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

<jats:p> 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 <jats:italic>Physarum polycephalum</jats:italic> , 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 <jats:italic>P. polycephalum</jats:italic> dynamics including path length, relocation time, and search efficiency at different spatial resolutions. These findings demonstrate how a traveling network model can capture <jats:italic>P. polycephalum</jats:italic> 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. </jats:p>