A universal growth trajectory of a 3D mechano-hydraulic model for plant cells

Growth is fundamental to many biological processes. Recently, we showed that cellular turgor pressure is highly heterogeneous in the shoot apical meristem (SAM) of Arabidopsis thaliana, balanced by mechanical and hydraulic parameters. We developed a 3D physical model of a single plant cell with classical mechanical and hydraulic properties, and recovered a typical, nonlinear growth trajectory. Depending on initial size, cells spontaneously go through consecutive phases of accelerating-then-decelerating growth separated by a critical cell size defined by the mechano-hydraulic balance and cell geometry. To test this model, we tracked long growth trajectories of Arabidopsis SAM cells treated with oryzalin, which blocks cell division but permeates continuous growth, and recovered the predicted growth trajectory using our 3D image analysis pipeline. Our theoretical and experimental analyses suggest that plant cells may follow a universal trajectory to autoregulate growth, which could potentially be applicable to other tissues and organisms.