[POS] Biomathematics

[POS-58] Mechanical properties of intercellular interactions enabling cone mosaic formation in fish retina

*Keiichi Yamamoto^1,2, Yuji Sakai³, Takashi Okada^2,4, Atsushi Mochizuki^1,2 (1. Graduate School of Science, Kyoto University (Japan), 2. Institute for Life and Medical Science, Kyoto University (Japan), 3. Yokohama city Univ. (Japan), 4. Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMs), Riken (Japan))

Keywords:

Pattern formation,Cell adhesion,Self-organized system,Zebrafish,Retina

Vision is crucial for the survival of animals. In particular, the types and arrangement of photoreceptor cells (cone cells) are important for visual function. In teleost fish, various types of cone cells are organized in regular patterns, known as cone mosaics, on the two-dimensional retinal sheet. A variety of mosaic patterns have been observed across species, possibly reflecting adaptations to the diverse underwater light environments. In zebrafish, for example, four distinct types of cone cells—each sensitive to ultraviolet, blue, green, or red light—are arranged in a regular, periodic square lattice. This highly ordered pattern can be formed through cone cell rearrangement, though the mechanisms underlying its formation are still not fully understood. Mochizuki and his colleagues previously used a mathematical model to analyze this rearrangement process and suggested that different adhesion strength between cell types could be an essential factor in cone mosaic formation (Mochizuki, 2002; Ogawa et al., 2017). However, their model simplified the retina into a two-dimensional square lattice. This lattice model assumes that cells are arranged in a square lattice, which may not accurately reflect biological reality. In this study, we developed and analyzed a mathematical model treating the retina as a two-dimensional continuous space, allowing cells to move freely. Building on previous research, we assumed that the strength of attraction between cells depends on the combination of cell types. Two candidate models of attraction have been proposed in previous studies: one in which attraction acts across the entire contact surface between adjacent cells and another in which it acts only at the edges of the contact area. To unify these models, we introduced a generalized attraction model that encompasses both surface- and edge-based interactions. Through mathematical simulation and stability analysis, we identified the general conditions of cell-cell interactions required for cone mosaic formation. Intuitively, if cell adhesion molecules (CAMs) are evenly distributed on the cell surface, the attraction would be expected to scale with the contact area. However, our findings suggest that the attractive forces act only at the contact edges. Assuming that CAM binding generates attraction, this implies that cell adhesion at the contact surface becomes fixed, with no further binding events occurring there, while new adhesion is formed only at the contact edges. Furthermore, we identified the required balance among forces between different cell types to achieve successful pattern formation.