Plenary Speakers

Plenary Speakers


A. Fogelson (University of Utah, USA)

P. Hogeweg (University of Utrecht, Netherlands)

L. Keshet (University of British Columbia, Canada)

P. Maini (University of Oxford, UK)

J.D. Murray (University of Washington, USA)

A. Stevens (Max Plank Institute, Leipzig, Germany)

The Okubo Prize Winner (2003) - Jonathan A. Sherratt (Heriot-Watt University, UK)


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

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

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

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

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.

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,

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

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.