Presentation Information
[SS01-04]Rules on Bifurcation and Unidirectionality in Transport Networks
*Dai Akita1 (1. The University of Tokyo (Japan))
Keywords:
Transport Network,Current Reinforcement Rule,Bifurcation,Branching,Unidirectionality
Transport networks play essential roles in many organisms by enabling the efficient circulation of vital substances such as nutrients, blood, or protoplasm. These biological systems often display robust designs that maintain effective distribution under varied conditions. Among the available model systems for studying biological transport networks, the true slime mold Physarum polycephalum stands out because it can be easily cultured and develops tubular networks overnight. This unique characteristic makes it an ideal platform for examining the self-organization, functionality, and adaptability of transport pathways.
One notable geometric characteristic of Physarum’s network can be found in a specific situation. When the plasmodium is placed in an arena with a single narrow exit and detects food outside, it begins evacuating the arena by channeling protoplasm through newly formed tubular structures. Observations at each branch reveal a law known as the cubic law. The cube of the parent tubes radius equals the sum of the cubes of the daughter tubes radii. This phenomenon can be explained by the current reinforcement rule, which states that tubes carrying greater flow expand while those with lower flow contract. Simulations based on this rule reproduce the observed branching patterns, and mathematical analysis indicates that the current reinforcement approach aligns with Murrays law, which describes a similar cubic relationship in blood vessels by optimizing frictional energy loss and metabolic maintenance costs.
In this presentation, we introduce the experimental findings and theoretical background of the cubic bifurcation law, and also explore unidirectionality as another important aspect of transport networks. Certain biological systems, such as blood vessels, have unidirectional flow, and graph-theoretic analyses provide insights into the geometric constraints of such one-way networks. We further discuss potential applications of the unidirectionality concept on experimental data.
One notable geometric characteristic of Physarum’s network can be found in a specific situation. When the plasmodium is placed in an arena with a single narrow exit and detects food outside, it begins evacuating the arena by channeling protoplasm through newly formed tubular structures. Observations at each branch reveal a law known as the cubic law. The cube of the parent tubes radius equals the sum of the cubes of the daughter tubes radii. This phenomenon can be explained by the current reinforcement rule, which states that tubes carrying greater flow expand while those with lower flow contract. Simulations based on this rule reproduce the observed branching patterns, and mathematical analysis indicates that the current reinforcement approach aligns with Murrays law, which describes a similar cubic relationship in blood vessels by optimizing frictional energy loss and metabolic maintenance costs.
In this presentation, we introduce the experimental findings and theoretical background of the cubic bifurcation law, and also explore unidirectionality as another important aspect of transport networks. Certain biological systems, such as blood vessels, have unidirectional flow, and graph-theoretic analyses provide insights into the geometric constraints of such one-way networks. We further discuss potential applications of the unidirectionality concept on experimental data.