Cellular heterogeneity in pressure and growth emerges from tissue topology and geometry

Cell-to-cell heterogeneity is observed in many biological phenomena like gene expression, signalling, cell size regulation and growth. Notably, heterogeneity in cell size and growth rate prevails in many systems and impacts tissue patterning and macroscopic growth robustness. From physical perspective, cell volume change is driven by osmosis and the subsequent intracellular hydrostatic pressure, which sustains cellular osmotic potential and is confined by peripheral constraints (plasma membrane, cytoskeletal cortex, extracellular matrix or cell wall) in plant, animal, tumorous and microbial cells. Despite numerous studies in unicellular systems, the spatial variation of hydrostatic pressure in multicellular tissues, and its relation with cell-to-cell growth variability, remain elusive. Here, using atomic force microscopy, we demonstrate that hydrostatic pressure is highly heterogeneous between adjacent cells in the epidermis of Arabidopsis shoot apical meristem, and it unexpectedly correlates either positively or negatively with cellular growth rate depending on growth conditions. Combining experimental arguments and physical modelling of cell wall mechanics and osmosis within multicellular tissues, we show that heterogeneities in pressure and growth are not random, and they spontaneously emerge from cell size and tissue topology. Together, we propose that cellular pressure build-up, a physical phenomenon, and growth rate, a biological property, are innately heterogeneous and modulate cell size homeostasis in any compact tissue with inhomogeneous topology.