In classic flexible-polymer networks chain conformations can be described by random coils and the properties are dominated by entropy. In such ideal, isotropic, and homogeneous networks it is often assumed that strain propagates in an affine way. However, biopolymers and their meso-scale assemblies -- from single polysaccharides through to DNA duplexes to protein fibrils -- are routinely found to be well-characterized by the worm-like chain model of semi-flexible polymers, and in some cases the global orientation of fibrils and local inhomogeneities play a crucial role in the response of the whole network against strain. ^{1}

In order to study the real architectures exhibited by biopolymer networks, we have applied a skeletonization process to the images obtained using different 3D microscopy techniques (TEM-tomography and CLSM) in order to obtain a spatial graph, which characterizes the network, and can be represented by an enriched connectivity matrix or adjancency list. From the spatial graph, some statistical distributions of its more important features can be studied, such as degree of nodes, length of edges, and angles between adjacent edges. These distributions subsequently allow us to perform in-silico network reconstruction. ^{2}

Despite the difference in scale between polysaccharide networks --such as pectin and carrageenan-- imaged with TEM, and fibrillar protein fibrils --such as collagen and actin-- imaged with confocal microscopy, interesting similarities are found. We compare the networks from a graph theory perspective, finding that some of the statistical distributions have the same functional form, but different parameters. This is valuable for a more precise characterization of these dissordered networks beyond the isotropic, homogeneus assumption, and will be interesting to investigate its impact in the mechanical properties of the network.

- Broedersz, Chase P., and Fred MacKintosh. “Modeling Semiflexible Polymer Networks.” arXiv Preprint arXiv:1404.4332, 2014. http://arxiv.org/abs/1404.4332.
- Lindström, Stefan B., David A. Vader, Artem Kulachenko, and David A. Weitz. “Biopolymer Network Geometries: Characterization, Regeneration, and Elastic Properties.” Physical Review E 82, no. 5 (November 2010). doi:10.1103/PhysRevE.82.051905.