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Abstract
Investigation of the dynamic structural changes in the actin cytoskeleton during cell migration provides crucial information about the physiological conditions of a stem cell during in-vitro culture. Here we proposed a quantitative analytical model associated with texture extraction with cell tracking techniques for in situ monitoring of the cytoskeletal density change of stem cells in phase-contrast microscopy without fluorescence staining. The reliability of the model in quantifying the texture density with different orientation was first validated using a series of simulated textural images. The capability of the method to reflect the spatiotemporal regulation of the cytoskeletal structure of a living stem cell was further proved by applying it to a set of 72 h phase-contrast microscopic video of the growth dynamics of mesenchymal stem cells in vitro culture.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Investigation of cell migration acts as a key in providing effective fill-ins in physiological and pathological phenomena [1,2]. In cell migration, cytoskeleton and cell-extracellular matrix adhesions are two major molecular machineries involved in mechano-chemical signal transduction [3]. Among the three types of cytoskeletons (actin microfilaments, microtubules, and intermediate filaments) that contribute to cell motility, actin microfilaments are the primary force-generating engine in the cell. The function of actin microfilaments depends on their area distribution and organization patterns. At the cell front, actin structures change dynamically during cell migration. A protrusive structure (filopodia) full of actin filaments, which are organized as spike-like bundles projected from the actin cross-linked mesh (lamellipodia), initially extends at the leading edge of the motile cell though actin polymerization to drive a pushing force on the cell membrane and direct the migrating cells [4,5]. By contrast, the actin microfilaments associated with myosin filaments across the cell body are the major components that modulate the shape of a migrating cell; they are termed as stress fibers. The viscoelasticity of stress fibers is found to provide the overall mechanical stability of the cell and interconnected extracellular matrix [6]. A study on the elastic property of living cells developed an elastic model of the human mesenchymal stem cell to demonstrate that the orientation of the stress fibers is parallel to the long axis of the cell, and the cellular force increases monotonically with the rigidity of the environment [7]. The findings suggest that the stress fibers predominantly aligned with the long axis of the cell when the rigidity of the cell was identical to its surrounding matrix. Furthermore, the maximized stress–fiber polarization optimized the stem cell differentiation. Thus, visualizing the structural variation of the actin cytoskeleton during cell migration can provide an insight into the cell interaction with the environment, mechanical properties of the cell membrane, and other key aspects of cell physiology. This has been a long-standing endeavor amongst biological researchers.
The actin cytoskeleton can be visualized by a wide range of microscopic techniques like scanning electron microscopy (SEM), transmission electron microscopy (TEM), or platinum replica electron microscopy (EM). These techniques are applied for high-resolution visualization of actin cytoskeleton ultrastructure of fixed cells [8–11]. In contrast to those sophisticated systems, light microscopy (bright-field or phase-contrast) is usually the first choice to observe a gross view of the actin filaments in fixed cells or actin structural variation of live cells. However, due to the inherent low-contrast property of light microscopy, fluorescence staining is usually implemented with it to increase the identification of actin filaments [7,12–15]. This is why most computational algorithms for analysis of the actin cytoskeleton based on fluorescence microscopy can skip the actin detection process and directly focus on precise filament segmentation for the measurement of orientation, position, and length of individual filaments [16–20]. However, despite the preciseness in actin identification, the time-consuming and complex procedure in fluorescence staining, which is likely to bring up inconsistency in staining specificity, and photo-toxicity in live cells, has been underestimated. In addition, the disadvantage of fluorescence microscopy in a dynamic study is the photo-bleaching effect that sets a time limitation for observations and hinders the investigation of the spatiotemporal regulation of actin filaments during cell culture. To solve these problems, machine-learning based approaches are being implemented to predict fluorescent labels [21–23]. However, numerous images with consistently good quality of fluorescence-staining are still pre-required for machine-learning network training.
As the dynamic variation in the actin cytoskeletal structure cannot be simultaneously acquired by more than one microscopy, inferences of actin dynamics were made by utilizing static images of fixed samples for rigorous multi-modality comparisons [4,9,24]. In the meantime, the capability of light microscopy to reveal the actin structure was validated. Even though the actin cytoskeleton ultrastructure is unresolvable by phase-contrast microscopy without fluorescence staining, the advantage of preservation of living cells in their natural state for long-term observation still appeals to the researchers, because the intact actin dynamics can be inspected. The early study of Wang [14] explored the tread milling movement of actin subunits from the leading edge of fibroblasts toward the cell’s center by associating the phase-contrast image with the corresponding fluorescence images. Verkhovsky et al. [13] verified the close correspondence of the static diagonal meshwork in the lamellipodia of a moving keratocyte exposed in the phase-contrast microscopy to the actin mesh, viewed through fluorescence and electron microscopy. Such evidence supports that the light microscopic meshwork results from subtle variations of actin filament density, solidifying the feasibility of using the time-lapse sequence of the unstained phase-contrast images to inspect the dynamic variation in actin network. Besides the qualitative inspection, the authors also pointed out the necessity of quantitative analysis of the fluctuations in filament density at the lower resolution of light microscopy for further understanding the actin dynamics at the leading edge.
The main principle of phase contrast microscopy is based on difference of the refractive index and therefore refraction. Unlike the fluorescence staining microscopy that only reveals the stained objects, the challenge in quantitative analysis of cytoskeleton in phase-contrast images is the poor identification of the cytoskeletal structures of multiple cells in an image with uneven brightness in the background full of debris and noise. To tackle this limitation, we proposed a large-scale meshwork enhancement method accomplished by texture extraction incorporated with cell tracking techniques. Subsequently, an analytical model using statistical physics was developed to quantify the textural fluctuation at different orientation during a cell movement. The fidelity of this model was first verified by synthetic images. The whole scheme was then applied to real biological video data from mesenchymal stem cells captured by the time-lapse phase-contrast microscope to monitor the textural variation in a mobile cell during in vitro culture. To demonstrate the potential of the extracted texture being the actin cytoskeleton, the dynamic variation revealed by the analytical scheme was discussed based on the mobility model of an individual cell [5,25].
2. Methods
2.1 Filament extraction from dynamic images
We input legacy data from a 72 h time-lapse experiment of the growth dynamics of mesenchymal stem cells (MSC) cultured in chitosan membranes. The videos were recorded by an ASTEC CCM-1.4XZY/CO2 system with a CCD camera mounted on a time-lapse microscope with a magnification ratio of 100:1. The acquisition rate was fixed at one acquisition every 15 min. The total recording time was 72 h. The image size was 1392 × 1040 pixels, and the intensity of each pixel was discretized into 8 bits with 256 levels. The video frames were converted from an AVI file into a series of frame images. The frames were simultaneously entered as inputs into our custom-developed software (written in Matlab) for cell detection, tracking, texture extraction and analyses.
Direct convolution of fluorescence-stained microscopic images with gradient kernels, such as Laplacian of Gaussian kernels [7,17] and synthetic fiber templates [16], and line Gaussians [19], is a common approach to enhance the actin cytoskeletal structure of the cells. However, a direct application of such a conventional method to the phase-contrast images containing multiple cells in a low-magnification not only reveals the whole diffraction pattern within the cells, but also cellular debris and background noise. In addition, the inhomogeneity occurs not only in the background but also inside the cells, resulting in an increase of the likelihood of false filament extraction from the phase-contrast images. To avoid these problems, cell segmentation, usually unnecessary for fluorescence microscopic images, is the essential step to isolate the cell region and by implementing it, the background noises can be identified and then removed. We adopted the previously proposed schematic method that combined texture extraction with cell detection techniques to satisfy these requirements [26,27]. Figure 1 depicts the overall procedure including the three phases: cell segmentation, texture extraction, and cell tracking. In cell segmentation, the Top-hat method [28] was first applied to correct non-uniformities in background luminance of the microscopic images. Subsequently, the cell entities including the single cells and cell aggregations in video frames were segmented using a fully automatic hybrid-thresholding segmentation technique with morphological operations. This two-phase cell segmentation method was especially designed to solve the problems of inhomogeneous background and intensity heterogeneity within a cell [26].
Fig. 1. (a) Overall procedure to track the dynamic structural variation of the actin filaments inside motile cells. (b)Two-dimensional Laws’ feature masks are used to extract the textures in (from left to right) horizontal (HT), vertical (VT), left diagonal (LD), and right diagonal (RD) directions.
The original image was convolved with a gradient mask to obtain the overall texture of the image. The original one-dimensional Laws’ texture masks can enhance the different texture patterns, including edges, spots, ripples, and waves [29]. Twenty-five two-dimensional 5 by 5 Laws’ feature masks can be derived according to a series of self-convolution procedures detailed in [30,31]. After careful assessment, we selected a specific feature mask, which is an edge detector, i.e., [-1, -2, 0, 2, 1], convolved with a local averaging filter, ${\mathrm{[1, 4, 6, 4, 1]}^t}$, owing to its better performance. This mask is identical to a Gaussian gradient filter for line detection and less sensitive to noise compared to Gaussian Laplacian filter. Rotating the mask by 0°, 45°, 90°, and 135° and convolving with the image, we can obtain the texture patterns in four directions, i.e., horizontal (HT), left diagonal (LD), vertical (VT), and right diagonal (RD). These four orientations were selected as considering the organization of actin filaments in protrusive structure [5] and its dynamic variation [12]. Figure 2 illustrates the three main orientations of the filament bundles separated mostly by an angle around ${\pm}$ 45° according to quantitative analysis of platinum replica electron microscopy [8]. The textures containing the noise and debris outside the cells were then removed by excluding the texture image outside the segmentation image that contained only the detected cells.
Fig. 2. Organization of actin filaments in protrusive structure: the tight extending actin bundles in the filopodium oriented in the direction of the protrusion lined by a thin sheet of lamellipodim with the two sets of filaments interwoven to each other. (Figure was created by BioRender.)
Cell detection was accomplished by cell tracking after cell segmentation. Subsequently, each connected object was labeled by a number according to its positional sequence. If the area of an object was smaller than a pre-set threshold and did not encounter any merging or splitting during the time-span of observation, the object was identified as a single cell, otherwise, it was assigned to a cell cluster. The centroid of each cell entity was detected after the segmentation. Tracking of the cell movement path was based on the cell matching with the minimum distance between two sequential frames. By combining cell detection and texture extraction, dynamic structural changes in the meshwork of the concerned cell can be quantitatively investigated.
2.2 Analytical model descriptions
Images of cells produced by phase-contrast microscopy exhibit enhanced results of light diffraction and scattering that occur at the edges between the cellular components and the surrounding medium. The intensity variation within a cell in phase contrast image is related to differences of the refractive index and optical path length between the components and cytoplasm. Thus, it can be interpreted as a density map between various structures within the cell. Based on that, we modeled this density map as follow:
$\textrm{s} = ({\textrm{x},\textrm{y}} )\in \textrm{U} \subset {\mathrm{\mathbb{R}}^2}$, denotes a point $\textrm{s}$ within a cell $\textrm{U}$ on an image space ${\mathrm{\mathbb{R}}^2}$. Let $f:\textrm{U} \to {\mathrm{\mathbb{R}}^2}$ be a density map.
Suppose those cellular components, such as actin microfilaments, microtubules, intermediate filaments, and other subcellular organelles, are independent to each other, then the density of a point on the image can be written as a linear combination of the component functions
where ${\mathrm{\omega }_i}$ is the strength of the wave disturbance from the corresponding cellular component ${g_i}$, which depends on the refractive index and optical path length of the component.The texture image we derived from the previous image processing procedures is the derivative of f(s) on variable s:
As the derived texture image would change with cytoskeleton reorganization during cell migration, it is a function of time ($t$) for a dynamic video. The spatial-temporal variation of the texture can be modeled as
Considering the reorganization of the protein components inside a motile cell as an inherently stochastic nature of a thermodynamic system, we can then apply the system's extensive parameters in statistical physics to measure bulk changes in those biomolecules. We define “energy” and “entropy” in this analytical model to quantify the structural variation of the extracted cellular textures.
Energy is an indicator of the textural strength. Because four-directional Laws’ feature masks are applied to extract the texture along four directions, the directional energy of the textural image at the corresponding direction is defined as
Entropy is originally a physical quantity, representing the level of disorder in a thermodynamic system. In this task, entropy is applied to indicate the degree of randomness in the intensity distributed in the ROI at a specific time frame t and is defined as
The time-dependent variation in ${E_{dir}}(t )$ and $S(t )\; $can be viewed as the derivatives of each of the functions at t. By applying the power rule and the sum rule of differentiation to Eqs. (4) and (5), the term involved the static components in texture $\nabla f({s,t} )$ becomes zero. In other words, the time-dependent variation in ${E_{dir}}(t )$ and $S(t )$ can only be contributed by the dynamic cellular components.
3. Results and discussion
3.1 Comparison to the existing state-of-the-art method
We adopted a simulated cytoskeleton (Simulate_cell_04) from the supplement material of [19] to test our algorithms. We first calculated the directional energy of the four texture orientations from the original image to form a directional energy bar chart. We then rotated the image by 45°, -45°, and 90° counterclockwise about the origin as in Fig. 3 to inspect if any change in the energy bar chart corresponds to the rotation.
Fig. 3. Quantitative analytical results of the simulated cytoskeleton. (Top) Four images demonstrate the original image and its counterclockwise rotations about the image center 45°, -45°, and 90°, respectively. (Middle) The corresponding directional energy bar charts derived from the four images. (Bottom) The inset shows a fusion of the bar chart of the original image with its angular histogram. Four angular forms of the bar chart were plotted in the same order of the images, proving a consistency of the rotational angle of the bar charts to the corresponding images.
The result of the original image in the inset of Fig. 3 shows that the pattern of the directional energy bar chart fitted the angular histograms revealing the accumulated pixel number of filaments per angular orientation [19]. When the image rotates, the associated bar chart rotates correspondingly to remain the same tendency of the fiber distribution along the four directions as seen in the middle panels of Fig. 3. We transformed the original bar charts to angular forms at the bottom panels of Fig. 3 for easy interpretation of the correspondence of the rotational angle with the image. These results verify the reliability of our proposed model to truly quantify the fiber density distribution at the quartile orientation.
3.2 Application to biological data
The tracking results of the time-lapse microscopy video (see Visualization 1) using our proposed methods in Fig. 1 is given in Visualization 2, which reveals the clear texture patterns inside the aggregated and single cells in comparison with the video without denoising process (see Visualization 3).
According to the mobility model of an individual cell, the cell moving over a two-dimensional substrate can be divided into five stages: protrusion of the leading edge, adhesion to the substratum, traction of the cell body, de-adhesion, and retraction [5]. Note that the formation of the leading edge of the motile cell is through actin polymerization beneath the cell cortex, thus except for actin textures other components are very few. Considering the texture pattern in the analytical model in Section 2.2, we boldly presume that the actin filaments significantly contribute to the extracted texture because they are the major components of the point density$\; f(s )$. In addition, the time-dependent variation in texture can only account for the dynamic components in ${E_{dir}}(t )$ and $S(t )$; thus, the static protein components only account for the direct current (DC) in directional energy and entropy, whereas the pulsatile variation in the alternating current (AC) can only stem from the dynamic components in the leading edge, i.e., actin filaments. Quantifiers were then used to track the structural variation of the extracted texture located at the leading edges of a cell and the cell body during the cell movement. The analytical results are presented as a static figure in Fig. 4 with 16 snapshots to demonstrate the perfect alignment of the protrusion direction with the orientation of the dominant energy curve and the relation of entropy variation to the degree of expansion of the leading edge. To clearly visualize the internal textures, an example image of frame 173 is enlarged and those extracted textures are highlighted by thresholding followed by morphological thinning in Fig. 5. In order to avoid erroneous measurements of the quantification parameters (i.e. texture energy and entropy) due to intensity enhancement, the calculations are performed using the original intensity value. The video (see Visualization 4) is also provided as a supplementary material to reveal the instantaneous correspondence. For clarity, we shall present and discuss the results from the aspect of directional energy and entropy separately.
Fig. 4. Quantitative analysis of a single motile cell with a leading edge (green) protruding from the cell body (red). Pseudo-colors are used to distinguish the leading edge from the cell body. Top panel plots the track of the four directional energy and entropy during the time-span where the single cell appeared in the video. Sixteen snapshots are given in the middle for comparison with those curves at the corresponding time-slot. Panel at the bottom, comparing the temporal variation of the directional energies of the cell body with that in the leading edge reveals the spatiotemporal regulation of the cell motility. The turning points (A’, B’, and C’) in the energy curve of the cell body lag behind the corresponding points (A, B, and C) of the leading edge, providing evidence that the leading edge steers the cell migration.
Fig. 5. Results display various intensities of extracted textures: (a) the original textures; (b) the colored textures as in Fig. 4; (c) internal textures highlighted by a single threshold value; (d) textures highlighted by combining the results with a range of thresholds.
First, following a long tracing span of the motile cell, we found that the dominant energy among the four directional energies indicates the orientation of the leading edge, even with sequential turns. At the beginning, the cell protruded toward horizontal direction but later wiggled to left-diagonal. The first eight snapshots between frame 151 to 176 in Fig. 4 demonstrate the firm correspondence between the orientations of the green leading edge and the dominant brown curve in the same direction. Later, the leading edge guided the cell march towards the left diagonal from the horizontal, indicated by a dominant red peak around frame 179. From frame 182, the filopodia started to shrink and reached a minimum at frame 186, where the four directional energy curves tend to overlap and converge to a local minimum. Within this time-span, the shrinkage of the leading edge is due to a brief pause in the proceeding, counter-balanced by the tail to prepare for a turning to the vertical. Subsequently, a new filopodium protrudes to steer the cell moving upward with an elevated energy in the same direction. A tango of green and red energy curves reflects the leading edge shift in the direction between left-diagonal and vertical till the end. Through a rigorous frame by frame checking of the supplemental video, we found evidence of the directional energy, revealing a 100% correspondence with the moving direction of a cell, tracked across each frame. Thus, the dominant directional energy exactly unveils the characteristic of the parallel actin bundles in the protrusion. This finding correlates to that reported in [5,24] regarding the structure of actin filaments at the leading edge. Thus, because actin polymerization in the cell migration direction is the key event that provides the protrusion force to extend the leading edge [3], our texture alignment findings provide quantitative evidence of the actin polymerization at the leading edge of a mobile cell.
Besides the dominant energy, we also found a regulation in the variation of the four direction energies, i.e., the secondary and the third directional energies below the dominant one are always at an angle of ${\pm}$ 45° relative to the dominant one. According to the geometry of actin array summarized by Svitkina [11], finer branch filaments interweaved between 0° and ${\pm}$ 70° with respect to the major actin filament bundles in the filopodia and a periodic rearrangement within these angles constantly occur to accommodate the membrane tension changes during the cell migration. The adjacent curves diagonal to the dominant one fall inside the arc range and, thus, agree with the Svitkina model. In addition, the closeness between the dominant and secondary curves, reflects a transition between two moving directions, and may result from a merging of the finer filaments, in terms of increasing the secondary directional energy to overcome the membrane resistance for protrusion formation [12]. Two segments of the curves, frame 167–173 and 190–198, exemplify this phenomenon.
By contrast, the entropy indicates the degree of extension/expansion of the leading edge. The shaded area in the top panel in Fig. 4, demonstrates that it increases with extension/expansion of the leading edge and decreases with its’ withdrawal. As entropy reveals the randomness of a texture distribution, the elevation of the entropy may suggest a disorganization process of the actin structure due to actin polymerization during protrusion formation. The fluctuation of the entropy also reflects a periodic rearrangement of the branch filaments in the actin mesh proposed by Svitkina [11].
In addition to the inspection of the leading edge, the directional energy of the cell body was also plotted for comparison. They are not as clear as those in the leading edge. We postulate that this could be because of higher interference from the other protein components in the cell body rather than only the refraction from the actin microfilament in the leading edge. However, sequential turns of the leading edge of a motile cell followed by the cell body can still be found in Fig. 4. At point A, the leading edge turns toward the left diagonal from the horizontal. By contrast, the cell body follows the same direction at point A’ after a three frame (45 min) delay. At point B, the original leading edge shrinks and protrudes again, continuously guiding the cell to move toward the left-diagonal direction, and making the LD curve dominant. During this time span (frame 185–190), the cell body maintains the movement and marches forward again at point B’. At point C, the leading edge turns toward the vertical direction from the left diagonal. However, the cell body succeeds in turning at point C’ after a seven frame (105 min) delay. All these points show that the occurrence of the turning points in the cell body lags behind those in the leading edge. According to the previous findings, the local minima of the energy curves suggest a reorganization of actin filaments to prepare for the change in moving direction; such delays prove that our model can truly respond to the spatiotemporal regulation of the actin filaments in the leading edge to guide stress fiber modification in the cell body during cell migration.
4. Conclusion
In this study, we demonstrated an image-based analytical method that enabled the usage of a conventional optical microscopy for stain-free, real time, and in situ monitoring of the reorganization of the actin-like cytoskeleton of living stem cells during in vitro culture. This method combined cell tracking, texture extraction, and gating with time-lapse microscopy to characterize structural changes in the intracellular textures associated with cell migration. We first used a set of synthetic images with four different orientations to test the reliability of the proposed model. Following that, based on the cell migration model, we focused on the behavioral analyses of the textures extracted from the leading edges and ascertained their identity of being the actin microfilaments by highlighting the supportive literature evidences. According to the analytical model described in Section 2.2, the results confirm that diffraction-induced texture patterns viewed in the phase-contrast images are majorly due to the contribution of actin network under the cell cortex and less by other subcellular organelles. Thus, with proper analytical design, the global information from the whole actin network rather than single filaments may render the big picture of the spatiotemporal variation in the actin structure of a motile cell during in-vitro culture. In summary, we demonstrated the potential of the proposed analytical model adding the extra-value to a phase-contrast microscopy for monitoring the spatiotemporal regulation of the cytoskeleton structure of a living stem cell for a long duration without the need for an additional fluorescence stain, thereby avoiding the photo-bleaching effect. Therefore, the proposed method provides a convenient way to monitor the density flow of the cytoskeleton during in vitro culture of stem cells.
Funding
Ministry of Science and Technology, Taiwan (MOST 109-2221-E-214 -006 –MY2).
Acknowledgments
We thank Prof. Shan-hui Hsu, the Biomaterials Laboratory of the Institute of Polymer Science and Engineering at the National Taiwan University, for providing the microscopic videos.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results of the simulated cytoskeleton presented in this paper are available in Ref. [19] and the biological data underlying the results are available in Video 1, Ref. [26].
References
1. C. M. Svensson, A. Medyukhina, I. Belyaev, N. Al-Zaben, and M. T. Figge, “Untangling cell tracks: Quantifying cell migration by time lapse image data analysis,” Cytometry A 93(3), 357–370 (2018). [CrossRef]
2. A. Aman and T. Piotrowski, “Cell migration during morphogenesis,” Dev. Biol. 341(1), 20–33 (2010). [CrossRef]
3. S. Li, J.-L. Guan, and S. Chien, “Biochemistry and biomechanics of cell motility,” Annu. Rev. Biomed. Eng. 7(1), 105–150 (2005). [CrossRef]
4. A. K. Lewis and P. C. Bridgman, “Nerve growth cone lamellipodia contain two populations of actin filaments that differ in organization and polarity,” J. Cell Biol. 119(5), 1219–1243 (1992). [CrossRef]
5. T. Mitchison and L. Cramer, “Actin-based cell motility and cell locomotion,” Cell 84(3), 371–379 (1996). [CrossRef]
6. S. Kumar, I. Z. Maxwell, A. Heisterkamp, T. R. Polte, T. P. Lele, M. Salanga, E. Mazur, and D. E. Ingber, “Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics,” Biophys. J. 90(10), 3762–3773 (2006). [CrossRef]
7. A. Zemel, F. Rehfeldt, A. Brown, D. Discher, and S. Safran, “Optimal matrix rigidity for stress-fibre polarization in stem cells,” Nat. Phys. 6(6), 468–473 (2010). [CrossRef]
8. I. V. Maly and G. G. Borisy, “Self-organization of a propulsive actin network as an evolutionary process,” Proc. Natl. Acad. Sci. 98(20), 11324–11329 (2001). [CrossRef]
9. T. D. Pollard and G. G. Borisy, “Cellular motility driven by assembly and disassembly of actin filaments,” Cell 112(4), 453–465 (2003). [CrossRef]
10. T. M. Svitkina, “Platinum replica electron microscopy: Imaging the cytoskeleton globally and locally,” Int. J. Biochem. Cell Biol. 86, 37–41 (2017). [CrossRef]
11. T. M. Svitkina, “Ultrastructure of the actin cytoskeleton,” Curr. Opin. Cell Biol. 54, 1–8 (2018). [CrossRef]
12. A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4(10), 789–793 (2008). [CrossRef]
13. A. B. Verkhovsky, O. Y. Chaga, S. Schaub, T. M. Svitkina, J.-J. Meister, and G. G. Borisy, “Orientational order of the lamellipodial actin network as demonstrated in living motile cells,” Mol. Biol. Cell 14(11), 4667–4675 (2003). [CrossRef]
14. Y.-L. Wang, “Exchange of actin subunits at the leading edge of living fibroblasts: possible role of treadmilling,” J. Cell Biol. 101(2), 597–602 (1985). [CrossRef]
15. S. Yonemura, M. Itoh, A. Nagafuchi, and S. Tsukita, “Cell-to-cell adherens junction formation and actin filament organization: similarities and differences between non-polarized fibroblasts and polarized epithelial cells,” J. Cell Sci. 108(1), 127–142 (1995). [CrossRef]
16. N. Lichtenstein, B. Geiger, and Z. Kam, “Quantitative analysis of cytoskeletal organization by digital fluorescent microscopy,” Cytometry A 54A(1), 8–18 (2003). [CrossRef]
17. M. Alioscha-Perez, C. Benadiba, K. Goossens, S. Kasas, G. Dietler, R. Willaert, and H. Sahli, “A robust actin filaments image analysis framework,” PLoS Comput. Biol. 12(8), e1005063 (2016). [CrossRef]
18. J. Nowak, K. Gennermann, S. Persson, and Z. Nikoloski, “CytoSeg 2.0: automated extraction of actin filaments,” Bioinformatics 36(9), 2950–2951 (2020). [CrossRef]
19. B. Eltzner, C. Wollnik, C. Gottschlich, S. Huckemann, and F. Rehfeldt, “The filament sensor for near real-time detection of cytoskeletal fiber structures,” PLoS One 10(5), e0126346 (2015). [CrossRef]
20. T. Xu, D. Vavylonis, and X. Huang, “3D actin network centerline extraction with multiple active contours,” Med. Image Anal. 18(2), 272–284 (2014). [CrossRef]
21. E. M. Christiansen, S. J. Yang, D. M. Ando, A. Javaherian, G. Skibinski, S. Lipnick, E. Mount, A. O’neil, K. Shah, and A. K. Lee, “In silico labeling: predicting fluorescent labels in unlabeled images,” Cell 173(3), 792–803.e19 (2018). [CrossRef]
22. J. LaChance and D. J. Cohen, “Practical fluorescence reconstruction microscopy for large samples and low-magnification imaging,” PLoS Comput. Biol. 16(12), e1008443 (2020). [CrossRef]
23. C. Ounkomol, S. Seshamani, M. M. Maleckar, F. Collman, and G. R. Johnson, “Label-free prediction of three-dimensional fluorescence images from transmitted-light microscopy,” Nat. Methods 15(11), 917–920 (2018). [CrossRef]
24. V. C. Abraham, V. Krishnamurthi, D. L. Taylor, and F. Lanni, “The actin-based nanomachine at the leading edge of migrating cells,” Biophys. J. 77(3), 1721–1732 (1999). [CrossRef]
25. S. R. K. Vedula, A. Ravasio, C. T. Lim, and B. Ladoux, “Collective cell migration: a mechanistic perspective,” Physiology 28(6), 370–379 (2013). [CrossRef]
26. C. F. Jiang, S. H. Hsu, K. P. Tsai, and M. H. Tsai, “Segmentation and tracking of stem cells in time lapse microscopy to quantify dynamic behavioral changes during spheroid formation,” Cytometry A 87(6), 491–502 (2015). [CrossRef]
27. C. F. Jiang and M.-H. Tsai, “Microscopic Image Recognition System and Method for Detecting Protein-Based Molecule,” US 10,274,711 B2 (2019).
28. M. A. A. Dewan, M. O. Ahmad, and M. Swamy, “Tracking biological cells in time-lapse microscopy: An adaptive technique combining motion and topological features,” IEEE Trans. Biomed. Eng. 58(6), 1637–1647 (2011). [CrossRef]
29. K. I. Laws, “Texture energy measures,” in Proc. Image understanding workshop (Los Angeles, CA: Sci. Appl., 1979), pp. 47–51.
30. C. F. Jiang, “3D image reconstruction of ovarian tumor in the ultrasonic images,” Biomed. Eng. Appl. Basis Commun. 13(02), 93–98 (2001). [CrossRef]
31. Y. C. Hsu, C. F. Jiang, and C. M. Uang, “Auto-segmentation of ultrasonic images by the genetic algorithm,” J. Med. Biol. Eng. 21(2), 151–157 (2001). [CrossRef]
