A traveling network model predicts emergent dynamics and search behavior from local remodeling in Physarum polycephalum

A variety of connected systems, ranging from the cytoskeleton to human organizations, dynamically rearrange themselves in order to move through physical or abstract space. However, our understanding of how systems-level behaviors arise from local restructuring actions remains limited, necessitating comparison of real-world data to models that predict network structure and dynamics. To understand these systems, we study an accessible example, the branching slime mold Physarum polycephalum, by imaging the organism as it travels and extracting key fundamental quantities from its continuously remodeling tubular network. By using these quantities as input parameters to a traveling network model, we find that with no further fitting, the model quantitatively matches key emergent properties from P. polycephalum dynamics including path length, relocation time, and search efficiency at different spatial resolutions. These findings demonstrate how a traveling network model can capture P. polycephalum behaviors, highlighting the potential to use traveling networks more broadly for understanding and predicting connected dynamic systems by linking local measurements to emergent, system-wide behaviors.