A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration.

It is now evident that the cell nucleus undergoes dramatic shape changes during important cellular processes such as cell transmigration through extracellular matrix and endothelium. Recent experimental data suggest that during cell transmigration the deformability of the nucleus could be a limiting factor, and the morphological and structural alterations that the nucleus encounters can perturb genomic organization that in turn influences cellular behavior. Despite its importance, a biophysical model that connects the experimentally observed nuclear morphological changes to the underlying biophysical factors during transmigration through small constrictions is still lacking. Here, we developed a universal chemomechanical model that describes nuclear strains and shapes and predicts thresholds for the rupture of the nuclear envelope and for nuclear plastic deformation during transmigration through small constrictions. The model includes actin contraction and cytosolic back pressure that squeeze the nucleus through constrictions and overcome the mechanical resistance from deformation of the nucleus and the constrictions. The nucleus is treated as an elastic shell encompassing a poroelastic material representing the nuclear envelope and inner nucleoplasm, respectively. Tuning the chemomechanical parameters of different components such as cell contractility and nuclear and matrix stiffnesses, our model predicts the lower bounds of constriction size for successful transmigration. Furthermore, treating the chromatin as a plastic material, our model faithfully reproduced the experimentally observed irreversible nuclear deformations after transmigration in lamin-A/C-deficient cells, whereas the wild-type cells show much less plastic deformation. Along with making testable predictions, which are in accord with our experiments and existing literature, our work provides a realistic framework to assess the biophysical modulators of nuclear deformation during cell transmigration.

Determination of cell elasticity through hybrid ray optics and continuum mechanics modeling of cell deformation in the optical stretcher.

The optical stretcher is a dual-beam trap capable of stretching individual cells. Previous studies have used either ray- or wave-optical models to compute the optical pressure on the surface of a spherical cell. We have extended the ray-optics model to account for focusing by the spherical interface and the effects of multiple internal reflections. Simulation results for red-blood cells (RBCs) show that internal reflections can lead to significant perturbation of the deformation, leading to a systematic error in the determination of cellular elasticity. Calibration studies show excellent agreement between the predicted and measured escape force, and RBC stiffness measurements are consistent with literature values. Measurements of the elasticity of murine osteogenic cells reveal that these cells are approximately 5.4 times stiffer than RBCs.