Shape optimization in lipid nanotube networks
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- Lobovkina, T., Dommersnes, P.G., Tiourine, S. et al. Eur. Phys. J. E (2008) 26: 295. doi:10.1140/epje/i2007-10325-x
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Starting from a high surface free-energy state, lipid nanotube networks are capable to self-organize into tree-like structures with particular geometrical features. In this work we analyze the process of self-organization in such networks, and report a strong similarity to the Euclidian Steiner Tree Problem (ESTP). ESTP is a well-known NP-hard optimization problem of finding a network connecting a given set of terminal points on a plane, allowing addition of auxiliary points, with the overall objective to minimize the total network length. The present study shows that aggregate lipid structures self-organize into geometries that correspond to locally optimal solutions to such problems.