A novel approach to actin bundle identification

and analysis in fluorescence microscopy images

Malek Hamed

Supervisory Committee:

Dr. Stephen Arce, Dr. David Gilland, and Dr. Yiider Tseng

Oral Defense Date:

March 27, 2017

H a m e d | 2

Structural and organizational analysis of filamentous actin structures in microscope images is a

frequent step in cell research. This analysis is commonly qualitative and based on human visual

inspection, limiting its accuracy and quantitative import. Current alternatives generally involve

specialized equipment, require high resolution images, or limit the structural information

regarding individual filaments that can be extracted. Here, a new approach is developed and

applied to wide-field fluorescence microscopy images of actin-stained cells. This analysis was

successfully used to extract information regarding individual filament bundles as well as to

produce distributional analyses useful in research. A few weaknesses are noted, including

occasional erroneous segmentation of intersecting filament bundles and poor results for

images with high levels of noise. Future work should investigate the relationships between

extracted structural information and physical parameters of actual filament bundles to

strengthen and broaden the conclusions that may be drawn using this analysis.

H a m e d | 3

Effective analysis of the filamentous actin cytoskeleton is an important step in many

areas of cell biology research. The relationship that the structure of the actin cytoskeleton has

with various other parameters, such as cell cycle progression [1], action of signaling molecules

[2], and extracellular attachment [3], is an active area of research. Analysis required in this

research frequently consists of qualitative visual inspection of fluorescence microscopy images

by a human investigator [4], which necessarily presents problems of consistency, accuracy, and

time expenditure. This approach also limits the degree of quantitative data that can be

gathered from biological samples, restricting the potential import of conclusions. Computerized

analysis methods offer advantages in such cases.

Actin filaments exist as double helix structures with diameters of approximately 7 nm

[5]. While these are too small to be observed individually usually typical fluorescence

microscopy, higher-order actin bundles can be observed and are the focus this work. The stress

fiber, an actin bundle structure of particular interest here, exists on the order of tenths of a

micrometer in diameter [6]; other types of actin bundles have similar diameters [7].

Current approaches for producing quantitative information about subcellular fibrillar

structures are diverse, and can be divided into pre- and post-imaging methods [4]. Pre-imaging

methods involve the use of specialized equipment to directly produce data related to filament

organization and structure. These approaches involved the use of polarization microscopy,

used, for example, to gain structural and organizational data for yeast septin filaments [8], and

x-ray scattering, as used by Müller and coworkers to study microfibril arrangements within

cellulose fibers [9]. These methods, however, require resources not readily available to most

labs in the field and are not as easily melded with the procedures and image-capture

techniques familiar to most researchers.

Post-imaging methods involve the processing of microscope images to identify regions

corresponding to the fibrillar structures of interest and analysis of signal to produce

information. Researchers have used computational methods based on skeletonization by

morphological thinning, as in [10] and [11], and intensity-based thresholding, as used in the

University of North Carolina’s Network Extractor (http://cismm.web.unc.edu/software/). These

H a m e d | 4

and alternative methods [12] tend to be designed for high-resolution images such as those

captured by scanning electron microscopy or electron tomography, where individual fibers are

clearly distinct. While they provide detailed information about network structure, they

generally are not designed to describe structural parameters such as fiber diameter and length.

Newer software tools have attempted to correct some of the problems of accuracy,

usability, and convenience associated with existing approaches. FibrilTool is an ImageJ plug-in

that works with readily-producible fluorescence microscope images to provide information

about orientation and anisotropy of fibrillar structures [4]. It is, however, not designed to

structurally describe individual fiber bundles. SOAX is another tool for describing fibrillar

networks in detail [13]; however, it derives data based on filament network centerlines and is

not designed to directly preserve the thickness of filamentous bundles; rather, bundle thickness

is inferred from pixel intensities along the centerline. An alternative approach is here

attempted.

In this study, I aim to design a computerized analysis tool able to identify filamentous

actin bundles in fluorescence microscopy images of cells and therewith extract structural and

organizational information involving bundle diameter, length, and orientation, with minimal

human input. It is hypothesized that, by appropriately subsampling cell images and extracting

orientation information from these subsamples, I will be able to reliably construct

segmentation masks for individual fiber bundles and, from these, produce useful descriptive

data.

Code was developed using Matlab (http://www.mathworks.com/) and utilizes some

functions provided in its Image Processing Toolbox.

Note that I will henceforth favor the term “filaments” rather than “actin filament

bundles” for conciseness and in reflection of the proposed potential to extend this technique to

other applications.

H a m e d | 5

The filament identification algorithm consists of:

1. Subsampling of the original image.

2. Identification of subsample principle orientations and associated filament subdivisions.

3. Filament reconstruction based on parameter matching between filament subdivisions.

This algorithm functions on the following premises:

1. By subsampling an image into appropriately-sized bins, filaments can be divided into

essentially straight subdivisions with identifiable principle axis orientations.

2. Using this directionality information, we can identify oriented filament subdivisions

otherwise indistinguishable with standard thresholding techniques.

The user sets the sampling bin size, in pixels, to begin the analysis, depending on the

pixel width-to-distance scaling factor associated with his or her microscopy setup. I report that

a bin size equivalent to approximately 1 µm × 1 µm is optimum for the sizes of actin bundles

commonly seen in fluorescence microscopy images.

The software begins by sampling a provided raw grayscale actin fluorescence image into

S/n2 subsamples, where S is the area in pixels of the provided image and n is the bin width in

pixels. By intensity thresholding, the program selects subsamples located within the cell area.

Within each subsample, the principle orientation (i.e. the prominent orientation of the

subdivided filament contained within the subsample) is determined considering two factors: (1)

the ratio of variations (ROV) and (2) peak prominences. ROV (Figure 1) is a novel parameter

that I here present for determining the principle orientation of filamentous signals. ROV is

based on the presumption that the signal intensity of an image sample containing an oriented

filamentous signal will show minimum variation when the sample is traversed along the

direction of the filament and maximum variation when traversed perpendicularly to the

direction of the filament.

Another parameter used in calculating ROV must here be defined. The mean directional

profile (MDP) of a given subsample at an angle α is defined as the array of mean intensities of

pixel cross sections (green segments in Figure 1) arranged perpendicularly to α. That is, the

H a m e d | 6

mean intensity of the pixels along each green line segment is calculated and arranged

consecutively into an MDP.

To calculate the ROV of a given subsample from the MDP, (1) the MDP at each 10-

degree interval in a 180-degree range of orientations is calculated. Then, (2) the MDP’s range (r,

i.e. maximum – minimum) is calculated at each angle to determine the variation of intensity

values along α. Finally, (3) the ROV at each angle is determine by finding the ratio of the range,

r0, at that angle to that calculated for the angle oriented perpendicularly to it, r90.

𝑅𝑂𝑉(𝛼) =𝑟0𝑟90

=max(𝑀𝐷𝑃0) − min(𝑀𝐷𝑃0)

max(𝑀𝐷𝑃90) − min(𝑀𝐷𝑃90)

H a m e d | 7

The algorithm also calculates the prominences of peaks within the MDP at each angle,

based on the assumption that more prominent peaks will be observable when the sample is

traversed perpendicular to the direction of its filament(s). ROVs and peak prominences

calculated for a representative subsample are shown in Figure 2. Finally, the principle

orientation of the filament subdivision within a subsample is determined by locating the

α

Figure 1. Illustration of the calculation of MDP and ROV for a representative subsample. The MDP at α is calculated by taking pixel cross sections (green lines) directed at α + 90° and calculating the mean intensities of pixels along each. For consistency and to reduce the influence of noise, all cross sections are set to be equal in length to the longest, central cross section (in this case, along the square’s diagonal), such that non-central cross sections extend beyond the subsample. This yields an MDP corresponding to the angle α, which is a profile of these mean values. To determine ROV, the MDP is calculated at each 10-degree interval along a 180-degree array of α values, and the range for each MDP is calculated. Then, the ratio of the MDP range at each α to that at α + 90° is calculated, resulting in the ROV profile for the subsample.

90°

H a m e d | 8

maximum of the element-wise multiplication of the ROV and peak prominence profiles and

adding 90° (Figure 2C).

The result of this process is an orientation matrix, which contains the principle

orientation (if applicable) of each subsample of the original image.

Figure 2. Determination of principle orientation for a given subsample. After calculating the ROV profile (A) and peak prominence profile (B) for a given subsample, these are multiplied element-by-element (C), the angle corresponding to the maximum of the resulting array (red dashed arrow) is located, and the principle orientation is identified at 90° greater (black arrow).

Angle (α, degrees)

Rat

io o

f va

riat

ion

(R

OV

)

Angle (α, degrees)

Pea

k p

rom

inen

ce

Angle (α, degrees)

RO

V *

Pea

k p

rom

inen

ce

+ 90°

H a m e d | 9

Identification of filament subdivisions

Having constructed the orientation matrix, the software then identifies filament

subdivisions oriented along the principle orientation of each subsample. Because a key

objective was to produce information regarding the structural characteristics of individual fiber

bundles, I have therefore attempted to produce a method that maintains information regarding

fiber diameter. I thus assume that a bundle’s diameter is related to the full width at half

maximum (FWHM) of its associated linear signal. I find that this is reasonable, although I have

not found studies clearly explicating this assumption. Pending further research, for the

purposes of this analysis, I assume that the FWHM of the MDP is equivalent to four times the

fiber diameter.

Therefore, for each subsample, the program calculates the maximum and FWHM of the

MDP perpendicular to the principle orientation. A value of ‘true’ is then assigned to a

corresponding linear segment in the processed image. Linear segments of adjacent subsamples

in contact with one another and with a difference in principle orientation less than a threshold

value are assigned to be segments of the same original filament bundle; these are given a

common integer identifier to distinguish them from segments belonging to other filaments

bundles. The result is a matrix of integer identifiers specifying grouped line segment

subdivisions of the original filament bundles. Due to image aberrations and other

imperfections, this step does not produce entirely unbroken regions associated with contiguous

filament bundles.

Rejoining of detached segment groups

The final step in the identification of individual filament bundles is to rejoin detached

segment groups that should be contiguous. This consists of two steps:

1. Assignment of an orientation to each segment group.

2. Reconnection based on adjacency and similarity of orientation.

Assignment of an orientation is performed by producing an ellipse with the same second

moments as the region of grouped segments and then determining the angle of its major axis

H a m e d | 10

with respect to the positive x axis. This is achieved using an inbuilt function of Matlab’s Image

Processing Toolbox.

Next, the program identifies grouped segment regions that (1) are adjacent (i.e. with

associated pixels in direct contact) and (2) have orientations differing by less than a threshold.

These are then assigned a common integer identifier to categorize them each as a unique

filament bundle. This image is processed to remove sufficiently small or abnormally shaped

regions.

Filament bundle analysis

To obtain useful organizational and structural information about the identified filament

bundles, the program analyzes each unique filament bundle connected component within the

processed image using Matlab’s Image Processing toolbox, yielding the following parameters

(among other potential data):

1. Orientation. The overall orientation of an actin filament bundle is determined by

calculating an ellipse with the same second moments and determining the angle that its

major axis makes with the positive x axis.

2. Length. A rough estimate of the filament length is obtained by calculating the length of

the corresponding ellipse’s major axis.

3. Diameter. Given that the width of the identified connected component is proportional

to the FWHM of the raw signal of the fiber bundle (as explained above), we can

estimate the diameter of the fiber bundle by dividing the area of the connected

component by its length (as explained in 2.).

From this primary information, we can then calculate additional useful higher-order

information about the actin cytoskeleton. For example, the orientation distribution of the

filament bundles can be determined by calculating the number of filament bundles oriented at

a range of different angles. From this we can make conclusions about the degree of anisotropy

or isotropy of the filament network. Another potentially useful set of data that can be

calculated using the primary data above is the distribution of filament bundle diameters

H a m e d | 11

relative to their orientations. Assuming that filament bundle diameter is related to tensile

strength, this might allow us to study the mechanical stress state of a cell at different angles.

Cell preparation and microscopy

This system was applied to two cell images for assessment. The cells were NIH 3T3

fibroblasts fluorescently stained for actin. Fixation buffer consisted of 4% paraformaldehyde

and 0.5% Triton X-100 in phosphate buffered saline (PBS), and blocking buffer consisted of 2%

bovine serum albumin and 0.02% Triton X-100 in PBS. Fixation buffer and blocking buffer were

applied consecutively to the cells on coverslips for 30 minutes each at room temperature. Cells

were then stained with a 1:40 dilution of Alexa Fluor 568-phalloidin (Sigma-Aldrich) in the

secondary antibody solution.

Cells were visualized using a TE-2000 imaging acquisition system with a 60× objective, a

Cascade:1K CCD camera, and an X-cite 120 PC fluorescent light source. Acquisitions were

conducted with a 500-ms exposure time, no binning, and 100% light intensity.

Filament Identification

The effectiveness of this tool was evaluated in identifying and analyzing a variety of test

images.

The tool was first tested upon the artificial image in Figure 3A, which depicts clearly

apparent lines against a dark background, representing well-defined, high-contrast actin

filament bundles against a darker background. The result after the first portion of the

identification process is shown in Figure 3B, and that after the final filament rejoining process is

shown in Figure 3C.

The tool is mostly successful when applied in this case. The four short parallel lines at

the upper left of the image are appropriately segmented as distinct, intact filaments. The three

segments to the right are each segmented into two portions. We observe that inappropriate

divisions tend to be identified at intersections between ‘fibers.’ The identified fibers are slightly

H a m e d | 12

jagged in shape relative to the original straight lines. The software was successfully able to

identify regions before and after the sharp curve at the far right as belonging to a single fiber.

The identification program was then applied to a cell image with clearly defined fibers.

Individual fibers are generally recognized correctly. As apparent in Figure 4, the closely spaced

parallel fibers at the center of the cell are identified as distinct. Occasional error in

A

C B

Figure 3. The filament identification system applied to a mock image. (A) shows the original. (B) is the image after the initial identification process. Unique colors indicate distinct identified filaments. The three linear segments at the top left are correctly identified as distinct and intact, while the overlapping segments to the right are each segmented into multiple fragments. (C) is the result after the rejoining process. Segmentation is correct except for three incorrect divisions occurring at intersections of the filaments at the right.

H a m e d | 13

distinguishing adjacent, parallel fibers is apparent as demonstrated in Figure 4C. Contiguous

fibers also generally remain intact after the final step of segmentation, although occasional

errors in this operation are also evident.

We finally tested the filament identification method on an image with high levels of

apparent noise and less clearly-defined actin bundles (Figure 5A). The resulting actin

segmentation is less successful than the previous. While the fibers of high intensity in the

Figure 4. The filament identification system applied to an image of a cell with fluorescently labeled actin. (A) shows the original. (B) is the image after the initial identification process. Unique colors indicate distinct identified filaments. After this step, incorrect intra-filament divisions remain. (C) Noise segments have been removed, and most intra-filament divisions have been corrected. Occasional joining of distinct filaments is noted (yellow arrow). Scale bar = 50 μm.

A

C B

H a m e d | 14

center of the cell are segmented mostly as distinct and intact, the fibers in the less intense

regions of the cell area are not consistently identified; rather, significant irrelevant information

is generated in these regions (Figure 5C).

Figure 5. The filament identification system applied to a cell image with high noise. (A) shows the original. (B) is the image after the initial identification process. Unique colors indicate distinct identified filaments. After this step, incorrect intra-filament divisions remain, as well as a large degree of irrelevant segmentation in areas corresponding to low contrast in the original image. (C) While most intra-filament divisions are corrected after this step, much noise remains, and most filaments in the low contrast regions remain unsegmented. Scale bar = 50 μm.

A

C B

H a m e d | 15

Individual filament analysis

The software allows the user to select individual filament representations in the

segmented image and receive descriptive parameters. The results when applied to

representative filaments are shown in Figure 6. The reported length and orientation agree with

a visual analysis of the raw image. The diameter, at this stage, cannot be confirmed definitively

because we have no conclusive information concerning the relationship between a signal’s

FWHM and the corresponding filament’s original diameter. It does, however, agree with a

rough visual estimate. The program is less successful in reporting diameters when adjacent

filaments are incorrectly adjoined.

Distributional and holistic analysis

The software can further be used to study distributions of filament parameters and to

investigate the relationships among sets of parameters. From the raw image in Figure 4A, we

produced: (1) an orientation distribution, (2) a length-weighted orientation distribution, (3) a

diameter distribution, (4) a distribution of filament diameters with respect to orientation.

Figure 6. Representative results of individual filament analysis. (A) Analysis of the filament outlined in white yields the estimated parameters shown, which are in approximate agreement with a visual inspection of the raw image. (B) shows the analysis applied where branching is identified, leading to overestimation of bundle diameter. Scale bar = 50 μm.

A Orientation: -65.5675° Length: 34.5031 µm Diameter: 0.77048 µm

Orientation: -67.3586° Length: 25.8975 µm Diameter: 1.2179 µm

B

H a m e d | 16

i. Orientation distribution

The filament analysis data was successfully applied to generate a distribution of filament

orientations, as shown in Figure 7A. The distribution agrees with a visual inspection of the raw

image, which suggests a preponderance of filaments oriented at approximately -60° and 40°

relative to the positive x axis.

ii. Length-weighted orientation distribution

Figure 7B shows that orientation data with frequency weighted with respect to filament

length at the given orientation, allowing the investigator to study the significance of filaments

at various directions. This emphasizes the -60° and 40° peaks observed previously in the test

raw cell image. This method of weighting can be applied with respect to other parameters

produced by the analysis program as well.

iii. Diameter distribution

A filament diameter distribution was produced (Figure 7C). We observe a skewed

distribution with a majority of low diameter filaments.

iv. Distribution of filament diameters with respect to orientation

This distribution (Figure 7D) was produced to assess the data’s potential to be used to

compare relationships between multiple parameters of filament structure. The data suggests

maximum filament diameters at orientations of approximately -60° and 50° relative to the

positive x axis, which agrees with a visual inspection of the raw image.

H a m e d | 17

No

rma

lize

d C

oun

t

Avg

. d

iam

ete

r (μ

m)

No

rma

lize

d

No

rma

lize

d C

oun

t

Orientation Orientation

Orientation Diameter

A B

Figure 5. Results of four illustrative distributional analyses. (A) shows an orientation distribution, showing the relative number of detected filament bundles at orientations relative to the positive x axis. Peaks are clearly apparent around -60° and 40°, which appears to agree with the raw image. (B) shows a length-weighted orientation distribution, such that the frequency of filaments at a given orientation is weighted with respect to the lengths of the corresponding filaments. The peaks previously observed at -60° and 40° are thus emphasized. (C) shows a diameter distribution, skewed with a majority of low diameter filaments. (D) shows a comparative distribution of average diameter relative to filament orientation. Maximum filament diameters are suggested to exist at approximately -60° and 50° relative to the positive x axis, apparently in agreement with the raw image.

1

.8

.6

0.6

0.5

0.4

0.3

0.2

0.1

-100 -80 -60 -40 -20 0 20 40 60 80 100

1

0.

8

0.

6

-100 -80 -60 -40 -20 0 20 40 60 80 100

1

0.8

0.6

0.4

0.2

-100 -80 -60 -40 -20 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4

C D

H a m e d | 18

The analysis of filamentous structures in microscope images of cells is an important step

in many areas of research. I have here developed and applied a novel method for identifying

and analyzing filamentous actin bundles in fluorescent microscope images of cells. The tool was

applied to segment and extract information from two distinct cell images, with success when

the raw image was low in noise.

The system allows for selection and description of individual actin filament bundles

within a segmented image, making it, to my knowledge, unique in this regard. More evidently

useful is its demonstrated ability to extract distributional information about filament structure

and orientation; potentially allowing investigators to study the effects of various factors on

cytoskeletal structure and, further, to study the relationships between various parameters of

filament organization. Whereas these types of analyses are commonly performed visually or

using ad hoc analysis tools, this system potentially allows for automated analyses of numerous

images, yielding quantitative data accessible to statistical analysis.

Segmentation of individual filament bundles is not perfect; parallel bundles in

particularly close adjacency are occasionally identified as contiguous bundles. In addition,

originally contiguous fibers are occasionally disjoined, especially at regions of filament

intersection, as demonstrated using a mock image. While the filament detection algorithm

employed here makes it difficult to guarantee the avoidance if these errors, it is expected that

methods of postprocessing can be developed to rectify these faults.

The generation of distribution data demonstrates a robust feature of this system. The

segmentation algorithm maximally preserves information present in the original raw image,

relying on minimal assumptions. From the segmented image, assumptions can then be made to

extract further information, and this can be studied collectively to make conclusions. The

production of weighted and unweighted orientation distributions illustrates this potential,

showing the ability to produce information in accordance with investigators’ research needs,

such as, in this case, filament orientations assessed with respect to their lengths. This data

could be used to investigate filament anisotropy, a key objective of this project. Additionally,

the construction of a filament diameter vs. orientation distribution illustrates how

H a m e d | 19

supplemental assumptions may be used to draw conclusions. For example, a clarification of the

relationship between filament diameter and filament tensile strength may allow investigators

to use this distributional information to study the mechanical strength of cells along various

orientations.

It is notable that, while it was expected that bundle diameters would follow a Gaussian

distribution within cells, the analysis yielded a skewed distribution. This may be the result of

processing error, whereby noise caused the identification of illusory filaments not correctly

eliminated from the final image. Further investigation is required.

This program holds a few notable weaknesses. Firstly, processing is lengthy, requiring

roughly one to two minutes per cell image. This may not be a practical problem, as users can

input necessary parameters, start the program, and leave it to function automatically. Secondly,

it cannot distinguish overlapping, parallel fibers as may occur in wide-field microscopy;

therefore, the program may be most effectively applied to images acquired using confocal

microscopy. Additionally, confocal microscopy images carry less noise from out-of-focus

structures, potentially making them particularly amenable to this approach.

Future work includes the investigation of the precise relationships between the

parameters outputted by this system and physical properties of cells, such as the association

between FWHM and filament diameter. It is notable that the bundle diameters calculated in

this study, while on the same order magnitude of those reported in the literature, were larger

by approximately a factor of three on average; this is likely mainly due to the use of an

unverified inference of bundle diameter (i.e. one-fourth the signal FWHM) as a placeholder for

more conclusive information regarding the meaning of the FWHM; this discrepancy is therefore

reasonable. More robust methods for analyzing filament segmentations might be developed to

allow for better and more consistent estimations of structural parameters such as diameter and

to allow for additional parameters to be extracted, such as curvature. Also, the system may be

better packaged into a user-friendly interface, considering ease-of-use while also maintaining

transparency.

H a m e d | 20

The novel approach to actin bundle identification and analysis developed in this project

constitutes a potentially powerful tool for extracting information about filamentous actin

bundles from the microscope images commonly produced in cell research labs. It allows both

for the study of distinct filament bundles and for distributional analysis, yielding quantitative

data amenable to statistical analysis. While additional investigation is required to correct the

occasional errors associated with this approach, it is believed that the accuracy, consistency,

and practicality of this method relative to existing techniques nevertheless make it a useful

tool. Its likely applicability to other types of filamentous structures, such as intermediate

filaments and microtubules, broadens its potential field of use.

H a m e d | 21

[1] T. Yamagishi and H. Kawai, "Cytoskeleton Organization during the Cell Cycle in Two

Stramenopile Microalgae, Ochromonas danica (Chrysophyceae) and Heterosigma akashiwo

(Raphidophyceae), with Special Reference to F-actin Organization and its Role in

Cytokinesis", Protist, vol. 163, no. 5, pp. 686-700, 2012.

[2] S. Mana-Capelli, M. Paramasivam, S. Dutta and D. McCollum, "Angiomotins link F-actin

architecture to Hippo pathway signaling", Molecular Biology of the Cell, vol. 25, no. 10, pp.

1676-1685, 2014.

[3] D. Hanein and A. Horwitz, "The structure of cell–matrix adhesions: the new frontier",

Current Opinion in Cell Biology, vol. 24, no. 1, pp. 134-140, 2012.

[4] Boudaoud, A. Burian, D. Borowska-Wykręt, M. Uyttewaal, R. Wrzalik, D. Kwiatkowska and

O. Hamant, "FibrilTool, an ImageJ plug-in to quantify fibrillar structures in raw microscopy

images", Nature Protocols, vol. 9, no. 2, pp. 457-463, 2014.

[5] V. Piazza, B. Weinhausen, A. Diaz, C. Dammann, C. Maurer, M. Reynolds, M. Burghammer

and S. Köster, "Revealing the Structure of Stereociliary Actin by X-ray Nanoimaging", ACS

Nano, vol. 8, no. 12, pp. 12228-12237, 2014.

[6] I. Herman, "Extracellular matrix-cytoskeletal interactions in vascular cells", Tissue and Cell,

vol. 19, no. 1, pp. 1-19, 1987.

[7] R. Ishikawa, T. Sakamoto, T. Ando, S. Higashi-Fujime and K. Kohama, "Polarized actin

bundles formed by human fascin-1: their sliding and disassembly on myosin II and myosin

V in vitro", Journal of Neurochemistry, vol. 87, no. 3, pp. 676-685, 2003.

[8] Vrabioiu and T. Mitchison, "Structural insights into yeast septin organization from polarized

fluorescence microscopy", Nature, vol. 443, no. 7110, pp. 466-469, 2006.

[9] M. Müller, C. Czihak, G. Vogl, P. Fratzl, H. Schober and C. Riekel, "Direct Observation of

Microfibril Arrangement in a Single Native Cellulose Fiber by Microbeam Small-Angle X-ray

Scattering", Macromolecules, vol. 31, no. 12, pp. 3953-3957, 1998.

[10] M. Beil, H. Braxmeier, F. Fleischer, V. Schmidt and P. Walther, "Quantitative analysis of

keratin filament networks in scanning electron microscopy images of cancer cells", Journal

of Microscopy, vol. 220, no. 2, pp. 84-95, 2005.

H a m e d | 22

[11] J. Weichsel, E. Urban, J. Small and U. Schwarz, "Reconstructing the orientation distribution

of actin filaments in the lamellipodium of migrating keratocytes from electron microscopy

tomography data", Cytometry Part A, vol. 81, no. 6, pp. 496-507, 2012.

[12] Rigort, D. Günther, R. Hegerl, D. Baum, B. Weber, S. Prohaska, O. Medalia, W. Baumeister

and H. Hege, "Automated segmentation of electron tomograms for a quantitative

description of actin filament networks", Journal of Structural Biology, vol. 177, no. 1, pp.

135-144, 2012.

[13] T. Xu, D. Vavylonis, F. Tsai, G. Koenderink, W. Nie, E. Yusuf, I-Ju Lee, J. Wu and X. Huang,

"SOAX: A software for quantification of 3D biopolymer networks", Scientific Reports, vol. 5,

p. 9081, 2015.