Mathematical Modelling of Cell Migration and Polarization
Doktorsavhandling, 2020

Cell migration plays a fundamental role in both development and disease. It is a complex process during which cells interact with one another and with their local environment. Mathematical modelling offers tools to investigate such processes and can give insights into the underlying biological details, and can also guide new experiments.

The first two papers of this thesis are concerned with modelling durotaxis, which is the phenomena where cells migrate preferentially up a stiffness gradient. Two distinct mechanisms which potentially drive durotaxis are investigated. One is based on the hypothesis that adhesion sites of migrating cells become reinforced and have a longer lifespan on stiffer substrates. The second mechanism is based on cells being able to generate traction forces, the magnitude of which depend on the stiffness of the substrate. We find that both mechanisms can indeed give rise to biased migration up a stiffness gradient. Our results encourages new experiments which could determine the importance of the two mechanisms in durotaxis.

The third paper is devoted to a population-level model of cancer cells in the brain of mice. The model incorporates diffusion tensor imaging data, which is used to guide the migration of the cells. Model simulations are compared to experimental data, and highlights the model’s difficulty in producing irregular growth patterns observed in the experiments. As a consequence, the findings encourage further model development.

The fourth paper is concerned with modelling cell polarization, in the absence of environmental cues, referred to as spontaneous symmetry breaking. Polarization is an important part of cell migration, but also plays a role during division and differentiation. The model takes the form of a reaction diffusion system in 3D and describes the spatio-temporal evolution of three forms of Cdc42 in the cell. The model is able to produce biologically relevant patterns, and numerical simulations show how model parameters influence key features such as pattern formation and time to polarization.

Opponent: Prof. Helen Byrne, Mathematical Institute, University of Oxford, United Kingdom.


Adam Malik

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis

Journal of Mathematical Biology,; Vol. 78(2019)p. 2289-2315

Artikel i vetenskaplig tidskrift

The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration

Bulletin of Mathematical Biology,; Vol. 82(2020)

Artikel i vetenskaplig tidskrift

Malik, A.A., Rosén, E., Kundu, S., Krona, C., Nelander, S., Gerlee, P. Modelling glioblastoma growth in a xenograft mouse model using diffusion tensor imaging.

Borgqvist, J., Malik, A.A., Lundholm, C., Logg, A., Gerlee, P., Cvijovic, M. Cell polarization in a bulk-surface model can be driven by both classic and non-classic Turing instability

Utveckling av homogeniseringsmetoder för multicellulära system

Vetenskapsrådet (VR), 2015-01-01 -- 2018-12-31.

Hierarkiska mixed effects-modeller av dynamiska system

Stiftelsen för Strategisk forskning (SSF), 2014-04-01 -- 2019-06-30.

Stiftelsen för Strategisk forskning (SSF), 2019-09-01 -- 2020-06-30.




Annan matematik


Grundläggande vetenskaper


Hälsa och teknik



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4814


Chalmers tekniska högskola



Opponent: Prof. Helen Byrne, Mathematical Institute, University of Oxford, United Kingdom.

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