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Quantitative and unbiased analysis of directional persistence in cell migration


The mechanism by which cells control directional persistence during migration is a major question. However, the common index measuring directional persistence, namely the ratio of displacement to trajectory length, is biased, particularly by cell speed. An unbiased method is to calculate direction autocorrelation as a function of time. This function depends only on the angles of the vectors tangent to the trajectory. This method has not been widely used, because it is more difficult to compute. Here we discuss biases of the classical index and introduce a custom-made open-source computer program, DiPer, which calculates direction autocorrelation. In addition, DiPer also plots and calculates other essential parameters to analyze cell migration in two dimensions: it displays cell trajectories individually and collectively, and it calculates average speed and mean square displacements (MSDs) to assess the area explored by cells over time. This user-friendly program is executable through Microsoft Excel, and it generates plots of publication-level quality. The protocol takes 15 min to complete. We have recently used DiPer to analyze cell migration of three different mammalian cell types in 2D cultures: the mammary carcinoma cell line MDA-MB-231, the motile amoeba Dictyostelium discoideum and fish-scale keratocytes. DiPer can potentially be used not only for random migration in 2D but also for directed migration and for migration in 3D (direction autocorrelation only). Moreover, it can be used for any types of tracked particles: cellular organelles, bacteria and whole organisms.

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Figure 1: Directionality ratio and its pitfalls.
Figure 2: Outputs of DiPer programs obtained from D. discoideum trajectories (Supplementary Data 4) for wild-type (WT), Arpin knockout (KO) and GFP-Arpin rescue amoeba.
Figure 3: Analysis of direction autocorrelation.
Figure 4: Outputs of DiPer autocorrelation programs for automatically tracked D. discoideum cells and manually tracked fish keratocytes (FK) cells.
Figure 5: Outputs of DiPer auxiliary programs obtained from D. discoideum trajectories for wild-type (WT), Arpin knockout (KO) and GFP-Arpin rescue amoeba.
Figure 6: Flowchart of DiPer procedure, highlighting the key steps in the column on the left.

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We thank N. Kurochkina, C. Merrifield, G. Romet-Lemonne, S. Shekhar and G. Taver for their technical advice. We acknowledge support from Fondation ARC (l'Association pour la Recherche sur le Cancer) pour la Recherche sur le Cancer (PDF20111204331 to R.G.) and from Agence Nationale pour la Recherche (ANR-11-BSV8-0010-02 to A.G.).

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Authors and Affiliations



R.G. and A.G. conceived the work; R.G. wrote all computer programs; A.G. supervised their development; and R.G. wrote the first draft of the manuscript, and a final version was reached through exchanges between both authors.

Corresponding authors

Correspondence to Roman Gorelik or Alexis Gautreau.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Data 1

'Plot_at_Origin' program source code. (TXT 9 kb)

Supplementary Data 2

'Make_Charts' program source code. (TXT 6 kb)

Supplementary Data 3

'Sparse_Data' program source code. (TXT 2 kb)

Supplementary Data 4

An example input file containing migration coordinates of amoeba Dictyostelium discoideum under three different conditions: wild-type (WT), Arpin KO (knock-out), and GFP-Arpin (rescue). Note that for each condition there is one worksheet, and all trajectories within a worksheet are listed one immediately below another without spaces. Columns 4, 5, and 6 contain frame number, X coordinate, and Y coordinate, respectively. This file was used to generate outputs in Figure 2, 4a, and 5. (XLSX 255 kb)

Supplementary Data 5

An example input file containing migration coordinates of fish scale keratocytes under two different conditions: microinjected with either buffer (Buffer), or full-length Arpin (FL). Note that for each condition there is one worksheet, and all trajectories within a worksheet are listed one immediately below another without spaces. Columns 4, 5, and 6 contain frame number, X coordinate, and Y coordinate, respectively. This file was used to generate outputs in Figure 4b. (XLSX 87 kb)

Supplementary Data 6

'Speed' program source code. (TXT 10 kb)

Supplementary Data 7

'Dir_Ratio' program source code. (TXT 19 kb)

Supplementary Data 8

'MSD' program source code. (TXT 13 kb)

Supplementary Data 9

'Autocorrel' program source code. (TXT 17 kb)

Supplementary Data 10

'Autocorrel No Gaps' program source code. (TXT 17 kb)

Supplementary Data 11

'Autocorrel 3D' program source code. (TXT 16 kb)

Supplementary Data 12

'Vel Cor' program source code. (TXT 15 kb)

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Gorelik, R., Gautreau, A. Quantitative and unbiased analysis of directional persistence in cell migration. Nat Protoc 9, 1931–1943 (2014).

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