Substrate Stiffness and Cell Area Predict Cellular Traction Stresses in Single Cells and Cells in Contact

Abstract

Cells generate traction stresses against their substrate during adhesion and migration, and traction stresses are used in part by the cell to sense the substrate. While it is clear that traction stresses, substrate stiffness, and cell area are related, it is unclear whether or how area and substrate stiffness affect force generation in cells. Moreover, multiple studies have investigated traction stresses of single cells, but few have focused on forces exerted by cells in contact, which more closely mimics the in vivo environment. Here, cellular traction forces were measured where cell area was modulated by ligand density or substrate stiffness. We coupled these measurements with a multilinear regression model to show that both projected cell area and underlying substrate stiffness are significant predictors of traction forces in endothelial cells, and interestingly, substrate ligand density is not. We further explored the effect of cell-cell contact on the interplay between cell area, substrate stiffness, and force generation and found that again both area and stiffness play a significant role in cell force generation. These data indicate that cellular traction force cannot be determined by cell area alone and that underlying substrate stiffness is a significant contributor to traction force generation.

Changes in E-cadherin rigidity sensing regulate cell adhesion

“…Quantification of morphological features of cells revealed that the cell area increased with increased ECM rigidity (Fig. 1B and Table S2), in agreement with previous studies (17,39,40). There were also relatively small, but statistically significant changes in the aspect ratio and circularity of cells with changes in ECM rigidity ( Fig.…”

“…This has been studied extensively in the context of cellular responses to increased ECM rigidity, which showed that integrin adhesions grow in size and are strengthened by local assembly of the actin cytoskeleton and activation of actomyosin contraction (17)(18)(19). These mechanical cues have physiological consequences, as ECM rigidity influences stem cell fate and cell differentiation (20).…”

Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion

“…The tractions predicted in the current study are strongly aligned with such experimental data. Furthermore, experimental studies have also reported that substrate stiffness influences cellular tractions; tractions for endothelial cells seeded on a 1 kPa substrate are reported to be ~200 Pa, whereas significantly higher tractions of ~1000 Pa are measured for endothelial cells on 5 kPa or 10 kPa substrates (Califano and Reinhart-King 2010). A similar dependence of shear tractions on substrate stiffness is predicted by the modelling framework used in the current study.…”

“…Different ranges of substrate stiffness that influence cytoskeletal remodelling have been reported for different cell phenotypes; particularly, more contractile cells, such as myoblasts, are most sensitive up to ~400 kPa (Ren et al 2008), but less contractile cells, such as fibroblasts, are sensitive up to ~20 kPa (Yeung et al 2005). Previous in-vitro studies have quantified the effect of different substrate stiffness on stress fibre (SF) formation (Solon et al 2007), FA area (Goffin et al 2006), cell traction (Califano and Reinhart-King 2010), and cell shape (Yeung et al 2005). However, the cellular mechanisms underlying these phenomena are poorly understood.…”

A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

“…Wang and Lin (2007) describe several experimental techniques to obtain cell traction forces. In the study by Califano and Reinhart-King (2010), cellular traction forces are determined by the combination of experiments and regression procedures. We use the input data from Table 1, unless stated otherwise.…”