Brückner Bastian Rouven, Nöding Helen, Janshoff Andreas
Georg-August-Universität Göttingen, Institute of Physical Chemistry, Göttingen, Germany.
Georg-August-Universität Göttingen, Institute of Physical Chemistry, Göttingen, Germany.
Biophys J. 2017 Feb 28;112(4):724-735. doi: 10.1016/j.bpj.2016.12.032.
The local mechanical properties of cells are frequently probed by force indentation experiments carried out with an atomic force microscope. Application of common contact models provides a single parameter, the Young's modulus, to describe the elastic properties of cells. The viscoelastic response of cells, however, is generally measured in separate microrheological experiments that provide complex shear moduli as a function of time or frequency. Here, we present a straightforward way to obtain rheological properties of cells from regular force distance curves collected in typical force indentation measurements. The method allows us to record the stress-strain relationship as well as changes in the weak power law of the viscoelastic moduli. We derive an analytical function based on the elastic-viscoelastic correspondence principle applied to Hertzian contact mechanics to model both indentation and retraction curves. Rheological properties are described by standard viscoelastic models and the paradigmatic weak power law found to interpret the viscoelastic properties of living cells best. We compare our method with atomic force microscopy-based active oscillatory microrheology and show that the method to determine the power law coefficient is robust against drift and largely independent of the indentation depth and indenter geometry. Cells were subject to Cytochalasin D treatment to provoke a drastic change in the power law coefficient and to demonstrate the feasibility of the approach to capture rheological changes extremely fast and precisely. The method is easily adaptable to different indenter geometries and acquires viscoelastic data with high spatiotemporal resolution.
细胞的局部力学特性通常通过原子力显微镜进行的力压痕实验来探测。应用常见的接触模型可提供一个单一参数——杨氏模量,以描述细胞的弹性特性。然而,细胞的粘弹性响应通常是在单独的微观流变学实验中测量的,这些实验提供了作为时间或频率函数的复剪切模量。在此,我们提出一种直接的方法,可从典型力压痕测量中收集的常规力-距离曲线获得细胞的流变特性。该方法使我们能够记录应力-应变关系以及粘弹性模量的弱幂律变化。我们基于应用于赫兹接触力学的弹性-粘弹性对应原理推导了一个解析函数,以对压痕和回缩曲线进行建模。流变特性由标准粘弹性模型描述,并且发现典型的弱幂律最能解释活细胞的粘弹性特性。我们将我们的方法与基于原子力显微镜的主动振荡微观流变学进行了比较,结果表明确定幂律系数的方法对漂移具有鲁棒性,并且在很大程度上与压痕深度和压头几何形状无关。对细胞进行细胞松弛素D处理,以引发幂律系数的剧烈变化,并证明该方法能够极其快速且精确地捕捉流变变化的可行性。该方法易于适应不同的压头几何形状,并以高时空分辨率获取粘弹性数据。