Department of Physics, Clarkson University, Potsdam, NY 13699, USA.
Ultramicroscopy. 2012 Oct;121:16-24. doi: 10.1016/j.ultramic.2012.06.014. Epub 2012 Jul 6.
Atomic force microscopy (AFM) can be used to study mechanics at the nanoscale. Biological surfaces and nanocomposites have typically heterogeneous surfaces, both mechanically and chemically. When studying such surfaces with AFM, one needs to collect a large amount of data to make statistically sound conclusions. It is time- and resource-consuming to process each force curve separately. The analysis of an averaged raw force data is a simple and time saving option, which also averages out the noise and measurement artifacts of the force curves being analyzed. Moreover, some biomedical applications require just an average number per biological cell. Here we investigate such averaging, study the possible artifacts due to the averaging, and demonstrate how to minimize or even to avoid them. We analyze two ways of doing the averaging: over the force data for each particular distance (method 1, the most commonly used way), and over the distances for each particular force (method 2). We derive the errors of the methods in finding to the true average rigidity modulus. We show that both methods are accurate (the error is <2%) when the heterogeneity of the surface rigidity is small (<50%). When the heterogeneity is large (>100×), method 2 underestimates the average rigidity modulus by a factor of 2, whereas the error of method 1 is only 15%. However, when analyzing the different surface chemistry, which reveals itself in the changing long-range forces, the accuracy of the methods behave oppositely: method 1 can produce a noticeable averaging artifact in the deriving of the long-range forces; whereas method 2 can be successfully used to derive the averaged long-range force parameters without artifacts. We exemplify our conclusions by the study of human cervical cancer and normal epithelial cells, which demonstrate different degrees of heterogeneity.
原子力显微镜（AFM）可用于研究纳米尺度的力学。生物表面和纳米复合材料通常具有机械和化学上不均匀的表面。当使用 AFM 研究此类表面时，需要收集大量数据才能得出统计学上合理的结论。分别处理每个力曲线既耗时又耗资源。对原始力数据进行平均分析是一种简单且节省时间的选择，它还可以平均分析的力曲线中的噪声和测量伪影。此外，一些生物医学应用只需要每个生物细胞的平均数量。在这里，我们研究了这种平均化，研究了由于平均化而产生的可能伪影，并演示了如何最小化甚至避免这些伪影。我们分析了两种进行平均化的方法：一种是对每个特定距离的力数据进行平均（方法 1，最常用的方法），另一种是对每个特定力的距离进行平均（方法 2）。我们推导出了这两种方法在寻找真实平均刚性模量时的误差。我们表明，当表面刚性的不均匀性较小时（<50%），这两种方法都是准确的（误差<2%）。当不均匀性较大（>100×）时，方法 2 会低估平均刚性模量的 2 倍，而方法 1 的误差仅为 15%。然而，当分析不同的表面化学性质时，表面化学性质会在变化的长程力中表现出来，这两种方法的准确性表现出相反的趋势：方法 1 会在推导长程力时产生明显的平均化伪影；而方法 2 可以成功地用于推导没有伪影的平均长程力参数。我们用人宫颈癌和正常上皮细胞的研究为例，证明了它们具有不同程度的不均匀性。
