A cell can be described as a complex viscoelastic material with structural relaxations that is modulated by thermal and chemically nonequilibrium processes. Tissue morphology and function rely upon cells' physical responses to mechanical force. We measured the frequency-dependent mechanical relaxation response of adherent human airway smooth muscle cells under adenosine triphosphate (ATP) depletion and normal ATP conditions. The frequency dependence of the complex compliance $J^{*}$ and modulus $G^{*}$ was measured over the frequencies ${10}^{-1}<f<{10}^3$ Hz at selected temperatures between $4<T<54{}^{\circ }\mathrm{C}$. Our results show characteristic relaxation features which can be interpreted by the mode-coupling theory (MCT) of viscoelastic liquids. We analyze the shape of the spectra in terms of a so-called $A_4$ scenario with logarithmic scaling laws. Characteristic timescales ${\tau }_{\beta }$ and ${\tau }_{\alpha }$ appear with corresponding energy barriers $E_{\beta }\approx \left(10\text{–}20\right)k_{\mathrm{B}}T$ and $E_{\alpha }\approx \left(20\text{–}30\right)k_{\mathrm{B}}T$. We demonstrate that cells are close to a glass transition. We find that the cell becomes softer around physiological temperatures, where its surface structure is more liquid-like with a plateau modulus around $0.1\text{–}0.8$ kPa compared with the more solid-like interior cytoskeletal structures with a plateau modulus $1\text{–}15$ kPa. Corresponding values for the viscosity are ${10}^2\text{–}{10}^3$ Pa s for the surface structures closer to the membrane and ${10}^4\text{–}{10}^6$ Pa s for the core cytoskeletal structures.

• Received 31 January 2019
• Accepted 24 January 2020

DOI:https://doi.org/10.1103/PhysRevE.101.032410