Cell Migration Driven by Cooperative Substrate Deformation Patterns

Most eukaryotic cells sense and respond to the mechanical properties of their surroundings. This can strongly influence their collective behavior in embryonic development, tissue function, and wound healing. We use a deformable substrate to measure collective behavior in cell motion due to substrate mediated cell-cell interactions. We quantify spatial and temporal correlations in migration velocity and substrate deformation, and show that cooperative cell-driven patterns of substrate deformation mediate long-distance mechanical coupling between cells and control collective cell migration.

Figure 1

Cell density is low and cell area is large at early times (a), and cells compact over time (b). Initially, cell area increases slightly, as island expansion just exceeds changing cell density due to proliferation. After 900 minutes, average cell area decreases and cell density steadily increases (c). $\mathrm{\text{Scalebar}}=100\mu \mathrm{m}$.

Figure 2

Substrate-displacement fields at low cell densities (a) and high cell densities (b) contain long-distance, complex patterns. $\mathrm{\text{Scalebar}}=248\mu \mathrm{m}$. The spatial autocorrelation function of displacement vectors, $C_{\mathrm{dd}}(r)$, decays exponentially (c), with a characteristic deformation correlation length, ${\xi }_d$, that grows over time as cell density increases (d).

Figure 3

Velocity fluctuation fields of cell migration show large-scale swirl patterns resembling the underlying substrate (a), low cell density; (b), high cell density; $\mathrm{\text{Scalebar}}=248\mu \mathrm{m}$. The spatial autocorrelation function of velocity fluctuation vectors, $C_{\mathrm{vv}}(r)$, decays over short distances and shows a clear negative minimum at larger distances (c). The position of this minimum defines a swirl correlation length, ${\xi }_s$, which grows over time as cell density increases (d).

Figure 4

${\xi }_d$ increases with the increasing ${\xi }_s$ (a). For cells on PA substrates, ${\xi }_s$ increases with increasing density (b); the opposite trend is seen on glass substrates (c). The temporal cross-correlation function of velocity fluctuations and substrate displacements, $C_{\mathbf{d}\mathbf{v}}(\tau )$, shows that velocity fluctuations lag substrate deformations in time [(d), inset]. The rate of these reorientations decreases throughout the experiment as cell density increases. In the inset, we shift the cross-correlation functions, $C_{\mathbf{d}\mathbf{v}}(\tau {)}^{*}=C_{\mathbf{d}\mathbf{v}}(\tau )-C_{\mathbf{d}\mathbf{v}}(0)$, preserving the trends in $C_{\mathbf{d}\mathbf{v}}(\tau )$, shifting all data to fit in one plot.