A model is presented to explain the development of flow channels within the cytoplasm of the plasmodium of the giant amoeba Physarum polycephalum. The formation of channels is related to the development of a self-organizing tubular network in large cells. Experiments indicate that the flow of cytoplasm is involved in the development and organization of these networks, and the mathematical model proposed here is motivated by recent experiments involving the observation of development of flow channel in small cells. A model of pressure-driven flow through a polymer network is presented in which the rate of flow increases the rate of depolymerization. Numerical solutions and asymptotic analysis of the model in one spatial dimension show that under very general assumptions this model predicts the formation of channels in response to flow.
Guy, Robert D.; Nakagaki, Toshiyuki; and Wright, Grady. (2011). "Flow-Induced Channel Formation in the Cytoplasm of Motile Cells". Physical Review E, 84(1), 016310-1 - 016310-13. http://dx.doi.org/10.1103/PhysRevE.84.016310