A strain-cue hypothesis for biological network formation.

The direction of migration of a cell invading a host population is assumed to be controlled by the magnitude of the strains in the host medium (cells plus extracellular matrix) that arise as the host medium deforms to accommodate the invader. The single assumption that invaders are cued by strains external to themselves is sufficient to generate network structures. The strain induced by a line of invaders is greatest at the extremity of the line and thus the strain field breaks symmetry, stabilizing branch formation. The strain cue also triggers sprouting from existing branches, with no further model assumption. Network characteristics depend primarily on the ratio of the rate of advance of the invaders to the rate of relaxation of the host cells after their initial deformation. Intra-cell mechanisms that govern these two rates control network morphology. The strain field that cues an individual invader is a collective response of the combined cell populations, involving the nearest 100 cells, to order of magnitude, to any invader. The mechanism does not rely on the pre-existence of the entire host medium prior to invasion; the host cells need only maintain a layer several cells thick around each invader. Consistent with recent experiments, networks result only from a strain cue that is based on strain magnitudes. Spatial strain gradients do not break symmetry and therefore cannot stabilize branch formation. The theory recreates most of the geometrical features of the nervous network in the mouse gut when the most influential adjustable parameter takes a value consistent with one inferred from human and mouse amelogenesis. Because of similarity in the guiding local strain fields, strain cues could also be a participating factor in the formation of vascular networks.