Morphogen Patterning in Dynamic Tissues.

Embryogenesis integrates morphogenesis-coordinated cell movements-with morphogen patterning and cell differentiation. While largely studied independently, morphogenesis and patterning often unfold simultaneously in early embryos. Yet, how cell movements affect morphogen transport and cells' exposure over time remains unclear, as most pattern formation models assume static tissues. Here, we develop a theoretical framework for morphogen patterning in dynamic tissues, recasting advection-reaction-diffusion equations in the cells' moving reference frames. This framework (i) elucidates how morphogenesis mediates morphogen transport and compartmentalization: cell-cell diffusive transport is enhanced at multicellular flow attractors, while repellers act as barriers, affecting cell fate induction and bifurcations. (ii) It formalizes cell-cell signaling ranges in dynamic tissues, deconfounding morphogenetic movements to identify which cells could communicate via morphogens. (iii) It provides two new nondimensional numbers to assess when and where morphogenesis affects morphogen transport. We demonstrate this framework by analyzing classical patterning models with common morphogenetic motifs as well as experimental tissue flows. Our work rationalizes dynamic tissue patterning in development, constraining candidate patterning mechanisms and parameters using accessible cell motion data.