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Andreas Buttenschoen

Assistant Professor

Research areas include building bridges between the mathematical, computational, and biological sciences.

Current Research

Dr. Buttenschoen is an applied mathematician, building bridges between the mathematical, computational, and biological sciences. His strong foundations in each allow him to identify key biological problems, draw on and contribute to theoretical mathematical foundations, and develop advanced computational tools.

One specific current focus of his research is a mathematical characterization of collective cell migration and invasion, whether by single cells, strands of cells, detached clusters or whole tissue fronts (as in wound healing) (see Friedl et. al. 2012). The primary significance is to foster a deeper understanding of metastatic cancer. His role would be to describe using rigorous mathematics the biological, physical and chemical forces at play in tissue dynamics.

In more detail, Dr. Buttenschoen is interested in three particular research directions: (1) development of digital-twins for in-vitro and in-vivo experiments; (2) development of the next generation continuum limits of cell-based models; and (3) statistical methods to compare experimental data, cell-based models, and continuum models.

Swarms, flocks, and human societies all exhibit complex collective behaviours. Dr. Buttenschoen is interested in collective cell behaviours, which he views as swarms with a twist:

(1) Cells are not simply point-like particles but have spatial extent;

(2) Interactions between cells go beyond simple attraction-repulsion; and

(3) Cells “live” in a regime where friction dominates over inertia.

Examples include: wound healing, embryogenesis (normal development), the immune response, and cancer metastasis. He uses mathematical modelling and computational biology to uncover the universal principles how biological, physical, and chemical factors shape biological tissues.

Interactions in tissues range over several orders of magnitude in time and spatial scales. Distinct mathematical frameworks are appropriate for specific levels of detail. For instance, differential equations (DEs), tracking changes in cell (or protein) densities, are suitable for describing large populations. He uses dynamical systems, bifurcation theory, and group theory to analyse nonlocal DEs. On the other hand, to track the motion, behaviour, or forces produced by individual cells, a more detailed cell-based computational framework is needed. He refers to such models as cell-based models (CBMs).

Learn more at https://www.buttenschoen.ca/

Academic Background

  • BS (2012) Physics and Mathematics at University of Alberta
  • BSH (2013) Applied Mathematics at University of Alberta
  • PhD (2017) Applied Mathematics at University of Alberta
  • Post doctoral fellow at University of British Columbia Department of Mathematics (2018-2022)
Buttenschön, Andreas, and Leah Edelstein-Keshet. "Bridging from single to collective cell migration: A review of models and links to experiments." PLoS computational biology 16.12 (2020): e1008411.
Buttenschön, Andreas, and Leah Edelstein-Keshet. "Cell repolarization: A bifurcation study of spatio-temporal perturbations of polar cells." Bulletin of Mathematical Biology 84.10 (2022): 114.
Andreas Buttenschön and Hillen, Thomas. Non-Local Cell Adhesion Models: Symmetries and Bifurcations in 1-D. Springer, 2021.
Buttenschön, Andreas, Yue Liu, and Leah Edelstein-Keshet. "Cell size, mechanical tension, and GTPase signaling in the single cell." Bulletin of mathematical biology 82 (2020): 1-33.
Contact Info

Department of Mathematics and Statistics
LGRT 1525
710 N. Pleasant Street
Amherst, MA 01003-9292

Email: abuttenschoe@umass.edu