Bausch A R, Ziemann F, Boulbitch A A, Jacobson K, Sackmann E
Physik Department E22 (Biophysics Group), Technische Universität München, D-85748 Garching, Germany.
Biophys J. 1998 Oct;75(4):2038-49. doi: 10.1016/S0006-3495(98)77646-5.
A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.
设计了一种磁珠微流变仪，它能够对直径4.5微米的顺磁珠施加高达10⁴皮牛的力。该仪器用于测量贴壁成纤维细胞表面的局部粘弹性特性。通过粒子跟踪记录施加在固定于细胞膜整合素受体上的磁珠上、大小为500 - 2500皮牛（持续时间约1秒）的切向力脉冲所引发的蠕变响应和松弛曲线。建立了由弹性偏转、应力松弛和粘性流动组成的线性三相蠕变响应。根据一个阻尼器和一个沃伊特体的串联组合来分析粘弹性响应曲线，这使得能够通过三个参数来表征贴壁细胞表面的粘弹性行为：有效弹性常数、粘度和松弛时间。通过观察固定在膜上的非磁性胶体探针组件的诱导运动，可视化细胞表面局部切向力产生的位移场。发现位移场随距磁珠的距离迅速衰减。确定了屏蔽弹性场的截止半径Rc约为7微米。通过观察细胞内区室的诱导偏转，确定剪切场部分穿透到细胞质中。细胞膜被建模为一个剪切模量为μ的薄弹性板，与一个粘弹性层相连，该粘弹性层在另一侧固定于固体支撑物上；前者代表膜/肌动蛋白皮质，后者代表细胞骨架对细胞膜变形的贡献。其特征在于表征细胞骨架弹性的耦合常数χ。耦合常数χ和表面剪切模量μ由磁珠和非磁珠的测量位移获得。根据该模型分析实验数据，发现表面剪切模量μ*约为2×10⁻³帕·米至4×10⁻³帕·米。假设板的厚度约为0.1微米，估算出平均体积剪切模量μ约为(2 / 4)×10⁻⁴帕，这与原子力显微镜获得的数据合理相符。阻尼器的粘度与细胞质的表观粘度相关，这是通过假设顶部膜通过粘性介质与底部（固定）膜相连而得到的。通过应用膜蛋白在支撑膜中的扩散理论，我们发现摩擦系数bc约为2×10⁹帕·秒/米，对应细胞质粘度为2×10³帕·秒。
