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

Plant cell morphology and growth are essential for plant development and adaptation, in particular the cell wall material deposition and rearrangement. As the wall is extended due to turgor pressure, the wall mechanical response, specifically the wall’s elastic properties, are not well understood. 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 the wall meridional outline on the assumption the cell is axisymmetric, an idea that does not align well with the reality of the cells. Instead, we developed a way to triangulate the surface of the cell using marker point locations that could be achieved experimentally with fluorescent labeling. After measuring the elastic stretch and curvatures from our triangulation, a mechanical model is used to measure the tensions and surface bulk modulus distribution. We simulated moss tip cells from experimental Physcomitrium patens plants to challenge the method with noise estimated from experiments. We discovered that increasing the discretization of the triangulation improved robustness against noise. With multiple cell sampling, we found that around 10 cells were sufficient to recover the elasticity distribution with noise, but only when the elastic stretches were high enough at the tip. With low elastic stretch at the tip, the appearance of non-physical modulus values led to underestimated inference values there, causing false-positive gradient results. This compelled us to study a range of cases, leading us to a dimensionless global phase map showing areas of good inference. This technique will open the field to more comprehensive measurements of tip cell elasticity, providing a key step in understanding tip cell growth and morphogenesis.