Gaussian Curvature Directs Stress Fiber Orientation and Cell Migration

Abstract

We show that substrates with nonzero Gaussian curvature influence the organization of stress fibers and direct the migration of cells. To study the role of Gaussian curvature, we developed a sphere-with-skirt surface in which a positive Gaussian curvature spherical cap is seamlessly surrounded by a negative Gaussian curvature draping skirt, both with principal radii similar to cell-length scales. We find significant reconfiguration of two subpopulations of stress fibers when fibroblasts are exposed to these curvatures. Apical stress fibers in cells on skirts align in the radial direction and avoid bending by forming chords across the concave gap, whereas basal stress fibers bend along the convex direction. Cell migration is also strongly influenced by the Gaussian curvature. Real-time imaging shows that cells migrating on skirts repolarize to establish a leading edge in the azimuthal direction. Thereafter, they migrate in that direction. This behavior is notably different from migration on planar surfaces, in which cells typically migrate in the same direction as the apical stress fiber orientation. Thus, this platform reveals that nonzero Gaussian curvature not only affects the positioning of cells and alignment of stress fiber subpopulations but also directs migration in a manner fundamentally distinct from that of migration on planar surfaces.

Cell‐Perceived Substrate Curvature Dynamically Coordinates the Direction, Speed, and Persistence of Stromal Cell Migration

“…Similar detachment and upward stretching on concave surfaces have been shown for single smooth muscle cells (SMC) and for SMC sheets . In mouse embryonic fibroblasts (MEFs) it was shown that apical stress fibers avoid bending by lifting away from the surface and bridge over a concave area of a curved surface . This implies that the curvature that cells perceive is additionally influenced by the attachment morphology on concave substrates.…”

“…Furthermore, cell migration speed was found to be significantly higher on concave spherical surfaces than on convex spherical surfaces . On sphere‐with‐skirt surfaces (i.e., a convex spherical cap, surrounded by a concave draping skirt), mouse embryonic fibroblasts were shown to primarily remain in the concave area of the substrate and migrate around the geometrical structure in the azimuthal direction . Recently, these findings were further corroborated by Pieuchot et al by plating cells on a substrate of a continuous landscape of spherical convex and concave topographies, demonstrating that the interplay between cell contractility and nuclear mechanics is responsible for active cell migration toward the concave valleys …”

A Biophysical Model for Curvature-Guided Cell Migration

“…More recent findings showed that cell migration is also directed by purely mechanical cues, such as stiffness gradients (durotaxis) (15), topographic pattern gradients (topotaxis) (16) and substrate anisotropy (ratchetaxis) (17)(18)(19). Lastly, microscopic curved topographies have gained greater interest for their resemblance with smooth biological tissues (20)(21)(22)(23). A recurrent factor in these directed migration mechanisms is the predominant role of the nucleus (24,25).…”

Three-dimensional Monolayer Stress Microscopy

“…The reported orientation patterns are consistent with the apical stress fibers but not the basal ones bearing tension, in agreement with bending creating mechanical tension in the apical surface and compression in the basal surface. How cells are able to withstand compressive stresses is less clear, although the nucleus and cytoplasmic pressure mediated by membrane curvature have been postulated as candidates 50, 51 . The fact that bending may result in compressive or tensile stress and deformation in different compartments of the cell based on their apical/basal localization could have implications for mechanotransduction.…”