Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations.

Collagen fibril is a major component of connective tissues such as bone, tendon, blood vessels, and skin. The mechanical properties of this highly hierarchical structure are greatly influenced by the presence of covalent cross-links between individual collagen molecules. This study investigates the viscoelastic behavior of a collagen lysine-lysine cross-link based on creep simulations with applied forces in the range or 10 to 2000pN using steered molecular dynamics (SMD). The viscoelastic model of the cross-link was combined with a system composed by two segments of adjacent collagen molecules hence representing a reduced viscoelastic model for a simplified micro-fibril. It was found that the collagen micro-fibril assembly had a steady-state Young׳s modulus ranging from 2.24 to 3.27GPa, which is in agreement with reported experimental measurements. The propagation of longitudinal force wave along the molecule was implemented by adding a delay element to the model. The force wave speed was found to be correlated with the speed of one-dimensional elastic waves in rods. The presented reduced model with three degrees of freedom can serve as a building block for developing models of the next level of hierarchy, i.e., a collagen fibril.