An equilibrium double-twist model for the radial structure of collagen fibrils

摘要

Mammalian tissues contain networks and ordered arrays of collagen fibrilsoriginating from the periodic self-assembly of helical 300 nm longtropocollagen complexes. The fibril radius is typically between 25 to 250 nm,and tropocollagen at the surface appears to exhibit a characteristictwist-angle with respect to the fibril axis. Similar fibril radii andtwist-angles at the surface are observed in vitro, suggesting that thesefeatures are controlled by a similar self-assembly process. In this work, wepropose a physical mechanism of equilibrium radius control for collagen fibrilsbased on a radially varying double-twist alignment of tropocollagen within acollagen fibril. The free-energy of alignment is similar to that of liquidcrystalline blue phases, and we employ an analytic Euler-Lagrange and numericalfree energy minimization to determine the twist-angle between the molecularaxis and the fibril axis along the radial direction. Competition between thedifferent elastic energy components, together with a surface energy, determinesthe equilibrium radius and twist-angle at the fibril surface. A simplifiedmodel with a twist-angle that is linear with radius is a reasonableapproximation in some parameter regimes, and explains a power-law dependence ofradius and twist-angle at the surface as parameters are varied. Fibril radiusand twist-angle at the surface corresponding to an equilibrium free-energyminimum are consistent with existing experimental measurements of collagenfibrils. Remarkably, in the experimental regime, all of our model parametersare important for controlling equilibrium structural parameters of collagenfibrils.