Does self-organized criticality drive leading edge protrusion?

Abstract

Arp2/3 complex nucleates dendritic actin networks and plays a pivotal role in the formation of lamellipodia at the leading edge of motile cells. Mouse fibroblasts lacking functional Arp2/3 complex have the characteristic smooth, veil-like lamellipodial leading edge of wild-type cells replaced by a massive, bifurcating filopodia-like protrusions (FLPs) with fractal geometry. The nanometer-scale actin-network organization of these FLPs can be linked to the fractal geometry of the cell boundary by a self-organized criticality through the bifurcation behavior of cross-linked actin bundles. Despite the pivotal role of the Arp2/3 complex in cell migration, the cells lacking functional Arp2/3 complex migrate at rates similar to wild-type cells. However, these cells display defects in the persistence of a directional movement. We suggest that Arp2/3 complex suppresses the formation of FLPs by locally fine-tuning actin networks and favoring dendritic geometry over bifurcating bundles, giving cells a distinct evolutionary edge by providing the means for a directed movement.

Keywords: Agent-based modeling; Arp2/3 complex; Filopodia-like protrusions; Fractal geometry; Lamellipodia; Self-organized criticality.

Fig. 1

Morphology of isogenic fibroblast cells. Still images from phase-contrast microscopy movies of spreading ARPC3^−/− and wild-type fibroblasts were converted to single-pixel wide boundary images for fractal analysis. Sample outlines of a ARPC3^−/− fibroblasts and b wild-type fibroblast cell boundaries. Bar is 30 μm

Fig. 2

Fractal analysis of ARPC3^−/− fibroblasts. The log-log plot of the boundary pixel count versus area size in light micrographs of ARPC3^−/− cells is a straight line, indicating the fractal nature of the cell boundary. The fractal dimension is equal to the negative slope of the fitted line, d = 1.32

Fig. 3

Fractal Morphology: Electron microscopy shows that the fractal behavior and bifurcation of FLPs of ARPC3^−/− fibroblasts extend to smaller nanoscales. The bars are 5 μm

Fig. 4

Nanoscale actin-morphology. a Cryotomographic reconstructions show dendritic networks at the edges of spreading wild-type fibroblasts. b Actin filaments in spreading ARPC3^−/− fibroblasts are organized as tight parallel bundles without branches. Traced actin filaments are shown in red, Arp2/3 branch junctions in orange and cell membranes in blue. Bar is 100 nm

Fig. 5

Agent-based modeling of the growth of actin filament bundles. The model encompassed the semiflexible nature of actin filaments, their tendency to cross-link in the presence of crosslinkers, and the fact that filaments cannot occupy the same space at the same time. Parallel actin filaments originated at the top of the field of view and grew towards the bottom. a Actin filaments in the presence of crosslinkers. The semiflexible nature of the filaments in conjunction with their tendency to form crosslinks leads to a bifurcation of bundles as an emergent property. b Actin filaments in the presence of crosslinkers and an agent that induces neighboring filaments to deviate from a parallel arrangement. This agent mimics the effect of Arp2/3 complex but does not create physical branches. The network is frayed rather than bifurcating into distinct bundles. c Same as b but with 10% of the concentration of the deviating agent in b. The concentration of the agent mimicking Arp2/3 complex fine-tunes the network architecture

Fig. 6

Actin-fascin assemblies. Slices through three-dimensional cryo-tomogram of reconstituted bundles of actin filaments cross-linked by fascin. Areas of paracrystalline order show evidence for bifurcation. Arrowheads in b mark some bifurcation points where actin bundles split into smaller sub-bundles. Slices are 3.8 nm thick. Bars are 100 nm