ICMS

Apr 14, 2010 - Apr 21, 2010

14 India Street, Edinburgh

Organisers

Name	Institution
Bournaveas, Nikolaos	University of Edinburgh
Painter, Kevin	Heriot-Watt University
Perthame, Benoit	Universite Pierre et Marie Curie

Scientific Committee

Nikolaos Bournaveas, University of Edinburgh
Peter Markowich, University of Cambridge
Kevin Painter, Heriot-Watt University
Benoit Perthame, Universite Pierre et Marie Curie
Christian Schmeiser, University of Vienna

Cell motion and tissue organisation are crucial to a range of biological processes, including tumour growth, tissue repair, embryonic development and biofilm development. Recent years have witnessed rapid growth in the modelling of these phenomena and have led to a number of novel mathematical models. Mathematical analysis can not only play a crucial role in understanding the resulting theoretical structures but directly impacts on the modelling and provides insight into the mechanistic bases of these processes.

A classical case example is chemotaxis, the directed motion of cells in response to chemical gradients. Mathematical attempts to model chemotaxis date to Patlak in the 1950s and Keller and Segel in the 1970s. The Keller and Segel model consists of a system of coupled parabolic equations for the cell density and the concentration of the chemical signal. The rigorous study of this parabolic system presents a multitude of challenges requiring significant use of methods from mathematical analysis, because blow-up may occur above a critical mass. While the Keller-Segel model provides a macroscopic description of cell migration in the presence of a chemical, it does not take into account the behaviour of individual cells and a variety of microscopic approaches have been developed, for example those using kinetic theory. Tissue mechanics also results from cell arrangements and most of the effects of biological interest have to take into account their movement and multiplication.

 

Arrangements

The workshop will be divided into two parts:

• Instructional Conference, Wednesday 14 April - Saturday 17 April
• Research Workshop, Monday 19 April - Wednesday 21 April

 

Instructional Conference arrangements 14-17 April

Mini courses during the instructional conference will be given by:

Vincent Calvez
Title: Mathematics for collective cell motion: analysis and modeling issues

Mark Chaplain
Title: Mathematical modelling of cell migration in cancer growth and development

Hans Othmer
Title: Modeling and analysis of individual and collective cell movement
Abstract

Thomas Hillen
Title: Mathematical modelling of cell movement in network tissues
Abstract

Luigi Preziosi
Title: Mechanical aspects of tumor growth
Abstract

The instructional part of the conference is intended for PG students wishing to learn more about the area. Places are limited. The workshop will cover the cost of accommodation throughout the duration of the two parts of the workshop, as well as some local costs. More details will be communicated to accepted participants.

The application period for the instructional conference has now closed. For questions please contact Helene Frossling; please see e-mail address below.

 

CANPDE Workshop arrangements 19-21 April

The participation in the workshop part of the conference is limited to particpants of the instructional workshop and to invitees.

Questions about both parts of the workshop can be sent to Helene Frossling (Conference Co-ordinator) by e-mail: helene.frossling@icms.org.uk.

Speakers at the workshop will be:

R. E. Goldstein (Cambridge)
K. Weijer (Dundee)
R. Voituriez (Paris VI)
J. Sherratt (Heriot-Watt)
J. R. King (Nottingham)
T. Suzuki (Osaka)
K. Ichikawa (Osaka)
Y. Murakami (Tokyo)
T. Souganidis (Chicago)
Y. Lou (Ohio State)
E. Grenier (Lyon)
C. Schmeiser (Vienna)
P. Markovich (Cambridge)
D. Oelz (Vienna)
R. Erban (Oxford)
M. Doumic Jauffret (INRIA)

Programme

The programme is currently under construction.

 Delegates are advised that the instructional conference is scheduled to start with registration at around 9.00 on Wednesday 14 April, and the research workshop at 9.00 on Monday 19 April. The workshop is expected to end around 17.00 on Wednesday 21 April. 

Presentations:

Presentation Details
Doumic Jauffret, Marie
Aggregation models for neurodegenerative diseases: direct and inverse problem
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abnormal protein aggregation is at the origin of a number of neuro-degenerative diseases, e.g. Prion (Madcow), Huntington or Alzheimer diseases. This phenomenon can be described mathematically either in a discrete or in a continuous setting, by equations of fragmentation-coagulation type. We review here some results and some open problems on the study of prion proliferation equations.
Erban, Radek
From Stochastic Models to Macroscopic PDEs
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I will analyse several stochastic simulation algorithms suitable for modelling reaction, diffusion and taxis processes in biology. Both on-lattice and off-lattice models, and their connections with deterministic (macroscopic) PDE models will be discussed.
Ichikawa, Kazuhisa
Molecular interactions and their modeling at the invasion front, invadopodia
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Invadopodium is a protrusion at the invasion front of a cancer cell. The formation of invadopodium is caused by the reorganization of cytoskeletal molecule actin. At the invadopodia, a protein MT1-MMP are expressed, and this causes the degradation of extracellular matrix (ECM), and finally the cell body is free from neighboring cells and ECM by cleaving adhesion molecules between them. Reorganization of actin, expression/activation of MT1-MMP and cleavage of adhesion are controlled through complicated enzymatic reactions. We will present a theory and simulation results of stochastic simulation for these events showing nonlinear molecular dynamics in the protein interactions.
King, John
PDE modelling of growing biological tissue
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Multiphase-continuum-mechanical approaches to the modelling of biological tissue growth will be described and some novel aspects of the resulting PDEs highlighted.
Lou, Yuan
Nonrandom dispersal of interacting species in heterogeneous landscapes
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Dispersals of organisms are key component of ecological and evolutionary processes and have a great deal of importance in solving conservation problems as well. From habitat degradation and climate change to spatial spread of invasive species, dispersals play a central role in determining how organisms cope with a changing environment. The dispersals of many organisms depend upon local biotic and abiotic factors and as such are often nonrandom. In contrast with random movements which are well understood from theoretical perspectives, we have limited knowledge of the consequences of nonrandom dispersal, especially in the context of the spatial dynamics of interacting species. This talk will focus on the effects of non-random dispersal on competing species in heterogeneous environments via reaction-diffusion advection models. Previous studies show that if two competing species adopt biased movement in response to habitat quality, there can be selection against both small and large advection rates. Is there some intermediate advection rate which is evolutionarily stable? If random dispersal rate and biased movement rate represent values for two different traits of species, how will two traits simultaneously evolve?
Murakami, Yoshinori
Involvement of a cell adhesion molecule CADM1/TSLC1 in oncogenesis
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Aberration of cell adhesion is a critical step in the invasion and metastasis of human cancer. A tumor suppressor gene, CADM1/TSLC1, was originally identified in non-small cell lung cancer (NSCLC) by functional complementation. CADM1 encodes an immunoglobulin superfamily cell adhesion molecule homologous to nectins and is expressed in the brain, testis, lung and many other epithelial tissues. In contrast, CADM1 is inactivated in 30-60% of various cancers in advanced stages, including NSCLC, suggesting that loss of CADM1 is involved in invasion and metastasis. Correspondingly, CADM1 is primarily involved in the formation of an epithelial cell structure and associates with an actin-binding protein, 4.1B, and the membrane associated guanylate kinase homologs, providing a novel tumor suppressor cascade. 　CADM1 also suppresses epithelial-mesenchymal transition (EMT) of MDCK cells treated with HGF. The Cadm1-gene deficient mice show male infertility caused by disruption of cell adhesion between spermatocytes and Sertoli cells. 　Furthermore, both Cadm1-/- and Cadm1+/- mice develop lung adenoma and adenocarcinoma spontaneously, indicating that this cascade is essential for lung tumor suppression. Unique features of CADM1-mediated cell adhesion in oncogenesis will be discussed.
Othmer, Hans G
Mathematical Problems in Embryonic Pattern Formation
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Pattern formation during development of an adult organism requires precise spatio-temporal control of gene expression, which involves complex signal transduction and control networks. In this talk we will first introduce techniques for the reduction of complex networks, for both deterministic and stochastic models of networks. We will then discuss the effects of various localization mechanisms on signaling and illustrate the interplay between reaction and transport in robust determination of boundaries between different tissue types.
Schmeiser, Christian
Analytic properties of a continuum model for the lamellipodium
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A two-phase continuum model for two families of locally parallel actin filaments describing the mechanics of the lamellipodium will be presented. Its variational nature and its relation to models for liquid crystals will be discussed.
Sherratt, Jonathan
Nonlocal Models for Pattern Formation and Cancer Invasion
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A number of key mechanisms regulating the dynamics of cell populations are intrinsically long-range. Examples are community effects in differentiation, and cellular adhesion, which is an important regulator of a variety of processes including cancer invasion. These long-range mechanisms have proved difficult to study using purely PDE models, and I will discuss a new approach to their study, via the inclusion of nonlocal terms. The resulting integrodifferential equations pose a range of numerical and analytical challenges, but provide a valuable tool for the study of the dynamics of cell populations. I will discuss specific IDE models for differentiation-controlled pattern formation and for cancer invasion. I will present new results, and will identify key challenges for future research. The work I will present is done in collaboration with Kevin Painter, Jenny Bloomfield and Nicola Armstrong (all Heriot-Watt University).
Suzuki, Takashi
ECM degradation - a topdown modeling of MT1-MMP metalloproteinase
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We present the method of bi-directed modeling in the study of the early stage of tissue invation at the cell level. First, several positive feedback loops are noticed in the integrated pathways and then the formation of peeks are recovered by the bottom up approach. Then a topdown model involving the switching process recovers this phenomenon.
Voituriez, Raphael
Modeling cytoskeleton dynamics : mechanisms of cell polarization and motility
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I will first present a phenomenological coarse-grained model of the cell cytoskeleton, viewed as a visco-elastic medium driven out-of-equilibrium by ATP hydrolysis. I will show that this model of "active gel" leads to a rich phase diagram, and in particular to spontaneous hydrodynamic flows -- and therefore macroscopic motion -- in absence of external forcing. Applications to cell motility will be discussed. Next I will discuss the effect of the out-of-equilibrium forcing by ATP hydrolysis on intracellular transport. I will show on a simple model that such "active" transport can give rise to instabilities in the distribution of molecular markers in cells, and therefore induce a mechanism of cell polarization.
Weijer, Kees
Cell-cell signalling and chemotactic cell movement during development
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We investigate the molecular mechanisms by which cells produce and detect chemotactic signals and translate this information in directed coordinated movement up or down chemical gradients in the social amoebae Dictyostelium discoideum, and during gastrulation in the chick embryo. During Dictyostelium development hundreds of thousands of cells aggregate chemotactically to form a fruiting body. Chemotactic cell migration during all stages of development is controlled by propagating waves of the chemo-attractant cAMP. Using a variety of imaging techniques we analyse the spatio-temporal dynamics of cAMP mediated cell-cell signalling and the resulting chemotactic cell movement responses to understand how the interactions beween cell-cell signalling and movement govern the multi-cellular organisation of this organism. Investigation of mutants that change cAMP cell-cell signalling dynamics and the organisation and function of the actin-myosin cytoskeleton affecting chemotactic movement, show how cellular heterogeneity in signalling dynamics and polarised activation of the actin-myosin cytoskeleton drive aggregation, cell sorting, slug formation and migration. Hypothesis are tested by detailed model calculations. Chemotactic cell movement also plays a critical role during gastrulation in the chick embryo. Our experiments show that epiblast cell movement during the formation of the primitive streak as well as the movement of the mesoderm cells after their ingression through the streak is controlled by a combination of attractive and repulsive guidance cues. We have identified FGF4 and VEGFA as attractive cues for mesoderm cells, while FGF8 and Wnt’s act as repulsive signals. We are currently trying to establish how signalling and movement interact and use models to design experimentally testable hypotheses.

Participants

Name	Institution
Bakshi, Suruchi	University of Oxford
Blasselle, Alexis	Laboratoire Jacques-Louis Lions
Bloomfield, Jenny	Heriot-Watt University
Bournaveas, Nikolaos	University of Edinburgh
Calvez, Vincent	CNRS and ENS Lyon
Calvez, Vincent	CNRS and ENS Lyon
Doumic Jauffret, Marie	INRIA
Ebde, Mohamed Abderrahman	Wolfgang Pauli Institute
Enault, Séverine	ENS-Lyon
Erban, Radek	University of Oxford
Gabriel, Pierre	Laboratoire Jacques-Louis LIONS
Goldstein, Raymond E.	University of Cambridge
Hillen, Thomas	University of Alberta
Hunt, Gordon	Heriot-Watt University
Ichikawa, Kazuhisa	University of Osaka
Kershaw, Sophie	University of Oxford
King, John	University of Nottingham
Kollar, Richard	Comenius University
Lorz, Alexander	University of Cambridge
Lou, Yuan	Ohio State University
Meunier, Nicolas	Université Paris Descartes
Mirrahimi, Sepidehsadat	Laboratoire J-L Lions
Murakami, Yoshinori	University of Tokyo
Oelz, Dietmar	University of Vienna
Othmer, Hans G	University of Minnesota
Painter, Kevin	Heriot-Watt University
Perthame, Benoit	Universite Pierre et Marie Curie
Preziosi, Luigi	Politecnico di Torino
Schmeiser, Christian	University of Vienna
Sherratt, Jonathan	Heriot-Watt University
Souganidis, Takis	University of Chicago
Surulescu, Christina	University of Stuttgart
Suzuki, Takashi	Osaka University
Tang, Min	Université Pierre et Marie Curie
Ulikowska, Agnieszka	University of Warsaw
Vasilopoulos, Georgios	Heriot-Watt University
Voituriez, Raphael	Universite Pierre et Marie Curie
Weijer, Kees	University of Dundee
Winkler, Christoph	Universität Wien, Fakultät für Mathematik
Yates, Christian	University of Oxford