br Schrader et al demonstrated that

Schrader et al. [52] demonstrated that vimentin expression was upregulated with increasing stiffness of substrate. So far, the in-duction of EMT is believed to promote tumor cell motility and in-vasion. In another study, Tsuji et al. [53] reported collective migration for the role of EMT in cancer invasion and metastasis, where EMT BCI-121 are responsible for invasion, and both EMT and non-EMT cells are responsible for intravasation. The linkage be-tween the acquisition of the mesenchymal phenotype in the cells and the promotion of cellular motility are likely to provide a more accurate understanding of broad cellular response to EMT in the stiffer microenvironment of the ECM. Our findings provide further indication that the linkage to the EMT phenotype and their motility mediated by substrate viscoelasticity may have a broad implication in cancer invasion and metastasis in therapeutic failure and relapse.
4. Conclusions
AC gel substrates with different viscoelasticity were used to evaluate the effect of viscoelasticity on the direct relation between cellular motility and mesenchymal properties with induction of EMT in two different types of breast cancer cells in hypoxia. The cellular morphological parameters (cytoplasm roundness, AN/AC, and nuclear elongation factor) were chosen to clarify the relation-ship between morphology induced by viscoelastic properties of substrates and cellular motility.
The cellular migration speed (S) values in MDA-MB-231 cells were upregulated with increase in deformability (cytoplasm roundness) and nuclear elongation factor of the cells on the sub-strates in both hypoxia and normoxia. The decrease in cytoskeletal stiffness (AN/AC) was also beneficial to understand the metastatic potential under both oxygen concentration conditions. r> The S value in MDA-MB-231 cells under hypoxia was signifi-cantly upregulated with decrease in the damping coefficient (tand), not in relative storage modulus (G0/r). For this fact, the tand value had robust correlation to the morphological parameters of cyto-plasm roundness (deformability), cellular spreading factor (AN/AC), and nuclear elongation factor in hypoxia. The response of MCF-7 cells did not follow the same trend, suggesting colonization in-hibits the deformation of cells.
The HIF-1a level under hypoxic condition was markedly increased in MDA-MB-231 cells incubated on stiffer substrates (AC-stiff and TCP-coat). The cells incubated on the TCP-coat showed significant increase in TGF-b and SNAI2 expression. The AC gel substrates were more favorable to enhance vimentin expression for MDA-MB-231 cells in comparison with those incubated on the stiffer substrate (TCP-coat), indicating vimentin expression has no effect on S.
The cellular morphologies as potential parameters of under-standing cellular motility and EMT induction emerged as the robust linkage to substrate damping.
Author contributions
The manuscript was written through contributions of all au-thors. All authors have given approval to the final version of the manuscripts.
Conflict of interest
The authors declare no competing financial interest.
Acknowledgments
This work was supported by the Grant in TTI as a Special Research Project (FY2017-2018). 
Data availability statement
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
Appendix A. Supplementary data
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