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.