Fig 1.
A pseudo-AFM image generation scheme and the search algorithm.
(A) The AFM probe tip (grey) is modeled as a hemisphere connected to a circular frustum of a cone. The shape of tip is determined by the tip radius (r) and a half-apex angle of cone (θ). The pseudo-AFM image represents the height of the tip when the tip collides with any atom (red circle) of the target molecule. (B) The exhaustive search finds the best match in the discrete space made of the orientation and the translation of the target molecule and the radius and the half-apex angle of the probe tip.
Fig 2.
Twin-experiments for a molecular model of dynein.
(A) One of the reference AFM images in the twin-experiment, with the 1 nm/10 degree probe. (B) The image generated from the predicted structure with the cosine similarity. (C) One of the reference AFM images with the 3 nm/20 degree probe. (D) The image generated from the predicted structure with the cosine similarity. The color bar shows the height in nm (shared by all of the images here). (E-L) The results of twin-experiment with the reference image generated by the 1 nm/10 degree probe. Results of 10 replicated runs are overlaid; each run uses different reference AFM images with independent noise. The row corresponds to the cost function. The leftmost 4 panels (E, G, I, K) show the lowest scores of images. The next 4 panels (F, H, J, L) show the structure-RMSD of the structures with the lowest score. Red vertical dashed lines show the ground-truth probe shape. Results from two probe angles, 10 degree in red and 20 degree in blue, are plotted in parallel. Solid lines connect the representative results from one reference AFM image. (M-T) The results of twin-experiment with the reference image generated by 3 nm/20 degree probe, shown in the same way as E-L. The cyan vertical dashed lines show the ground-truth probe shape.
Fig 3.
Twin-experiments for an actin monomer.
(A) One of the reference images in the twin-experiment, generated with the 1 nm/10 degree probe. (B) The image generated from the predicted structure with the cosine similarity-based cost function. (C) One of the reference images in the twin-experiment with the 3 nm/20 degree probe. (D) The image generated from the predicted structure with the cosine similarity-based cost function. The color bar shows the height in nm (shared by all of the images here). (E-L) The results of twin-experiment with a reference image generated by the 1 nm/10 degree probe. Results of 10 replicated runs are overlaid; each run uses different reference AFM images with independent noise. The row corresponds to the cost function. The leftmost 4 panels (E, G, I, K) show the lowest scores of images. The next 4 panels (F, H, J, L) show the structure-RMSD of the structures with the lowest score. Red vertical dashed lines show the ground-truth probe shape. Results from two probe angles, 10 degree in red and 20 degree in blue, are plotted in parallel. Solid lines connect the representative results from one reference AFM image. (M-T) The results of twin-experiment with the reference image generated by the 3 nm/20 degree probe, shown in the same way as E-L. The cyan vertical dashed lines show the ground-truth probe shape.
Fig 4.
Twin-experiment for actin filament.
(A) One of the reference images used in this twin experiment, generated by a 3 nm/20 degree probe, with the pixel width 1 nm. (B) The image generated using the structure predicted from the image (A) with the cosine similarity-based cost function. (C) The difference between (A) and (B). (D) One of the reference images used in this twin experiment, generated by a 3 nm/20 degree probe. Unlike the panel (A), the pixel width is 2 nm, which is twice as large as that of panel (A). (E) The image generated from the structure predicted from the image (D) with the cosine similarity-based cost function. (F) The difference between panel (D) and (E). (A, B, D, E) The colormap of all the pseudo-AFM images is shared. (C, F) The color-bar of the difference maps is shared. (G) The resulting best scores of the prediction from the image with 1 nm pixel. (H) The structure-RMSD between the ground-truth structure and the predicted structure from the image with 1nm pixel. (I) The resulting best scores of the prediction from the image with 2 nm-wide pixels. (J) The structure-RMSD between the ground-truth structure and the predicted structure from the image with 2 nm-wide pixels. (G-J) Results from two probe angles, 10 degree in red and 20 degree in blue, are plotted in parallel. Solid lines connect the representative results from one reference AFM image. The cyan line shows the ground-truth probe shape.
Fig 5.
Exhaustive search rigid body fitting to an experimental HS-AFM image of actin filament.
(A) The stage plane estimated from the background regions of experimental AFM image. (B) The AFM image after the correction of stage position. (C) The reference image used in the rigid-body fitting. It is taken from the lower left rectangular region of the image in B. (D) The pseudo-AFM image generated by the best estimation with the cosine similarity score with the 3 nm/16 degree probe that shows the best score. (E) The absolute value of difference between C and D. (F) The resulting actin filament structure model on top of the reference AFM image. In (A-F), the color map is given in nm unit. In (D) and (F), the orientation of the generated actin filament model is indicated by (+) and (-) labels. (G-I) The cost values of the best fit using varying probe shape. From left to right, the result using the cosine similarity (G), the pixel-RMSD (H), and the correlation coefficient (I) are plotted. In (G-I), the marker color and shape represent the probe angle and three consecutive markers have the same probe radius. (J, K) The results of finer-grid search of probe angle with radius 3.0, using the cosine similarity score (J) and the pixel-RMSD score (K).
Fig 6.
Exhaustive search rigid body fitting to an HS-AFM experimental image of FlhAC ring [36].
(A) The stage plane estimated from the background regions of experimental AFM image. (B) The AFM image after the correction of stage plane. (C) The reference image used in the rigid-body fitting. It is taken from the left middle rectangular region of the image in (B). (D) The pseudo-AFM image generated by the estimation result with the correlation coefficient. (E) The absolute value of differences between (C) and (D). (F) The resulting FlhAC nonamer ring structure model on top of the reference AFM image. (G-I) The result of fitting using cosine similarity (G), pixel-RMSD (H), and correlation coefficient (I). The colors and shapes of the marker represents the angle of the probe. The angle is 5 (dot), 10 (triangle), 15 (diamond), 20 (thin diamond), 25 (x), and 30 degrees (hexagon), respectively. Within 6 trials using varying probe angles, the same probe radius is used.