| Cornelis Storm1*, Jennifer J. Pastore2, Fred C. MacKintosh3, Tom C. Lubensky1,2 and Paul A. Janmey1,2
The article discusses the nonlinear elastic response, specifically strain stiffening, in biological gels composed of semiflexible filamentous proteins. Unlike synthetic materials, biological materials often stiffen as they are deformed, a property crucial for the physiological function of tissues. The authors present a simple molecular theory that explains this behavior in a wide range of biopolymer gels formed from purified cytoskeletal and extracellular proteins. This theory shows that systems of semi-flexible chains, such as filamentous proteins arranged in an open crosslinked meshwork, stiffen at low strains without requiring a specific architecture or multiple elements with different intrinsic stiffnesses.
The response of a single elastic filament to an applied force is dominated by entropy, leading to a nonlinear elastic behavior. The authors use a theoretical framework based on the force-extension curve of individual filaments, assuming that networks composed of these filaments are homogeneous and isotropic, and that their elastic response is affine. They derive a universal scaling relation for the shear modulus as a function of strain, which agrees well with experimental data.
The theory is further extended to account for high-strain deviations from the simple entropic model, introducing a stretch modulus to capture enthalpic contributions. The model is fit to experimental data for fibrin at different mass concentrations, showing good agreement. The results suggest that the degree of strain stiffening can be quite large, with increases in shear moduli of up to 10-fold under modest strains as small as 20%. The strain at which stiffening becomes significant depends on the persistence length of the filament and weakly on the mesh size of the network.
The implications of these findings for the design of artificial biomaterials and the active manipulation of stiffness in biological systems are discussed, highlighting the potential for using motor proteins to locally adjust the stiffness of networks like the cytoskeleton.The article discusses the nonlinear elastic response, specifically strain stiffening, in biological gels composed of semiflexible filamentous proteins. Unlike synthetic materials, biological materials often stiffen as they are deformed, a property crucial for the physiological function of tissues. The authors present a simple molecular theory that explains this behavior in a wide range of biopolymer gels formed from purified cytoskeletal and extracellular proteins. This theory shows that systems of semi-flexible chains, such as filamentous proteins arranged in an open crosslinked meshwork, stiffen at low strains without requiring a specific architecture or multiple elements with different intrinsic stiffnesses.
The response of a single elastic filament to an applied force is dominated by entropy, leading to a nonlinear elastic behavior. The authors use a theoretical framework based on the force-extension curve of individual filaments, assuming that networks composed of these filaments are homogeneous and isotropic, and that their elastic response is affine. They derive a universal scaling relation for the shear modulus as a function of strain, which agrees well with experimental data.
The theory is further extended to account for high-strain deviations from the simple entropic model, introducing a stretch modulus to capture enthalpic contributions. The model is fit to experimental data for fibrin at different mass concentrations, showing good agreement. The results suggest that the degree of strain stiffening can be quite large, with increases in shear moduli of up to 10-fold under modest strains as small as 20%. The strain at which stiffening becomes significant depends on the persistence length of the filament and weakly on the mesh size of the network.
The implications of these findings for the design of artificial biomaterials and the active manipulation of stiffness in biological systems are discussed, highlighting the potential for using motor proteins to locally adjust the stiffness of networks like the cytoskeleton.