Flow-network adaptation and behavior in slime molds

The slime mold Physarum polycephalum is an amoebozoa that grows forming a cytoplasm network that adapts its geometry to external stimuli. The cytoplasm is made of ectoplasm tubes in which the endoplasmic fluid flows. Endoplasmic flow is due to the rhythmic contraction of the actomyosin fibers of the ectoplasm, which induces a peristaltic wave that can be tracked through the spatiotemporal variations of the tube diameters. Slime mold behavior depends on many periodic modes of tube diameter variation, which is believed to allow a smooth transition between migration directions. Physarum polycephalum can solve mazes and grow optimal networks to solve traveling salesman and Steiner tree problems. Slime mold network dynamics have been modeled through cell automata and stochastic approaches, as well as fluid flow equations, electronic analogs, and multi-agent systems. Here, we examine the modeling strategies available to date to simulate flow-network adaptation in slime molds. However, we found no theoretical framework that can properly predict the evolution of the network as it morphs from an initial configuration to a pseudo-asymptotic optimum or explain the physical phenomena that drive endoplasmic flow or memory encoding at the scale of the entire network. Multi-frame object tracking by k-partite graphs holds promise for slime mold network analysis and tracking, whereas deep learning could be used to classify sequences of latent features to help characterize the behavior of Physarum polycephalum. The combination of the two could pave the way to a new class of predictive behavior models for slime molds.