Communications in Mathematical Sciences

Volume 17 (2019)

Number 5

Dedicated to the memory of Professor David Shen Ou Cai

An optimization principle for initiation and adaptation of biological transport networks

Pages: 1427 – 1436



Dan Hu (School of Mathematical Sciences, Institute of Natural Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai, China)

David Cai (Shanghai Jiao Tong University, Shanghai, China; Courant Institute and Center for Neural Science, New York University, New York, N.Y., U.S.A; and NYUAD Institute, New York University, Abu Dhabi, United Arab Emirates)


Structural optimization of biological transport networks, such as leaf venation and blood vessel systems, can be regarded as a consequence of natural selection. Many studies have examined the important question of whether an adaptation dynamics of edges can be responsible for structural optimization. However, what role the initiation process plays in structural optimization remains to be clarified. Here we propose an optimization principle that potentially underlies common mechanisms that drive the formation of biological transport networks. Associated with the optimization principle is an adaptation dynamics of cell polarization that unifies initiation processes and segment formation of transport networks. In our model, the competition between the reduction of transport energy cost and the reduction of material and metabolic consumptions is sufficient to induce optimal structures: a tree-like network as well as loops under different states of fluctuating drives.


biological transport networks, initiation, adaptation

2010 Mathematics Subject Classification

60F10, 60J75, 62P10, 92C37

Received 12 May 2018

Accepted 4 April 2019

Published 6 December 2019