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A Phyllotactic Approach to the Structure of Collagen Fibrils

Collagen fibrils, cable-like assemblies of long biological molecules, are dominant components of connective tissues. Their determinant morphological and functional roles motivated a large number of studies concerning their formation and structure. However, these two points are still open questions and, particularly, that of their organization which is certainly dense but not strictly that of a crystal. We examine here how the algorithm of phyllotaxis could contribute to the analysis of the structure of collagen fibrils. Such an algorithm indeed leads to organizations giving to each element of the assembly the most homogeneous and isotropic dense environment in a situation of cylindrical symmetry. The scattered intensity expected from a phyllotactic distribution of triple helices in collagen fibrils well agrees with the major features observed along the equatorial direction of their X ray patterns. Following this approach, the aggregation of triple helices in fibrils should be considered within the frame of soft condensed matter studies rather than that of molecular crystal studies.