Emergent Collective Chemotaxis without Single-Cell Gradient Sensing

Abstract

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.

FIG. 1. Signal-dependent contact inhibition of locomotion creates directed motion

a, Schematic picture of model and origin of directed motion. Cell polarities are biased away from the cluster toward the direction qⁱ = ∑_j~i r̂^ij by contact inhibition of locomotion (CIL); the strength of this bias is proportional to the local chemoattractant value S(r), leading to cells being more polarized at higher S. See text for details. b, One hundred trajectories of a single cell and c, cluster of seven cells. Trajectories are six persistence times in length (120 min). Scalebar is one cell diameter. Gradient strength |∇S| = 0.025, with the gradient in the x direction.

FIG. 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 θ between the cell-cell axis and the chemotactic gradient. Cell pairs also drift perpendicular to the gradient, 〈V_y〉_c ≠ 0. V₀ ≡ β̄τ|∇S| is the velocity scale; |∇S| = 0.025. Simulations are of Eqs. 1–2. We compute 〈V_μ〉_c by tracking the instantaneous angle, then averaging over all velocities within the appropriate angle bin. Error bars here and throughout are one standard deviation of the mean, calculated from a bootstrap. Over n = 13, 000 trajectories of 6τ (120 minutes) are simulated.

FIG. 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 V₀ ≡ β̄τ|∇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 Eq. 3 and Eq. 6. Colored symbols are full model simulations with strong adhesion. Cell cluster shape may influence 〈V_x〉 (Supplementary Information Fig. S4); our calculations are for the shapes in Table S1. Error bars here are symbol size or smaller; n ≥ 2000 trajectories of 6τ are used for each point.

FIG. 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, Chemotactic index approaches unity, but slower than in a rigid cluster. Rigid cluster theory assumes the same cluster geometries as in Fig. 3. Averages in a–b are over n ≥ 20 trajectories (ranging from n = 20 for N = 217 to n = 4000 for N = 1, 2), over the time 12.5τ to 50τ. c, Breakdown of a cluster as it moves up the chemoattractant gradient. X marks the initial cluster center of mass, O the current center. |∇S| = 0.1, β̄ = 1 in this simulation.