Emergent symmetries and phase phenomenology in an individual-based model of cell-like particles with internal mobility.

We investigate the phase behaviour and structural organisation of a novel individual-based particle model designed to capture the core geometric and mechanical constraints of densely packed cells. Specifically, the model represents epithelial cells as coaxial spherocylinders composed of a rigid core and an axially mobile, wider component that mimics the nucleus. This internal degree of freedom is inspired by the phenomenon of pseudostratification in biological tissues, where dense packing and mechanical constraints compel nuclei to occupy different heights along the thickness of the tissue. Through Monte Carlo simulations in the isothermal-isotension ensemble, we systematically characterise the rich phase phenomenology of these fluids across various geometric parameters and pressure regimes. Our results demonstrate that the internal axial mobility induces vertical staggering, which stabilises crystalline phases with hexagonal as well as square symmetry, the latter being notably absent in standard two-dimensional hard-disk fluids. Furthermore, we identify transitions between hexagonal and square lattices depending on the vertical freedom of the particles. These findings provide a general physical framework to explore how internal degrees of freedom dictate structural symmetries, offering insights into passive packing features in pseudostratified tissues and suggesting new pathways for the design of colloidal materials with complex structural organisation.