Modeling the effect of substrate topography on cellular and nuclear deformations

As they navigate complex extracellular environments, cells and their nuclei undergo extensive deformation. Recent experiments have demonstrated that vascular endothelial cells cultured on microgroove substrates, which mimic the anisotropic topography of the basement membrane, exhibit complex nuclear deformations, leading to partial or even complete nuclear penetration into the microgrooves. Interestingly, the experiments suggest that nuclear entry into the microgrooves is driven mainly by cellular adhesion and spreading rather than by cytoskeleton-mediated pulling and/or pushing forces. In the present work, we develop a phase-field model to describe endothelial cell deformation on microgroove substrates and characterize the conditions necessary for nuclear confinement within the grooves, a process that has been termed "caging" in the experiments. The model introduces a novel non-local term that prevents the cellular body from fragmenting under conditions of strong adhesion and high curvature. Our numerical simulations show that significant nuclear deformation and partial caging occur for strong cell-substrate adhesion and for nuclear membrane stiffness close to or inferior to that of the cell membrane. We further show that the dimensions of the grooves are critical for the caging process, with increasing groove depth and width favoring nuclear penetration into and caging within the grooves. These results are in close agreement with experimental observations, thus corroborating the notion that cell-substrate adhesion forces can drive large-scale nuclear deformations without the need for cytoskeleton-generated forces.