Work and Tension: New Evidence that Adherent Cells of the Same Area Do the Same Work Independent of Stiffness and Focal Adhesions

Recent observations in single cellular mechanics suggest that spread, attached cells have a set tension, and will work to maintain that tension in an environment of changing extracellular matrix stiffness, focal adhesion formations, and applied strains. The negative feedback loop that maintains tension in a cell has been dubbed “tensional homeostasis” (1). The maintenance of active tension in an attached, spread cell is critical for mechanosensing changes in the cell’s mechanical environment, which can regulate everything from cell motility (1), metastasis of cancer cells (2), cell proliferation and survival (3), stem cell fate (4), and maturation of cardiac cells (5). Hence, it is important to understand correlations between the sensing of mechanical cues and the subsequent biochemical response to preserve tensional homeostasis.

One trend in modeling cell tension has been modeling at the level of the focal adhesion and actin cytoskeleton. However, the article by Oakes et al. (6), in this issue, helps to define and simplify the control of cell tension, and presents evidence that the work done by the cell, measured as strain energy, has little dependence on the substrate stiffness and number of focal adhesions. Instead, they find that the strain energy is most strongly related to a cell’s spread area. From this data, the authors were able to model the total strain energy in the cell using three terms: one assuming the cell is a homogeneous elastic medium with a homogeneous contractile stress, one accounting for the energy from the elastic behavior of the substrate, and one that scales with the cell perimeter, applying a contractile force per perimeter unit length. This allowed a fit to only three parameters: the elastic modulus of the cell, the cell contractility, and the perimeter line tension.

This simple model contrasts previous models that considered the cell a series of tensioned actin filaments between focal adhesions (7), which could better determine stress distribution, but requires specific knowledge of the size, spatial orientation, and strength of focal adhesions. The findings presented by Oakes et al. (6) must also be considered in light of the work of Han et al. (8), which used silicone-post arrays to demonstrate that the total force generated by a cell increases with the number of posts, and thus, increases the number of possible focal adhesions. In contrast, Oakes et al. (6) found that the number of focal adhesions on these continuous hydrogel substrates increased as the cell area increased, independent of the increase in strain energy. These articles are difficult to compare, inasmuch as the cell contact and measurements are different. However, these divergent results seem to indicate differing cell mechanotransduction on post array experiments, where cells may generate more force against an individual post than in a continuous matrix.

To broaden the applicability of this model, future studies may want to investigate the assumption of constant internal stiffness of the cell held across the spread areas, and times in this system of fibroblasts with relatively low contact areas. A study from Tee et al. (9) demonstrated that substrate stiffness and cell stiffness interact with each other. They found a tripling of cell stiffness in human mesenchymal stem cells plated on gels, with elastic moduli varying from 5 to 30 kPa, the same range as the study by Oakes et al. (6). This result suggests that a constant strain energy, as modeled here, may not hold in situations where a cell changes internal stiffness in response to external modulus.

In conclusion, the approach taken by Oakes et al. (6), and the finding that strain energy is conserved across substrates of differing elastic modulus, by alterations in both the force and the strain, has implications in cellular control of tension and in mechanosensing. A cell of a given area may seek to maintain constant work done in maintaining tension, with signaling arising from tensions and displacements on a constant number of focal adhesions. Future studies will likely want to compute and report strain energy, and investigate the effect of changes in the cell structure and internal stiffness.