Non-Gaussian Elastic Properties in Biopolymer Networks
Highly extensible biomaterials containing rubber-like, crosslinked protein networks usually exhibit non-linear stress-strain curves that are matched to functional requirements, and it is commonly accepted that non-linear elastic properties arise from a composite of rubber-like protein reinforced by stiff fibres. It is possible, however, for protein rubbers to function as non-Gaussian networks and directly provide the non-linear elastic properties. This paper summarizes work on the analysis of non-Gaussian elastic properties in two biomaterials.
The elastic fibres in cephalopod arteries contain network chains that are relatively inflexible when compared with those in elastin, the rubber-like protein of the vertebrates. The equivalent random link in the cephalopod protein is about 12 amino acid residues long, whereas it is only about 8 amino acid residues for elastin. Although the crosslink density of these two protein networks is essentially identical, the difference in backbone flexibility creates significant differences in mechanical properties. Cephalopod elastic fibres exhibit non-Gaussian elastic properties at small strains that match the range of extensions seen in the living tissue, and thus contribute to the functionally important non-linear elastic properties. Elastin, in contrast, does not enter its non-Gaussian region until it is stretched by more than 100%, well beyond the biological range of extension, and thus it behaves as a linear elastic system.
Spider’s frame silk is a high strength protein fibre that contains a short-chain polymer network reinforced by extremely small crystalline inclusions. When hydrated in water, this silk exhibits rubber-like elastic properties, and analysis of its non-Gaussian properties provides the basis for a molecular model of the material. Network chains are about 15 amino acid residues long and contain two equivalent random links. The crystalline regions in silk occupy about 25% of the volume and appear to be elongated structures with a length—width ratio of about 5.
KeywordsElastic Fibre Spider Silk Elastic Artery Random Chain Small Amino Acid
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