Physics of active jamming during collective cellular motion in a monolayer Simon Garciaa,b, Edouard Hannezoa,c, Jens Elgetid, Jean-François Joannya, Pascal Silberzana,b,1, and Nir S. Gove,1 aLaboratoire PhysicoChimie Curie, Institut Curie, Paris Sciences et Lettres Research University - Sorbonne Universités, Université Pierre et Marie Curie - Centre National de la recherche Scientifique, 75005 Paris, France; bEquipe “Biology-inspired physics at mesoscales” labellisée Ligue Contre le Cancer, Institut Curie, 75248 Paris, France; cCavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom; dTheoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany; and eDepartment of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved November 3, 2015 (received for review June 4, 2015) Although collective cell motion plays an important role, for cell shape (15) have also been considered. Any of these parame- example during wound healing, embryogenesis, or cancer pro- ters could a priori contribute to the jamming transition, and dis- gression, the fundamental rules governing this motion are still not criminating between each contribution is not possible at present. well understood, in particular at high cell density. We study here In the present study, we investigate the motion of a proliferating, the motion of human bronchial epithelial cells within a monolayer, motile, population of immortalized human bronchial epithelial cells over long times. We observe that, as the monolayer ages, the cells (HBEC) (29). Even though cellular density increases during the time slow down monotonously, while the velocity correlation length course of our experiments, we find that it is not the main control first increases as the cells slow down but eventually decreases at parameter to describe the collective motion of these cells. Rather, we the slowest motions. By comparing experiments, analytic model, observe that the decrease in cell motility is due to the maturation of and detailed particle-based simulations, we shed light on this cell−cell and cell−substrate junctions. We find that the HBEC cellular biological amorphous solidification process, demonstrating that monolayer changes from a fluid-like regime of fast motion at early the observed dynamics can be explained as a consequence of the times to an amorphous solid-like (“glassy”)regimeatlatetimes,and − − combined maturation and strengthening of cell cell and cell sub- this transition is mainly driven by changes in the cell−cell adhesion and strate adhesions. Surprisingly, the increase of cell surface density friction. This transition can be formalized in a simple analytical model due to proliferation is only secondary in this process. This analysis andinnumericalsimulationsthatboth describe well our experimental is confirmed with two other cell types. The very general relations observations. We furthermore demonstrate that the same framework between the mean cell velocity and velocity correlation lengths, describes cells that do not develop cell−cell adhesions (NIH 3T3 fi- which apply for aggregates of self-propelled particles, as well as broblasts), as well as strongly adherent epithelial cells [Madin Darby motile cells, can possibly be used to discriminate between various Canine Kidney (MDCK)]. We thereby identify a cellular mechanism parameter changes in vivo, from noninvasive microscopy data. where the path to glassiness is dominated by increasing the effective interaction potentials, rather than density (18, 22). collective cell migration | jamming | glass transition | − dynamic inhomogeneity | cell cell adhesion Results Cellular Slowing Down and Evolution of the Velocity Correlations. ollective motion of cells is crucial in many biological phe- We have experimentally studied the dynamics of immortalized Cnomena, including embryonic development (1), wound heal- HBEC cells in a monolayer and its evolution over time. For these ing (2, 3), tissue repair (1, 4), and cancer (1, 4). Therefore, understanding the physics underlying how individually migrating Significance cells combine their motion to collectively migrate is presently a matter of intense study. In this context, several studies have re- cently shown, by numerical simulations, that local alignment rules Collective cell motion is very important in many biological pro- can result in the emergence of strongly correlated cellular motions cesses such as wound healing, embryogenesis, or cancer pro- in a confluent monolayer (5–9). gression. Nevertheless, it is not clear which parameters control As time passes, these cell movements in the monolayer slow the transition from freely moving single cells to collective jam- down. This classic observation is usually associated with the so- med motion. In this article, we uncover complex dynamics as a called “density-mediated contact inhibition of locomotion” (10, cell monolayer ages, where cell motion is shown to gradually 11). To go further in the analysis of this phenomenon, several slow down with time, while the distance over which cell dis- observations (6, 12, 13) and simulations (7, 14, 15) give an in- placements are correlated first increases drastically and then de- teresting new angle by emphasizing the analogy between a cell creases. This change of behavior is not controlled by cell density − − monolayer and a bidimensional “jammed” colloidal system, where but rather by a maturation of the cell cell and cell substrate the individual motions of the particles are confined in “cages” of contacts. By comparing experiments, analytic model, and detailed the size of the particles, and where the whole system behaves as a particle-based simulations, we shed light on this biological solid (16–19). In particular, the increase in the characteristic length amorphous solidification process. scales describing the velocity field as well as the presence of “giant” Author contributions: P.S. and N.S.G. designed research; S.G., E.H., J.E., P.S., and N.S.G. density fluctuations (20, 21) appear to validate this analogy. As a performed research; J.-F.J., P.S., and N.S.G. contributed new reagents/analytic tools; S.G., consequence, several theoretical descriptions have been proposed E.H., J.E., P.S., and N.S.G. analyzed data; and S.G., E.H., J.E., P.S., and N.S.G. wrote for these cell assemblies within the conceptual framework used to the paper. describe jamming in active systems (6, 12, 13, 22–24). The authors declare no conflict of interest. Cellular density (the equivalent of the packing fraction in col- This article is a PNAS Direct Submission. loidal systems) is often assumed to be the principal control pa- Freely available online through the PNAS open access option. – rameter in these systems (6, 12, 25 27). However, because cellular 1To whom correspondence may be addressed. Email: [email protected] or pascal. densities vary between cell types and growing conditions, other [email protected]. − parameters such as (i)cell cell adhesion energy, (ii)magnitudeof This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. cellular forces and persistence time for these forces (28), or (iii) 1073/pnas.1510973112/-/DCSupplemental. 15314–15319 | PNAS | December 15, 2015 | vol. 112 | no. 50 www.pnas.org/cgi/doi/10.1073/pnas.1510973112 Downloaded by guest on September 25, 2021 weakly cohesive cells, confluence could not be accurately defined AB because, at low density, the cells were very dynamic, the population 160 120 being best described as a cellular gas with low interactions between 140 particles. This state was followed by a situation where the cells 100 remained very motile but with no more voids between them because 120 of the larger cell density (“fluid phase”), at which point the velocity 100 80 gradually decreased. This system therefore exhibits fast keratinocyte- 80 60 like motion at early times and epithelium-like motion at late 60 Correlation length (μm) Correlation length (μm) times. Of note is that, by analyzing the density fluctuations in the 40 40 layer, we found the characteristic signature of nonequilibrium -5 0 5 10 15 20 25 1.4 1.6 1.8 2 Shifted time (h) Density (cell·cm-2) (×105) dynamics, namely giant number fluctuations (30) (Fig. S1). By mapping the displacement field within the monolayer over time Time (h) C D 45 (3) (Movie S1 and Fig. 1A), we first measured the overall cell speed, 180 180 or root-mean-square (rms) velocity vrms, in the layer and observed 140 140 that it decreased monotonously (Fig. 1B) with time until it became -1 too small to measure. We then computed the velocity−velocity 100 100 20 spatial correlation function CvvðrÞ for each time, from which we ξ ð Þ extracted a correlation length vv t (Fig. 1C; see details in Mate- 60 60 rials and Methods). This correlation length was small (of order two Correlation length (μm) Correlation length (μm) to three cell sizes) at the beginning of the experiment (Fig. 1D), 40 40 10 100 10 100 and then increased to a value corresponding to approximately rms velocity (μm/h) rms velocity (μm/h) seven cell sizes over the course of several hours. Eventually, at ξ ξ ð Þ later times, vv decreased again to the single cell size. Fig. 1C, Fig. 2. Velocity controls the correlation. (A) Comparison of the vv t evo- Inset, demonstrates that a single exponential decay allowed us to lution curves for different seeding densities. The times have been shifted to ξ ξ superimpose the early evolutions. (B) No significant correlation between vv extract vv throughout the whole process of cellular slowing down. ρ Inspired by previous work (6, 12, 26), we first tried to correlate and cell density cell was found for given time points. Here, eight FOVs were picked among the wells seeded with 640,000 cells at t = 21 h. Pearson’s this progressive slowing down of the cells with their surface density = ξ ð Þ ρ ρ correlation coefficient is r 0.34.