Rigid-body fitting to atomic force microscopy images for inferring probe shape and biomolecular structure

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 FlhAC, 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.Author summary: Observation of functional dynamics of individual biomolecules is important to understand molecular mechanisms of cellular phenomena. High-speed (HS) atomic force microscopy (AFM) is a powerful tool that enables us to visualize the real-time dynamics of working biomolecules under near-physiological conditions. However, the information available by the AFM images is limited to the two-dimensional surface shape detected via the force to the probe. While the surface information is affected by the shape of the probe tip, the probe shape itself cannot be directly measured before each AFM measurement. To overcome this problem, we have developed a computational method to simultaneously infer the probe tip shape and the molecular placement from an AFM image. We show that our method successfully estimates the effective AFM tip shape and visualizes a structure with a more accurate placement. The estimation of a molecular placement with the correct probe tip shape enables us to obtain more insights into functional dynamics of the molecule from HS-AFM images.