Type-I collagen fibrils: From growth morphology to local order

The length of type-I collagen fibrils in solution increases through the development and progress of pointed tips appearing successively at the two ends of an axis-symmetric shaft with constant diameter. Those tips, respectively fine ($\alpha$) or coarse ($\beta$) have opposite molecular orientations. The $\alpha$-pointed tips, the first to appear, are particularly remarkable as they all show, on most of their length, a common parabolic profile which stays constant during the growth. Assuming that the latter occurs by lateral accretion of individual molecules in staggered configuration, we propose to give account of this prominent morphological feature along a purely geometrical argument, the profile of a tip being linked to the shape of the trajectories followed all along the accretion process. Among several possible trajectories, Fermat spirals lead to a parabolic profile in perfect agreement with the one observed for $\alpha$-pointed tips. This is to be put in relation with the presence of such spirals in phyllotactic patterns which ensure the best packing efficiency in cases of axis-symmetry, which is indeed that of dense collagen fibrils. Moreover, those patterns are structured by concentric circles of dislocations, constitutive of the structure itself, whose behaviour might contribute to the mechanical properties of the fibrils. Graphical abstract:

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