Actin flow versus cell velocity analysis. For Figs. 1e–g, 4e–g, Extended
Data Figs. 1l, 4b, 5g, 8a, kymographs were generated along the cell
trajectories, and both cell and actin velocities were extracted from
those kymographs. To follow cells migrating in a channel with a high
magnification (Fig. 4e–g, Supplementary Video 10), the channel was
realigned with a homemade script (MATLAB, MathWorks).
Microchannel assay analysis. Cells going in both directions of the
microchannels were analysed, and channels containing more than one
cell were excluded. Kymographs were generated along the channel, and
cell velocity was calculated for each cell in the different zones.
Actin flow in primary T cells confined on nanoridges. Actin flow
vectors were measured by two methods: A, which was automatic par-
ticle tracking with TrackMate plugin (3.8.0) of FIJI^31 (ImageJ 1.52p, java
1.8.0), and B, which was optical flow analysis (using a custom MATLAB
code). Only frames where optical flow analysis was confirming auto-
matic particle tracking (deviation of <30°) were subjected to further
analysis. To estimate vectors of forwards cell movement, cell contours
were segmented with Ilastik^32 , and cell displacement was measured by
tracking the centroids. Angular distributions of actin flow vectors and
angular distributions of cell forwards movement vectors were then
analysed and plotted with respect to the orientation of nanoridges
using a custom MATLAB code.
Curvature analysis. For Extended Data Fig. 8, we set up a home-
made script that performs binarization of fluorescent images of
Lifeact-GFP-expressing cells. The local curvature was calculated from
a spline fit to the cell outline, and the cortical actin flow was quantified
with optical flow analysis (MATLAB, MathWorks).
Statistical analysis
All statistical analyses were performed with GraphPad Prism (Graph-
Pad Software). The normality test was performed, and the statistical
strategy used accordingly (for example, non-parametric Mann–Whit-
ney U-test and one-way ANOVA with Kruskal–Wallis test with post hoc
Dunn’s test) as indicated in Supplementary Table 1. For the box and
whiskers graphs in Fig. 4d, g and Extended Data Figs. 2f, 4a, 4b, 5g, 6f, the
box extends from the 25th to the 75th percentiles, with the middle line
showing the median, and the whiskers indicating the minimum to maxi-
mum values. See Supplementary Table 1 for additional information.
Reporting summary
Further information on research design is available in the Nature
Research Reporting Summary linked to this paper.
Data availability
Data that support the findings of this study are available within the
Article and its Supplementary Information. Source data for Figs. 1, 2,
4 and Extended Data Figs. 1–8 are provided with the paper. Original
videos will be made available on reasonable request due to the large
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Acknowledgements We thank A. Leithner and J. Renkawitz for discussion and critical reading
of the manuscript; J. Schwarz and M. Mehling for establishing the microfluidic setups; the
Bioimaging Facility of IST Austria for excellent support, as well as the Life Science Facility and
the Miba Machine Shop of IST Austria; and F. N. Arslan, L. E. Burnett and L. Li for their work
during their rotation in the IST PhD programme. This work was supported by the European
Research Council (ERC StG 281556 and CoG 724373) to M.S. and grants from the Austrian
Science Fund (FWF P29911) and the WWTF to M.S. M.H. was supported by the European
Regional Development Fund Project (CZ.02.1.01/0.0/0.0/15_003/0000476). F.G. received
funding from the European Union’s Horizon 2020 research and innovation programme under
the Marie Skłodowska-Curie grant agreement no. 747687.
Author contributions A.R. and M.S. conceived the experiments and wrote the manuscript, with
critical feedback from all authors. A.R. designed, performed and analysed the experiments,
with the help of I.d.V., J.S., M.H., R.H. and S.T. A.R. and J.M. designed the microfluidic devices.
J.M. performed the photolithography. F.G. designed and performed the nanoridge
experiments. J.A. fabricated the nanoridge substrates. R.H. wrote the image analysis scripts.
A.C.-J., R.V., J.M., R.H., M.S. and A.R. discussed the physical model. A.C.-J. and R.V. wrote the
physical model.Competing interests The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41586-020-
2283-z.
Correspondence and requests for materials should be addressed to A.R. or M.S.
Peer review information Nature thanks Kenneth Yamada and the other, anonymous,
reviewer(s) for their contribution to the peer review of this work.
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