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Conceived and designed the experiments: YT KA TN YS. Performed the experiments: KA MM. Analyzed the data: YT. Contributed reagents/materials/analysis tools: YT. Wrote the paper: YT KA TN YS MM SI.

The authors have declared that no competing interests exist.

Advances in time-lapse fluorescence microscopy have enabled us to directly observe dynamic cellular phenomena. Although the techniques themselves have promoted the understanding of dynamic cellular functions, the vast number of images acquired has generated a need for automated processing tools to extract statistical information. A problem underlying the analysis of time-lapse cell images is the lack of rigorous methods to extract morphodynamic properties. Here, we propose an algorithm called edge evolution tracking (EET) to quantify the relationship between local morphological changes and local fluorescence intensities around a cell edge using time-lapse microscopy images. This algorithm enables us to trace the local edge extension and contraction by defining subdivided edges and their corresponding positions in successive frames. Thus, this algorithm enables the investigation of cross-correlations between local morphological changes and local intensity of fluorescent signals by considering the time shifts. By applying EET to fluorescence resonance energy transfer images of the Rho-family GTPases Rac1, Cdc42, and RhoA, we examined the cross-correlation between the local area difference and GTPase activity. The calculated correlations changed with time-shifts as expected, but surprisingly, the peak of the correlation coefficients appeared with a 6–8 min time shift of morphological changes and preceded the Rac1 or Cdc42 activities. Our method enables the quantification of the dynamics of local morphological change and local protein activity and statistical investigation of the relationship between them by considering time shifts in the relationship. Thus, this algorithm extends the value of time-lapse imaging data to better understand dynamics of cellular function.

Morphological change is a key indicator of various cellular functions such as migration and construction of specific structures. Time-lapse image microscopy permits the visualization of changes in morphology and spatio-temporal protein activity related to dynamic cellular functions. However, an unsolved problem is the development of an automated analytical method to handle the vast amount of associated image data. This article describes a novel approach for analysis of time-lapse microscopy data. We automated the quantification of morphological change and cell edge protein activity and then performed statistical analysis to explore the relationship between local morphological change and spatio-temporal protein activity. Our results reveal that morphological change precedes specific protein activity by 6–8 min, which prompts a new hypothesis for cellular morphodynamics regulated by molecular signaling. Use of our method thus allows for detailed analysis of time-lapse images emphasizing the value of computer-assisted high-throughput analysis for time-lapse microscopy images and statistical analysis of morphological properties.

Cell morphological change is a key process in the development and homeostasis of multicellular organisms

Quantitative approaches are helping to unveil cellular morphodynamic systems, and they are generating new technical requirements. Because cellular morphological change is highly dynamic, time-lapse imaging is necessary to understand the mechanism of cell morphology regulation. Progress in the development of fluorescent probes has enabled the direct observation of cell morphological changes and/or the localization and activity of specific proteins

Indeed, computational methods have been used to determine the properties of morphological dynamics, protein activity and gene expression

Although previous methodologies have successfully described the specific aspects of cellular morphodynamics, there remain challenges to quantify the relationship between morphodynamics and signaling events. One representative problem is the association between regions in different frames. To scrutinize the dynamic relationship between morphological change and molecular signaling, we need to cross-correlate them in a time-dependent manner (

(A) General scheme of cellular morphological changes. The diagram shows part of a cell's edge expanding continuously over time (frame number)

We focused on the Rho-family small GTPases, or Rho GTPases, as signaling molecules associated with cell morphodynamics. Rho GTPases, which act as binary switches by cycling between inactive and active states (

Various upstream signals trigger the activation of Cdc42, Rac, and Rho GTPases and induce morphological and cytoskeletal changes such as formation of filopodia, lamellipodia, and stress fibers, respectively. The ratio of the inactive GDP-bound state to active GTP-bound state is regulated by guanine nucleotide exchange factors (GEFs) and the GTPase-activating proteins (GAPs). Many studies have shown crosstalk between these GTPases; however, direct links between these GTPases are still to be clarified.

The objective of this study was to uncover the relationship between spatio-temporal activities of Rho GTPases and morphological changes of the cells. To achieve this, we needed a data analysis tool to assess the link between biochemical signaling and biophysical phenomena. However, we do not focus on unveiling the orchestration of the complete signaling pathways that regulate cell morphology. In addition, we elucidated how Rho GTPases regulate “two-dimensional” morphological changes of cells, rather than “three-dimensional” changes. These findings will however be meaningful because the results can be compared with earlier findings

The EET algorithm describes the time course of local cell morphological changes based on area differences of sequential images. We focused on the local area change, rather than the local structural change as a morphological property; therefore, EET analysis did not make clear distinctions between filopodia and lamellipodia. Subdivided regions along the cell edge boundaries are connected to the corresponding subdivided regions in the next frame, and movements of the subdivided regions are then defined by these connected subregions. Thus, the subdivided regions called “segments” are basic units in EET for quantification of morphological changes. EET describes the time course of local protrusion and retraction as follows:

Sequential cell edge boundaries and area differences are obtained by applying an appropriate binary filter to time-lapse microscopy images as a preprocess (see Preprocessing section). Each area difference is typically represented as a positive or negative number of pixels.

The traced cell boundary is divided into segments according to the area differences between two consecutive frames (see

The boundary points of each segment are identified as “anchor points” (lowercase letters in

The identified segments and the anchor points are projected into time and position along the cell perimeter coordinates (

The corresponding anchor points, described in

(A) Identification of morphodynamic properties. Solid lines denote cellular edge at each frame and the shaded regions A, B, and C indicate area differences between consecutive frames. We define two properties for a local morphological status transition: segments and anchor points. The segments are subdivided along the cellular edges, which are determined by the area differences between neighboring frames. The anchor points are segment terminals (closed circles) and are projected into the previous frame (open circles). Open squares l and r represent the edge terminals. (B) All of the segments identified and anchor points are mapped two-dimensionally. Horizontal and vertical axes denote the time and position along the cell edge, respectively. Connections between anchor points (dashed lines) illustrate the corresponding points between neighboring frames. (C) We can then construct a graph to represent segment evolution. A node and link denote each segment and the connection between temporally consecutive segments. (D) Flow chart of the EET algorithm. (E) All colored nodes show the ancestry of the colored node at ‘

These connected anchor points indicate the spatial associations between neighboring time frames, and allow us to trace the corresponding regions along the time course by means of the graph structure, which represents the lineage of the segments along the time course. A flow chart of the EET procedure above is shown in

It should be noted that EET defines how the ancestral segments of a certain segment at a certain time behave along the time course (

Local activity along a cell boundary is defined as the mean FRET ratio inside a circle, which has its center on the cell boundary and radius ^{N}.

We calculated cross-correlation coefficients between local area changes and activities based on the defined segments. Vector data {^{(t)}|^{(t)}|^{(t)} and ^{(t)} represent local activities at time ^{(t)}},{^{(t)}},^{t}^{(t)} and ^{(t+1)} have the same dimensionality ^{t}^{(t)}}, {^{(t)}}, N) is defined as_{j}^{(t)}|_{d}^{(t)}|_{a}^{(t)}|_{a} the number of ranks in {^{(t)}|

We investigated ^{t,t+τ}^{(t,t+τ)} could be defined. Because the graph structure was obtained under the basic assumption that each local event is defined in terms of ‘segment’, a morphological property, we calculate the ^{(t,t+1)}, ^{(t,t+2)}, ^{(t,t+3)},…, denotes the time course of edge evolution; ^{(t,t+τ)} is defined below. The transition between ^{t}^{t+}^{1} segments at time ^{t}×M^{t+}^{1} matrix ^{t,t+}^{1}, which consists of 0 and 1 denoting unconnected and connected segments, respectively, in the ancestry graph (^{(t,t+τ)} denotes the summation of area differences among the segments at ^{(T)} = {la, ab, br} and ^{(T+1)} = {lc, cd, de, ef, fr}, where each element in the sets denotes an area difference (typically, a number of pixels). The transition matrix is given by:^{(T+1,T)} = (^{T,T+1} (^{(T+1)})’)’ = {lc+cd+de, de+ef+fr, fr}, where the addition is applied to the area difference values. Based on these time-shifted corresponding area differences, a one-to-one relationship between the segments in different frames is constructed. The cross-correlation coefficient with a time-shift of τ is thus obtained by calculating ^{(t)}}, {^{(t, t+τ)}},

In this study, cell boundaries and area differences were all extracted from fluorescence time-lapse images. To emphasize the cell edges, the images were filtered with an unsharp mask (implemented by the image-processing software MetaMorph [Universal Imaging, Sunnyvale, CA]), which subtracts a low-pass filtered and scaled image from its original image. The Gradient Anisotropic Diffusion filter

For this study, we used neurite outgrowth of rat pheochromocytoma PC12 cells as an example of cells displaying complex morphological dynamics, while random migration of human fibrosarcoma HT1080 cells was used for analysis of the cross-correlation between morphological changes and Rho GTPase activity. PC12 cells were plated on polyethyleneimine- and laminin-coated 35-mm glass-base dishes (Asahi Techno Glass, Chiba, Japan), and then transfected with pRaichu-1011x encoding Rac1 FRET probe. One day after transfection, the cells were stimulated with 50 ng/ml NGF in phenol red-free Dulbecco's modified Eagle's medium/F12 containing 0.1% bovine serum albumin for 48 h to induce neurite outgrowth. HT1080 cells were transfected with pRaichu-1011x, pRaichu-1054x encoding a Cdc42 FRET probe, or pRaichu-1294x encoding RhoA FRET probe and, after 24 h, cells were plated on collagen-coated 35-mm glass-base dishes. The medium was then changed to phenol red-free Dulbecco's modified Eagle's medium/F12 containing 10% fetal bovine serum, overlaid with mineral oil to prevent evaporation, and image acquisition was started. The cells were imaged with an inverted microscope (IX81 or IX71; Olympus, Tokyo, Japan) equipped with a cooled charge-coupled device camera (Cool SNAP-K4 or Cool SNAP-HQ; Roper Scientific, Duluth, GA), and a laser-based auto-focusing system at 37°C. The filters used for the dual-emission imaging were purchased from Omega Optical (Brattleboro, VT): an XF1071 (440AF21) excitation filter, an XF2034 (455DRLP) dichroic mirror, and two emission filters (XF3075 [480AF30] for CFP and XF3079 [535AF26] for FRET). The cells were illuminated with a 75-W xenon lamp through a 6%, 10% or 12% ND filter and viewed through a 60× oil-immersion objective lens (PlanApo 60×/1.4). The exposure times for 2×2 or 3×3 binning were 400 or 500 ms for CFP and FRET images. After background subtraction, FRET/CFP ratio images were created with MetaMorph software, and the images were used to represent FRET efficiency. Further details of microscopy and sample preparation can be found in previous reports

We executed a permutation test between positive (6 min), negative (−6 min) and non time-shifted correlations according to the following procedure. Letters/numbers in bold fonts represent vectors.

Correlations are obtained at positive (

For each pair of the three labels:

Calculate the difference between the two correlation vectors, for example, the difference between positive and negative labels is given as

Resample permutated differences of correlations (for example ^{per}

Calculate the rates (i.e., permutation

Calculate the permutation

For example, if we have ^{per}^{3} = 8 in the above example, with uniform probability. The permuted difference vectors whose mean is larger than that of the original difference vector are thus {[0.3 0.1 0.2], [0.3 −0.1 0.2]} and number 2. In this particular example, the permutation

We applied EET to branching PC12 cells to validate its usefulness for quantifying complex cell morphological changes. As shown in

(A) Time-lapse fluorescence images of a PC12 cell. (B) Expanding, retracting, and stationary regions of the cell edge boundary in the subsection of (A) (white square) are colored red, blue and green, respectively. Each colored region along the cell edge corresponds to a single segment in panel (C). Red arrows show the correspondence between colored regions in (B) and segments in (C). (C) The cell boundary state profile of (A), in which each segment is colored red, blue and green according to the status of expansion, retraction and stasis, respectively. Black lines connect the corresponding anchor points to represent the correspondence between subdivided regions in successive frames. The plot shows the total cell area and complexity {(total cell boundary length)^{2} /(total cell area)} of the cell. Note that the total cell area and the total length of the cell boundary are highly independent. (D) Local area difference map of (C), in which the magnitude of area difference for each segment is depicted by a color gradation from protrusion (red) to retraction (blue).

Because previous studies have shown the localization of GTPase activities at peripheral regions

(A) Time-lapse FRET images of an HT1080 cell. The colored bar illustrates the FRET/CFP ratio, which is assumed to indicate Rac1 activity. (B) Area difference images are acquired by subtracting neighboring frames (see

Next, we applied EET to precisely examine the spatio-temporal relationships between morphological changes and GTPase activities in motile HT1080 cells. As with PC12 cells (

Visual inspection of the local area difference map (

We further investigated this spatio-temporal cross-correlation between morphological changes and Rho-family GTPase activity. First, we summarized their statistical characteristics to examine the cross-correlation.

(A) A scatter plot of the local activity and area difference of each segment. Each point represents the local activity and area difference of a single segment identified by EET. The overall property of all the segments in the dataset is portrayed, excluding temporal and positional information. (B) Histogram of GTPase activities (YFP/CFP ratio) approximated by Gaussian distribution. Vertical and horizontal axes denote the number of segments and local activity within each segment, respectively. (C) Histogram of area differences in each segment. Zero values occur frequently because the majority of edge segments do not move. (D) Time-shifted relationship between local area differences and GTPase activity. The top panels show the time-shifted scatter plots of the local area difference and the GTPase activity. Each point represents the mean local activity and summation of the area difference of the ancestry segments (see

We next examined the effects of time-shifts on cross-correlation between the activity and the area difference. The graphical structures of EET profiles display local area differences in the corresponding time-shifted segments. The middle panels of

We calculated time-shifted cross-correlations between the local activities of Cdc42/Rac1/RhoA and local morphological changes, as shown in

Rho family small GTPases Cdc42, Rac1 and RhoA were analyzed in terms of the time-shifted cross-correlation. We examined several cells for each GTPase. Each boxplot shows the first quartile (bottom of the box), third quartile (top of the box), median (red line) and outliers (red plus marks) for several cells (N = 9 for Cdc42, N = 6 for Rac1 and N = 6 for RhoA). Where there were no outliers, a red dot is shown at the bottom of the whisker. For Cdc42 and Rac1, the time-shifted correlation is significantly increased with negative time-shifts (results of the permutation test are shown in

The results do not appear to be intuitive with regard to the causal relationship between morphological changes and molecular signaling; upstream molecular signaling should control downstream morphological changes, for example via actin reorganization, adhesion and/or retrograde flow. In the cases of both Rac1 and Cdc42, the time-shifted correlations showed that morphological change preceded local GTPase activity. Cdc42 activity, in particular, showed large deviations when the preceding time-shifts were short, and the correlation decayed steeply when the time-shifts were longer. Rac1 activity, on the other hand, elicited small deviations and the decay of the correlation was less steep when the preceding time-shifts were longer. It should be noted that the time-shifted correlation generally approaches zero over long time-shifts owing to an increase in the number of connections between the original segment and time-shifted segments (see

We further examined the spatial property of the relationship between GTPase activity and morphology change by comparing the original EET profile with rotated (see

We compared EET analysis to polar coordinate-based analysis to further prove the utility of EET. We first performed polar coordinate-based analysis to the cell in

(A) Polar coordinate-based analysis was performed by setting the origin of coordinates at the mean mass center of the binary images. (B) Time-shifted cross-correlation analysis by polar coordinates and EET for the cell depicted in

A similar tendency was observed when a population of the cells in

We also compared EET analysis with simple implementation of marker-tracking-based analysis. In this marker-tracking-based analysis, virtually defined markers were aligned uniformly along the spline-fitted cellular edge in the first frame of time-lapse FRET images. Then, the movements of markers in the direction perpendicular to the cellular edge during a single time-frame were measured according to the current marker position and the intersection of the perpendicular axes of the current cellular edge and the next cellular edge (

Marker-tracking-based analysis was performed using virtually-defined markers, and their movements perpendicular to the cellular edge were measured. (A) Cellular edges changing with time (blue: 6 min; indigo: 7 min; light blue: 8 min; green: 9 min; yellow: 10 min; red: 11 min). The cell analyzed was the same as that used in

The time-shifted cross-correlations in

We have developed an algorithm called EET, which describes changes in cell morphology using time-lapse live cell imaging. Spatio-temporal area difference maps revealed morphodynamic properties as patterns of extension and retraction, and the correspondence between time-shifted segments, achieved using anchor points, ensured that the related subdivided edges were connected between time-shifted frames. Therefore, EET effectively accounts for complex morphodynamics that include persistent extension or retraction, and arborization. This property is realized by the graphical representation of edge evolution, and ensures EET is suitable for depicting changes in cell shape, such as the branching that occurs during neural development. Application of EET to the extending neurites of PC12 cells provided a clear evidence of its utility by precisely revealing the persistent protrusion and retraction patterns. Besides, a second application to motile HT1080 cells illuminated distributions of local area differences and corresponding local activity of GTPases. Although the graph structure itself potentially generates biases when correlating the one-to-multi segments between temporally distant frames, we confirmed that our results were consistent even when we obtained our result differently by associating the area change in each segment with the average molecular activities over the corresponding segments (see

It has been established that Rho-family GTPases (Rac1, Cdc42 and RhoA) play key roles in morphological changes through cytoskeletal reorganization

The precise mechanism by which local area changes precede local activity around the cell boundary remains unclear from our current analysis. However, we speculate four possible mechanisms based on our results. The first explanation is the existence of upstream signaling molecules that regulate extension in parallel with GTPase activity. If the reactions of the signaling cascades involved with extension are faster than those linked to GTPase activation, extension could precede GTPase activity. In this respect, it would be interesting to conduct a study similar to the current one for PI3K, which activates many signaling molecules including Rac1 activators

The second explanation is that protrusion site-specific stimulation activates the GTPases. There are several mechanisms by which physical force can be converted into biochemical responses

The third possibility is that signaling crosstalk regulates the timing of extension and retraction

The fourth possibility is the existence of different mechanisms for cell edge extension. EGF-stimulated initial protrusion in MTLn3 rat adenocarcinoma cells is caused by cofilin activation and severing of F-actin, which is coincident with actin polymerization and formation of lamellipodia

Quantitative analysis of live cell microscopy images is invaluable for better understanding of the dynamic properties of processes such as chemotaxis and development. Such quantitative data can go beyond descriptions of the dynamic features of cellular behavior to serve as a scaffold for theoretical study and to enhance system-level understanding. Based on quantitative data acquired by polar coordinate-based analysis of neurons, for example, Betz et al. discussed a bistable stochastic process derived from velocity histograms and calculated potential distribution

Effect of radius. (A) Activity maps with several radius lengths are shown in the upper panels. Maps become increasingly blurred with increasing radius due to the averaging effect within each circle. Histograms of activity for each segment (lower panels) become sharper with increasing radius because an increase in the circle size leads to both a decrease in the population of outliers and an increase in the population of mean segments. A few zero-activity segments occur as a result of failure of cell edge tracing in preprocessing. (B) Time-shifted correlations for several radii. Qualitatively similar profiles are shown for four radii. To precisely determine the length of the radius, however, there is a trade-off between noise reduction and retention of map clarity. For subsequent analysis, we set the length at

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Sample numbers with time-shifts. Cross-correlation between local activity and area difference (black line) and sample number (red line) was plotted against time-shift. Because we executed statistical analysis segment-wise, the sample number for calculating the cross-correlation is the same as the number of all segments ∑^{N−1}_{t = 1}^{t}. Although the sample number decreases as the time-shift increases, a statistically sufficient number of samples (more than 2000) were obtained with EET.

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Effect of time-lapse length. (A) We examined how the time-shifted correlation behaves when the time-lapse length (i.e., number of images) changes. The time-shifted correlation was calculated for different time-lapse values with the same cell. We made a series of different time-lapse images by extracting selected images. For example, from seven frames of 1-min time-lapse images {1 2 3 4 5 6 7}, we extracted 2-min {1 3 5 7} and 3-min time-lapse images {1 4 7}. All profiles show quantitatively the same behavior; that is, a high correlation for around −7 to −13 min time-shifts and no correlation for positive time-shifts. (B) The relationship between various time-lapse values (1 to 3 min) and sample numbers (segment numbers) decreases with increasing time lapse. Longer time lapses tend to show higher correlation owing to the tight relationship between persistently extending cell peripheries and GTPase activities. On the other hand, we should choose a time-lapse length considering the decrease in the sample number, which may reduce the statistical significance of cross-correlation values.

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Figure S4. Time-shifted cross-correlations for the original and modified data obtained from the same cell as in

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Validation of EET by permutation and rotation. The time-shifted correlation was calculated when the locations of the identified segments were rotated about the cell boundary (A) and randomly permutated (B). Each circle schematically denotes the segments we identified, and the cell edge boundary is represented by the entire linked circle. (C) The time-shifted correlations reveal that the correlation coefficients decrease with increasing rotation (blue to green lines). Red and pink lines indicate absence of correlation for permutated segments and an inverse correlation for halfway-rotated segments, respectively.

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Comparison of morphodynamic maps and activity maps. (A) Local area difference map of a motile HT1080 cell, acquired by EET (same figure as

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Original time-shifted correlations of EET and reversely calculated time-shifted correlations. To examine the effects of the graph structure on time-shifted correlations, we obtained differently calculated time-shifted cross-correlations for the cell depicted in

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P-values of permutation tests for two-sided test.

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We thank Naoki Honda, Shigeyuki Oba, and Justin Dauwels for helpful discussions and Yuko Fujisawa and Ian Smith for reviewing the manuscript.