Periodic Reporting for period 2 - HexaTissue (Hexatic hydrodynamics: from driven soft matter to biological tissues)
Reporting period: 2022-03-01 to 2023-08-31
The epithelium is one of the most important and versatile tissue in animals. It comprises the external layer of most of our organs and body cavities and, depending on the circumstances, can behave both as a solid or a liquid material. The epithelium liquid-like behaviour, in particular, can be observed in a number of biological processes that are instrumental for the development and maintenance of life — such as the embryonic development and wound healing — but also in the presence of life-threatening conditions, such as metastatic cancer. The project HexaTissue aims at delivering a theoretical framework to describe, understand and predict the collective motion of epithelial cell layers, using concepts from fluid mechanics and the physics of liquid crystals.
The central strategy behind the project HexaTissue consists of leveraging on the “hidden” structure of epithelial cell layers to compute the forces driving cellular motion during collective migration. Unlike normal fluids, which flow only when subject to external stimuli — such as a pressure difference or applied shear — the cells embedded in a tissue move in response of the contractile forces exerted by neighbouring cells, as well as of their internally-generated driving force, which allows them to self-propelled when in contact with a solid substrate. All these forces, in turn, are mediated by the cell shape as well as the architecture of cell clusters, through a hierarchy of structures spanning a range of length scales that goes from the typical size of a cell (e.g. 10 microns) to that of an entire organism. The main task of the HexaTissue project was to identify such a multi-scale structure and exploit it to calculate the forces driving the cells’ collective motion. This was achieved by leveraging on the physics and the mathematics of liquid crystals, that is fluids comprising anisotropic building blocks, whose mechanical properties are crucially affected by the building blocks shape and spatial organisation. Within the HexaTissue project, this multi-scale organisation is accounted for using the language of p-atic liquid crystals, that is two-dimensional liquid crystals whose local orientation is invariant with respect to rotations by 2π/p, with p an integer. During the first half of the project, the researchers involved in HexaTissue achieved the following objectives.
1) Construct a mathematical framework suited to describe generic p-atic liquid crystals (thus, not necessarily cells).
2) Construct a hydrodynamic theory able to describe how “passive” p-atic liquid crystals — that is p-atic liquid crystals whose building blocks are unable to autonomously generate force — flow in response to external forces.
3) Extend the aforementioned theory to “active” p-atic liquid crystals, where forces can be both externally and internally generated.
4) Develop a set of mathematical tool to identify p-atic order in experimental data sets consisting of in vitro layers of epithelial cells and compare the outcome of the theoretical predictions with experimental evidence.
5) Perform in-depth theoretical and experimental studies to consolidate and calibrate the theoretical framework.
1) Construct a mathematical framework suited to describe generic p-atic liquid crystals (thus, not necessarily cells).
2) Construct a hydrodynamic theory able to describe how “passive” p-atic liquid crystals — that is p-atic liquid crystals whose building blocks are unable to autonomously generate force — flow in response to external forces.
3) Extend the aforementioned theory to “active” p-atic liquid crystals, where forces can be both externally and internally generated.
4) Develop a set of mathematical tool to identify p-atic order in experimental data sets consisting of in vitro layers of epithelial cells and compare the outcome of the theoretical predictions with experimental evidence.
5) Perform in-depth theoretical and experimental studies to consolidate and calibrate the theoretical framework.
The first batch of results of the HexaTissue project was beyond the PI’s most optimistic expectations. The multi-scale structure of epithelia, which was inaccessible to previous theoretical approaches, being these either cell- or organism-resolved, emerged naturally within the new framework while combining multiple types of liquid crystal order — corresponding to different values of the integer p — with activity, that is the ability of generating forces. In particular, this construction highlighted the possibility that both nematic (i.e. p=2) and hexatic (i.e. p=6) could coexist at different length scales, with the former being dominant at the large and the former at the small scale. This prediction, named “hexanematic” order in the publications where it was reported, was confirmed by numerical simulations of two different cell-resolved model of epithelia — the so-called Voronoi model and Multi Phase-field Model — and, later, by a direct comparison with in vitro layers of Madin-Darby canine kidney cells (MDCK). The first experimental work, currently under review in Nature Physics, showed that the crossover between hexatic and nematic order occurred at a length scale corresponding to clusters of approximatively 20 cells. A follow-up experimental study — currently under review in Nature Communications — demonstrated that such a hexanematic crossover scale depends on the mechanical and biochemical properties of both the cells and the substrate, such as the cell density, the substate stiffness and the level of expression of adhesion proteins, such as E-cadherin. It was speculated — and it will next be investigated — that such a peculiar multi-scale organisation, as well as the possibility of tuning the hexanematic crossover scale, could be instrumental to the versatility of epithelial tissues and complement the complex set of singling pathways that cells have a their disposal to achieve biological functionality. For instance, collective cell migration in epithelia relies on both remodelling events at the small scale — such as cell intercalation and the rearrangement of multicellular rosettes — as well as large scale flows. Therefore, the underlying hexanematic multscagle organisation and the specific magnitude of the crossover scale are expected to have a profound impact on how the geometry of the environment affects the specific migration strategy. E.g. metastatic cells traveling through micron-sized channels in the extracellular matrix during cancer invasion will more likely rely on local hexatic-controlled remodelling events, whereas unconfined wound healing processes are more likely to leverage on system-wide nematic-driven collective flows.