Mechanochemical modeling of morphogenesis in cell polarization for budding yeast

Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.