We have measured the elastic properties of live cells by Atomic Force Microscope (AFM) using different tip geometries commonly used in AFM studies. Soft 4-sided pyramidal probes (spring constant = 12 and 30 mN/m, radius 20 nm), 3-sided pyramidal probes (spring constant = 100 mN/m, radius 65-75 nm), flat (circular) probes (spring constant = 63 mN/m, radius 290 nm) and spherical probes (spring constant = 43 mN/m, radius 5 μm) have been used. Cells (3T3 fibroblasts) having elastic moduli around 0.5 kPa were investigated. We found that cell measured stiffness shows a systematic dependence on tip geometry: the sharper the tip, the higher the average modulus values. We hypothesize that the blunter the tip, the larger the contact area over which the mechanical response is measured or averaged. If there are small-scale stiffer areas (like actin bundles) they will be easier to pick up by a sharp probe. This effect can be seen in the wider distribution of the histograms of the measured elastic moduli on cells. Furthermore, non-linear responses of cells may be present due to the high average pressures applied by sharp probes, which would lead to an overestimation of the Young's modulus. Pressure versus contact radius simulations for the different tip geometries for a 0.5 kPa sample suggested similar average pressure for Bio-MLCTs, PFQNM and cut tips, except spherical tips that showed much lower average pressure at the same 400 nm indentation. However, real data of the cells suggested different results. Using the same indentation depth (400 nm), PFQNM and Bio-MLCTs showed similar average pressure and it decreased for cut and spherical tips. The calculated contact area at 400 nm cell indentation, using the obtained apparent Young's modulus for each tip geometry, showed the following distribution: Bio-MLCTs < PFQNM < cut << spherical. In summary, tip geometry as well as average pressure and tip-sample contact area are important parameters to take into account when measuring mechanical properties of soft samples. The larger the tip radius, the larger the contact area that will lead to a more evenly distribution of the applied pressure.

中文翻译：

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悬臂尖端几何形状和接触模型对细胞 AFM 弹性测量的影响

我们通过原子力显微镜 (AFM) 使用 AFM 研究中常用的不同尖端几何形状测量了活细胞的弹性特性。软 4 面锥体探头（弹簧常数 = 12 和 30 mN/m，半径 20 nm）、3 面锥体探头（弹簧常数 = 100 mN/m，半径 65-75 nm）、扁平（圆形）探头（弹簧使用了弹簧常数 = 63 mN/m，半径 290 nm）和球形探针（弹簧常数 = 43 mN/m，半径 5 μm）。研究了弹性模量约为0.5 kPa的细胞（3T3成纤维细胞）。我们发现，细胞测量的刚度显示出对尖端几何形状的系统依赖性：尖端越锋利，平均模量值越高。我们假设尖端越钝，测量或平均机械响应的接触面积就越大。如果存在小范围较硬的区域（如肌动蛋白束），则它们将更容易被锋利的探针拾取。这种效应可以从细胞上测量的弹性模量的直方图的更广泛分布中看出。此外，由于尖锐探针施加的高平均压力，可能会出现细胞的非线性响应，这将导致杨氏模量的高估。对 0.5 kPa 样品的不同尖端几何形状的压力与接触半径模拟表明，Bio-MLCT、PFQNM 和切割尖端的平均压力相似，但球形尖端在相同的 400 nm 压痕下显示出低得多的平均压力。然而，细胞的真实数据表明了不同的结果。使用相同的压痕深度（400 nm），PFQNM 和 Bio-MLCT 显示出相似的平均压力，并且对于切割尖端和球形尖端而言，平均压力有所下降。使用获得的每个尖端几何形状的表观杨氏模量计算出 400 nm 细胞压痕处的接触面积，显示出以下分布：Bio-MLCT < PFQNM < 切口 << 球形。总之，尖端几何形状以及平均压力和尖端与样品接触面积是测量软样品机械性能时需要考虑的重要参数。尖端半径越大，接触面积就越大，从而使施加的压力分布更均匀。尖端几何形状以及平均压力和尖端与样品接触面积是测量软样品机械性能时需要考虑的重要参数。尖端半径越大，接触面积就越大，从而使施加的压力分布更均匀。尖端几何形状以及平均压力和尖端与样品接触面积是测量软样品机械性能时需要考虑的重要参数。尖端半径越大，接触面积就越大，从而使施加的压力分布更均匀。