1. Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
2. Institute for Medicine and Engineering, University of Pennsylvania, 3340 Smith Walk, Philadelphia, Pennsylvania 19104, USA
3. Division of Physics and Astronomy, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081HV Amsterdam, The Netherlands
4. *Present address: Instituut-Lorentz for Theoretical Physics, LION, Universiteit Leiden, PO Box 9506, NL-2300RA Leiden, The Netherlands

Correspondence to: Cornelis Storm^1,4 Correspondence and requests for materials should be addressed to C.S. (Email: cstorm@lorentz.leidenuniv.nl).

Abstract

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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