GROWSIZE

This project investigates how organisms reach a specific size, focusing on the role of residual stress, which remains in tissues even after external forces are removed. Currently, the respective role of mechanics and biochemical processes in determining organ size is an open question, and it is unknown how stress is actively built and maintained in tissues during growth. Our hypothesis suggests growth incompatibility as the missing link between tissue growth, size, and residual stress. Growth incompatibility represents the challenge of fitting parts of a grown tissue without voids or overlaps, acting as the geometric "seed" of residual stress. We use the Ricci curvature of the growth metric tensor to approximate incompatibility at both tissue and cell levels. The project will blend theory, simulations, and experiments in the Drosophila wing disc as well as in multicellular spheroids to investigate the concept of incompatibility across cell and tissue scales. At the tissue level, we will fully integrate the idea of growth incompatibility into the theoretical framework of solid mechanics of growing tissues (morphoelasticity) by considering the dissipation of Ricci curvature and giving incompatibility a thermodynamical basis. This introduces significant computational challenges as highly nonlinear and nonlocal PDEs must be solved due to Ricci curvature. At the cell level, we adapt the concept of Ricci curvature for the vertex model, aiming to differentiate between inherent cell incompatibility and that caused by cell network connections, termed "topological incompatibility." To test our theory we will measure the spatio temporal evolution of incompatibility in the Drosophila wing disc and in multicellular spheroids. By cutting small tissue samples and observing their opening due to ablations, we can infer Ricci curvature. This demands a new laser ablation protocol, bringing the "Volterra cuts" of biomechanics to the embryonic scales of mechanobiology.