Positional information and information flows in dynamic tissues

During development, embryos store, transmit, and transform information to generate spatial patterns. Positional information (PI) quantifies how precisely cells form patterns at a given time, but cell motion has limited its application to static tissues. We introduce a framework for PI in dynamic tissues by decomposing mutual information between cells' positions and properties over time into information flows contributing to PI preservation, loss and generation. These reveal information-theoretic signatures of ubiquitous developmental processes, including instruction, sorting and mixing, directly from data. Applying this framework to whole-embryo cell trajectories in Drosophila, mouse and zebrafish gastrulation, we provide local and global information-theoretic quantification of cell mixing and derive bounds on PI preservation imposed by tissue dynamics. Analyzing tissue flows as dynamical systems, we further show that morphogenesis structures mixing, preferentially preserving specific patterns. Finally, we derive inequality conditions for tracing generated PI to candidate information sources and distinguishing among alternative pattern-formation mechanisms, from programmed extracellular cues to self-organizing intercellular interactions.