Nonlinear elasticity in biological gels

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Abstract
Unlike most synthetic materials, biological materials often stiffen as they are strained. This property, critical for the physiological function of tissues such as blood vessels, lung parenchyma and blood clots, has been documented since the nineteenth century, but the molecular structures and design principles responsible for it are unknown. Storm et al. now show that a much simpler theory can account for strain stiffening in a wide range of biopolymer gels formed from cytoskeletal and extracellular proteins. According to this theory, systems of semiflexible chains such as filamentous proteins arranged in an open crosslinked meshwork invariably stiffen at low strains without the need for a specific architecture or multiple elements with different intrinsic stiffnesses. The mechanical properties of soft biological tissues are essential to their physiological function and cannot easily be duplicated by synthetic materials. Unlike simple polymer gels, many biological materials—including blood vessels1, mesentery tissue2, lung parenchyma3, cornea4 and blood clots5—stiffen as they are strained, thereby preventing large deformations that could threaten tissue integrity. The molecular structures and design principles responsible for this nonlinear elasticity are unknown. Here we report a molecular theory that accounts for strain-stiffening in a range of molecularly distinct gels formed from cytoskeletal and extracellular proteins and that reveals universal stress–strain relations at low to intermediate strains. The input to this theory is the force–extension curve for individual semi-flexible filaments and the assumptions that biological networks composed of these filaments are homogeneous, isotropic, and that they strain uniformly. This theory shows that systems of filamentous proteins arranged in an open crosslinked mesh invariably stiffen at low strains without requiring a specific architecture or multiple elements with different intrinsic stiffness.
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