Our algorithm was written efficiently in C++ to allow researchers to run data sets of any size (varying number of time frames) in minutes. The algorithm variables can be easily fine-tuned to quantify collective migration behavior for any cell type. For example, it is easy to adjust parameters such as the number of frames to be analyzed (based on how tortuous the cell migration path is) and the size of radii increments (based on average cell width). The program is fully automated, allowing analysis of the data for all of the wells from a 96-well plate with a single instruction, which is useful for integration with a high-content screening platform. On average, the program can run data containing ~2400 cells (one site of a confluent well imaged at 4× magnification) over 24 time frames in ~20 s. Vast numbers of cells can therefore be analyzed in a short time period, which is important as often computational time is an analysis bottleneck.
We assessed the accuracy of our algorithm in estimating stream width by comparing its output to manual measures of stream width from our directionally colored images for randomly selected cells. Specifically, the stream widths of thirty randomly selected cells from three wells were evaluated manually for each cell type. Accuracy was computed as
The average accuracy is displayed on the bar chart in Figure 4A and was not significantly different for each test case. The algorithm had a calculated accuracy of 89.7% ± 8.9% for ARPE-19 cells, of 85.1% ± 10.1% for BJ cells, 75.5% ± 12.5% for ARPE-19 GFP-N-cadherin expressing cells, and 82.2% ± 10.5% for the ARPE-19 cells in the wound healing assay. The inaccuracy was a result of a combination of factors. First, manually estimating the stream widths by hand was incredibly difficult due to the number of surrounding tracks, making our accuracy benchmark inherently inaccurate. This was a major contribution to the large deviation in accuracy, and further illustrates the need for an algorithm to evaluate stream widths. Secondly, errors may arise from cells that are not exactly in the center or edge of a stream. In the algorithm used for all our experiments, to account for situations where the comparison cell being analyzed is exactly in the center of a stream, the radius is doubled if both arcs finish at the same time; this was computationally easy to implement and was expected to improve the accuracy of the measurement. A similar calculation for cells located between the edge and center of a stream would have unnecessarily increased the complexity of the code and hence was not implemented; therefore, these cells will report narrower stream widths. We do not expect this effect to be significantly detrimental to overall accuracy, however, unless assessing very wide streams. Still, this could be improved in future iterations of the algorithm. Thirdly, the algorithm may be too lenient when classifying neighboring cells as correlated. If a nearby cell moved in the same orientation for less than ~5 µm, our observations determined the cell movement to be uncorrelated, whereas the program marked it as correlated, for that time point. This could be adjusted in the future by only considering data from pairs of cells that both movea minimum distance. Despite these factors, our algorithm reported stream widths that were much closer to those measured in experimental images than achieved using the standard velocity correlation function method.
We also performed a sensitivity analysis to determine the impact of the different algorithm variables on the results. Figure 4B shows a histogram comparing the stream width outputs for ARPE-19 cells if the radius increment is changed. The 10-µm radius increment data shows similar peaking characteristics as the 20-µm radius increment, but fails to detect larger stream widths, whereas the 40-µm radius increment returns stream widths that are too high and inaccurate. The major differences arise due to under-sampling versus over-sampling. In smaller increments, the algorithm does not detect enough correlated cells to continue searching. In larger increments, the algorithm potentially assesses multiple streams within one arc. Increment size should be selected to correspond approximately to the width of one cell to get the most accurate results. We also assessed the impact of the angle used to define correlated movement (Figure 4C). We selected ±10° for correlation based on visual estimates of the angle between cells in a stream from our live imaging movies, but this could easily be adjusted to be more or less stringent. Decreasing this angle to 5° did not significantly change the shape of the stream width distribution or peak location, but did slightly increase the number of cells considered to be part of very narrow streams. Increasing this angle to 50°, however, significantly impacted the stream width distribution. Selection of an appropriate angle to define correlated movement, therefore, is also an important parameter for obtaining accurate results.
The GFP-N-cadherin lentiviral plasmid was a gift from W. James Nelson at Stanford University. The authors thank Maria Jimena Loureiro and Sahar Javaherian for technical contributions. This work was funded by a National Science and Engineering Research Council (NSERC) Discovery grant (to A.M.)
The authors declare no competing interests.
Address correspondence to Alison P McGuigan, Dept. of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College St., Toronto, Ontario, M5T 3J9, Canada. e-mail: [email protected]
1.) Weber, G., M. Bjerke, and D. DeSimone. 2012. A mechanoresponsive cadherin-keratin complex directs polarized protrusive behavior and collective cell migration. Dev. Cell 22:104-115. 2.) Migeotte, I., T. Omelchenko, A. Hall, and K.V. Anderson. 2010. Rac1-dependent collective cell migration is required for specification of the anterior-posterior body axis of the mouse. PLoS Biol 8:e1000442. 3.) Arima, S., K. Nishiyama, T. Ko, Y. Arima, Y. Hakozaki, K. Sugihara, H. Koseki, Y. Uchijima. 2011. Angiogenic morphogenesis driven by dynamic and heterogeneous collective endothelial cell movement. Development 138:4763-4776. 4.) Honda, H., Y. Ogita, S. Higuchi, and K. Kani. 1982. Cell movements in a living mammalian tissue: long-term observation of individual cells in wounded corneal endothelia of cats. J. Morphol. 174:25-39. 5.) Wolf, K., Y.I. Wu, Y. Liu, J. Geiger, E. Tam, C. Overall, S.M. Stack, and P. Friedl. 2007. Multi-step pericellular proteolysis controls the transition from individual to collective cancer cell invasion. Nat. Cell Biol. 9:893-904. 6.) Szabó, A., R. Ünnep, E. Méhes, W.O. Twal, W.S. Argraves, Y. Cao, and A. Czirók. 2010. Collective cell motion in endothelial monolayers. Phys. Biol. 7:046007. 7.) Aman, A., and T. Piotrowski. 2009. Multiple signaling interactions coordinate collective cell migration of the posterior lateral line primordium. Cell Adh. Migr. 3:365-368. 8.) Ewald, A.J., A. Brenot, M. Duong, B.S. Chan, and Z. Werb. 2008. Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis. Dev. Cell 14:570-581. 9.) Prasad, M., X. Wang, L. He, and D.J. Montell. 2011. Border cell migration: a model system for live imaging and genetic analysis of collective cell movement. Methods Mol. Biol. 769:277-286. 10.) Farooqui, R., and G. Fenteany. 2005. Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement. J. Cell Sci. 118:51-63. 11.) Zaman, M.H., L.M. Trapani, A.L. Sieminski, D. MacKellar, H. Gong, R.D. Kamm, A. Wells, D.A. Lauffenburger, and P. Matsudaira. 2006. Migration of tumor cells in 3D matrices is governed by matrix stiffness along with cell-matrix adhesion and proteolysis. Proc. Natl. Acad. Sci. USA 103:10889-10894. 12.) Vaughan, R.B., and J.P. Trinkaus. 1966. Movements of epithelial cell sheets in vitro. J. Cell Sci. 1:407-413. 13.) Friedl, P., and D. Gilmour. 2009. Collective cell migration in morphogenesis, regeneration and cancer. Nat. Rev. Mol. Cell Biol. 10:445-457. 14.) Vitorino, P., M. Hammer, J. Kim, and T. Meyer. 2011. A steering model of endothelial sheet migration recapitulates monolayer integrity and directed collective migration. Mol. Cell. Biol. 31:342-350. 15.) Vitorino, P., and T. Meyer. 2008. Modular control of endothelial sheet migration. Genes Dev. 22:3268-3281. 16.) Angelini, T.E., E. Hannezo, X. Trepat, M. Marquez, J.J. Fredberg, and D.A. Weitz. 2011. Glass-like dynamics of collective cell migration. Proc. Natl. Acad. Sci. USA 108:4714-4719. 17.) Szabó, B., G.J. Szöllösi, B. Gönci, Z. Jurányi, D. Selmeczi, and T. Vicsek. 2006. Phase transition in the collective migration of tissue cells: experiment and model. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74:061908. 18.) Vedula, S.R.K., M.C. Leong, T.L. Lai, P. Hersen, A.J. Kabla, C.T. Lim, and B. Ladoux. 2012. Emerging modes of collective cell migration induced by geometrical constraints. Proc. Natl. Acad. Sci. USA 109:12974-12979. 19.) Vedula, S.R.K., M.C. Leong, T.L. Lai, P. Hersen, A.J. Kabla, C.T. Lim, and B. Ladoux. 2012. Emerging modes of collective cell migration induced by geometrical constraints. Proc. Natl. Acad. Sci. USA 109:12974-12979. 20.) Angelini, T.E., E. Hannezo, X. Trepat, J.J. Fredberg, and D.A. Weitz. 2010. Cell migration driven by cooperative substrate deformation patterns. Phys. Rev. Lett. 104:168104. 21.) Haga, H., C. Irahara, R. Kobayashi, T. Nakagaki, and K. Kawabata. 2005. Collective movement of epithelial cells on a collagen gel substrate. Biophys. J. 88:2250-2256. 22.) Kabla, A.J. 2012. Collective cell migration: leadership, invasion and segregation. J. R. Soc. Interface 9:3268-3278. 23.) Parish, C.R. 1999. Fluorescent dyes for lymphocyte migration and proliferation studies. Immunol. Cell Biol. 77:499-508. 24.) Peyton, S.R., and A.J. Putnam. 2005. Extracellular matrix rigidity governs smooth muscle cell motility in a biphasic fashion. J. Cell. Physiol. 204:198-209. 25.) Cimini, D., B. Howell, P. Maddox, A. Khodjakov, F. Degrassi, and E.D. Salmon. 2001. Merotelic kinetochore orientation is a major mechanism of aneuploidy in mitotic mammalian tissue cells. J. Cell Biol. 153:517-528. 26.) Ng, M.R., A. Besser, G. Danuser, and J.S. Brugge. 2012. Substrate stiffness regulates cadherin-dependent collective migration through myosin-II contractility. J. Cell Biol. 199:545-563.