COVariant Fluctuating hydrodynamics of Epithelial Flows – COVFEFE

Recent advances in microscopy make it possible to image the entire embryonic development of a drosophila embryo with high spatial (sub-cellular) and temporal (second) resolution. Interpreting these new data requires new multi-scale theoretical approaches to unravel the relationship between embryonic tissue flow and cellular biochemical activity. In this project, I propose to develop numerical and analytical tools to describe the global dynamics of these flows in terms of local mechanical properties at cellular interfaces. In connection with experimental groups, we will seek to understand the appearance of reproducible spontaneous tissue flows in curved environments typically encountered during embryogenesis but also in artificial systems such as organoids or model epithelium systems.

Our first objective is to build a new numerical model based on a hydrodynamic theory of cell interfaces to predict the macroscopic dynamics of epithelial tissues. Our model will be based on the hydrodynamic active gel theory which includes viscous dissipation of the cell cortex. Since epithelial tissues are fundamentally non-equilibrium materials due to the constant injection of chemical energy required to maintain the cell metabolic activity, the choice of a realistic dynamics will affect the steady-state reached by the system. With this tool, I will identify the role of mechanical stress fluctuations at the cell junctions in the statistics of cellular rearrangements and, consequently, in determining the larger-scale mechanical properties of tissues.

Our second objective is to develop non-invasive techniques for inferring the mechanical properties of biological tissues from image sequences obtained by optical microscopy. We propose to extend the application regime of micro-rheology to active materials based on the tracking of endogenous biological tracers (e.g. nuclei or tri-cellular junctions).

Our third objective is to develop a covariant (i.e. valid in curved geometry) hydrodynamic theory to predict the relation between the local cell-level contractility and global tissue flows. In particular, in the context of in vitro models of intestinal epithelial tissues (intestinal stem cell organoids), we will seek to establish the role of mechanical factors in the partitioning of characteristic cellular events (division, elimination) within regions of specific curvature. While the behaviour of single cells within curved geometries is under scrutiny, the question of collective flows within curved confluent epithelial tissues remains largely unexplored; such study is now becoming possible thanks to the design of new 3D micropatterning and imaging techniques. Furthermore, motivated by experimental observations that increased levels in fluctuations precedes global tissue flows (e.g. during the drosophila germ band extension), we will consider the mechanical impact of fluctuating active stress tensor within our curved hydrodynamic equations. Such fluctuations could play a previously unexpected role in a curvature detection mechanism, allowing for example the initiation of organogenesis at a specific and reproducible position within the embryo.

Understanding the physical mechanisms contributing to organogenesis reproducibility is of key interest to understand normal vs. pathological organ development in vivo but also to understand how to generate organoids in a reproducible fashion in the medical context of artificial organ design.