Mathematical models of living tissues

24.10.2018, 14:00 Uhr  –  Haus 9, Raum 2.22

Anna Marciniak-Czochra (Universität Heidelberg), Marie Doumic (Inria, CNRS and Sorbonne Université, Paris)

14:00 Marie Doumic: Modelling protein polymerisation: results and open questions
15:00 Tea and Coffee break
15:30 Anna Marciniak-Czochra: Mathematics of stem cells


Marie Doumic: Modelling protein polymerisation: results and open questions
Mathematical modelling of protein polymerisation is a challenging topic, with wide applications, from actin filaments in myocytes (muscle tissues) to the so-called amyloid diseases (e.g. Alzheimer's, Parkinson's or Creuzfeldt-Jakob's diseases).
In this talk, we will give an overview of recent results for both deterministic - where statistical mechanical fluctuations arising from intrinsic noise are negligible - and stochastic approaches, envisaged as giving complementary insights on the still largely mysterious intrinsic mechanisms of polymerisation. A data assimilation approach is developed in parallel of more specific methods for fragmentation estimation.

Anna Marciniak-Czochra: Mathematics of stem cells
In this talk I will discuss two different approaches in modelling of cell self-renewal and differentiation in a regenerating tissue. Hierarchical structures of cell production systems are usually modelled using systems of ordinary differential equations, each of which describes a discrete differentiation stage. However, there is evidence that cell fate transitions may be continuous processes, which can be described using transport equations. A crucial question is whether the continuous nature of these transitions may have an impact on the observed system dynamics. I will present two classes of mathematical models describing the production of white blood cells and discuss the differences in model dynamics stemming from the different mathematical structure. In the second part, I will discuss computer experiments using an optimal design approach. Here, one typical application is black-box optimization: Consider a complicated computer code (the black-box function), which takes several inputs and requires several hours to return a single output. We want to maximize the black-box, using a limited number of function calls by means of a sequential approach. This approach requires solving large-scale optimal design problems, and I will discuss new efficient algorithms to do so.

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