Modelling Intermolecular Cross-Linking in Collagen Fibrils

Collagen fibrils are microscopic molecular ropes that are structural components in many animal tissues. We present an equilibrium coarse-grained model for the structural and mechanical properties of these cross-linked fibrils. We model enzymatic cross-links as anisotropic Gaussian chains, which allows us to approximate their free-energy contributions. We add additional terms in the free energy for the Frank elastic energy due to the orientation of collagen molecules within the fibril, for the surface tension, and phase-field crystal terms which account for the D-band density modulations observed along the length of collagen fibrils. We computationally minimize the sum of these free-energy terms with respect to imposed strain fields acting on the fibril to obtain equilibrium structures. Using this framework we investigate the effect of strain on various important structural and mechanical properties of the fibril, such as the molecular director field and the stress-strain curve.