Filament displacement image analytics tool for use in investigating dynamics of dense microtubule networks

The fate and motion of cells is influenced by a variety of physical characteristics of their microenvironments. Traditionally, mechanobiology focuses on external mechanical phenomena such as cell movement and environmental sensing. However, cells are inherently dynamic, where internal waves and internal oscillations are a hallmark of living cells observed under a microscope. We propose that these internal mechanical rhythms provide valuable information about cell health. Therefore, it is valuable to capture the rhythms inside cells and quantify how drugs or physical interventions affect a cell's internal dynamics. One of the key dynamical entities inside cells is the microtubule network. Typically, microtubule dynamics are measured by end-protein tracking. In contrast, this paper introduces an easy-to-implement approach to measure the lateral motion of the microtubule filaments embedded within dense networks with (at least) confocal resolution image sequences. Our tool couples the computer vision algorithm Optical Flow with an anisotropic, rotating Laplacian of Gaussian filtering to characterize the lateral motion of dense microtubule networks. We then showcase additional image analytics used to understand the effect of microtubule orientation and regional location on lateral motion. We argue that our tool and these additional metrics provide a fuller picture of the active forcing environment within cells.

Figure 1

LoG algorithm extracts MT filaments in every frame. (a) NG108 cell line with fluorescently labeled microtubule filaments. This confocal image displays a MT network with representative density of filaments. (b) Cytoskeletal networks containing filaments oriented in different directions. Even with the relatively low image resolution, the variety of microtubule orientations (some filaments are tilted while others are horizontal) is apparent. (c) Anisotropic, rotating Laplacian of Gaussian (LoG) filter with some rotation steps. The rods (right leaning, left leaning, and vertical) in each of the three images represent the LoG kernel with angle prescribed as the closest area on the color wheel (different shading represents different angles). These rods resemble the shapes of microtubules, which showcases how microtubules are detected. Note that once microtubule pixels are found above a threshold, each pixel is ascribed an associated angle belonging to which kernel causes maximal value in the max projection step. (d) Filament orientation map output from convolving data in (a) with kernel in (c). This final output shows all microtubule filaments detected. Note that there are spatial homogeneities with neighboring pixels which amounts to filament detection. Moreover, note that there are regions of white (corresponding to pixels not valued as microtubules) within the image; areas not white (different colors and shades) represent regions where the algorithm has identified a filamentous pixel and has prescribed an angle for this pixel. We found that LoG paramters of Refs. [1, 7] for the sigma in $\widehat{x}$ and $\widehat{y}$ as well as 30 rotations work well with our data. Our scripts are provided in the GitHub link at the end of the paper. Scale bars are $10\mu \mathrm{m}$ for (a) and (d); scale bar is $5\mu \mathrm{m}$ for (b).

Figure 2

Lateral motion of detected filaments is quantified by coupling OF with LoG. (a) Two frames separated by time are shown overlaid on top of each other. The minimal differences between the frames are shown by the green and magenta pixels (grayer shades–lighter from one frame, darker for the other–correspond to differences in either frame, white regions are pixels shared by both frames). (b) The frame overlay in (a) can be better represented as a difference image (a frame earlier in time subtracted from a frame later in time) where the pixels now correspond to the magnitude of intensity changes over time. (c) Using Eq. (2), we generate vectors of motion as represented by the yellow arrows [lighter regions with clusters of activity (arrows)]. Similarly to LoG, we find local neighborhoods for assessing motion. For our results, we use a kernel width, in both $\widehat{x}$ and $\widehat{y}$, as 5. [(d), (e)] These masks showcase horizontal and vertical filaments, respectively. Notice that with our rotating LoG kernel, we are able to separately partition filaments to focus on specific orientations for analysis. (f) This schematic shows filaments in one frame (tan undashed lines) and a subsequent frame (brown dashed lines). Due to the crosslinking of filaments, the overall OF motion would normally be quantified by the larger black arrow. However, since we have access to the filament information (for which the two tan undashed lines are oriented in different directions), we can decompose that larger black vector into components perpendicular to each filament as shown by the smaller blue (lighter) arrows and analyze them separately (and we have access to the different filaments despite the crosslinking based upon the different orientation output). In this regard, we overcome the difficulty of analyzing dense MT networks and assess lateral motion. Scale bars are $3.5\mu \mathrm{m}$.

Figure 3

Manual verification of FIDI. Comparison of the strips of CHO filaments reveals the small (sub)pixel-level movements of these clearly defined filaments. (a) Two frames at difference time points, t0 and t1, separated vertically. The overlay of the two frames shows the differences in movement. Most of this movement is small; pixels from t0 and t1 are identified as green and magenta, respectively [shades more gray but not dark represent regions of activity from either frame; white represents regions of overlap. See (c) for more detail]. (b) For the t0 and t1 frames shown in (a), we show the LoG generated output (different colors and shades represent different angles). The slight heterogeneity of angles within the filaments is due to our pixel-level detection of filaments. Overall, however, the general angle of the filament is well-defined by eye. The LoG output overlaid below t1 showcases the agreement of our kernel parameters with the actual data. (c) To verify whether our algorithm is assessing motion with realistic output, a difference image of the detected filaments [using the LoG outputs from (b)] is generated. We further notice subpixel level differences. We quantify the area of these objects, which correspond to motion, and take the square root to mimic perpendicular motion relative to a filament. (d) We compare the values of our algorithm with a manual calculation of the square root of difference objects found. We notice that FIDI captures with subpixel-level accuracy the movements of filaments across frames.

Figure 4

Composite dynamic microtubules in CHO cells reveal differences in lateral motion based upon orientation and location. (a) Strips of CHO microtubules are taken. These strips have a higher frame rate and resolution than achieved with more standard confocal imaging. We concatenate the strips as each strip contains different information of microtubule dynamics. Despite concatenating, we separately analyze each strip to maximize the information from each cell. (b) To separate filaments into different groups, we find each filament's orientation relative to its closest boundary point. Given a pixel's LoG outputted angle, we find the relative angle between the angle created from the vector normal to the boundary and the unit vector created from the LoG angle. The leftmost arrow with the axis (dotted flat line) creates the boundary angle (lowermost theta). The rightmost arrow with the axis represents the filament angle. The relative angle is represented by the theta in between the two arrows. (c) The relative angle output from the composite image in (a) is shown. The color wheel displays angle colors corresponding to [0, $\pi /2$] (lighter shades represent perpendicular angles, darker shades represent parallel angles). (d) The composite cell image is used to generate mask from which angles relative to the boundary of the mask are generated. These regions are not meant to be exact but to provide a qualitative assessment of regional differences. (e) We show the boundaries of the regions in (d) overlaid on the output in (c). (f) We compare the mean speed of lateral motion for filaments that are considered parallel to the boundary versus filaments considered perpendicular to the boundary. We display the mean speeds side by side to demonstrate differences. From left to right: Boundary, middle, and innermost dynamics as shown in (d) above. (g) We find that only in the boundary region is there a significant difference. Filaments that are oriented parallel to the boundary seem to have a higher motion than those perpendicular. (h) We assess the variability of the mean speed across differently oriented filaments for both parallel and perpendicular filaments. We represent the difference similarly to (f). (i) We compute the difference in this variability and find a statistically significant difference in the variability in both the boundary and middle regions of the composite cells. Scale bars are $10\mu \mathrm{m}$.