Metastatic cancer cells squeeze through small pores, often smaller than their nucleus, in order to reach a secondary site of proliferation. This constriction exerts forces on the nucleus, leading to deformations. Our previous work showed that A375 melanoma cells that have passed through 10 rounds of constricted migration exhibit stable differences in migratory phenotype, gene expression, and 3D genome structure (Golloshi et al. EMBO Reports, 2022). We are now investigating what combination of selection and induction forces lead to this stable difference. We have identified a cell surface protein, Integrin-β4 (ITGB4), as a marker whose RNA and protein expression level closely associates with cellular constricted migration proficiency over the course of sequential rounds of constriction. Sorting cells for expression of ITGB4 revealed a subpopulation of cells that, before constriction, already possess some of the phenotypic and 3D genome structure characteristics of proficient migrators. We next carefully tracked ITGB4 protein levels over a timecourse of sequential constricted migration, compared to unconstricted migration, in both the initial A375 population and a clonal population. We found evidence for both selection of ITGB4 expressing cells and also induction of ITGB4 expression after multiple constrictions. Intriguingly, this careful timecourse revealed that it consistently takes 3-4 rounds of constriction before a dramatic and stable shift in cell migratory phenotype. To investigate the molecular underpinnings of this lag, we collected nucleus images, Hi-C chromosome contact data, and gene expression data after 1 and 4 rounds of constriction. We propose that stable phenotypic differences after sequential constricted migration are the product of selection from a continuously regenerated heterogeneity combined with changes induced by the cumulative impact of multiple rounds of cell and nucleus constriction.