Emergent Collective Chemotaxis without Single-Cell Gradient Sensing

Many eukaryotic cells chemotax, sensing and following chemical gradients. However, experiments show that even under conditions when single cells cannot chemotax, small clusters may still follow a gradient. This behavior is observed in neural crest cells, in lymphocytes, and during border cell migration in Drosophila, but its origin remains puzzling. Here, we propose a new mechanism underlying this “collective guidance,” and study a model based on this mechanism both analytically and computationally. Our approach posits that contact inhibition of locomotion, where cells polarize away from cell-cell contact, is regulated by the chemoattractant. Individual cells must measure the mean attractant value, but need not measure its gradient, to give rise to directional motility for a cell cluster. We present analytic formulas for how the cluster velocity and chemotactic index depend on the number and organization of cells in the cluster. The presence of strong orientation effects provides a simple test for our theory of collective guidance.

Figure 1

Signal-dependent contact inhibition of locomotion creates directed motion. (a) Schematic picture of the model and origin of directed motion. Cell polarities are biased away from the cluster toward the direction ${\mathbf{q}}^i=\sum _{j\sim i}{\widehat{\mathbf{r}}}^{ij}$ by contact inhibition of locomotion (CIL); the strength of this bias is proportional to the local chemoattractant value $S(\mathbf{r})$, leading to cells being more polarized at higher $S$. See the text for details. (b) One hundred trajectories of a single cell and (c) a cluster of seven cells. Trajectories are six persistence times in length (120 min). Scale bar is one cell diameter. The gradient strength $|\nabla S|=0.025$, with the gradient in the $x$ direction.

Figure 2

Adherent pairs of cells undergo highly anisotropic chemotaxis. The average chemotactic velocity of a cell pair $⟨V_x{⟩}_c$ depends strongly on the angle $\theta$ between the cell-cell axis and the chemotactic gradient. Cell pairs also drift perpendicular to the gradient; $⟨V_y{⟩}_c\ne 0$. $V_0\equiv \overline{\beta }\tau |\nabla S|$ is the velocity scale; $|\nabla S|=0.025$. Simulations are of Eqs. (1) and (2). We compute $⟨V_{\mu }{⟩}_c$ by tracking the instantaneous angle and then averaging over all velocities within the appropriate angle bin. Error bars here and throughout are 1 standard deviation of the mean, calculated from a bootstrap. Over $n=13000$ trajectories of $6\tau$ (120 min) are simulated.

Figure 3

Larger cell clusters chemotax more effectively, but their velocity saturates (a) As the number of cells $N$ in a cluster increases, the mean velocity $⟨V_x⟩$ increases with $N$ but then saturates; the mean velocity can be collapsed onto a single curve by rescaling by $V_0\equiv \overline{\beta }\tau |\nabla S|$. (b) The chemotactic index CI also saturates to its maximum value. Black squares and lines are the orientationally averaged drift velocity computed for rigid clusters by Eqs. (3) and (6). Colored symbols are full model simulations with strong adhesion. Cell cluster shape may influence $⟨V_x⟩$ (Supplemental Material [22], Fig. S4); our calculations are for the shapes in Table S1 [22]. Error bars here are symbol size or smaller; $n\ge 2000$ trajectories of $6\tau$ are used for each point.

Figure 4

Nonrigid clusters may also chemotax via collective guidance. (a) As the number of cells $N$ in a cluster increases, the mean velocity $⟨V_x⟩$ increases with $N$ but then saturates. (b) The chemotactic index approaches unity, but more slowly than in a rigid cluster. Rigid cluster theory assumes the same cluster geometries as in Fig. 3. Averages in (a) and (b) are over $n\ge 20$ trajectories (ranging from $n=20$ for $N=217$ to $n=4000$ for $N=1,2$), over the time $12.5\tau$ to $50\tau$. (c) Breakdown of a cluster as it moves up the chemoattractant gradient. $X$ marks the initial cluster center of mass, $O$ the current center. $|\nabla S|=0.1$, $\overline{\beta }=1$ in this simulation.