Internship proposal MASTER 2:   Mathematical modeling of biological tissue architecture emergence

Supervisors:  Sophie Hecht (CNRS, sophie.hecht@sorbonne-unviersite.fr ), Diane Peurichard (Inria Paris, diane.a.peurichard@inria.fr )

Location: LJLL, Sorbonne Université

Duration: 4 month starting march 2024

Scientific description: 

The objective of this internship is to develop and study a mathematical model for the modeling of various types of biological tissues (muscles, tendons, etc.). We

propose to develop an agent-centered 2D model involving a network of fibers dynamically connected and interacting via repulsion with their relatives

neighbors. In the context of adipose tissues [1], this modeling was used for the ECM matrix and made it possible to highlight the importance of mechanical constraints

in the emergence of fabric architecture. Initially, this internship will aim of going further in the analysis of this model, in particular on the influence of

edge conditions on the emergence of the overall organization of the network. This will allow subject the fabric to various types of mechanical challenges (tests of

traction/compression for example) and study the effect of external stresses on these reorganization capabilities. Secondly, we will focus on the co-

evolution of such a network with an increasing population of cells of various shapes (discs, segments, ellipses), to study the influence of the shape of the agents on

the emergence of patterns. By generalizing the known results in the case of interactions of spherical populations [2,3], this internship will allow us to go further into the

understanding of the emergence of complex architectures and will create a framework theory applicable to a large number of biological tissues.

Missions:

- Development of models and digital implementation of optimized code

(parallelization, GPU etc.). 

- Study of models by sensitivity analysis of parameters (numerical simulations)

via innovative methods based on machine learning (SHAP values).

- In-silico experiments and calibration and validation of models on data

experimental

Context

This internship will be developed in an interdisciplinary framework involving mathematicians. (LJLL, Paris) and biologists (RESTORE, Toulouse) who will provide data

experimental to validate the modeling hypotheses. The intern will be located at LJLL (Paris) and visits to our collaborators (Toulouse) will be considered according to the

project needs. The internship requires an advanced level of programming (matlab, python, Fortran90, C++ of your choice) and sensitivity to mathematical modeling for

biology. If the trainee wishes, a thesis can be considered for the start of the 2025 school year (it there is no funding at the moment but we will respond to calls for tenders).

How to apply

To apply, please send an email to sophie.hecht@sorbonne-unviersite.fr and to diane.a.perichard@inria.fr with a CV, a cover letter, your transcripts

and possible letters of recommendation.

References

[1] D. Peurichard, F. Delebecque, A. Lorsignol, C. Barreau, J. Rouquette , X. Descombes, L. Casteilla and P. Degond, Simple mechanical cues could explain adipose tissue

morphology, Journal of Theoretical Biology (2017).  https://doi.org/10.1016/j.jtbi.2017.06.030

[2] J. Barré, J.A. Carillo, P. Degond, E. Zatorska, D. Peurichard, Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions,   Journal of Nonlinear Sci ence (2017), 1-34, doi:10.1007/s00332-017-9408-z

[3] J. A. Carrillo, H. Murakawa, M. Sato, H. Togashi, O. Trush, A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation , J. Theor. Biology 474, 14-24, 2019. of active particles, https://arxiv.org/pdf/1706.05666.pdf