Master's thesis defense by Steven Rønhild – Niels Bohr Institute - University of Copenhagen

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Master's thesis defense by Steven Rønhild

Title: Self-organisation of Multicellular Systems through Cell Polarity

Recently a new, two dimensional model was proposed by [1] for the development of the blastocyst. In this study they took an agent-based approach and modelled the cells as unit spheres and the cell polarities as unit vectors. By collecting the information about the local configuration of the position of the cells and their polarity into one mathematical quantity and introducing a novel rule of assigning neighbours they were able to generate a circle of cells, where the polarities pointed radially outward.

The purpose of this study is to generalise this aspect of their model to three dimensions. More precisely, we want to examine the following questions: Is it possible to generate a sphere of cells in three dimensions, where each cell carries one polarity? If yes, how stable is the sphere? Is it possible to make any deformations of the sphere? We used analytical methods to derive the gradient of the potential and the Euler method to solve the equations of motion numerically.

Our simulations show that it is indeed possible to make a sphere of cells in three dimen- sions. The sphere is topologically stable under modifications to the shape of the potential. However, the new rule of assigning neighbours to each cell is essential to get a sphere. If we change this rule the resulting global structure of cells are mostly going to be planes. It is possible to deform the sphere into other stable, global structures: a cylinder with caps at the ends and an ellisoid. Furthermore this study has also proposed and shown that it is possible to generate other stable, global structures of cells: loops and strings. Finally, we breifly studied a system of cells, where the cells have two polarities. In this model we get the cells to once again form a sphere using the old polarity. However, the cells use their second polarity to self-organised and make a dipole structure across the sphere. Thus the cells introduce an axis into the sytem with a direction they choose.

[1] S. B. Nissen, M. Perera, J. M. Gonzalez, S. M. Morgani, M. H. Jensen, K. Sneppen, J. M. Brickman, and A. Trusina, “Four simple rules that are sufficient to generate the mammalian blastocyst”, PLOS Biology, vol. 15, no. 7, pp. 1–30, Jul. 2017.