Nonlinear Elasticity in Biological Gels

Nonlinear Elasticity in Biological Gels

| Cornelis Storm*, Jennifer J. Pastore, Fred C. MacKintosh, Tom C. Lubensky, Paul A. Janmey
Nonlinear elasticity in biological gels is a phenomenon where biological materials stiffen as they are deformed, a behavior critical for physiological functions. This strain stiffening has been observed in various tissues like blood vessels, mesentery, lung parenchyma, and cornea. The study presents a molecular theory explaining this behavior in a wide range of biopolymer gels formed from purified cytoskeletal and extracellular proteins. The theory shows that systems of semi-flexible chains, such as filamentous proteins arranged in an open crosslinked meshwork, invariably stiffen at low strains without requiring a specific architecture or multiple elements with different intrinsic stiffnesses. The response of biological networks to deformation depends strongly on the magnitude of the deformation. Strain stiffening allows biological tissues to adaptively respond to varying mechanical conditions. The theory considers the force-extension curve of individual filaments and assumes that networks are homogeneous, isotropic, and have an affine elastic response. Theoretical predictions for the shear modulus as a function of strain agree with experimental measurements. The study also explores the force-response of semiflexible filaments, which are neither fully flexible nor fully rigid. These filaments have comparable persistence length and contour length. A theory for the force-response of such filaments and the corresponding network shear modulus was proposed, showing that the range of strain over which the material has linear elasticity decreases with increasing concentration. The study introduces a model for the geometry of the network, assuming isotropic networks with random crosslink points connected by semi-flexible filaments. The model assumes affine deformations, where the deformation tensor is uniform across the network. The stress tensor is calculated by averaging the force per area exerted by a single link over all magnitudes and directions of separation between crosslink points. The model is fitted to experimental data for fibrin at different mass concentrations, showing good agreement with the theoretical predictions. The results suggest that the initial stages of strain stiffening in biopolymer networks are dominated by entropic effects. However, the theory has limitations, particularly at high strains where enthalpic contributions become significant. The study also discusses the implications of these findings for the design of artificial biomaterials that mimic the nonlinear elastic response of biological tissues. The results highlight the importance of understanding the molecular structure and design principles of biological materials to develop effective biomaterials. The study concludes that the inherent strain-stiffening of semiflexible polymer networks is a starting point for the complex designs that have evolved to endow biological materials with their mechanical properties.Nonlinear elasticity in biological gels is a phenomenon where biological materials stiffen as they are deformed, a behavior critical for physiological functions. This strain stiffening has been observed in various tissues like blood vessels, mesentery, lung parenchyma, and cornea. The study presents a molecular theory explaining this behavior in a wide range of biopolymer gels formed from purified cytoskeletal and extracellular proteins. The theory shows that systems of semi-flexible chains, such as filamentous proteins arranged in an open crosslinked meshwork, invariably stiffen at low strains without requiring a specific architecture or multiple elements with different intrinsic stiffnesses. The response of biological networks to deformation depends strongly on the magnitude of the deformation. Strain stiffening allows biological tissues to adaptively respond to varying mechanical conditions. The theory considers the force-extension curve of individual filaments and assumes that networks are homogeneous, isotropic, and have an affine elastic response. Theoretical predictions for the shear modulus as a function of strain agree with experimental measurements. The study also explores the force-response of semiflexible filaments, which are neither fully flexible nor fully rigid. These filaments have comparable persistence length and contour length. A theory for the force-response of such filaments and the corresponding network shear modulus was proposed, showing that the range of strain over which the material has linear elasticity decreases with increasing concentration. The study introduces a model for the geometry of the network, assuming isotropic networks with random crosslink points connected by semi-flexible filaments. The model assumes affine deformations, where the deformation tensor is uniform across the network. The stress tensor is calculated by averaging the force per area exerted by a single link over all magnitudes and directions of separation between crosslink points. The model is fitted to experimental data for fibrin at different mass concentrations, showing good agreement with the theoretical predictions. The results suggest that the initial stages of strain stiffening in biopolymer networks are dominated by entropic effects. However, the theory has limitations, particularly at high strains where enthalpic contributions become significant. The study also discusses the implications of these findings for the design of artificial biomaterials that mimic the nonlinear elastic response of biological tissues. The results highlight the importance of understanding the molecular structure and design principles of biological materials to develop effective biomaterials. The study concludes that the inherent strain-stiffening of semiflexible polymer networks is a starting point for the complex designs that have evolved to endow biological materials with their mechanical properties.
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