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Graduate Seminar on Modeling and Simulation with PDE - Selected Topics from cell biology and immunology

Biological organisms, and cells within multicellular organisms, critically depend on their microenvironment constituted by diverse chemical species as well as other cells and organisms. How can cells efficiently communicate by means of chemical ligands in conditions of fast diffusion? How can cells sense subtle concentration gradients given their small size? And how do stable spatio-temporal structures form and persist, as in the cases of cell polarization or the immunological synapse? All those questions lead to reaction-diffusion equations, often with high-dimensional and highly non-linear reaction terms. In this seminar, we consider examples from classic theoretical biophysics as well as recent data-driven models, and we will discuss mathematical and biological implications.

An important goal of the seminar will be to derive an understanding of how scientific questions in bio-medicine can be addressed using mathematical models, in this case PDE models.  Students will select a paper to present and discuss from a prepared list or based on their own interests (together with the instructor). The seminar will be broadly organized as follows:

  1. Introductory lecture – space-time problems in biology 
  2.  Biological pattern formation – Turing structures, cell polarization and the immunological synapse 
  3.  Morphogen gradients, detection limits and cell-to-cell signaling 
  4.  Optional additional topic: Chemotaxis 

Prerequisites: Bsc-level courses such as "Introduction to partial differential equations". Regarding the biological background, assistance will be provided by the instructor.