3D geometry and mechanics of a single apical stem cell ensure helically symmetric plant body in multicellular models

Self-renewing divisions of stem cells at the growing tip universally govern plant development. In basal land plants, a single apical stem cell (AC) undergoes successive 120-degree rotational divisions while maintaining a self-similar tetrahedral geometry with three division walls, recapitulating the helically symmetric body architecture. The mechanisms by which AC geometry and mechanics determine the division axis and its rotation are largely unknown. Here, we develop two 3D multicellular mathematical models to address these questions. Our geometrical model reveals that the least area rule, coordinated with the AC surface curvature, is sufficient to drive rotational divisions by rotating the geometric proportion of the AC. Furthermore, by incorporating biologically plausible cell growth mechanics, we show that the tetrahedral AC and its rotational division spontaneously emerge from a spherical cell. Notably, the maximal tension rule confers superior robustness against stochastic fluctuations in division orientation compared to the least area rule, because the sequential formation of division walls continuously updates the tension distribution to guide subsequent orientation. These results suggest that the tetrahedral AC and the helically symmetric body plan are natural consequences of self-renewing cell divisions, imposed by 3D geometry and/or mechanics.