Differentiation and stemmness, in cell migration, cancer invasion, and development

eSMB2020 eSMB2020 Follow Wednesday at 9:30am EDT
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Nikolaos Sfakianakis, Linnea C. Franssen


As the mathematical research of cancer is entering a mature stage, the efforts of the community focus on the transfer of information between the various relevant biological scales. With this in mind, we bring together researcher working in experimental and theoretical biology as well as mathematics in the aim to shed some light in mathematical approaches that are able to bridge the different scales. Central role in our minisymposium will play the presentation by Robert Insall —experimental and theoretical biologist working on cell migration— where he will be speaking about the most recent work in his lab in reverse chemotaxis. Subsequently Niklas Kolbe —mathematician working in epithelial-to- mesenchymal transition— will discuss an intracellular stochastic model describing of TGF-β signalling that they have developed in collaboration with the Institute of Molecular Biology in Mainz. In a higher scale, Cicely Macnamara— mathematician working on multiscale cancer invasion models— will discuss a hybrid atomistic-macroscopic coupling atomistic cancer cell migration with collective cancer cell invasion. In the higher scale, Filip Klawe —mathematician working on the macroscopic description of stem cells specification— will provide a mathematical framework for the study of evolving signal concentrations in evolving domains. It is expected that during this mini-symposium the participants (speakers and organisers) will establish a communication network between them and foster new research collaborations. It is moreover expected that it will draw the attention of the participants as it addresses several of the current difficulties in the mathematical study in cell differentiation and stemmness.

Luke Tweedy

Beaton Institute of Cancer Research, Glasgow
"Seeing around corners: Cell migration is determined by the complex interaction of environmental topology and attractant degradation"
Cell migration is often guided by gradients of attractants. Many cells are known to degrade the molecules that attract them, creating dynamic gradients that evolve and change as the cells migrate up them. In unrestricted environments, this enables more robust directed migration over much greater distances than can be explained by chemotaxis to an externally imposed gradient. However, its effects in a complex topology remain unclear. This is important to understand, because the in-vivo topologies in which cells migrate are almost invariably complex. We therefore modelled the behaviour of cells solving a variety of mazes, varying dead end lengths and complexities. We then tested each design experimentally. We found specific rules governing the collective decisions of cells connecting cell speed, attractant diffusivity and dead-end length and complexity. We even found topologies in which a majority of cells would favour a dead end over a path to a large attractant reservoir. This self-generated view of chemotaxis in complex environments will help us better understand immune responses and the patterns of metastasis for some cancers.

Niklas Kolbe

Faculty of Mathematics and Physics, Kanazawa University, Japan
"Stochastic modelling of TGF-β signalling in single cells"
The cytokine TGFb plays an important role in cancer progression as it can both prevent uncontrolled tissue growth and trigger epithelial-to-mesenchymal transition. To better understand the intracellular responses of the cells to the cytokine we have developed a stochastic model that we present in this talk. This model explains heterogeneous signaling dynamics between the cells found in experimental data where time-resolved measurements at the single-cell level were taken. We elaborate on our parameter estimation technique considering the distribution of features in the time paths and demonstrate the accordance of model simulation and measurement data. Joint work with Lukas-Malte Bammert (JGU Mainz), Stefan Legewie (IMB Mainz), Maria Lukacova (JGU Mainz), Lorenz Ripka (IMB Mainz)

Cicely Macnamara

School of Mathematics and Statistics, University of St. Andrews, UK
"Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue"
The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individual-based model which allows one to simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary blood-vessel network or along the striations of fibrous tissue.

Filip Klawe

Institute of Applied Mathematics, Heidelberg University, Germany
"Mathematical model of stem cell specification in a growing domain"
We will study a mathematical framework for analysis and simulation of development of stem cell based, growing organs with cell self-renewal and differentiation regulated by signalling factors. Considered model consists of PDEs which describe concentrations of signals in moving domain Ω(t) and ODEs. One of the ODEs describes evolution of domain Ω(t) The main novelty of our work is a coupling between of PDEs solutions and deformation of the domain. There is no general approach which allow us to obtain mathematical results for such phenomena. However, assuming that Ω(t) is a circle and it is changing uniformly in all directions we are able to prove existence and uniqueness of solution. The considered model may be used to describe the signal concentration (and domain evolution) of shoot apical meristem of arabidopsis thaliana. We present numerical simulations which show that model fits to its biological origin.

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