  The macroscopic properties, the properties of individual components and how
those components interact with each other are three important aspects of a
composited structure. An understanding of the interplay between them is
essential in the study of complex systems. Using axonal cytoskeleton as an
example system, here we perform a theoretical study of slender structures that
can be coarse-grained as a simple smooth 3-dimensional curve. We first present
a generic model for such systems based on the fundamental theorem of curves. We
use this generic model to demonstrate the applicability of the well-known
worm-like chain (WLC) model to the network level and investigate the situation
when the system is stretched by strong forces (weakly bending limit). We
specifically studied recent experimental observations that revealed the
hitherto unknown periodic cytoskeleton structure of axons and measured the
longitudinal fluctuations. Instead of focusing on single molecules, we apply
analytical results from the WLC model to both single molecule and network
levels and focus on the relations between extensions and fluctuations. We show
how this approach introduces constraints to possible local dynamics of the
spectrin tetramers in the axonal cytoskeleton and finally suggests simple but
self-consistent dynamics of spectrins in which the spectrins in one spatial
period of axons fluctuate in-sync.
