Open-system force-elongation relationship of collagen in chemo-mechanical equilibrium with water

A significant deformation mechanism of collagen at low loads is molecular uncoiling and rearrangement. Although the effect of hydration and cross-linking has been investigated at larger loads when collagen undergoes molecular sliding, their effects on collagen molecular reorganization remain unclear. Here we develop two thermodynamic models that use the notion of open-system elasticity to elucidate the effect of swelling due to water uptake during deformation of collagen networks under low and high cross-linking conditions. With low crosslinking, entropic contributions dominate resulting in rejection of solvent from the polymer network leading to reduced collagen stiffness with increased loads. Contrarily, high cross-linking inhibits initial coiling and structural kinking and the mechanical behavior is dominated by elastic energy. In this configuration, the solvent content depends on the sign of the applied load resulting in a non-linear open-system stress-strain relationship. The models provide insight on the parameters that impact the stress-strain relationships of hydrated collagen and can inform the way collagenous matrices are treated both in medical and laboratory settings.