Fig 1.
Images are processed and reduced to polymer backbone coordinates, then individual features are separated based upon architecture. Usually, only measurements of linear polymers are considered when calculating persistence length, lp.
Fig 2.
Polymer backbone isolation procedure.
The first steps to perform PS-Poly calculations on an AFM image of candidalysin are shown. Scale bars (yellow) are 100 nm. (A) Raw AFM image with topographic height, z, shown in greyscale. (B) Mask created from the AFM data. (C) New mask that has been expanded to a higher pixel density. (D) Skeleton created from the expanded mask. (E) Each molecule is registered as a unique object (pink circles).
Fig 3.
Examples of the different particle types identified through PS-Poly. Raw AFM image data of CL is shown next to processed skeleton images for Linear, Looped, Branched, and Branched-Looped polymers. The scale bar spans 50 nm and applies to all images.
Fig 4.
Convolutional filtering for end point determination.
(A) shows 9 x 9 pixel grids that are created from points i, ii, and iii on a skeletonized polymer. (B) shows the sixteen different shapes that were used in the convolutional filter that finds endpoint coordinates. Shapes are clustered via number of neighbors.
Fig 5.
(A) Each pixel in the image is centered in a 3 x 3 grid and a string of 1’s and 0’s begins at any point neighboring the centrally located reference pixel. In this example three unique paths (blue triangles) are found, identifying the reference pixel as a branch point. (B) Technique for prevention of branch point overcounting. Test point D has 3 neighboring 1-valued pixels, each of which corresponds to a unique path. Test point C also has 3 neighboring 1-valued pixels, but it does not exhibit three unique paths and is thus not a branch point. The non-unique path is marked by the orange triangle.
Fig 6.
Process for determining overlapped polymers.
(A) Cartoon showing an example of how an overlapped polymer may form via twisting upon surface adsorption. (B) AFM image of CL polymer. The height is shown in greyscale, the lateral scale bar (yellow) is 20 nm. (C) Skeleton created from the data in panel B shows a potential branch point junction (arrow) comprising the intersection of 4 branches. (D) New skeleton that incorporates height information. (E) Skeleton created at a threshold of 1.5 times the average height of the polymer distal from the junction identifies the polymer as overlapped.
Fig 7.
Skeletonization and interpolation of different polymer topologies.
Examples of linear, looped, and branched polymers are shown along with the skeleton (green) and interpolation (red).
Table 1.
Comparison of PS-Poly to previous work. Results were obtained via the end-to-end distance method for persistence length.
Fig 8.
The output of PS-Poly for shape categorization.
(A) Input AFM image of Candidalysin. The scale bar is 200 nm and the greyscale spans 12 nm. (B) Output for shape categorization is shown in tabular format. Two types of artifacts are identified, high points, defined as any point on a particle that is above 1.5 times the average height of the polymer backbone in the image and noise particles, defined as any particle in which 80% or more of the pixels are above 1.5 times the average height of the polymers in the image.
Fig 9.
Limiting the contour length fitting window provides robust persistence length calculations for CL.
Plot of mean-square end-to-end distance versus contour length for CL polymers. The persistence length was found to be 12.0 ± 0.9 nm. A 95% confidence interval (CI, teal shaded region) and 95% prediction band (pink shaded region) are shown.
Fig 10.
Persistence length calculations appear stable in the face of noise.
(A) Image sequence showing the addition of noise. The second-row images are detailed views of the region indicated in upper images (red rectangles). The added noise levels for each plot are indicated and range between 0 and 0.03 (std). Calculations of persistence length using different methods: (B) end-to-end distance and (C) tangent-tangent correlation. As before, only data within 10–30 nm contour windows were included in the fits. The expected range for new observations are indicated by the 95% prediction bands.
Fig 11.
Persistence length output in the presence of noise.
Persistence length results, as a function of added image noise, obtained by using the (A) R2 or (B) TTC methods. Rows in the tables are defined: noise std = noise level added to each image; All = total number of polymer features detected; Linear = number of features identified as Linear; 10 < L < 30 = number of Linear features exhibiting contour lengths within the 10–30 nm fitting window; = value of persistence length; 95% CI = confidence interval;
statistical goodness of fit parameter.
Fig 12.
The dependence of the radius of gyration () on contour length (L) for linear (top) and branched (bottom) candidalysin polymers. The WLC model predictions based on the persistence lengths (
) obtained from fitting the corresponding end-to-end distance data are overlaid.