Natural networks, such as collagen gels or cytoskeletal webs, have the ability to increase their stiffness with increasing strain. This unique feature is an advantage over most synthetic fibers. If blood vessels were made of rubber tubing, for example, the pressure from a heart beat would vastly increase vessel diameter. But collagen's nonlinear elasticity prevents such a drastic endothelial deformation.
This ability is usually explained by the heterogeneous nature of biological gels—perhaps tauter filaments take over at increasing strains. But in vitro measurements by Storm et al. now show that uniform biopolymer gels also exhibit nonlinear elasticity. The authors then produced a mathematical model that explains this behavior based on the characteristics of the individual polymer filaments within a cross-linked network.
“We show that strain stiffening comes about automatically because of the semiflexible nature of the chains in the biomaterials,” says Janmey. “They're not exactly straight, but they're not randomly highly coiled either.” That flexibility allows for short range movement under mild strain, but under greater strain the filaments reach the end of their leash and stop extending. Slightly stiffer polymers (actin, collagen), with shorter leashes, stop extending at lower strains. Softer gels, such as intermediate filaments, take larger deformations before they stiffen.
The model makes certain assumptions that might not hold true in vivo. For one, networks were assumed to form randomly. But Arp2/3 complexes, for instance, bias actin filament branching at specific angles. Additionally, cross-links were assumed to stay put under strain, although they are probably labile in cells. Determining the effects of these variations on strain stiffening will require further modeling.
Beyond biological interests, the findings might also prove useful to engineers. “If you wanted to make a material that stiffens as you deform it,” says Janmey, “filaments as stiff as intermediate filaments would create a new type of [synthetic] polymer.”