A predictive mechanochemical modeling framework for the deformation and remodeling of the nuclear lamina

1Nuclear envelope stretch and rupture are common to cell spreading and migration in a variety of microenvironments, leading to marked changes in nucleocytoplasmic transport. Predicting cell response to different mechanochemical cues that are transmitted to the nucleus remains an open problem in the field of mechanomedicine. We developed a predictive modeling framework to examine how nuclear deformation on substrates with different nanotopographies influences nucleocytoplasmic transport and rearrangement of the nuclear lamina. Using the finite element method, we simulated nuclear compression by the perinuclear actin cap on substrates with arrays of nanopillars, modeling the nuclear envelope as a nonlinear elastic structure and coupling deformations to a biochemical model of lamin remodeling and nucleocytoplasmic transport. These simulations predicted regions of high nuclear envelope stretch adjacent to cell-nanopillar contacts, leading to maximized nuclear envelope tension on small nanopillars spaced by 4-5 microns. We then considered the effects on nuclear transport of YAP and TAZ and found that increased nuclear compression led to YAP/TAZ nuclear localization in agreement with previous experiments. Furthermore, the simulated force load per lamin was maximized on nanopillar substrates with high nuclear stretch. The magnitude of this load was modulated by the rate of actin cap assembly and the overall expression level of lamin A/C - decreasing lamin content in the nuclear envelope led to a higher likelihood of rupture. We validated this prediction in subsequent experiments with lamin-depleted U2OS cells, establishing the central importance of lamin transport and microenvironment nanotopography to nuclear mechanotransduction. 2 SignificanceCell nuclei commonly experience large strains, but existing computational models do not explain the coupling between such deformations and molecular transport. Here, we present a modeling framework that includes the mechanics of nuclear deformations and the reaction-transport of molecules within the cytoplasm, nuclear envelope, and nuclear interior. As a well-controlled setup for comparing experiments and simulations, we consider nuclear indentations exhibited by cells on nanopillar substrates. Our simulations recapitulate measurements of nuclear YAP/TAZ localization from the literature and predict that low-lamin cells experience higher force loads at the nuclear envelope. We validate this prediction experimentally, showing that lamin-depleted cells are more likely to exhibit nuclear rupture. Overall, our framework presents opportunities to predict nuclear mechanoadaptation to different microenvironments.