Mathematical Immunology
Org: Beni Sahai (Cadham Provincial Laboratory) and Robert Smith (Ottawa) [PDF]
 CATHERINE BEAUCHEMIN, Los Alamos National Laboratory, Los Alamos, NM, USA
Characterizing T Cell Movement within Lymph Nodes
[PDF] 
The recent application of twophoton microscopy to the visualization
of T cell movement has presented trajectories of individual T cells
within lymphoid organs both in the presence and in the absence of
antigenloaded dendritic cells. Remarkably, even though T cells
largely move along conduits of the fibroblastic reticular cell (FRC)
network, they appear to execute random walks in lymphoid organs rather
than chemotaxis. Here, we will present results from our analysis of
experimental trajectories of T cells using computer simulations of
idealized random walks. Comparisons of simulations with experimental
data provide estimates of key parameters that characterize T cell
motion in vivo. For example, we find that the distance moved before
turning is about twice the distance between intersections in the FRC
network, suggesting that at an intersection a T cell will turn onto a
new fibre about 50% of the time. Finally, recent, more detailed
models from other groups will also be discussed.
 DANIEL COOMBS, Department of Mathematics, University of British Columbia,
Vancouver, British Columbia, V6T 1Z2
Virus competition and evolution at multiple scales
[PDF] 
Viruses compete and are subject to natural selection at multiple
levels: withincell, withinhost and withinpopulation (of hosts). We
examine how viruses can optimally exploit their hosts and how this
behaviour may influence the most successful strategy at the
betweenhost, or epidemiological level. I will present a fairly
general way to consistently combine models of disease process and
disease spread with the goal of understanding the net selection
pressure on a model virus. The method is illustrated using two
popular models at the within and betweenhost levels.
 VITALY GANUSOV, Utrecht University, Padualaan 8, 3584CH Utrecht, The
Netherlands
Modeling CD8 T cell dynamics following acute and chronic
viral infections
[PDF] 
Mathematical modeling is a reemerging field of current immunology. I
review some of our work in which we have used mathematical models to
address interesting questions in immunology. First, I show how simple
models can be used to quantify and compare the dynamics of T cell
responses following acute and chronic viral infections. Second, I
will demonstrate how one can use models to discriminate between
different hypotheses on the generation of memory CD8 T cells following
an acute infection. Finally, I discuss how models can be used to
investigate validity of a verbal hypothesis on whether and how
crossreactivity of memory CD8 T cells influences the rate of loss of
immunological memory.
 BENI SAHAI, Cadham Provincial Laboratory, Winnipeg, Manitoba, R3C 0Y1
A Basis for Immunological Protection from Death Upon
Pandemic Influenza Infection
[PDF] 
While infection with interpandemic influenza virus strains threatens
survival among the elderly and other immunocompromised individuals,
the infection with pandemic viral strains frequently proves fatal
among immunocompetent adults. Although a precise reason for this
contrast is not fully understood, the cause of death in the latter
case is attributed to a cytokine storm triggered by the pandemic
strains.
However, it is important to note that while an unacceptably large
numbers of individuals die, a large majority of infected individuals
do survive during each pandemic. It is unclear how the latter escape
or survive virusinduced cytokine storm. Understanding the basis for
their survival may aid in designing strategies that could minimize the
impact of influenza pandemics. To explore an immunological basis for
survival, we devised a multidimensional mathematical model that
monitors the dynamics of interaction between influenza virus and
uninfected and infected respiratory epithelial cells, in the presence
of innate and virusinduced adaptive immunities. The results of our
simulations indicate that the rate of death of infected epithelial
cells can be a major determinant of the course of disease and survival
after infection with a pandemic viral strain. This rate may be
affected by innate immunity, MHC make up of the individual, and any
preexisting adaptive immunity.
 ROBERT SMITH, The University of Ottawa, 585 King Edward Ave
Predicting the potential impact of a cyctotoxic Tlymphocyte
HIV vaccine: how often should you vaccinate and how strong
should the vaccine be?
[PDF] 
To stimulate the immune system's natural defences, a HIV vaccination
program consisting of regular boosts of cytotoxic Tlymphocytes (CTLs)
has been proposed. We develop a mathematical model to describe such a
vaccination program, where the strength of the vaccine and the
vaccination intervals are constant. We apply the theory of impulsive
differential equations to show that the model has an orbitally
asymptotically stable periodic orbit. We show that, on this orbit, it
is possible to determine vaccine strength and vaccination intervals so
that the number of infected CD4^{+} T cells remains below a maximal
threshold. We also show that the outcome is more sensitive to changes
in the vaccine strength than the vaccination interval and illustrate
the results with numerical simulations.
 DOMINIK WODARZ, University of California Irvine, Dept. of Ecology and
Evolution, 321 Steinhaus Hall, Irvine, CA 92697
HIV coinfection, immunity, and virus evolution in vivo
[PDF] 
It is commonly thought that virus evolution in vivo can contribute to
or correlate with the progression of HIV infection from the
asymptomatic phase towards AIDS. The virus evolves towards immune
escape, increased replication kinetics, and a higher degree of cell
killing, leading to the depletion of the T helper cell population.
Mathematical models of in vivo HIV evolution have been useful in
shaping our understanding of the disease process. However, the models
considered so far assume that one cell can only harbor one virus
particle. Recent data, however, indicate that one cell can be infected
by more than one virus particle, a process called coinfection. I will
discuss a mathematical model that studies the effect of coinfection
on HIV evolution in vivo and on the process of disease progression.
This gives rise to some counterintuitive insights that find some
support in experimental data. It also gives rise to a theory for why
natural SIV infection does not progress to AIDS despite the presence
of high virus loads and high virus diversity in some cases.
