Non-local models of cell-cell adhesion
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When cells in a tissue exert traction forces, they pull on one another and on the underlying matrix, much like a tug of war. I describe this process using non-local PDEs.
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Published:
When cells in a tissue exert traction forces, they pull on one another and on the underlying matrix, much like a tug of war. I describe this process using non-local PDEs.
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Published:
I consider models of intra-cellular signalling in cell polarization, that control how a cell determines its front and back. The objective is to uncover how cell-cell interactions, intracellular signalling, forces, and adhesion affect cell polarity and lead to the emergence of collective cell behaviour, in small to large cell groups.
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Published in Theortical Ecology, 2017
This paper investigates the suitability of a castrating barnacle parasite for control of the European green crab. Read more
Recommended citation: Bateman, A.W., Buttenschön, A., Erickson, K.D., Marculis, N.G. Theor Ecol (2017) 10: 305. http://dx.doi.org/10.1007/s12080-017-0332-5
Published in Journal of Mathematical Biology, 2017
Derivation of non-local cell-cell adhesion models from a stochastic space-jump process. Read more
Recommended citation: Buttenschön, A., Hillen, T., Gerisch, A., Painter, K.J. J. Math. Biol. (2018) 76: 429. https://doi.org/10.1007/s00285-017-1144-3
Published in Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes, 2017
Agent-based models (ABMs) of multicellular systems are models in which each cell is represented individually. These models allow taking the variability between individual cells and the spatial heterogeneity of tissues on histological scales into account. In this chapter we present an overview and methodology of ABMs that are used to simulate mechanical and physiological phenomena in cells and tissues. Read more
Recommended citation: Drasdo, D., Buttenschön, A. and Van Liedekerke, P., 2018. Agent-based lattice models of multicellular systems: numerical methods, implementation, and applications. In Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes (pp. 223-238). Academic Press. https://doi.org/10.1016/B978-0-12-811718-7.00012-5
Published in Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes, 2017
Lattice-free agent-based models (ABMs) of multicellular systems are mathematical models in which each cell is represented individually and can move continuously in space. In this chapter we present an overview of the methodology of ABMs that are used to simulate mechanical and physiological phenomena in cells and tissues. Read more
Recommended citation: Van Liedekerke, P., Buttenschön, A. and Drasdo, D., 2018. Off-lattice agent-based models for cell and tumor growth: numerical methods, implementation, and applications. In Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes (pp. 245-267). Academic Press. http://doi.org/10.1016/B978-0-12-811718-7.00014-9
Published in University of Alberta, 2018
In my dissertation, I explore models of non-local effects in biological systems. To study these nonlocal phenomena, I use iPDEs. The thesis has three chapters: (1) a derivation of non-local models from an underlying stochastic random walk; (2) an analysis of the steady-states of a non-local model of cell-cell adhesion; and (3) the construction of no-flux boundary conditions for a non-local model of cell-cell adhesion. Read more
Recommended citation: Buttenschoen, A. (2018). Integro-partial differential equation models for cell-cell adhesion and its application. https://doi.org/10.7939/R3M902J30
Published in European Journal of Applied Mathematics, 2018
In a singularly perturbed limit, we analyze the existence and linear stability of steady-state hotspot solutions for an extension of the 1-D three-component reaction-diffusion (RD) system … Read more
Recommended citation: Buttenschoen, A., Kolokolnikov, T., Ward, M.J. and Wei, J., 2019. Cops-on-the-dots: The linear stability of crime hotspots for a 1-D reaction-diffusion model of urban crime. European Journal of Applied Mathematics, pp.1-47. https://doi.org/10.1017/S0956792519000305
Published in SIAM Journal on Applied Mathematics, 2019
For the one dimensional Armstrong model of cell-cell adhesion, we derive various types of adhesive, repulsive, and no-flux boundary conditions. We prove local and global existence and uniqueness for the resulting integro-differential equations. Read more
Recommended citation: Hillen T., Buttenschön, A. SIAM Journal on Applied Mathematics (2020) https://epubs.siam.org/doi/abs/10.1137/19M1250315
Published in Journal of Mathematical Biology, 2019
Correlated random walks (CRW) have been explored in many settings, most notably in the motion of individuals in a swarm or flock. But some subcellular systems such as growth or disassembly of bio-polymers can also be described with similar models and understood using related mathematical methods. Here we consider two examples of growing cytoskeletal elements, actin and microtubules. Read more
Recommended citation: Buttenschön, A. & Edelstein-Keshet, L. J. Math. Biol. (2019) https://doi.org/10.1007/s00285-019-01416-6
Published in Bulletin of Mathematical Biology, 2019
Intra-cellular pattern formation determines single cell migration in a mechanochemical model. Read more
Recommended citation: Buttenschön, A., Liu Y., Edelstein-Keshet, L. Bull. Math. Bio. (2020) https://link.springer.com/article/10.1007/s11538-020-00702-5
Published in arXiv, 2020
Symmetries and global bifurcations of the linear cell-cell adhesion model. Read more
Recommended citation: Buttenschön, A., and Hillen, T. arXiv preprint arXiv:2001.00286. (2020) https://arxiv.org/abs/2001.00286
Published in arXiv, 2020
Cancer cells exhibit increased motility and proliferation, which are instrumental in the formation of tumours and metastases. These pathological changes can be traced back to malfunctions of cellular signalling pathways, and calcium signalling plays a prominent role in these. We formulate a new model for cancer cell movement which for the first time explicitly accounts for the dependence of cell proliferation and cell-cell adhesion on calcium. Read more
Recommended citation: Kaouri, K., Bitsouni, V., Buttenschön, A., & Thul, R. arXiv preprint arXiv:2003.00612. (2020) https://arxiv.org/abs/2003.00612
Published in PLOS Computational Biology, 2020
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. Read more
Recommended citation: Buttenschön A, Edelstein-Keshet L PLOS Computational Biology 16(12): e1008411 (2020)
Published in CMS/CAIMS Books in Mathematics, 2021
Symmetries and global bifurcations for non-local models of cell adhesion. Read more
Recommended citation: Buttenschön, A., and Hillen, T. (2021) https://www.springer.com/gp/book/9783030671105
Published in Bulletin of Mathematical Biology, 2021
Recommended citation: Buttenschön, A., Edelstein-Keshet, L. Bull. Math. Bio. (2022) https://link.springer.com/article/10.1007/s11538-022-01053-z
Published:
Talk on my thesis work on the steady-states of a non-local model for cell-cell adhesion at “Mathematical Challenges in the Analysis of Continuum Models for Cancer Growth, Evolution and Therapy”. Read more
Undergraduate courses, University of Alberta, Department of Mathematics and Statistical Sciences, 2013
Teaching Assistant at the University of Alberta. Read more
Undergraduate courses, University of British Columbia, Department of Mathematics, 2018
Instructor at University of British Columbia. Read more
Undergraduate courses, University of Massachusetts Amherst, Department of Mathematics and Statistics, 2022
Instructor at University of Massachusetts Amherst. Read more
Undergraduate course, University of Massachusetts Amherst, Department of Mathematics and Statistics, 2024
A second applied course in linear algebra. Read more