  The lysyl oxidase (LOX) enzyme that catalyses cross-link formation during the
assembly of collagen fibrils in vivo is too large to diffuse within assembled
fibrils, and so is incompatible with a fully equilibrium mechanism for fibril
formation. We propose that enzymatic cross-links are formed at the fibril
surface during the growth of collagen fibrils; as a consequence no significant
reorientation of previously cross-linked collagen molecules occurs inside
collagen fibrils during fibril growth in vivo. By imposing local equilibrium
only at the fibril surface, we develop a coarse-grained quantitative model of
in vivo fibril structure that incorporates a double-twist orientation of
collagen molecules and a periodic D-band density modulation along the fibril
axis. Radial growth is controlled by the density of available collagen
molecules around the fibril. In contrast with earlier equilibrium models of
fibril structure, we find that all fibrils can exhibit a core-shell structure
that is controlled only by the fibril radius. At small radii a core is
developed with a linear double-twist structure as a function of radius. Within
the core the double-twist structure is largely independent of the D-band.
Within the shell at larger radii, the structure approaches a constant twist
configuration that is strongly coupled with the D-band. We suggest a stable
radius control mechanism that corneal fibrils can exploit near the edge of the
linear core regime; while larger tendon fibrils can use a cruder version of
growth control that does not select a preferred radius.
