Kinetic signature of fractal-like filament networks formed by orientational linear epitaxy.

We study a broad class of epitaxial assembly of filament networks on lattice surfaces. Over time, a scale-free behavior emerges with a 2.5-3 power-law exponent in filament length distribution. Partitioning between the power-law and exponential behaviors in a network can be used to find the stage and kinetic parameters of the assembly process. To analyze real-world networks, we develop a computer program that measures the network architecture in experimental images. Application to triaxial networks of collagen fibrils shows quantitative agreement with our model. Our unifying approach can be used for characterizing and controlling the network formation that is observed across biological and nonbiological systems.