Double twist liquid crystal model of collagen structure

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Collagen is the main component of connective tissue and the most abundant protein in mammals. The structure of collagen is hierarchical with the triple-helical molecules organizing into fibrils and fibrils contained in higher-order arrangements. A fibril may be considered as a liquid crystal of individual triple helices. Their chiral molecular structure can lead to a macroscopic helical arrangement known as the cholesteric phase which has been observed in fragments of collagen fibrils. The cholesteric orientation can vary with radial distance in the fibril as a double twist. We numerically minimize mean-field Frank free energy in the bulk to solve for the liquid crystal orientation as a function of radial distance (r). By also considering surface terms the overall energy per fibril area is minimized to find the optimal fibril radius R and molecule orientation on the fibril surface (R) both of which may be compared to experimental measurements.