Nondimensional nucleus shape parameters reveal mechanostasis during confined migration

Nucleus shape is a sensitive indicator of cell state, influenced by numerous bio-chemical and physiological factors. While prior work has cataloged how perturbations alter nucleus morphology, we address the inverse: inferring underlying molecular changes from nucleus shape alone. We previously developed a mechanical model yielding two nondimensional parameters: flatness index and scale factor, which are surrogate measures for cortical actin tension and nuclear envelope compliance respectively. In this study, we apply these parameters to investigate the dynamics in cellular mechanics during confined migration. We fabricated polydimethylsiloxane (PDMS) microchannels with widths of 3 {micro}m (high confinement) and 10 {micro}m (low confinement) and tracked cells migrating through them. We captured high-frequency 3D nucleus shapes via double fluorescence exclusion microscopy and custom image analysis. Fitting the model and estimating flatness index and scale factor to time-resolved shapes revealed dynamic regulation in 3 {micro}m channels: actin tension decreased and nucleus compliance increased immediately before nucleus entry into the constriction, with rapid restoration to baseline upon exit. No such changes occurred in 10 {micro}m channels, indicating active, confinement-dependent cytoskeletal adaptation. Immunostaining for YAP and lamin-A,C confirmed these model inferences. Our results uncover mechanostasis, active mechanical homeostasis, during confined migration and establish the combination of double fluorescence exclusion microscopy and nondimensional nucleus shape parameters as a powerful, non-invasive tool for single-cell mechanobiology studies.