Title: Coordination Without a Nervous System: A Mechanochemical Model of Physarum polycephalum

Abstract: The slime mold Physarum polycephalum is a single giant cell with no nervous system, yet it migrates toward food, builds efficient transport networks, and balances exploration against exploitation. How does such a cell encode, transmit, and integrate information about its environment? We present a proposal in which calcium oscillations, whose strength is tuned locally by the environment, and which are coupled by diffusion, drive changes in the mechanics of the cell's actin cortex. Experiments show that locally weakening the cortex with a depolymerizing agent biases the cell toward the weakened side, even without a nutritional cue. We use a one-dimensional model to show that a local change in a single parameter produces traveling waves and a corresponding redistribution of biomass. The model also predicts that perturbing actin alone should move biomass without directed waves. Then, using a phase-field framework, we show the same mechanism explains chemotaxis, network formation, and solving of the two-armed bandit problem without a programmed decision rule. Finally, we discuss what the models do and do not explain, and open mathematical questions about wave selection and the role of diffusion in coordinating a whole cell.