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Plenary
Speakers
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A. Fogelson (University of Utah, USA)
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P. Hogeweg (University of Utrecht, Netherlands)
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L. Keshet (University of British Columbia, Canada)
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P. Maini (University of Oxford, UK)
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J.D. Murray (University of Washington, USA)
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A. Stevens (Max Plank Institute, Leipzig, Germany)
Computational Modelling
of Blood Clotting: Platelet
Aggregation and Coagulation: A multiscale story of cells, flow,
mechanics, transport, and chemistry
Aaron Fogelson
University of Utah, USA
fogelson@math.utah.edu
Blood clotting
is an essential defence mechanism in response to trauma. Thrombosis is the
formation of clots within blood vessels and is the immediate cause of most
heart attacks and many other severe cardiovascular problems. The main components
of this process are platelet aggregation and coagulation. Platelet aggregation
involves processes of cell-cell and cell-substrate adhesion and cell signalling
and response, all within the moving blood. Coagulation involves a tightly-regulated
network of enzyme reactions with the important feature that many of the
key reactions occur on surfaces (e.g. platelet surfaces), not in the bulk
fluid, while transport of the reactants occurs in the fluid. Coagulation
results in the formation of a polymer mesh around the aggregating platelets.
Relevant scales range from the nanometer molecular scale to the micron cellular
scale to the millimeter blood vessel scale. This talk will introduce several
aspects of our efforts to model these complex dynamic biological systems,
discuss some of the modelling and computational challenges in this work,
describe some predictions made by the modelling, and outline plans for developing
more comprehensive models with which to further probe these critical processes.
Evolution of Morphogenesis:
The interface between generic and informatic processes
Paulien
Hogeweg
Utrecht University, Netherlands
p.hogeweg@bio.uu.nl
A hallmark
of biotic systems is the occurrence of interactions between processes at
different space and time scales. I will discuss models that try to capture
this property of biotic systems and explore its consequences. I will focus
on morphogenesis, examining models that explore the interface between mechanical
interactions between cells and informatic processes on the time scales of
gene regulation and evolution. I analyze the model behavior in terms of
mechanisms of morphogenesis, cell differentiation, and evolutionary dynamics.
I will show that inheritance of phenotype is not automatic, even in non-varying
environment. However, during evolution the inheritance of phenotype, and
thus the primacy of inherited information, will increase.
Modelling
Type-1 (autoimmune) Diabetes
Leah Keshet
University of British Columbia, Canada
keshet@math.ubc.ca
Coauthor(s): A.F.M.
Maree, P. Santamaria, D. Finegood, B. O'Brien, M Labecki
Type-1 Diabetes
(T1D) is an autoimmune disease that affects predominantly young people,
with severe consequences. In this disease, the body's immune system destroys
the essential insulin-producing pancreatic beta cells.
Our group has worked on a number of modelling efforts directed at understanding
T1D, and interpreting experiments and data. I will survey some of our problems
and results, including models of avidity maturation of autotoxic T-cells that
kill the beta cells (work by Stan Maree), and implications for artificial
peptide therapy (experiments by the group of Pere Santamaria). I will also
discuss our work on the differences in macrophages in normal (Balb/c) and
diabetes-prone (NOD) mice (experiments by group of Finegood).
Finally, I will show how simple models also help to interpret experimental
measurements with tetramers that are used to find the on- and off-rates for
the T-cell receptors (TCR's) binding to MHC-peptide.
A
multiple scale model for tumour growth
Philip Maini
Oxford University, UK
maini@maths.ox.ac.uk
Coauthor(s): T. Alarcon
and H.M. Byrne
We have recently
started to work on modelling tumour growth on the multiple scale level,
with a view to understanding how processes at the molecular level affect
tissue dynamics. This is achieved via a hybrid cellular automaton approach,
in which sub-cellular processes are modelled by ordinary differential equations,
cells are modelled as automaton elements, and extracellular processes are
represented by partial differential equations. Preliminary results of this
work will be presented.
Modelling Marital
Interaction: divorce prediction and marital therapy
James Murray
University of Washington & University of Oxford, U.S.A.
murrayjd@amath.washington.edu
Mathematical
modelling is now found in practically all branches of the biomedical sciences
with the glaring exception of psychology. I shall describe one such application
and suggest that psychology is another fruitful field for the application
of mathematical modelling.
About two thirds of marriages end in divorce in a 40 year period with the
divorce rate for second marriages even worse, about 75%. Previous attempts
at predicting marriage dissolution tend to be based on mismatches in the couple's
personalities or areas of agreement; these attempts have not been very successful.
We have developed a simple mathematical model based on only a few parameters
descriptive of specific marital interaction patterns, such as the difference
between positivity and negativity. The model has turned out to be surprisingly
accurate in its predictions.
I shall describe the model and how a couple's interaction data are collected
and built into the model. I shall show graphically how the model is used and
a couple's parameters determined. Armed with these, I shall then show what
they predict for a couple's marital future. Analysis of the model and data
show that there are essentially only five types of marriage interaction styles
each with its own prediction as to marital permanence. In a large sample of
marriages in Washington State our prediction as to which couples would divorce
within a 4-year period was 94% accurate.
A practical consequence of this mathematical approach is that it suggests
specific marital therapy, an example of which I shall describe. The procedure
is currently being used in clinical practice with encouraging results.
Structure and Function:
Interacting Cell Systems
Angela Stevens
Max-Planck-Institute for Mathematics in the Sciences, Leipzig,
Germany
stevens@mis.mpg.de
Cell
systems, which build up defined structures, as in tissues, organs and in self-organizing
microbiological populations, do so by a complex interplay of several mechanisms.
Among them are, cell signalling, cell growth, cell death, and cell motion,
whose specific functioning and malfunctioning often results in clearly distinguishable
patterns at the population level. A major question in this context is, how
can the underlying functioning of the respective cell system be deduced from
this macroscopic information observed by experimentalists?
Examples will be presented for the analysis of such kind of inverse questions
for signal dependent motion in interacting cell systems.
Spatiotemporal
Patterning of Cyclic Field Voles
Jonathan
Sherratt
Heriot-Watt University, UK
jas@ma.hw.ac.uk
Field
data from Kielder Forest (Northern UK) reveals patterns of periodic travelling
waves in the population of field voles (Microtus agrestis). I will discuss
the use of mathematical modelling to study the mechanism underlying this
spatiotemporal pattern. I will show that the wave can be explained by the
large reservoir, Kielder Water, in the centre of the forest. Moreover, I
will show that such large-scale landscape features act as a generic mechanism
for periodic wave formation in cyclic populations. I will discuss how the
size and shape of the landscape feature affects the wave speed and wave
length, and how two waves generated by different landscape features interact.
