engleski

Structuring of the epithelial tissue

Structural properties of space tessellations are important to understand various problems in many fields of science and industry. One of the existing questions is how to tessellate space with the maximized centrality of the cells, usually known as Quantizer problem. Here we study stable solutions of Quantizer problem by applying Lloyd's algorithm on various disordered random point processes. We find that Lloyd's algorithm converges to a universal amorphous structure with a long-range order. Furthermore, we investigate the role of cell centrality in the epithelium tissue. First we find that the tissue can be represented by the tessellation based on the nuclear shape of constituting cells. In the following we explore the interplay between finite size effects and the Lloyd minimisation and find that during the epithelial tissue development, centrality as a concept may play a role and is tightly controlled by the activity of the cell.

Lloyds algorithm ; optimization ; hyperuniform ; tissue modeling

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