We report a scaling law that governs both the elastic and frictional properties of a wide variety of living cell types, over a wide range of time scales and under a variety of biological interventions. This scaling identifies these cells as soft glassy materials existing close to a glass transition, and implies that cytoskeletal proteins may regulate cell mechanical properties mainly by modulating the effective noise temperature of the matrix. The practical implications are that the effective noise temperature is an easily quantified measure of the ability of the cytoskeleton to deform, flow, and reorganize.

Adherent cells exert tractions on their surroundings. These tractions can be measured by observing the displacements of beads embedded on a flexible gel substrate on which the cells are cultured. This paper presents an exact solution to the problem of computing the traction field from the observed displacement field. The solution rests on recasting the relationship between displacements and tractions into Fourier space, where the recovery of the traction field is especially simple. We present two subcases of the solution, depending on whether or not tractions outside the observed cell boundaries are set to be zero. The implementation is computationally efficient. We also give the solution for the traction field in a representative human airway smooth muscle cell contracted by treatment with histamine. Finally, we give explicit formulas for reducing the traction and displacement fields to contraction moments, the orientation of the principal axes of traction, and the strain energy imparted by the cell to the substrate.

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.

The cytoskeleton (CSK) is a crowded network of structural proteins that stabilizes cell shape and drives cell motions. Recent studies on the dynamics of the CSK have established that a wide variety of cell types exhibit rheology in which responses are not tied to any particular relaxation times and are thus scale-free. Scale-free rheology is often found in a class of materials called soft glasses, but not all materials expressing scale-free rheology are glassy (see plastics, wood, concrete or some metals for example). As such, the extent to which dynamics of the CSK might be regarded as glassy remained an open question. Here we report both forced and spontaneous motions of microbeads tightly bound to the CSK of human muscle cells. Large oscillatory shear fluidized the CSK matrix, which was followed by slow scale-free recovery of rheological properties (aging). Spontaneous bead motions were subdiffusive at short times but superdiffusive at longer times; intermittent motions reflecting nanoscale CSK rearrangements depended on both the approach to kinetic arrest and energy release due to ATP hydrolysis. Aging, intermittency, and approach to kinetic arrest establish a striking analogy between the behaviour of the living CSK and that of inert non-equilibrium systems, including soft glasses, but with important differences that are highly ATP-dependent. These mesoscale dynamics link integrative CSK functions to underlying molecular events, and represent an important intersection of topical issues in condensed matter physics and systems biology.