A surface morphology-based inference method for the cell wall elasticity profile in tip-growing cells

Plant development and adaptation are highly dependent on cell morphology and growth. High turgor pressure in plants causes stress on the cell wall, followed by cell extension. In tip-growing cells, the localization of vesicles and cytoskeleton components has been well studied. However, there has been a lack of attention to the spatial profile of mechanical properties, specifically the cell wall elasticity. In this study, we introduce a new surface morphology-based method to measure the elasticity of the cell wall in tip-growing cells. Previous work is based on measurements from the wall meridional outline, a technique that cannot track the elastic deformation of the cell wall experimentally. Instead, we developed a way to infer the bulk modulus distribution from the cell surface by triangulating experimental marker points coming from fluorescent labeling. To justify the use of our protocol in tip-growing cells from the moss Physcomitrium patens, we replicated the experimental noise and moss morphology in simulated cells. In practice, we found that a larger triangulation improved robustness against noise, which agreed with our theoretical study. With multiple cell sampling, we determined that 10 cells were sufficient to recover the elasticity distribution with noise, but only when the elastic stretches were high enough. We then created a dimensionless map of inference error to verify a spatial change of P. patens bulk modulus within two folds. This technique will open the field to more comprehensive measurements of cell wall elasticity, providing a key step in understanding tip cell growth and morphogenesis. Author summaryTip-growing cells can be characterized by their fast growth concentrated at the cells apex. Their growth and morphogenesis are tightly regulated processes involving cell wall addition and rearrangement while the cell wall is under stress originating from the cells internal turgor pressure. We start by studying the cell walls elastic properties, one aspect of the cell growth process. We use a method of marker point tracking across the surface of the tip-growing cell to measure the walls elasticity profile. In this work, we present a parameter sensitivity study of this method on synthetic cells and report our results on experimental moss tip-growing cells. Our results suggest that this inference method can reliably measure a cell wall elasticity gradient under combined geometric and mechanical conditions that create elastic strains within 5% at the tip.