Valeria Caliaro, A 2D hybrid agent-based/continuum model for the regeneration of axolotl spinal cord
Tissue response after amputation induces either scar formation or regeneration and, in particular, regeneration has been observed and described in axolotl. However, what are the mechanisms implicated in the regulation of regenerative processes and what is their role remains poorly understood. Our goal is to develop a numerical model for tissue regeneration and to use it to explore the main mechanisms influencing spinal cord regeneration in axolotl. In particular, we developed a 2D hybrid model where individual 2D spheres interact via mechanical repulsion with their close neighbours (agent-based model) and divide randomly with a division rate depending on a chemical signal diffusing through the tissue (continuous field). In this talk, first we will recapitulate some results obtained in previous works. Then, we will describe our model and validate it by recovering experimental results. Finally, we will numerically explore the behaviour of solutions as function of the parameters in order to identify the main mechanisms in tissue regeneration.
Mete Demircigil, Aerotactic Waves in Dictyostelium discoideum : When Self-Generated Gradients engage with Expansion by Cell Division
Using a self-generated hypoxic assay, it is shown that Dictyostelium discoideum displays a remarkable collective aerotactic behavior: when a cell colony is covered, cells quickly consume the available oxygen and form a dense ring moving outwards at constant speed and density.
We propose a simple, yet original PDE model with the hypothesis that cells have two distinct behaviors depending on the surrounding oxygen levels : either they undergo cell division, or they move upwards the oxygen gradient. This leads to a system of parabolic PDEs, with one having coefficients constant by piece. The approach is very fruitful as it leads to an explicit characterization of traveling wave solutions, a qualitative analysis of the phenomenon, as well as an explicit and novel formula of the collective migration speed of cells that encapsulates a surprising combination of expansion by cell divison, such as described by the Fisher/KPP equation, and aerotaxis. Furthermore, the model exhibits a remarkable dichotomy between pulled waves and pushed waves as a function of the parameters of the model. The analysis shows that collective migration is caused by the interaction between cell division and the modulation of aerotaxis. The modeling approach and its conclusions complement and are in turn confirmed by an experimental study of the collective behavior of cells. This is joint work with Christophe ANJARD Vincent CALVEZ, Jean-Paul RIEU, Olivier COCHET-ESCARTIN and is a subpart of the work presented in the preprint bioRxiv 2020.08.17.246082; doi: https://doi.org/10.1101/2020.08.17.246082.
Sophie Hecht, On the modelling of the morphogenesis of bacteria micro-colony
Bacteria are abundant organisms whose roles are included in many processes such as medicine, agriculture, ecology, industry… From a single organism, they quickly develop into organised micro-colonies and biofilm structures. The formation of these microcolonies, while broadly studied in the past decade, is still poorly understood. We first consider an individual-based model for the growth of rod-shaped micro-colony. Each bacterium is modelled by a spherocylinder and bacteria interact only through non-overlapping constraints. Introducing asymmetric friction and mass for the bacterium, which are taking into account the asymmetry of the pole of the bacteria, we retrieve mechanical behaviours of micro-colony growth, this without implementing attraction or adhesion. We compare our model to various sets of experiments, discuss our results, and propose several quantifiers to compare model to data in a systematic way. We then investigate the micro-macro limit for these type of individual-based model.