Buckling and Torsional Instabilities of a Nanoscale Biological Rope Bound to an Elastic Substrate.

Abstract

Rope-like structures are ubiquitous in Nature. They are supermolecular assemblies of macromolecules responsible for the structural and mechanical integrity of plant and animal tissues. Collagen fibrils with diameters between 50 and 500 nm and their helical supermolecular structure are good examples of such nanoscale biological ropes. Like man-made laid ropes, fibrils are typically loaded in tension, and due to their large aspect ratio, they are, in principle, prone to buckling and torsional instabilities. One way to study buckling of a rigid rod is to attach it to a stretched elastic substrate that is then returned to its original length. In the case of single collagen fibrils, the observed behavior depends on the degree of hydration. By going from buckling in ambient conditions to immersed in a buffer, fibrils go from the well-known sine wave response to a localized behavior reminiscent of the bird-caging of laid ropes. In addition, in ambient conditions, the sine wave response coexists with the formation of loops along the length of the fibrils, as observed for the torsional instability of a twisted filament when tension is decreased. This work provides direct evidence that single collagen fibrils are highly susceptible to axial compression because of their helical supermolecular structure. As a result, mammals that use collagen fibrils as their main load-bearing element in many tissues have evolved mitigating strategies that protect single fibrils from axial compression damage.