Abstract
The interplay between cellular mechanics and biochemical processes in the cell cycle is not well understood. We propose a quantitative model of cell budding in Saccharomyces cerevisiae as a "weaken-fill-repair" process, linking Newtonian mechanics of the cell wall with biochemical changes that affect its properties. Our model reveals that (1) oscillations in mother cell size during budding are an inevitable outcome of the process; (2) asymmetric division is necessary for the daughter cell to maintain mechanical stiffness; and (3) although various aspects of the cell are constrained and interconnected, the budding process is governed by a single reduced parameter, ψ, which balances osmolyte accumulation with enzymatic wall-weakening to ensure homeostasis. This model provides insights into the evolution of cell walls and their role in cell division, offering a system-level perspective on cell morphology.