Mathematics Colloquia and Seminars

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Animal cells use an unknown mechanism to control their growth and physical size. Here, using the fluorescence exclusion method, we quantitatively measure cell volume for adherent cells on substrates of varying stiffness. We find that the cell volume has a complex dependence on substrate stiffness, and is positively correlated with the size of the cell adhesion to the substrate. From a mechanical force balance condition that determines the geometry of the cell surface, we find the observed cell volume variation can be quantitatively predicted from the distribution of active myosin throughout the cell cortex. To connect cell mechanical tension with cell size homeostasis, we quantified the nuclear localization of YAP/TAZ, a transcription factor involved in cell growth and proliferation and the Hippo pathway. We find that the level of nuclear YAP/TAZ is positively correlated with the average cell volume. Moreover, the level of nuclear YAP/TAZ is also connected to cell tension, as measured by the amount of phosphorylated myosin. Cells with greater apical tension tend to have higher levels of nuclear YAP/TAZ and a larger cell volume. These results are also confirmed by examining YAP KO cells, which displays pronounced size change. We will discuss some simple mathematical models that can rationalize some of these results. These results also point to a size-sensing mechanism based on mechanical tension: the cell tension increases as the cell grows and increasing tension biochemically feeds back to growth and proliferation control.