Patterning and Information Flows in Dynamic Tissues

In early embryonic development, thousands of cells coordinate their motion and biochemical properties to form precisely shaped and patterned tissues. Classic pattern-formation theories—reaction–diffusion models and positional information—have illuminated how patterns arise in static tissues. However, simultaneous data on cell motion and properties (e.g., gene expression) are now becoming increasingly available in dynamic tissues. I will present our recent mathematical frameworks for rationalizing pattern formation in dynamic tissues, with a focus on generalizing positional information to these settings. Our framework decomposes the mutual information between cells' positions and properties over time into interpretable components that quantify the preservation and generation of positional information. It enables: (i) quantifying information flows from data—e.g., whether initial cell properties influence final positions and vice versa—and tracing these flows back to underlying mechanisms; (ii) defining an information-theoretic measure of cell mixing and bounds for pattern preservation; and (iii) elucidating how tissue flows mediate pattern transmission. I will show applications to canonical patterning processes and experimental data. Broadly, while inspired by living embryos, our framework can be adapted to general flowing active matter.