Epithelial geometry reveals how positive tension feedback drives active cell intercalations during tissue convergence extension: Theory

During morphogenesis, tissues reshape to create the forms required by the adult body plan. One basic motif of morphogenesis is convergent extension, where a tissue sheet narrows and elongates as cells exchange neighbors (intercalations). How do cells coordinate the active stress generation required for coherent tissue flow?

Based on analysis of a model organism, the gastrulating Drosophila embryo, we present a minimal model of intercalations, both active – driven locally by motor molecules on cell-cell junctions – and passive – driven by forces applied at the tissue boundary. We propose a positive tension feedback loop, primed by initial tension anisotropy, that leads to spatially coordinated junction collapses and thus cell intercalations. Force balance links tensions and epithelial geometry by fixing the angles at which junctions meet at vertices, but leaves room for isogonal, or angle preserving, modes. We specify the dynamics of these isogonal modes by minimizing an elastic energy for the cell shapes.

Solving this model for a single quartet of cells reproduces the experimentally observed dynamics of tension and shape, both for active and passive intercalations. Next, a mean field calculation explains the dynamics of the entire distribution of the tensions at each vertex, pooled across the tissue. Finally, we present an agent-based simulation of a complete tissue, in which we can investigate the coupling of active and passive regions. Remarkably, in our model, convergent extension eventually halts, in a way that depends on the geometry and topology of the initial condition. Our results suggest that morphogenetic behavior can self-organize and encode target shape geometrically, and and lay the foundation for a continuum theory for active tissue remodeling.