br Cellular migration analysis by the PRW model br
3.3.2. Cellular migration analysis by the PRW model
To discuss the diffusion of the seeded PPT on the substrates (Fig. S5: Supplementary data), the calculated MSD values and characteristic parameters, cellular migration speed (S), persistent time (P), and cellular diffusivity (D) given by Eqn (4) are presented
in Fig. 5. MDA-MB-231 cells cultured on the TCP-coat under hyp-oxia exhibit the highest value of S (0.87 mm/min) at day 3, while slight increase in S under normoxic condition (0.96 mm/min) was observed on the same substrate. The S value of MDA-MB-231 cells on AC gel substrates under hypoxia changes obviously higher with increase in gel stiffness (3-fold change between AC-stiff and AC-soft) accompanied by an enhancement in the vitality (P). The D value is the balance between S and P. The TCP-coat substrate ex-hibits a one order of magnitude larger D value in comparison with AC-stiff and two orders of magnitude larger D value than those of AC-soft or AC-mid. Overall, D is significantly upregulated under both oxygen concentration conditions, and the cellular motility is enhanced.
The D value is important to understand how quick the cancer cells can invade to the vasculature or lymph node. In general, metastatic cells can be distinguished from non-invasive cancer cells by reduced cytoskeletal stiffness (ratio of AN and AC: Fig. 3(b)) and increased deformability (Fig. 3(a)).
For MCF-7 cells both in hypoxia and normoxia, a significant motility reduction of the cells on the TCP-coat reflects the sup-pression of S and P, followed by the decrease in D. In this regard, MCF-7 cells are rather less invasive cancer cells presumably because of multicellular aggregation (Fig. 2).
3.4. Linkage to substrate viscoelasticity and motility of cells in cellular morphologies
The cellular morphological parameters are chosen to clarify the relationship between morphology induced by physical properties of substrates and cellular motility.
Cellular migration speed (S) is plotted as a function of morphological parameters of cytoplasm roundness, AN/AC, and nuclear elongation factor. For MDA-MB-231 cells in both hypoxia and normoxia, linear relations between three cellular morphol-ogies and migration speed are found on all substrates with different stiffness (except TCP), indicating the elongation of cells enhances the cellular motility (Fig. 6 and Fig. S6 [Supplementary data]). The S values are upregulated with increase in deformability (cytoplasm roundness) (Fig. 6(a) and Fig. S6(a): [Supplementary data]) and nuclear elongation factor (Fig. 6(c) and Fig. S6(c): [Supplementary data]) of the cells on the substrates. The effect of cytoskeletal stiffness (AN/AC) on cellular migration speed is plotted in Fig. 6(b) and Fig. S6(b) (Supplementary data). The decrease in cytoskeletal stiffness, which is equal to the increase in cellular spreading factor, is also beneficial to understand the metastatic potential under both oxygen concentration conditions. For MCF-7 cells, such robust correlation is not obtained (Fig. 6(d)-(f) and Fig. S6(e)-(f): Supple-mentary data) except for Fig. S6(d) (Supplementary data).
Cellular migration speed (S) in MDA-MB-231 cells under hyp-oxia was significantly upregulated with decrease in damping co-efficient (tand) (Fig. 7(a)). Although the stiff substrate increased cellular motility, as discussed in Section 3.3, our results found that migration speed is not robustly correlated with substrate stiffness (relative storage modulus [G0/r] in Fig. 7(d)). This result suggests that damping is the driving force of the cellular migration in rather more invasive MDA-MB-231 cells. In addition, interestingly, tand promotes the persistent time (P) in a log-log linear relation compared with G0/r (Fig. 7(e)). This behavior is consistent with the results of cellular diffusivity (D) (Fig. 7(c) and (f)).
Extensive studies have been made in mechanotransduction via surface topography and stiffness on the substrates, in which the cells respond to applied forces and exert forces in the substrate (ECM) [28e31]. Such forces can change cell morphology and cytoskeletal structure because of traction force (contractility) generation, which influence cell response and cell fate. Essentially,
Fig. 4. Representative trajectory of MDA-MB-231 and MCF-7 cells cultured on five different substrates under hypoxic condition over 16 h at day 3. The data were obtained in (aee) 300 300 mm2 and (gek) 200 200 mm2 . AC, acrylamideeN-acryloyl-6-aminocaproic acid copolymer; TCP-coat, tissue culture plate coated with type I collagen.
Fig. 5. Summary of the cellular migration parameters calculated from MSD of MDA-MB-231 and MCF-7 cells in both hypoxia and normoxia: (a and d) cellular migration speed (S), (b and e) persistent time (P), and (c and f) cellular diffusivity (D) at day 3 cultured on five different substrates. AC, acrylamideeN-acryloyl-6-aminocaproic acid copolymer; MSD, mean squared displacement; TCP-coat, tissue culture plate coated with type I collagen.