Spontaneous contractility-mediated cortical flow generates cell migration in three-dimensional environments

Abstract

We present a model of cell motility generated by actomyosin contraction of the cell cortex. We identify, analytically, dynamical instabilities of the cortex and show that they yield steady-state cortical flows, which, in turn, can induce cell migration in three-dimensional environments. This mechanism relies on the regulation of contractility by myosin, whose transport is explicitly taken into account in the model. Theoretical predictions are compared to experimental data of tumor cells migrating in three-dimensional matrigel and suggest that this mechanism could be a general mode of cell migration in three-dimensional environments.

Figure 1

Cell migration in three-dimensional environments. (a) Confocal section of an MDA-MB-231 cell migrating in three-dimensional matrigel. The cell expresses mCherry-Lifeact, a fluorescent probe that labels F-actin (12). (White arrow) Direction of movement. (Arrowhead) Accumulation of F-actin at the rear of the cell. (Curved blue arrows) Direction of observed cortical flow analyzed in Fig. 3. Scale bar, 10 μm. (b) Cartoon of the model in the first unstable mode Y_1,0, with the actin cortex around the edge (purple). (Arrows) Velocity of the gel.

Figure 2

Dispersion relation s(l) in log scale. (Blue lines) One dimension (where k = $\sqrt{l\left(l+1\right)}/R$). (Red crosses) Three dimensions. Pairs of curves in ascending order are for Pe = 500, 2500, and 5000 (where Pe is defined in Eq. 15). (Inset) Most unstable integer mode number l_max against Pe. Order-of-magnitude estimates of biologically relevant parameters values taken from the indicated articles are as follows: k^on = 1 μm s⁻¹ (23); k^off = 0.1 s⁻¹ (23); D_c = 10 μm² s⁻¹ (21,22); D_μ = 1 μm² s⁻¹, k_d = 0.1 s⁻¹ (17,21,22); α = 1000 kg μm⁻¹ s⁻² (24); β = 1000 kg μm s⁻², ξ = 0.1 kg μm⁻³ s⁻¹ (17); and R = 10 μm and μ₀ = 10⁴μm⁻² (25,26).

Figure 3

(a) Experimental data of MDA-MB-231 tumor cells seeded in three-dimensional matrigel (average of 19 cells) (12). Intensity of mCherry-Lifeact labeled cortical actin and labeled myosin are compared to the simulated steady state for ρ and μ with Pe = 2500. Maximum and background intensities are fitted. (b) (Red triangles) Experimental velocity of actin (12) (average of nine cells). (Green line) Simulated steady state for v. (c) Typical patterns for $\tilde{\mu }$ obtained analytically (Eq. 17 with $\tilde{\nu }=1$): (blue) Pe = 2; (red) Pe = 5. Here θ ∈ [−π, π] runs over a given meridian.