Figure 1.
Contour expansion method for cell boundary detection.
(A) It is assumed that most cells have illustrated height profiles with one peak located above the cell nucleus. In negative phase contrast images, the light intensity of cells is proportional to cell height. Therefore, the light intensity distribution over cell surface is similar to a height profile of cells with one peak located above each cell body. (B) Mesh plot of the light intensity for a selected cell (shown in Fig. 1D), which demonstrates the distribution of light intensity over cell surface. (C) Quiver plot of the gradient of light intensity for the selected cell. Over cell surface, the gradient of light intensity is pointing outwards. (D) Demonstration of contour expansion method for cell segmentation. The first figure shows the negative phase contrast image. The threshold method is used to get a preliminary mask for the selected cell, as shown in the second figure. The boundary of the mask is extracted and taken as the initial contour (the third figure). With contour expansion method, the initial contour is driven by the field of gradient of light intensity to gradually converge to the cell boundary (the fourth figure). The contour is finally converged at the boundary of the cell, where the contour achieves the minimum energy (the fifth figure).
Figure 2.
Cell localization, contour detection, and separation of aggregated cells.
(A) Based on negative phase contrast image, peaks of light intensity are detected for all cells, as indicated by red circles. (B) Preliminary masks are obtained with the threshold method. Masks in green are areas with multiple peaks indicating aggregated cells. Masks in yellow are areas with single cell. (C) The boundaries of the preliminary masks are extracted to serve as initial contours for individual cells. (D) The contour expansion method is applied to detect cell boundaries for all cells in the field of view. (E) Steps taken to separate three aggregated cells selected in figure (A). The first figure shows three peaks detected, indicating three cells in the selected area. The second figure shows the mask area defined by the threshold method and locations of three detected peaks. The third figure shows division of the mask area into three sub-areas based on shortest distance between any given pixels and the three detected peaks. The fourth figure shows contour initiation by extracting the outlines of sub-areas. The fifth figure shows the final contours of three cells after contour expansion.
Figure 3.
Peripheral protrusions may not be included in the final contours.
The segmentation program can capture cell bodies and some parts of protrusion structures. However, peripheral protrusion structures with locally increased light intensity (marked by a red arrow in figure A) connected with thin extensions would not be included in the final contours (“A” in figure B). Similarly, thin lamellipodia of low image contrast would not be included in the final contours (“B” in figure B). Finally, the contour could not converge to a sharp protrusion structure due to the constraint of internal energy of the contour (“C” in figure B).
Figure 4.
Cell association and detection of cell division.
(A) Three detected cells in frame i. (B) Four detected cells in frame i+1. Cells 1′ and cell 2′ are the same cells of cell 1 and cell 2 in frame i, respectively. Cell 3 in frame i is divided into cell 3′ and 4′ in frame i+1. The cells can be associated based on the overlapping areas between the two consecutive frames. The two divided cells 3′ and 4′ in frame i+1 have large overlapping areas with their mother cell 3 in frame i. Moreover, the sum of the two areas has large overlapping area with the mother cell. This one-to-two association relationship is utilized to detect cell division. (C) The overlapping rate is defined as the ratio of the overlapping area to the minimum area of the two areas under investigation. (D) A cell association matrix is constructed with the calculated overlapping rate. (E), (F) Cell segmentation results for two consecutive frames. (G) The association matrix between two consecutive frames after calculating the overlapping rate. The x and y axes denote cell labels for cells in Frame i+1 and Frame i, respectively. The color of each point represents the overlapping rate (range from 0 to 1.0) of a given cell between two consecutive frames, as indicated by the color bar in the image.
Figure 5.
Illustration of temporal changes in cell area and cell shape along with cell cycle progression.
After division, cell area gradually increases with change in cell shape from time point A to time point D. Thereafter, the cell becomes rounded with decreased cell area (time point F), marking the entry of mitotic stage. The cell is elongated with slightly increased area and subsequently a characteristic bottleneck structure appears and cell division occurs.
Figure 6.
Cell behaviors during cell division for MCF-10A, MCF-7, and MDA-MB-231 cells.
(A) MCF-10A cells divide horizontally with smooth separation after cell division. (B) Some MCF-7 cells divide vertically and remain vertically overlapping for a long time before the cell on the top slides down and gradually attaches to the substrate. (C) MDA-MB-231 cells are unique in that divided cells often underwent rapid motion and irregular geometry change, as shown with green contours from the fifth to the seventh figures.
Table 1.
False tracking rate of selected MCF-10A, MCF-7, and MDA-MB-231 cells.
Figure 7.
Cell lineage construction and associated cell behaviors after offline editing.
(A) Cell trajectories for all tracked cells in the-field-of-view. The color of trajectories indicates cell generations. Blue, green, red, cyan, and magenta represent trajectories from the first to the fifth generations, respectively. (B) Cell trajectories for cells presented in the first video frame and their offspring cells. (C) Trajectories for cells from a selected cell lineage family. (D) Cell lineage families constructed with automated cell tracking program followed by offline editing. (E) A selected cell lineage family with cell migration speed, cell area, and cell axis ratio aligned with cell cycle progression. Note that a maximum of 5 generations and 11 cell divisions in total are observed in this family during 40 hrs of monitoring. (F) The enlarged figure for the selected area in figure (E).
Figure 8.
Calculation of mean square displacement (MSD) and determination of motion type.
(A) Schematic showing the selected pairs of data point along a trajectory with different time interval for the calculation of MSD. (B) MSD calculation. (C) MSD as function of time interval to determine motion type. The linear increase of the MSD with the time interval indicates the motion type of random walk. Directional motion leads to a MSD curve deflected upward, whereas depressed motion results in a MSD curve deflected downward.
Figure 9.
Correlation between cell area and cell axis ratio in a constructed 2D geometry space.
For any point in the 2D space, the x coordinate and the y coordinate represent cell area and cell axis ratio of a given cell at each video frame, respectively. Summation of all entry data in the 2D space for all video frames results in the overall 2D geometry distribution maps. The frequency of cells appears at each point in the 2D space is indicated with corresponding color bar. (A) MCF-10A cells have a narrow distribution of cell area, while (B) MCF-7 cells show a wider distribution of cell area. (C) MDA-MB-231 cells have a wider distribution of axis ratio. Moreover, the axis ratio for MDA-MB-231 cells slightly increases with increasing cell areas.
Figure 10.
Temporal change of cell area and cell axis ratio along cell cycle progression for MCF-10A, MCF-7, and MDA-MB-231 cells.
The cell cycle was scaled to 0–1 to facilitate comparison among different cells within the same cell-line. Values of cell area or cell axis ratio for each cell examined (blue curves) were lined up with the scaled cell cycle and the mean value for each parameter was shown by the red curve in each figure. (A–C) A rapid increase in mean size of cell area occurred shortly after cell division, which reflects cell attachment on the substrate after cell division. Thereafter, mean size of cell area gradually increased. A rapid decrease in mean size of cell area occurred before the end of cell cycle, which reflects cells becoming rounded in preparation of cell division. (D–F) The mean axis ratio was lowest before and after cell division for the three cell lines, reflecting cells rounded up before and after cell division. Otherwise, the mean axis ratio did not change much at the interphase of cell cycle for both MCF-10A cells and MCF-7 cells. In comparison, the mean axis ratio for MDA-MB-231 cells slightly increased with cell cycle progression.
Figure 11.
Boxplots of median cell area and median cell axis ratio for cells undergoing an entire cell cycle.
(A) MCF-7 cells have highest median value of cell area, while the median value for MDA-MB-231 cells is slightly larger than that for MCF-10A cells. The Wilcoxon rank sum test showed that there is statistically significant difference in distribution shift of median cell areas between MCF-10A and MCF-7, and between MDA-MB-231 and MCF-7 cells. (B) MDA-MB-231 cells have the highest median value of cell axis ratio followed by MCF-10A cells. MCF-7 cells have the lowest median value of cell axis ratio among the three cell lines. The Wilcoxon rank rum test showed that there is statistically significant difference in distribution shift of median cell axis ratios between MCF-10A and MCF-7, and between MDA-MB-231 and MCF-7 cells.
Table 2.
Unadjusted p-values of Wilcoxon rank sum test.
Figure 12.
Instantaneous migration speed for cells undergoing an entire cell cycle.
(A–C) Temporal change of instantaneous migration speed along cell cycle progression for MCF-10A, MCF-7, and MDA-MB-231 cells. The cell cycle was scaled to 0–1 to facilitate comparison among different cells within the same cell-line. Values of instantaneous migration speed for each cell examined (blue curves) were lined up with the scaled cell cycle and the mean value of all cells examined was shown by the red curve in each figure. (D) Boxplot of median instantaneous migration speed. MDA-MB-231 cells have highest median value, whereas MCF-10A and MCF-7 cells have comparable migration speed. The Wilcoxon rank rum test showed that there is statistically significant difference in distribution shift of median instantaneous migration speed between MCF-10A and MDA-MB-231, and between MDA-MB-231 and MCF-7 cells.
Figure 13.
Motion types for cells undergoing an entire cell cycle.
(A–C) show mean square displacement (MSD) as a function of time interval for a cell of MCF-10A, MCF-7, and MDA-MB-231, respectively. From left to right, the MSD curves show directional motion, depressed motion, and random walk, respectively. The inset in each figure is cell trajectories during the entire cell cycle for the selected cell. Blue and green dots represent the starting and ending points along cell trajectories, respectively. (D) Motion types for MCF-10A, MCF-7, and MDA-MB-231 cells undergoing an entire cell cycle. For MCF-10A cells (N = 128), over 50% of cells examined belong to directional motion. For MCF-7 cells (N = 11), over 80% of cells examined belong to depressed motion. For MDA-MB-231 cells (N = 11), 54.5% of cells examined are depressed motion. Fisher's Exact test indicates that motion types are significantly different among the three cell-lines (p-value = 0.0001413).
Figure 14.
Motion range for cells undergoing an entire cell cycle.
(A–C) The starting points of cell trajectories are shifted to the origin of the coordinate. MCF-10A and MDA-MB-231 cells show larger motion range than MCF-7 cells. (D) Boxplot of maximum displacement for the three cell-lines. MCF-10A and MDA-MB-231 cells have comparable mean values of their maximum displacement, whereas MCF-7 cells have much smaller mean value in maximum displacement. The Wilcoxon rank rum test showed that there is statistically significant difference in distribution shift of median maximum displacement between MCF-10A and MCF-7, and between MDA-MB-231 and MCF-7 cells.
Figure 15.
Negative phase contrast images of MCF-10A, MCF-7, and MDA-MB-231 cells.
(A) MCF-10A cells have polarized protrusion structures of leading edge versus trailing edge. (B) MCF-7 cells have multiple protrusion structures around cell boundaries. (C) MDA-MB-231 cells have protrusion structures at the two ends of the long axes.
Figure 16.
Correlation between direction of cell migration and cell long axis for MCF-10A and MDA-MB-231 cells.
The direction of cell long axis along cell trajectories is shown with green arrows. (A) For the MCF-10A cell, the direction of cell long axis is mostly perpendicular to the direction of the cell trajectory. (B) For the MDA-MB-231 cell, the direction of cell long axis is mostly parallel to that of the cell trajectory. As shown in the inset of figure A, we used the unit vector v1 and v2 to indicate the direction of cell long axis and the direction of migration, respectively. (C, D) The histograms of the angle between the two unit vectors are shown for MCF-10A and MDA-MB-231 cells, respectively. The majority of data points for the MDA-MB-231 cell are close to zero degree, while the data points for the MCF-10A cell are distributed between 0 and 90 degree.