Molina-Par?s C., Lythe G. (editors) Mathematical Models and Immune Cell Biology
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x Contents
9 Multivariate Competition Processes: A Model for Two
Competing T Cell Clonotypes ...............................................187
Carmen Molina-Par´ıs, Grant Lythe, and Emily Stirk
10 Stochastic Modelling of T Cell Homeostasis for Two
Competing Clonotypes Via the Master Equation .........................207
Shev MacNamara and Kevin Burrage
11 Dendritic Cell Migration in the Intestinal Tract ..........................227
Rowann Bowcutt and Sheena Cruickshank
12 Reassessing Germinal Centre Reaction Concepts ........................241
Jose Faro and Michal Or-Guil
13 B Cell Strategies of Ag Recognition in a Stratified
Immune System ...............................................................259
Belen de Andr´es, Ana R. S´anchez-Archidona,
Isabel Cortegano, Natalia Serrano, Sharmili Jagtap,
Mar´ıa-Luisa Gaspar, and Miguel-Angel Rodr´ıguez Marcos
14 Dynamics of Peripheral Regulatory and Effector T Cells
Competing for Antigen Presenting Cells ...................................275
Nuno Sep´ulveda and Jorge Carneiro
15 Mathematical Models of the Role of IL-2
in the Interactions Between Helper
and Regulatory CD4
C
T Cells...............................................305
Kalet Le´on and Karina Garc´ıa-Mart´ınez
16 A Physicist’s Approach to Immunology ....................................339
Mario Castro
17 Timescales of the Adaptive Immune Response ............................351
Mark Day and Grant Lythe
18 Using Mathematical Models to Explore the Role
of Cytotoxic T Lymphocytes in HIV Infection ............................363
Helen Fryer and Angela McLean
19 Viral Immunity and Persistence ............................................383
Stephen Hickling and Rodney Phillips
Index .................................................................................405
Contributors
Asma Ahmed Department of Biochemistry, Indian Institute of Science,
Bangalore 560012, India, asma.127@gmail.com
Graham Anderson Medical Research Council Centre for Immune Regulation,
Institute for Biomedical Research, Medical School, University of Birmingham,
Birmingham B15 2TT, UK, g.anderson@bham.ac.uk
Belen de Andr
´
es Centro Nacional de Microbiolog´ıa, ISCIII, Majadahonda,
28220 Madrid, Spain, bdandres@isciii.es
Becca Asquith Department of Immunology, Wright-Fleming Institute, Imperial
College London, Norfolk Place, London W2 1PG, UK, b.asquith@imperial.ac.uk
Jos
´
e A.M. Borghans Department of Immunology, University Medical Center
Utrecht, Lundlaan 6, Utrecht, The Netherlands, j.borghans@umcutrecht.nl
Rowann Bowcutt Faculty of Life Sciences, AV Hill Building, University of
Manchester, Oxford Road, Manchester M13 9PL, UK,
Rowann.Bowcutt@postgrad.manchester.ac.uk
Kevin Burrage The Oxford Computing Laboratory and Oxford Centre for
Integrative Systems Biology, University of Oxford, Oxford OX1 2JD, UK,
and
The Institute for Molecular Biosciences, The University of Queensland,
Queensland, Brisbane, QLD 4072, Australia, kevin.burrage@comlab.ox.ac.uk
Jorge Carneiro Instituto Gulbenkian de Ciˆencia, Oeiras, Portugal,
nunosep@igc.gulbenkian.pt
Mario Castro Grupo Interdisciplinar de Sistemas Complejos (GISC), Grupo de
Din´amica No Lineal, Universidad Pontificia Comillas, Madrid E-28015,
Spain, mariocastro73@gmail.com
Daniel Coombs Department of Mathematics and Institute of Applied
Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2,
coombs@math.ubc.ca
Isabel Cortegano Centro de Biolog´ıa Molecular, CSIC-UAM, Campus, de
Cantoblanco, 28049 Madrid, Spain, icortegano@isciii.es
xi
xii Contributors
Sheena Cruickshank Faculty of Life Sciences, AV Hill Building,
University of Manchester, Oxford Road, Manchester M13 9PL, UK,
sheena.cruickshank@manchester.ac.uk
Mark Day Department of Applied Mathematics, University of Leeds,
Leeds LS29JT, UK, jhs5msd@leeds.ac.uk
Omer Dushek Centre for Mathematical Biology, University of Oxford,
Oxford OX1 3LB, UK
and
Sir William Dunn School of Pathology, University of Oxford, Oxford OX1 3RE,
UK, omer.dushek@path.ox.ac.uk
Jose Faro Edificio de Ciencias Experiment´ais, Universidade de Vigo, Campus
As Lagoas-Marcosende, 36310 Vigo, Spain,
and
Estudos Avanc¸ados de Oeiras, Instituto Gulbenkian de Ciˆencia, Apartado 14,
2781-901 Oeiras, Portugal, jfaro@uvigo.es; jfaro@igc.gulbenkian.pt
Marc Thilo Figge Applied Systems Biology, Friedrich Schiller University Jena,
Leibniz Institute for Natural Product Research and Infection Biology – Hans Kn¨oll
Institute, Beutenbergstrasse 11a, 07745 Jena, Germany, thilo.figge@hki-jena.de
Helen Fryer The Institute for Emerging Infections, The Oxford Martin School,
Department of Zoology, University of Oxford, Oxford OX13PS, UK,
helen.fryer@zoo.ox.ac.uk
Karina Garc´ıa-Mart´ınez Center of Molecular Immunology, Havana, Cuba,
karina@cim.sld.cu
Mar´ıa-Luisa Gaspar Centro Nacional de Microbiolog´ıa, ISCIII, Majadahonda,
28220 Madrid, Spain, mlgaspar@isciii.es
Edwin D. Hawkins The Walter and Eliza Hall Institute of Medical Research,
1G Royal Parade, Parkville, Victoria 3052, Australia
and
Department of Medical Biology, The University of Melbourne, Parkville,
Victoria 3010, Australia, Edwin.Hawkins@petermac.org
Stephen Hickling Peter Medawar Building for Pathogen Research, University
of Oxford, South Parks Road, Oxford OX1 3SY, UK,
stephen.hickling@lincoln.ox.ac.uk
Phillip D. Hodgkin The Walter and Eliza Hall Institute of Medical Research,
1G Royal Parade, Parkville, Victoria 3052, Australia
and
Department of Medical Biology, The University of Melbourne, Parkville,
Victoria 3010, Australia, wellard@wehi.edu.au
Sharmili Jagtap Centro de Biolog´ıa Molecular, CSIC-UAM, Campus de
Cantoblanco, 28049 Madrid, Spain, Sharmili.Jagtap@dartmouth.edu
Contributors xiii
Eric Jenkinson Medical Research Council Centre for Immune Regulation,
Institute for Biomedical Research, Medical School, University of Birmingham,
Birmingham B15 2TT, UK, e.j.jenkinson@bham.ac.uk
William Jenkinson Medical Research Council Centre for Immune Regulation,
Institute for Biomedical Research, Medical School, University of Birmingham,
Birmingham B15 2TT, UK, w.e.jenkinson@bham.ac.uk
Kalet Le
´
on Center of Molecular Immunology, Havana, Cuba, kalet@cim.sld.cu
Grant Lythe Department of Applied Mathematics, University of Leeds,
LS29JT, UK, grant@maths.leeds.ac.uk
Shev MacNamara The Oxford Computing Laboratory and Oxford Centre for
Integrative Systems Biology, The University of Oxford, Oxford OX1 2JD, UK
and
The Institute for Molecular Biosciences, The University of Queensland, Brisbane,
QLD 4072, Australia, shev.macnamara@maths.ox.ac.uk
Miguel-Angel Rodr´ıguez Marcos Centro de Biolog´ıa Molecular, CSIC-UAM,
Campus de Cantoblanco, 28049 Madrid, Spain
John F. Markham The Walter and Eliza Hall Institute of Medical Research,
1G Royal Parade, Parkville, Victoria 3052, Australia
and
Department of Medical Biology, The University of Melbourne, Parkville,
Victoria 3010, Australia, jmarkham@wehi.edu.au
Angela McLean The Institute for Emerging Infections, The James Martin 21st
Century School, Department of Zoology, University of Oxford, Oxford OX13PS,
UK, angela.mclean@zoo.ox.ac.uk
Michael Meyer-Hermann Department of Systems Immunology, Helmholtz
Centre for Infection Research (HZI), Inhoffenstr. 7, D-38124 Braunschweig,
Germany, michael.meyer-hermann@helmholtz-hzi.de
Carmen Molina-Par´ıs Department of Applied Mathematics, University of Leeds,
Leeds LS29JT, UK, carmen@maths.leeds.ac.uk
Dipankar Nandi Department of Biochemistry, Indian Institute of Science,
Bangalore 560012, India, nandi@biochem.iisc.ernet.in
Michal Or-Guil Systems Immunology Research Group, Institute for Theoretical
Biology, Humboldt University, 10115 Berlin, Germany
and
Research Center ImmunoSciences, Charit´e, 10115 Berlin, Germany,
m.orguil@biologie.hu-berlin.de
Rodney Phillips Peter Medawar Building for Pathogen Research, University of
Oxford, South Parks Road, Oxford OX1 3SY, UK, rodney.phillips@ndm.ox.ac.uk
Katie Quinn Department of Applied Mathematics, University of Leeds,
Leeds LS29JT, UK
xiv Contributors
Ana R. S
´
anchez-Archidona Centro Nacional de Microbiolog´ıa, ISCIII,
Majadahonda, 28220 Madrid, Spain, asarchidona@sanfordburnham.org
Nuno Sep´ulveda Instituto Gulbenkian de Ciˆencia, Oeiras, Portugal
and
London School of Hygiene and Tropical Medicine, Keppel Street,
London WC1E 7HT, UK, nuno.sepulveda@lshtm.ac.uk
Natalia Serrano Centro Nacional de Microbiolog´ıa, ISCIII, Majadahonda,
28220 Madrid, Spain
Andrew K. Sewell Department of Infection, Immunity and Biochemistry,
Cardiff University School of Medicine, Henry Wellcome Building, Heath Park,
Cardiff CF14 4XN, UK, sewellak@cardiff.ac.uk
Emily Stirk Department of Applied Mathematics, University of Leeds,
Leeds LS29JT, UK, emily@maths.leeds.ac.uk
Hugo A. van den Berg Warwick Systems Biology Centre, University of Warwick,
Coventry CV47AL, UK, hugo@maths.warwick.ac.uk
P. Anton van der Merwe Sir William Dunn School of Pathology, University
of British Columbia, Oxford OX1 3RE, UK, anton.vandermerwe@path.ox.ac.uk
Cameron Wellard The Walter and Eliza Hall Institute of Medical Research,
1G Royal Parade, Parkville, Victoria 3052, Australia
and
Department of Medical Biology, The University of Melbourne, Parkville,
Victoria 3010, Australia, wellard@wehi.edu.au
List of Abbreviations
Ab antibody
ACE abundance coverage estimator
AID activation-induced deaminase
APC antigen-presenting cell
APP antigen presentation profiles
BCR B cell antigen receptor
BM bone marrow
BrdU 5-bromo-2’-deoxyuridine
CD cluster of determination cell surface molecules
CDR complementarity-determining region of the TCR
CFSE carboxyfluorescein diacetate succinimidyl ester
CP colonic patch
CpG C–phosphate–G region of DNA
CSR class switch recombination
cTEC cortical thymic epithelial cells
CTL cytotoxic T lymphocyte
DC dendritic cell
DN double negative
DP double positive
EBV Epstein-Barr virus
ER endoplasmic reticulum
FDC follicular dendritic cell
FSP finite state projection
GC germinal centre
GIT gastrointestinal tract
HCMV human cytomegalovirus
HIV human immunodeficiency virus
HLA human leukocyte antigens
HSC haematopoietic stem cells
IEC intestinal epithelial cell
IFN interferon
Ig immunoglobulin
ILF isolated lymphoid follicle
xv
xvi List of Abbreviations
IL-2 interleukin-2
IL-7 interleukin 7
IR immune response
IS immune system
ITAM immunoreceptor tyrosine-based activation motif
ITIM immunoreceptor tyrosine-based inhibition motif
MAP methionine aminopeptidas
mTEC medullary thymic nepithelial cells
LCD limiting conditional probability distribution
ME master equation
MHC major histocompatibility complex
MHCI class I MHC
MHCII class II MHC
MLN mesenteric lymph node
MZ marginal zone
NK natural killer cell
NP nitrophenyl
ODE ordinary differential equation
PCR polymerase chain reaction
PDE partial differential equation
PDF probability density function
PGF probability generating function
PLC peptide loading complex
pMHC peptide-MHC
PRR pattern recognition receptor
QSD quasi-stationary distribution
RAG recombinase activating gene
SHM somatic hypermutation
SHIV simian-human immunodeficiency virus
SIV simian immunodeficiency virus
SP single positive
SSA stochastic simulation algorithm
TAP transporter associated with antigen presentation
TCR T cell antigen receptor
TDL thoracic duct lymphocyte
TNF tumour necrosis factor
TREC T cell receptor excision circle
V immunoglobulin variable region
Chapter 1
Thymocyte Development
William Jenkinson, Eric Jenkinson, and Graham Anderson
Abstract T cell developmentwithin the thymus involves the dynamic interaction of
thymocytes with a unique heterogeneous microenvironment formed predominantly
by a three-dimensional network of specialized thymic epithelium. Multiple devel-
opmental checkpoints have been identified during thymocyte maturation, including
selective recruitment to the thymus, ˛ˇ versus ı T cell fate decisions, positive
and negative selection and finally regulated egress of mature T cells from the thy-
mus to the periphery. The controlled migration of thymocytes within the thymus
ensures that developing T cells undergo a series of tightly-regulated interactions
with stromal cells of the thymus, ensuring that, firstly, only cells bearing a func-
tional TCR are selected for survival and onward differentiation via positive selection
and, secondly, that autoreactive T cells capable of responding to self-antigens and
causing autoimmune disease are deleted via negative selection. The stringent selec-
tion mechanisms enforced within the thymus are demonstrated by the fact that only
2–5% of thymocytes generated within the thymus mature to form na¨ıve T cells ca-
pable of forming a functional, self-tolerant component of the peripheral adaptive
immune system. Whilst many of the developmental processes occurring during thy-
mocyte development have become elucidated over the past several years, systems
directed towards modelling the dynamic migratory patterns and real-time cellular
interactions will radically advance our understanding of how such pivotal cells of
the immune system are generated.
Introduction
During T cell development, thymocytes undergo a programme of sequential
interactions with stromal cells of the thymus, predominantly of an epithelial na-
ture, providing essential developmental cues to ensure a carefully orchestrated
W. Jenkinson (
)
Medical Research Council Centre for Immune Regulation, Institute for Biomedical Research,
Medical School, University of Birmingham, Birmingham B15 2TT, UK
e-mail: w.e.jenkinson@bham.ac.uk
C. Molina-Par´ıs and G. Lythe (eds.), Mathematical Models and Immune Cell Biology,
DOI 10.1007/978-1-4419-7725-0
1,
c
Springer Science+Business Media, LLC 2011
1
2 W. Jenkinson et al.
maturational programme lasting 3–4 weeks [1]. Similar to B cells, thymocytes bear
a cell surface receptor capable of recognizing antigen, inducing cellular activation
and driving adaptive immune responses, although unlike B cells, T cells require
presentation of antigen by MHC class I and II. The huge diversity of potential
antigen that a single individual may encounter over the course of a lifetime requires
a highly efficient and specialized mechanism to ensure the production of sufficient
T cells, each bearing a receptor of a single specificity, to confer the ability to rec-
ognize and respond to such diversity of antigen. This variety of T cell receptors
(TCR) is generated during thymocyte development via the ability of individual cells
to rearrange multiple gene segments encoding the ˛ and ˇ-chains of the TCR in
a random fashion. Whilst the capacity to generate TCR diversity via random gene
recombination provides the capacity to produce a huge range of TCR specificities,
estimated at 10
15
, an intrinsic drawback of such a system is the potential to generate
multiple non-functional TCR arrangements and also TCRs capable of recognizing
the host’s own tissue and driving potential autoimmune responses. It is therefore
essential that a strict quality-control mechanism operates within organisms capable
of generating lymphocytes bearing randomly generated receptors. In most verte-
brates the thymus represents the site of selection, sorting the good from the bad and
ensuring that only useful T cells progress to populate the periphery and contribute
to immunological defence. As a result of this, while approximately 50 million thy-
mocytes are generated within the thymus every day, only around 1 in 20 thymocytes
survive the stringent selection events required to become a mature T cell.
The thymus until relatively recently, remained an organ of mystery. The essen-
tial function of the thymus in the generation of lymphocytes was established in the
1960s through pioneering research by Jacques Miller, demonstrating that neonatal
thymectomy resulted in immunodeficiency and furthermore indicating that the thy-
mus was a site where lymphocytes were selected and tolerance induced. Extensive
research into thymocyte developmentand thymus biology have begun to uncover the
nature of the mechanisms regulating T cell developmentand the cellular interactions
involved in this process. In this chapter, an overview of thymocyte development will
be provided summarizing the relationship between thymocyte and thymic microen-
vironment resulting in the generation of functional, self-tolerant T cells.
Thymic Microenvironments
The thymus represents a bilobed organ, located in the superior mediastinum of
the thorax anterior to the outflow tract of the heart. The mature thymus shows a
clear degree of compartmentalization, displaying both anatomically and function-
ally distinct regions of cortex and medulla (Fig. 1.1). A fibrous capsule surroundsthe
mature thymus, with a rich vascular network penetrating throughout the organ. The
parenchyma of the thymus consists predominantly of a unique three-dimensional
arrangement of epithelial cells providing a mesh-like network, within which de-
veloping T cells are able to migrate and receive essential signalling interactions.