supported by clinical observations in which both strains were shown to
coexist late in infection [27, 7] We analysed the effect of six parameters on the outcome
of the system. We choose these parameters because we thought they we important determinants of the properties of the system we were looking at. The properties were (1)
the presents or absence of a switch from R5 to X4, (2) if there is a switch , the time that
lapses before it occurs. We found that while some parameters affected either of the two
properties, other parameters affect both the occurrence and the time lapse of the switch.
The important feature of this model is the inclusion of the both the CD4 cells and macrophages
and distinguishing of the virus tropisms. This model gives a better insight on how HIV
adapts to its environment by making use of the different properties of the tropisms. During the primary stage, the immune response is generally stronger. A slow replicating
40
3.3 Discussion
41
virus and an escape from the lytic responses of CD8 cells gives the virus a better survival chance. Experiments [60, 48], have shown that the R5 strain dominates the initial
population even if the X4 strains are transmitted as well. This has been shown to be the
case if infection was via drug injection or blood transfusion [51]. As the immune system
weakens, the virus slowly evolves towards a faster replicating strain. When the immune
system goes below a critical threshold, the faster replicating strain then dominates the
system paving way for accelerated disease progression.
From this model we conclude that macrophages are essential for maintaining viral persistence in the presence of an immune response. We also conclude that the cytopathicity
of the different HIV strains play an important role in progression of the disease by determining the success of HIV in switching from a slow replicating strain to a faster one. On
the other hand, the rate of evolution, the strength of the immune response, infection rate
and again the cytopathicity are major determinants of the time taken for the switch to a
faster replicating strain to occur.The following is a table of parameter values used in the
simulations of our model.[39]
41
3.3 Discussion
42
Parameter
Value
Description
λ
600 day −1mm−3
Production rate of resting T cells
µ
300 day −1mm−3
Production rate of macrophages
g
0.000001 day −1 mm3
rate of T cell activation
N
100 day −1mm−3
amount of antigen present for back ground activation
β
2.4 ∗ 10−5 day −1 mm3
infection rate
KR5
15000 day −1
number of new viral particles produced from infected
macrophages
KX4
20000day −1
number of new viral particles produced from infected
CD4 cells
ev
varies (10−5 )∗∗
evolution rate
p
1 day −1 mm−3
rate of T cell killing by CTLs
H
20
efficiency of non-lytic response inhibition of entry into
macrophages
f
0.001
rate of differentiation from CD8 precursors to CD8
effectors
r
5 ∗ 10−8
CD8 responsiveness
ds
0.00001day −1
death rate of resting T cells
dT
0.001day −1
death rate of active but uninfected T cells
dT ∗
varies (0.01)∗∗
death rate of infected T cells
dm
0.001 day −1
death rate of uninfected macrophages
dm∗
varies (0.005)∗∗
death rate of infected macrophages
dv
2.4 day −1
decay rate of free viral particles
dc
0.005
decay rate of CD8 effectors
dw
0.0001
decay rate of CD8 precursors
∗∗default value.
42
Chapter 4
Conclusions
In this paper, we reviewed models and imperical evidence presented to explain the dynamics of HIV infections and progression to AIDS. The subject proved to be highly controversial as there remain a lot of unanswered questions. However from the review, assuming
CD8 cells play some role in HIV infection, we established the following: (1). CD8 responses can reduce the viral set point value. (2). Persistent CD8 responses are required
for successful viral control. (3). CD4 helper cells are efficient in establishing a persistent
CD8 responses. (4). Lytic CD8 responses (CTLs) can be detrimental to the host hence a
cooperation with non-lytic CD8 responses results in a more beneficial outcome. (5). HIV
can escape CTL responses through variations with in the virus for instance mutations in
epitopes. (6). HIV makes use of different viral tropisms to adapt to its environment. (7).
Switching of viral tropics can be a mechanism for disease progression.
We developed a model to investigate the factors that contribute to the switching of viral
tropisms. We considered a case where the R5 strain dominated the viral population at the
beginning of an infection while the X4 strains evolves from the R5 strain at a later stage.
We found that a successful switch from the R5 strain to the X4 strain depended on the
cytopathicity of the individual strains. However if the switch does occur, strength of the
CD8 response, infection rate and the evolution rate had an effect on the time lapse before
the switch occurs. We conclude that these factors may be important determinants of the
43
44
length of the asymptomatic period of infection.
However our analysis of the model showed that background activation had no effect on
switching of tropisms. This does not conform with experiments that have shown that
disease progression is associated with an increased T cell activation[15]. We therefore
suggest that the activation term be some other function other than a function of the resting T cells as suggested in our model. A possible candidate would be a function that
peaks later during the asymptomatic period. This will account for the role of opportunistic infections which arise just before the onset of AIDS [49]. We used the ‘one at a time’
analysis technique whereby we varied the value of a single parameter and noted its individual effect. We suggest that a detailed analysis be carried out, for example an analysis
of an interactions between different parameters.
To extend this model we suggest the inclusion of some mechanism for viral escape from
CD8 responses for instance variation within epitopes. As discussed earlier, HIV can
evade the immune response through such variations [32]. Our model observations where
based on the case where a CTL memory failed to establish since in the presence of a CTL
memory the virus was always driven to extinction. This extension may give insight on the
dynamics of the virus in the presence of an established CTL memory (in our model when
T > f /r). Another problem faced with our model was the exhaustion of target cells. In
some cases the observed result could have been a due to target cell limitation rather than
a variation in the parameters. For this reason we suggest a extension of the model which
maintains the availability of target cells for longer in the absence of an immune response.
44
Bibliography
[1] Altes.H.K, Wodarz.D and Jansen.V.A.A.The dual role of CD4 T helper cells in the
infection dynamics of HIV and their importance for vaccination. Journal of theoretical Biology Vol 14, (2002):633-646.
[2] Altfeld.M, Rosenberg.E.S, Shankarappad.R, Mukherjeea.J.S, Frederick M. Hechtc,
Robert L. Eldridgea, Marylyn M. Addoa, Samuel H. Poona, Mary N. Phillipsa,
Gregory K. Robbinsa, Paul E. Saxe, Steve Boswellf, James O. Kahnb,c, Christian
Brandera, Philip J.R. Gouldera, Jay A. Levyb, James I. Mullinsd, and Bruce D.
Walkera . Cellular Immune Responses and Viral Diversity in Individuals Treated
during Acute and Early HIV-1 Infection. The Journal of Experimental Medicine,
Vol 193(2), (2001):169-180.
[3] Biti.R, Ffrench.R, Young.J, Bennetts.B, Stewart.G, Liang.T. HIV-1 infection in an
individual homozygous for the CCR5 deletion allele. Nat Med, Vol 3, (1997):252253.
[4] Binder.D, van den Broek, M. F, Kagi.D, Bluethmann.H, Fehr.J, Hengartner.H,
Zinkernagel.R.M. Aplastic Anemia Rescued by Exhaustion of Cytokine-secreting
CD8+ T Cells in Persistent Infection with Lymphocytic Choriomeningitis Virus. J.
Exp. Med, Vol 187, (1998):1903-1920.
[5] Berger.E.A HIV-1 entry and tropism: the chemikine receptor connection. AIDS, 11,
(1997): s3-s16.
45
BIBLIOGRAPHY
46
[6] Borrow, P., H. Lewicki, B. H. Hahn, G. M. Shaw, and M. B. Oldstone. Virus-specific
CD8+ cytotoxic T-lymphocyte activity associated with control of viremia in primary
human immunodeficiency virus type 1 infection. J. Virol, Vol 68, (1994):6103-6110.
[7] Callaway, Ducan S, Ribeiro, Ruy M, Nowak, Martin A. Virus phenotype switching
and disease progression in HIV-1 infection. Proc.RSoc.Lond.B Biol. Sci., Vol 266,
(1999):2523-2530.
[8] Collman.R, Balliet.J.W, Gregory.S.A, Friedman.H, Kolson.D.L, Nathanson.N,
Srinivasan.A. An infectious molecular clone of an unusual macrophage-tropic and
highly cytopathic strain of human immunodeficiency virus type 1. J Virol, Vol 66,
(1992):7517-7521.
[9] Connor,R.I, H.Mohri, Y.Cao, D.D. Ho. Increased viral burden and cytopathicity
correlate temporally with CD4+ T-lymphocyte decline and clinical progression
in human immunodeficiency virus type 1-infected individuals. J Virol, Vol 67,
(1993):1772-1777.
[10] Connor.R.I, and Ho.D.D. Human immunodeficiency virus type 1 variants with increased replicative capacity develop during the asymptomatic stage before disease
progression. J. Virol, Vol 68, (1994):4400-4408.
[11] Dimitrov.D.S, Xiao.X, Chabot.D, Broder.C.C. HIV coreceptors. J. Membr. Biol, Vol
166, (1998):75-90.
[12] Doms.R.W, and Moore.J.P. HIV-1 Coreceptor Use: A Molecular Window into Viral
Tropism.
[13] De Boer.R.J, Boucher.C.A.B, and Perelson.A.S. Target cell availability and the
successful suppression of HIV by hydroxyurea and didanosine. AIDS, Vol 12,
(1998):1567-1570.
[14] Gotch.F.M, Nixon.D.F, Alp.N, McMicheal.A.J, and Borysiewicz.L.K. High frequency of memory and effector Gag-specific cytotoxic T lymphocytes in HIVseropositive individuals. Int.Immunol, Vol 2, (1990):707-712.
46
BIBLIOGRAPHY
47
[15] Giorgi.J.V, Hultin.L.E, McKeating.J.A, et al. Shorter survival in advanced human
immunodeficiency virus type 1 infection is more closely associated with T lymphocyte activation than with plasma virus burden or virus chemokine coreceptor usage.
J Infect Dis, Vol 179, (1999):859-870.
[16] Guidotti.L.G and Chisari.F.V. To kill or cure-options in host defence against viral
infection. Curr.Opin.Immunol, Vol 8, (1996):478-483.
[17] Haynes.B.f, Plantaleo.G, and Fauci.A.S. Towards an understanding of the correlates
of protective immunity to HIV infection. science, Vol 271, (1996):324-328.
[18] Harrer.T, Harrer.E, Kalams.S. A, Barbosa.P, Trocha.A, Johnson.R. P, Elbeik.T, Feinberg.M. B, Buchbinder.S. P. Walker.B. D. CytotoxicT lymphocytes in asymptomatic
long-term non progressing HIV-1 infection. Breadth and specificity of the response
and relation to in vivo viral quasi species in a person with prolonged infection and
low viral load. J. Immunol, Vol 156, (1996):2616-2623.
[19] Hou.S, Hyland.L, Ryan.K.W, Portner.A. Doherty.P. C. Virus-specic CD8+ T-cell
memory determined by clonal burst size. Nature, Vol 369, (1994):652-654.
[20] Ho.D.D, Neumann.A.U, Perelson.A.S, Chen W, Leonard.J.M, Markowitz M. Rapid
turnover of plasma virion and CD4 lymphocytes in HIV-1 infection. Nature, Vol
373, (1995):123-126.
[21] Jamieson.B.D. Ahmed.R. T cell memory. Long-term persistence of virus-specific
cytotoxic T cells. J. Exp. Med, Vol 169, (1989)1993-2005.
[22] Jin.X, Bauer.D.E,.Tuttleton.S.E, Lewin.S, Gettie.A, Blanchard.J, Irwin.C.J,
Safrit.J.T, Mittler.J, Weinberger.L, Kostrikis.L.G, Zhang.L, Perelson.A.S, and
David.D.H. J.Exp.Med, Vol 189(6), (The Rockefeller University Press,15
March.1999):991-998.
[23] Kalams.S.A,
Buchbinder.S.P,
Rosenberg.E.S,
Billingsley.J.M,
Colbert.D.S,
Jones.N.G, Shea.A. K, Trocha.A.K, and Walker.B.D. Association between
Virus-Specific Cytotoxic T-Lymphocyte and Helper Responses in Human Im47
BIBLIOGRAPHY
48
munodeficiency Virus Type 1 Infection Journal of Virology, Vol. 73.No. 8
(1999):6715-6720.
[24] Kagi.D, and Hengattner.H. Different role of cytotoxic T cells in the control of infections with cytopathic versus non-cytopathic viruses. Curr.Opin.Immunol, Vol 8,
(1996):472-477.
[25] Klein.M.R, van der Burg.S.H.b, Pontesilli.O, Miedema.F. Cytotoxic T lymphocytes
in HIV-1 infection: a killing paradox? Immunology Today, Vol: 19(7), (1998):317324
[26] Koup.R.A, Safrit.J.T, Cao.Y, Andrews.C.A, McLeod.G, Borkowsky.W, Farthing.C,
and Ho.D.D Temporal association of cellular immune responses with the initial control of viremia in primary human immunodeficiency virus type 1 syndrome. J. Virol,
Vol 68, (1994):4650-4655.
[27] Koot.M, Van’t Wout.A.B, Kootstra.N.A, de Goede.R. E, Tersmette.M, and
Schuitemaker.H. Relation between changes in cellular load .evlution of phenotype.and the clonal composition of virus populations in the course HIV-1 infection.
J.Infect.Dis, Vol 173, (1996):349-354.
[28] Kundig.M, Bachmann.M.F, Oehen.S, Hoffmann.U.W, Simard.J.J.L, Kalberer.C.P,
Pircher.H, Ohashi.P.S, Hengartner.H, and Zinkernagel.R.M. On the Role of Antigen
in Maintaining Cytotoxic T-Cell Memory. Proc Natl Acad Sci U S A, Vol 93(18),
(1996):9716-9723.
[29] McMicheal.A.J and Rowland-jones.S.L Cellular immune responses to HIV. Nature,
Vol 410, (2001):980-987.
[30] Muller.V, Maree.A.F, De Boer.R.J. Small variations in multiple parameters account
for wide variations in HIV-1 set-points: a novel modelling approach. Proc R Soc
Lond B Biol Sci, Vol 268(1464), (2001):235-42.
[31] Moskophidis.D, Lechner.F, Pircher.H. and Zinkernagel.R.M. Virus persistence in
acutely infected immunocompetent mice by exhaustion of antiviral cytotoxic
e¡ectorTcells. Nature, Vol 362, (1993):758-761.
48
BIBLIOGRAPHY
49
[32] Nowak.M.A, and Bangham.C.R. Population dynamics of immune responses to persistent viruses. Science, Vol 272(5258), (1996):74-79.
[33] Nowak.M.A, and May.R.M Virus Dynamics, Oxford University Press (2000):
[34] Ogg.G.S, Jin.X, Bonhoeffer.S, Moss.P, Nowak.M.A, Monard.S, Segal.J.P, Cao.Y,
Rowland-Jones.S.L, and Hurley.A. et al. Decay kinetics of human immunodeficiency virus-specific effector cytotoxic T lymphocytes after combination antiretroviral therapy. J. Virol, Vol 73, (1999):797-800.
[35] Oehen.S, Waldner.H, Kundig.T.M, Hengartner.H, and Zinkernagel.R. M. Antivirally
protective cytotoxic T cell memory to lymphocytic choriomeningitis virus is governed by persisting antigen. J. Exp. Med, Vol 176, (1992):1273-1281.
[36] Perelson.A.S and P.W. Nelson Mathematical analysis of HIV-1 dynamics in vivo.
SIAM , Rev. 41, (1999): 3-44.
[37] Price.D.A, Goulder.P.J, Klenerman.P, Sewell.A.K, Easterbrook.P.J, Troop.M, Bangham.C.R, and Phillips.R.E. Positive selection of HIV-1 cytotoxic T lymphocyte
escape variants during primary infection. Proc. Natl. Acad. Sci. USA, Vol 94,
(1997):1890-1895.
[38] Perelson.A.S, Neumann,D.C, Markowitz,M, Leonard,J.M, and Ho,D.D. HIV-1 dynamics in vivo:virion clearance rate.infected cell lifespan.viral genaration time Science, Vol 271, (1996):1582-1586.
[39] Perelson.A.S, Kirschner.D.E, and De Boer.R.J. Dynamics of HIV infection of CD4+
T cells. Math. Biosciences, Vol 114, (1993):81-125.
[40] Phillips.R.E, Rowlland-Jones.S, Nixon,D.F, Gotch,F.M, Edrwards.G.p, Ogunlesi.A.O., et al. Human immunodeficiency virus genetic variation that can escape
cytotoxic T cells recognition. Nature, Vol 354(6353), (1991):453-459.
[41] Regoes.R.R, Wodarz.D, and Nowak.M.A. Virus dynamics: the effect of target cell
limitation and immune responses on virus evolution. J Theor Biol, Vol 191 (10),
(1998):451-462.
49
BIBLIOGRAPHY
50
[42] Rosenberg.E.S, Billingsley.J.M, Caliendo.A.M, Boswell.S.L, Sax.P.L, Kalams.S.A,
and Walker.B.D Vigorous HIV-1-specific CD4+ T cell responses associated with
control of viremia. Science, Vol 278, (1997):1447-1450.
[43] Schmitz.J.E, Kuroda.M.J, Santra.S, Sasseville.V.G, Simon.M.A, Lifton.M.A,
Racz.P, Tenner-Racz.K, Dalesandro.M, and Scallon.B.J. et al. Control of viremia
in simian immunodeficiency virus infection by CD8+ lymphocytes. Science, Vol
283, (1999):857-860.
[44] Stafford.M.A, Corey.L, Cao.Y, Daar.E, Ho.D.D. and Perelson.A.S. Modeling
plasma virus concentration during primary HIV infection. J. Theoret. Biol, Vol 203,
(2000):285-301.
[45] Schuitemaker.H, Koot.M, Kootstra.N.A, Dercksen.W.A, Lange.J.M, Schattenkerk.J.K, Miedema.F, and Tersmette.M. Biological phenotype of human
immunodeficiency virus type 1 clones at different stages of infection: progression
of disease is associated with a shift from monocytotropic to : T-cell-tropic: virus
population. J Virol, Vol 66, (1992):1354-1360.
[46] Thomsen.R.A, Nansen.A, Andreasen.S.O, Wodarz.D. and Christensen.J.P. Host
factors influencing viral persistence. Phil. Trans. Roy. Soc. Lond. B, Vol 355,
(2000):1031-1041.
[47] van den Broek.M.F, Muller.U, Huang.S, Aguet.M, Zinkernagel.R.M. Antiviral defense in mice lacking both alpha/beta and gamma interferon receptors. J Virol, Vol
69(8), (1995):4792-6.
[48] van’t
Wout.A.B,
Kootstra.N.A,
Mulder-Kampinga.G.A,
Albrecht-van
Lent.N, Scherpbier.H.J, Veenstra.J, Boer.K, Coutinho.R.K, Miedema.F, and
Schuitemaker.H. Macrophage-tropic variants initiate human immunodeficiency
virus type 1 infection after sexual.parenteral and vertical transmission. J. Clin.
Invest, Vol 94, (1994):2060-2067.
[49] Witten.G. Q and Perelson.A.S. Modelling the cellular-level interaction between the
immune system and HIV. to be published
50
BIBLIOGRAPHY
51
[50] Wodarz.D and Jansen.V.A.A. The role of T cell help for anti-viral CTL responses.
Journal of theoretical Biology Vol 211, (2001):419-432 .
[51] Wodarz.D, Lloyd.A.L, Jansen.V.A.A, and Nowak.M.A. Dynamics of macrophage
and T-cell infection by HIV. Journal of theoretical Biology. Vol 196, (1999):101113.
[52] Wodarz.D. Helper dependent versus helper independent CTL responses in HIV
infection: Implications for drug therapy and resistance. J. Theor. Biol, Vol 213
(2001):447-459.
[53] Wodarz.D, Christensen.J.P, and Thomsen.R.A. The importance of lytic and nonlytic immune responses in viral infections. Trends Immunol. Vol 23(4) (2002): 194200.
[54] Wodarz.D, and Krakauer.D.C. Defining CTL-induced pathology: implications for
HIV Virology Vol 274, (2000):94-104.
[55] Wodarz.D, May.R. M. and Nowak.M. A. The role of antigen-independent persistence of memory cytotoxic T lymphocytes. Int Immunol, 12, (2000):467-77.
[56] Wodarz.D. and Nowak.M.A. CD8 memory.immunodominance.and antigenic escape. Eur. J. Immunol, Vol 30, (2000):2704-2712.
[57] Wodarz.D, Page.K.M, Arnaout.R.A, Thomsen.A.R, Lifson.J.D. and Nowak.M.A. A
new theory of cytotoxic T-lymphocyte memory: implications for HIV treatment.
Philos Trans R Soc Lond B Biol Sci, Vol 355, (2000):329-43.
[58] Wodarz.D, Klenerman.P, and Nowak.M.A. Dynamics of cytotoxic T-lymphocyte exhaustion. Proc R Soc Lond B Biol Sci Vol 265, (1998):191-203.
[59] Wei.X.P, Ghosh.S.K, Taylor.M.E, Johnson.V.A, Emini.E.A, Deutsch.P, Lifson.J.D,
Bonhoeier.S, Nowak.M.A, Hahn.B.H, Saag.M.S. and Shaw.J.M. Viral dynamics in
human immunodeficiency type-1 infection. Nature, Vol 373, (1995):117-122.
51
BIBLIOGRAPHY
52
[60] Zhu.T, Mo.H, Wang.N, Nam.D.S, Cao.Y, Koup.R.A, Ho.D.D. Genotypic and phenotypic characterization of HIV-1 patients with primary infection. Science, Vol 261,
(1993):1179-1181.
[61] Zinkernagel.R.M, Bachmann.M.F, Kundig.T.M, Oehen.S, Pirchet.H. and Hengartner.H. On immunological memory. A. Rev. Immunol, Vol 14, (1996):333-367.
52