Positional information in dynamic tissues

In developing embryos, positional information (PI) quantifies how precisely cells i) form patterns and ii) can infer their positions from external cues. PI has illuminated pattern formation in static systems where cells relative positions remain fixed. We present a general framework for PI in dynamic tissues, decomposing mutual information between cells' positions and properties over time into interpretable components reflecting PI preservation and generation. The framework identifies the shared information-theoretic signatures of large classes of processes---including mixing, instructing, and sorting---from data. When only cell motion data is available, it predicts how random cell motility amid morphogenetic movements constrains pattern preservation, enabling the first information-theoretic quantification of mixing in embryos. Instead, when motion and property data are both available, it enables causal hypothesis testing, tracing the origins of generated PI to distinct mechanisms. We show applications to Drosophila, mouse, and zebrafish gastrulation data.