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.

Investigation of mechanisms of viscoelastic behavior of collagen molecule

Unique mechanical properties of collagen molecule make it one of the most important and abundant proteins in animals. Many tissues such as connective tissues rely on these properties to function properly. In the past decade, molecular dynamics (MD) simulations have been used extensively to study the mechanical behavior of molecules. For collagen, MD simulations were primarily used to determine its elastic properties. In this study, constant force steered MD simulations were used to perform creep tests on collagen molecule segments. The mechanical behavior of the segments, with lengths of approximately 20 (1X), 38 (2X), 74 (4X), and 290 nm (16X), was characterized using a quasi-linear model to describe the observed viscoelastic responses. To investigate the mechanisms of the viscoelastic behavior, hydrogen bonds (H-bonds) rupture/formation time history of the segments were analyzed and it was shown that the formation growth rate of H-bonds in the system is correlated with the creep growth rate of the segment (β=2.41βH). In addition, a linear relationship between H-bonds formation growth rate and the length of the segment was quantified. Based on these findings, a general viscoelastic model was developed and verified here, using the smallest segment as a building block, the viscoelastic properties of larger segments could be predicted. In addition, the effect of temperature control methods on the mechanical properties were studied, and it was shown that application of Langevin Dynamics had adverse effect on these properties while the Lowe-Anderson method was shown to be more appropriate for this application. This study provides information that is essential for multi-scale modeling of collagen fibrils using a bottom-up approach.