Analysis Modelling Simulation Multiscale – NEMATIC

The objective of the project is to experimentally characterize, analyse, model and simulate the multi-scale dynamics of complex and growing branching random networks. Both analytical and numerical means as well as experimental realizations are used and developed. In a biological context, the growth of the filamentous fungus Podospora anserina will be used as a model, by systematically comparing modeling and experiments. The project brings together the project's biologists, who are specialists in this field, as well as physicists and mathematicians in charge of acquiring and analyzing experimental data and designing the models as well as simulations.

On the one hand, we plan to develop the numerical reconstruction of the network, by transforming the raw experimental data into a spatio-temporal graph, the dynamics of which will be included in an efficient labelling of the temporal evolution of the nodes, capable of interpreting anastomosis and branching, and thus of following through time and space a node of the network.
By varying the type of constraints applied during model validation, we expect a fine-grained understanding of emergent processes (such as branching) and resilience. NEMATIC aims to provide the scientific community with the experimental, theoretical and numerical data and tools necessary for such analyses.

We plan to develop simulations of network growth based on two approaches:
-- The first is based on "parsimony of means", while remaining as close as possible to the experimental data to extract the salient parameters driving the morphology of the filamentous network, as well as its dynamics.
-- The second is based on probabilistic tools, PDE and PDES, and will aim at a multi-scale description. This yields:
i) At the macroscopic level, to a fluid dynamics-type system (advection/reaction/diffusion equations with a memory source term) for the description of the thallus propagation front; ii) At the mesoscopic level with a multi-type stochastic growth-fragmentation model in which each "individual" represents a hypha segment between two branching points of the network, or between a branching point and an apex; iii) At the microscopic/molecular level with the modelling of the aggregation process of molecules generating a branching point by an approach based on Markov chains.