Inferring exocytosis profiles from cell shapes using a dual-configuration model of walled cell tip growth

Tip growth in filamentous cells, such as root hairs, moss protonemata, and fungal hyphae, depends on coordinated cell wall extension driven by turgor pressure, wall mechanics, and exocytosis. We introduce a dual-configuration model that incorporates both turgid and unturgid states to describe cell wall growth as the combined effect of elastic deformation and irreversible extension. This framework infers exocytosis profiles directly from cell morphology and elastic stretches, formulated as an initial value problem based on the self-similarity condition. Applying the model to Medicago truncatula root hairs, moss Physcomitrium patens protonemata, and hyphoid-like shapes, we find that exocytosis peaks at the tip in tapered cells but shifts to an annular region away from the apex in flatter-tip cells beyond a threshold. The model generalizes previous fluid models and provides a mechanistic link between exocytosis distribution and cell shape, explaining observed variations in tip-growing cells across species.