Mahaffy R E, Park S, Gerde E, Käs J, Shih C K
Department of Physics, Center for Nonlinear Dynamics, University of Texas, Austin, Texas, USA.
Biophys J. 2004 Mar;86(3):1777-93. doi: 10.1016/S0006-3495(04)74245-9.
Viscoelasticity of the leading edge, i.e., the lamellipodium, of a cell is the key property for a deeper understanding of the active extension of a cell's leading edge. The fact that the lamellipodium of a cell is very thin (<1000 nm) imparts special challenges for accurate measurements of its viscoelastic behavior. It requires addressing strong substrate effects and comparatively high stresses (>1 kPa) on thin samples. We present the method for an atomic force microscopy-based microrheology that allows us to fully quantify the viscoelastic constants (elastic storage modulus, viscous loss modulus, and the Poisson ratio) of thin areas of a cell (<1000 nm) as well as those of thick areas. We account for substrate effects by applying two different models-a model for well-adhered regions (Chen model) and a model for nonadhered regions (Tu model). This method also provides detailed information about the adhered regions of a cell. The very thin regions relatively near the edge of NIH 3T3 fibroblasts can be identified by the Chen model as strongly adherent with an elastic strength of approximately 1.6 +/- 0.2 kPa and with an experimentally determined Poisson ratio of approximately 0.4 to 0.5. Further from the edge of these cells, the adherence decreases, and the Tu model is effective in evaluating its elastic strength ( approximately 0.6 +/- 0.1 kPa). Thus, our AFM-based microrheology allows us to correlate two key parameters of cell motility by relating elastic strength and the Poisson ratio to the adhesive state of a cell. This frequency-dependent measurement allows for the decomposition of the elastic modulus into loss and storage modulus. Applying this decomposition and Tu's and Chen's finite depth models allow us to obtain viscoelastic signatures in a frequency range from 50 to 300 Hz, showing a rubber plateau-like behavior.
细胞前缘（即片状伪足）的粘弹性是深入理解细胞前缘主动延伸的关键特性。细胞的片状伪足非常薄（<1000纳米），这给精确测量其粘弹性行为带来了特殊挑战。这需要解决强基底效应以及薄样品上相对较高的应力（>1千帕）问题。我们提出了一种基于原子力显微镜的微观流变学方法，该方法使我们能够全面量化细胞薄区域（<1000纳米）以及厚区域的粘弹性常数（弹性储能模量、粘性损耗模量和泊松比）。我们通过应用两种不同模型——一种用于良好粘附区域的模型（陈模型）和一种用于未粘附区域的模型（涂模型）来考虑基底效应。该方法还提供了关于细胞粘附区域的详细信息。靠近NIH 3T3成纤维细胞边缘的非常薄的区域可以通过陈模型确定为强粘附区域，其弹性强度约为1.6±0.2千帕，实验测定的泊松比约为0.4至0.5。离这些细胞边缘更远的地方，粘附性降低，涂模型可有效评估其弹性强度（约0.6±0.1千帕）。因此，我们基于原子力显微镜的微观流变学使我们能够通过将弹性强度和泊松比与细胞的粘附状态相关联，来关联细胞运动的两个关键参数。这种频率依赖性测量允许将弹性模量分解为损耗模量和储能模量。应用这种分解以及涂氏和陈氏有限深度模型，使我们能够在50至300赫兹的频率范围内获得粘弹性特征，呈现出类似橡胶平台的行为。
