Spontaneous shear flow in confined cellular nematics

Abstract

In embryonic development or tumor evolution, cells often migrate collectively within confining tracks defined by their microenvironment 1,2. In some of these situations, the displacements within a cell strand are antiparallel 3, giving rise to shear flows. However, the mechanisms underlying these spontaneous flows remain poorly understood. Here, we show that an ensemble of spindle-shaped cells plated in a well-defined stripe spontaneously develop a shear flow whose characteristics depend on the width of the stripe. On wide stripes, the cells self-organize in a nematic phase with a director at a well-defined angle with the stripe’s direction, and develop a shear flow close to the stripe’s edges. However, on stripes narrower than a critical width, the cells perfectly align with the stripe’s direction and the net flow vanishes. A hydrodynamic active gel theory provides an understanding of these observations and identifies the transition between the non-flowing phase oriented along the stripe and the tilted phase exhibiting shear flow as a Fréedericksz transition driven by the activity of the cells. This physical theory is grounded in the active nature of the cells and based on symmetries and conservation laws, providing a generic mechanism to interpret in vivo antiparallel cell displacements.

Chiral stresses in nematic cell monolayers

“…only one of the two branches of the pitchfork bifurcation is connected to the trivial solution, which may then be the only one observed experimentally. This latter result could potentially explain the experimental observations by Duclos et al [8], who found that NIH 3T3 cells are more likely to tilt clockwise then counterclockwise once the spontaneous flow transition sets up.…”

“…[15]). * Corresponding author: giomi@lorentz.leidenuniv.nl Another remarkable demonstration of active hydrodynamic behavior in eukaryotic cell layers has been recently reported by Duclos et al, upon confining spindle-like RPE1 and C2C12 cells within adhesive stripe-shaped domains [8]. Depending on the width of the stripe the system was found either in a stationary state, with the cells parallel to the longitudinal direction of the confining region, or in a collectively flowing state characterized by a spontaneous tilt of the cells toward the center of the stripe.…”

“…Furthermore, since the cells used in Ref. [8] were only weakly chiral the effects of chirality were not as pronounced. Performing similar experiments with cells with stronger chirality and for different boundary conditions would enable further tests of the presented theory.…”

“…As in the adhesive stripes used in Ref. [8], the channel walls do not comprise a real physical barrier, but represent instead the interface between two regions of the substrate with different coating. As the walls now do not exert any force on the cells σ xy (0) = σ xy (L) = 0.…”

“…Refs. [2][3][4][5][6][7][8]). Among these, monolayers of clotured spindle-like cells, such as NIH 3T3 mouse embryo fibroblasts [4], murine neural progenitor cells (NPCs) [6], human bronchial epithelial cells (HBEC) [7], Retinal Pigment Epithelial (RPE1) cells [8] and C2C12 mouse myoblasts [8] represent an especially promising class of model systems, because of their connection with active nematic liquid crystals (see e.g.…”