Fibre crosslinking drives the emergence of order in a three-dimensional dynamical network model

Abstract

The extracellular-matrix (ECM) is a complex interconnected three-dimensional network that provides structural support for the cells and tissues and defines organ architecture as key for their healthy functioning. However, the intimate mechanisms by which ECM acquire their three-dimensional architecture are still largely unknown. In this paper, we study this question by means of a simple three-dimensional individual based model of interacting fibres able to spontaneously crosslink or unlink to each other and align at the crosslinks. We show that such systems are able to spontaneously generate different types of architectures. We provide a thorough analysis of the emerging structures by an exhaustive parametric analysis and the use of appropriate visualization tools and quantifiers in three dimensions. The most striking result is that the emergence of ordered structures can be fully explained by a single emerging variable: the number of links per fibre in the network. If validated on real tissues, this simple variable could become an important putative target to control and predict the structuring of biological tissues, to suggest possible new therapeutic strategies to restore tissue functions after disruption, and to help in the development of collagen-based scaffolds for tissue engineering. Moreover, the model reveals that the emergence of architecture is a spatially homogeneous process following a unique evolutionary path, and highlights the essential role of dynamical crosslinking in tissue structuring.

Keywords

• interaction networks
• three-dimensional mathematical modelling
• self-organization
• extracellular matrix
• dynamical crosslinking
• architecture emergence