Atomic force microscopy (AFM) can visualize functional biomolecules near the physiological condition, but the observed data are limited to the surface height of specimens. Since the AFM images highly depend on the probe tip shape, for successful inference of molecular structures from the measurement, the knowledge of the probe shape is required, but is often missing. Here, we developed a method of the rigid-body fitting to AFM images, which simultaneously finds the shape of the probe tip and the placement of the molecular structure via an exhaustive search. First, we examined four similarity scores via twin-experiments for four test proteins, finding that the cosine similarity score generally worked best, whereas the pixel-RMSD and the correlation coefficient were also useful. We then applied the method to two experimental high-speed-AFM images inferring the probe shape and the molecular placement. The results suggest that the appropriate similarity score can differ between target systems. For an actin filament image, the cosine similarity apparently worked best. For an image of the flagellar protein FlhA_C, we found the correlation coefficient gave better results. This difference may partly be attributed to the flexibility in the target molecule, ignored in the rigid-body fitting. The inferred tip shape and placement results can be further refined by other methods, such as the flexible fitting molecular dynamics simulations. The developed software is publicly available.

中文翻译：

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刚体拟合原子力显微镜图像以推断探针形状和生物分子结构

原子力显微镜 (AFM) 可以在生理条件附近可视化功能生物分子，但观察到的数据仅限于标本的表面高度。由于 AFM 图像高度依赖于探针尖端的形状，为了从测量中成功推断分子结构，需要探针形状的知识，但通常会丢失。在这里，我们开发了一种刚体拟合 AFM 图像的方法，该方法通过详尽的搜索同时找到探针尖端的形状和分子结构的位置。首先，我们通过四个测试蛋白质的双实验检查了四个相似性分数，发现余弦相似性分数通常效果最好，而像素-RMSD 和相关系数也很有用。然后，我们将该方法应用于两个实验性高速 AFM 图像，推断探针形状和分子位置。结果表明，目标系统之间适当的相似性分数可能不同。对于肌动蛋白丝图像，余弦相似性显然效果最好。鞭毛蛋白 FlhA 的图像_C，我们发现相关系数给出了更好的结果。这种差异可能部分归因于目标分子的灵活性，在刚体拟合中被忽略。推断的尖端形状和放置结果可以通过其他方法进一步细化，例如灵活的拟合分子动力学模拟。开发的软件是公开可用的。