Confinement-Induced Transition between Wavelike Collective Cell Migration Modes

Vanni Petrolli, Magali Le Goff, Monika Tadrous, Kirsten Martens, Cédric Allier, Ondrej Mandula, Lionel Hervé, Silke Henkes, Rastko Sknepnek, Thomas Boudou, Giovanni Cappello, and Martial Balland

Phys. Rev. Lett. 122, 168101 – Published 24 April 2019

Abstract

The structural and functional organization of biological tissues relies on the intricate interplay between chemical and mechanical signaling. Whereas the role of constant and transient mechanical perturbations is generally accepted, several studies recently highlighted the existence of long-range mechanical excitations (i.e., waves) at the supracellular level. Here, we confine epithelial cell monolayers to quasi-one-dimensional geometries, to force the establishment of tissue-level waves of well-defined wavelength and period. Numerical simulations based on a self-propelled Voronoi model reproduce the observed waves and exhibit a phase transition between a global and a multinodal wave, controlled by the confinement size. We confirm experimentally the existence of such a phase transition, and show that wavelength and period are independent of the confinement length. Together, these results demonstrate the intrinsic origin of tissue oscillations, which could provide cells with a mechanism to accurately measure distances at the supracellular level.

Received 17 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.168101

Physics Subject Headings (PhySH)

Biological self-organization Cell locomotion Cell mechanics Cell migration Emergence of patterns Patterns in complex systems

Cell membrane

Interdisciplinary PhysicsPolymers & Soft MatterPhysics of Living Systems

Authors & Affiliations

Vanni Petrolli¹, Magali Le Goff¹, Monika Tadrous^1,*, Kirsten Martens¹, Cédric Allier², Ondrej Mandula², Lionel Hervé², Silke Henkes³, Rastko Sknepnek^4,5, Thomas Boudou¹, Giovanni Cappello^1,†, and Martial Balland^1,‡

¹Université Grenoble Alpes, Laboratoire Interdisciplinaire de Physique, CNRS, F-38000 Grenoble, France
²CEA, LETI, MINATEC, 17 rue des Martyrs, 38054 Grenoble cedex 9, France
³Department of Mathematics, University of Bristol, Bristol BS81TW, United Kingdom
⁴School of Science and Engineering, University of Dundee, Dundee DD1 4HN, United Kingdom
⁵School of Life Sciences, University of Dundee, Dundee DD1 5EH, United Kingdom

^*Present address: Mechanical Engineering Department, California State University, Fullerton, CA 92831, USA.
^†Giovanni.Cappello@univ-grenoble-alpes.fr
^‡Martial.Balland@univ-grenoble-alpes.fr

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Issue

Vol. 122, Iss. 16 — 26 April 2019

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Images

Figure 1
(a) Top: MDCK cells are seeded onto a polyacrylamide (PA) gel patterned with fibronectin stripes (width: $L_{Y} = 40 μ m$ , length: $L_{X} = 1500 μ m$ ). Middle: phase-contrast image of a confluent tissue. Bottom: velocity field measured by PIV. Velocities pointing in the positive (negative) $x$ -axis direction are shown in red (blue), in agreement with the arrows reported under the image. (b) Left: kymograph representing the average horizontal velocity $v_{∥} (x; t)$ in time. Right: an example of velocity profile along the dashed line. We removed low frequency drifts using a Gaussian high-pass filter. (c) To quantify the periodicity of oscillations, we calculate the spatiotemporal autocorrelation of the kymograph (left) and measure peak spacing along the spatial (top-right) and temporal (bottom-right) coordinates (insets: distribution of peak periodicity for $n = 59$ independent stripes). Images in panels (b), (left) and (c), (left) were smoothed for visualization purposes with a low-pass Gaussian filter ( $σ_{x} = 15 μ m$ , $σ_{t} = 30 \min$ ).
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Figure 2
Self-propelled Voronoi model for collective oscillations in confluent tissues.(a) Top: Example of tissue configuration obtained from the integration of the SPV model. Voronoi tessellation of the plane and centroid positions. Bottom: Velocity field of the centroids of the tesselation. Velocities pointing to the positive direction on the $x$ axis are represented in red and to the negative direction in blue. (b) Left: Kymograph representing the average horizontal velocity [ $v_{∥} (x; t)$ ] over time and right: its profile along the dotted line. (c) Phase diagram of oscillation patterns in the SPV model in the ( $τ_{a l} - L_{X}$ ) plane. Two types of oscillations are observed depending upon the system size $L_{X} (τ_{a l})$ : Top left: For large systems where $L_{X} > L_{X}^{c} (τ_{a l})$ the autocorrelation of the kymograph shows multinodal oscillations whereas for small systems (bottom, left) where $L_{X} < L_{X}^{c} (τ_{a l})$ the autocorrelation exhibits global oscillations. Right: Simulation data points indicating whether the system exhibits global (blue disks), multinodal (red diamond), or no oscillations (gray squares symbols) for large values of the feedback timescale ( $τ_{a l} > τ_{a l}^{c} \approx 17$ model time units). The solid line delimiting the global and multinodal oscillation phases is a power-law fit of the transition data points [ $L_{X}^{c} (τ_{a l}) = a τ_{a l}^{b} + c$ with $a ≃ 32$ , $b ≃ 0.62$ , $c ≃ 13$ ].
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Figure 3
Dependence of oscillatory behavior on the stripe length. (a) The velocity field superimposed on phase contrast images for short stripes of length 200 and $300 μ m$ displays global oscillations, generating a characteristic two-dimensional autocorrelation (right). Longer lines (500 and $1000 μ m$ ) display multinodal oscillations (b), which give rise to a different pattern in the autocorrelation image (right). Velocities pointing in the positive $x$ -axis direction are represented in blue, those pointing in the negative $x$ -axis direction are represented in red, in agreement with the arrows reported in the schemes under each image. For each length, we display the frequency of each phenotype (c) and the characteristic time and space periodicity (d) calculated. Bars represent the standard error of the mean.
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