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.

中文翻译：

---

气道平滑肌细胞的复数模量和顺应性

单元可以描述为具有结构弛豫的复杂粘弹性材料，其受热和化学非平衡过程调节。组织的形态和功能取决于细胞对机械力的物理反应。我们测量了三磷酸腺苷（ATP）耗竭和正常ATP条件下贴壁人气道平滑肌细胞的频率依赖性机械弛豫响应。复杂依从性的频率依赖性${Ĵ}^{*}$ 和模量 $G^{*}$ 在整个频率上测量 ${10}^{-\mathrm{1个}}<F<{10}^3$ 在选定温度之间的Hz $4<Ť<54{}^{\circ }\mathrm{C}$。我们的结果显示出特征弛豫特征，可以通过粘弹性液体的模式耦合理论（MCT）来解释。我们根据所谓的频谱分析频谱的形状${\mathrm{一种}}_4$对数缩放定律的场景。特征时标${\tau }_{\beta }$ 和 ${\tau }_{\alpha }$ 出现相应的能垒 ${Ë}_{\beta }\approx （10\text{–}20）{ķ}_{\mathrm{乙}}Ť$ 和 ${Ë}_{\alpha }\approx （20\text{–}30）{ķ}_{\mathrm{乙}}Ť$。我们证明细胞接近玻璃化转变。我们发现细胞在生理温度下变得更软，其表面结构更像液体，平台模量约为$0.1\text{–}0.8$ kPa与具有平稳模量的更固态的内部细胞骨架结构相比 $\mathrm{1个}\text{–}15$千帕 相应的粘度值为${10}^2\text{–}{10}^3$ Pa s接近于膜的表面结构 ${10}^4\text{–}{10}^6$ Pa s为核心细胞骨架结构。