Multiscale Characterization of Type I Collagen Fibril Stress-Strain Behavior under Tensile Load: Analytical vs. MD Approaches.

Type I collagen is one of the most important proteins in the human body because of its role in providing structural support to the extracellular matrix of the connective tissues. Understanding its mechanical properties was widely investigated using experimental testing as well as molecular and finite element simulations. In this work, we present a new approach for defining the properties of the type I collagen fibrils by analytically formulating its response when subjected to a tensile load and investigating the effects of enzymatic crosslinks on the behavioral response. We reveal some of the shortcomings of the molecular dynamics (MD) method and how they affect the obtained stress-strain behavior of the fibril, and we prove that not only does MD underestimate the Young's modulus and the ultimate tensile strength of the collagen fibrils, but also fails to detect the mechanics of some stretching phases of the fibril. We prove that non-crosslinked fibrils have three tension phases: (i) an initial elastic deformation corresponding to the collagen molecule uncoiling, (ii) a linear regime related to the stretching of the backbone of the tropocollagen molecules, and (iii) a plastic regime dominated by molecular sliding. We also show that for crosslinked fibrils, the second regime can be subdivided into three sub-regimes, and we define the properties of each regime. We also prove, analytically, the alleged MD quadratic relation between the ultimate tensile strength of the fibril and the concentration of enzymatic crosslinks (