Optimizing Nutrient Uptake in Biological Transport Networks

Many biological systems employ complex networks of vascular tubes to facilitate transport of solute nutrients, examples include the vascular system of plants (phloem), some fungi, and the slime-mold \emph{Physarum}. It is believed that such networks are optimized through evolution for carrying out their designated task. We propose a set of hydrodynamic governing equations for solute transport in a complex network, and obtain the optimal network architecture for various classes of optimizing functionals. We finally discuss the topological properties and statistical mechanics of the resulting complex networks, and examine correspondence of the obtained networks to those found in actual biological systems.