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Multi-stranded plies : from collagen to cables
Application : mechanical properties of collagen, metal cables.
Collagen is a very abundant fibrous protein that constitutes 1/4 of all protein in the human body. It is an extracellular filament unlike actin of intermediate filaments. It forms a matrix that holds and supports cells. The basic unit of structure is a triple helix structure called tropocollagen. Along each of the strands (1000 residus longs), each third residu is a glycine. The Gly residus form H-bonding to lock the chains in the conformation. This stabilises the unusual structure. Without the H-bonds the structure is unstable and un-winds. The three left handed helices are stretched and more opened than the coiled alpha-helix.
To get the mechanical equilibrium equations right, one first has to work out the geometry : the way the 3 strands touch each other. The contact set is nolonger a straight line but helices. The two touching conditions are (rho is the ratio of the thickness of on strand to the radius of the carrying cylinder, delta is the difference in arc length between contacting points):
Nevertheless when considering one strand, the total pressure force coming from the 2 other strands still is orthogonal to the helix axis. We get the equilibrium equation relation the helix angle (theta) to the external forces (ft and fc) and the total twist :
For the collagen, in order to model the Hydrogen bonds involving the Glycine residus, only equilibrium configurations with a negative pressure force will be studied.
Remark : The fact that there is a gap in the middle of the ply is also found in a proposed model for how a Gap Junction may close.