Automated characterization and parameter-free classification of cell tracks based on local migration behavior

Abstract

Cell migration is the driving force behind the dynamics of many diverse biological processes. Even though microscopy experiments are routinely performed today by which populations of cells are visualized in space and time, valuable information contained in image data is often disregarded because statistical analyses are performed at the level of cell populations rather than at the single-cell level. Image-based systems biology is a modern approach that aims at quantitatively analyzing and modeling biological processes by developing novel strategies and tools for the interpretation of image data. In this study, we take first steps towards a fully automated characterization and parameter-free classification of cell track data that can be generally applied to tracked objects as obtained from image data. The requirements to achieve this aim include: (i) combination of different measures for single cell tracks, such as the confinement ratio and the asphericity of the track volume, and (ii) computation of these measures in a staggered fashion to retrieve local information from all possible combinations of track segments. We demonstrate for a population of synthetic cell tracks as well as for in vitro neutrophil tracks obtained from microscopy experiment that the information contained in the track data is fully exploited in this way and does not require any prior knowledge, which keeps the analysis unbiased and general. The identification of cells that show the same type of migration behavior within the population of all cells is achieved via agglomerative hierarchical clustering of cell tracks in the parameter space of the staggered measures. The recognition of characteristic patterns is highly desired to advance our knowledge about the dynamics of biological processes.

Figure 1. Schematic cell track characterization.

(A) Example of a cell track segment. (B) The volume asphericity is determined by the cell positions of the track segment that are viewed as uncorrelated data points. (C) Track segments with different time-orderings are compatible with one and the same volume, including time-ordering based on closest data points (top) and time-ordering based on farthest data points (bottom). (D) The confinement ratio is determined by the displacement over the length of the cell track segment. (E) The displacement ratio is determined by the displacement over the maximal displacement of the cell track segment. (F) The outreach ratio is determined by the maximal displacement over the length of the cell track segment.

Figure 2. Cell population analyses of cell track data consisting of three sub-populations with distinct types of migration behavior.

(A) Instantaneous speed distribution with average speed m/min. (B) Turning angle distribution with average angle . (C) Displacement curve showing linear dependence on the square-root of time for the overall cell population. Error bars correspond to the standard deviation and are only shown at selected time points to enhance clarity. (D) Displacement curves for each sub-population separately: 100 cell tracks of type 1 (red, see Fig. S1), 100 cell tracks of type 2 (green, see Fig. S2) and 300 cell tracks of type 3 (blue, see Fig. S3). Error bars correspond to the standard deviation.

Figure 3. Characterization of cell populations by linear measures.

Results are presented as time-dependent averages over the relevant cell populations for each type of migration behavior (type 1: red curve, type 2: green curve, type 3: blue curve) and for the overall population (grey curve). Error bars correspond to the standard deviation and are only shown at selected time points to enhance clarity. (A) Confinement ratio. (B) Volume asphericity. (C) Outreach ratio. (D) Displacement ratio.

Figure 4. Examples of cell tracks from different sub-populations.

One cell track for each type of migration behavior is shown: a fairly straight cell track (type 1, red), a strongly confined cell track (type 2, green) and a purely random cell track (type 3, blue).

Figure 5. Linear measures for the three types of cell tracks shown in Fig.(type 1: red, type 2: green, type 3: blue).

(A) Confinement ratio as a function of time. (B) Volume asphericity as a function of time. (C) Outreach ratio as a function of time. (D) Displacement ratio as a function of time.

Figure 6. Heat maps of the staggered confinement ratio, staggered volume asphericity, staggered outreach ratio and staggered displacement ratio for the three types of cell tracks shown in Fig. 4.

(A) Type 1: fairly straight cell track. (B) Type 2: strongly confined cell track. (C) Type 3: purely random cell track.

Figure 7. Hierarchical clustering of synthetic cell tracks in the parameter space of staggered measures.

(A) Cell tracks from the three sub-populations with different types of migration behavior, i.e. fairly straight (type 1: red), strongly confined (type 2: green) and purely random (type 3: blue), form distinct clusters in the space spanned by the average confinement ratio and the average volume asphericity. (B) Dendrogram obtained from the agglomerative hierarchical clustering based on the euclidean distance between the centroids of groups of data points.

Figure 8. Cell population analyses of cell track data obtained from neutrophil migration.

(A) Instantaneous speed distribution with average speed m/min. (B) Turning angle distribution with average angle . (C) Displacement curve showing linear dependence on the square-root of time. Error bars correspond to the standard deviation and are only shown at selected time points to enhance clarity. (D) Number of cell tracks as a function of time.

Figure 9. Hierarchical clustering of neutrophil cell tracks in the parameter space of two staggered measures.

(A) Sub-populations of cell tracks in the space spanned by the average confinement ratio and the average volume asphericity: fairly straight cell tracks (type 1: red), strongly confined cell tracks (type 2: green) and purely random cell tracks (type 3: blue). In going from 2D to 4D clustering, eleven cell tracks change sup-populations from type 1 to type 3 and from type 3 to type 2 (indicated in black). (B) Dendrogram obtained from the agglomerative hierarchical clustering based on the euclidean distance between the centroids of groups of data points.

Figure 10. Hierarchical clustering of neutrophil cell tracks in the parameter space of four staggered measures.

(A) Dendrogram obtained from the agglomerative hierarchical clustering based on the euclidean distance between the centroids of groups of data points. The clustering was performed in the space spanned by the average confinement ratio, average volume asphericity, average displacement ratio and average outreach ratio. (B) Representative cell tracks of the cluster with fairly straight cell tracks. (C) Representative cell tracks of the cluster with strongly confined cell tracks. (D) Representative cell tracks of the cluster with purely random cell tracks.

Figure 11. Neutrophil cell track with ID 1 switching sub-populations in going from 2D to 4D clustering.

(A) Neutrophil with track ID 1 switched from sub-population of type 3 (random migration) to type 2 (strongly confined migration). (B) Heat maps of the staggered confinement ratio, staggered volume asphericity, staggered outreach ratio and staggered displacement ratio.

Figure 12. Neutrophil cell track with ID 245 switching sub-populations in going from 2D to 4D clustering.

(A) Neutrophil with track ID 245 switched from sub-population of type 1 (fairly straight migration) to type 3 (random migration). (B) Heat maps of the staggered confinement ratio, staggered volume asphericity, staggered outreach ratio and staggered displacement ratio.