Propagating strain pulses built on strain-cued strain transformations and strain-cued motility transformations can segment an initially homogeneous cell population

Abstract

Transformations in cell shape and motility triggered by strain cues impinging on individual cells within a large population are shown to offer a distinct alternative to chemical cues as a pathway to periodic patterns or sequential segmentation. Interacting transformations can raise up solitary wave-like strain pulses that propagate across a population, providing the cells all the timing and positional information necessary for templating segmentation. Candidate strain-cued transformations include a cell transforming into a secretory state, wherein it changes the organ's geometry; a change in a cell's shape; the onset of proliferation; and surges in cell motility, being either a change in the rate at which cells minimize density gradients or the onset of positive velocity feedback. If the wave response excited by transformations is assumed to be nonlinear, biologically interesting solution spaces emerge. When multiple transformations are pinned to different strain levels by switching criteria in a nonlinear system, their transformation fronts propagate at different velocities. When positive velocity feedback acts between a pair of such fronts, a cycling system can arise, timed by jumps in the location of one of the pair. The period of the cyclic pattern is approximately λ = 1.43Lexcl/εc, where Lexcl is a length scale related to velocity feedback and εc is the critical strain for the primary (driving) transformation. Remarkably but consistently with one small set of data, λ is independent of the velocity of the pulse system and the type of transformation that drives the system. Reasonable values of εc and the assumption that Lexcl must be at least the cell width if velocity feedback is effected by discrete cells yield an approximate lower bound for λ, free of adjustable parameters. The lower bound approximately predicts the lengths of rugae that form in palatal development in the mouse, somites that form during body axis extension in a bird embryo, and cell cohorts that form among pre-ameloblasts in the mouse or rat incisor.