Elasticity in Physically Cross-Linked Amyloid Fibril Networks

We provide a constitutive model of semiflexible and rigid amyloid fibril networks by combining the affine thermal model of network elasticity with the Derjaguin-Landau-Vervey-Overbeek (DLVO) theory of electrostatically charged colloids. When compared to rheological experiments on β-lactoglobulin and lysozyme amyloid networks, this approach provides the correct scaling of elasticity versus both concentration (G∼c^{2.2} and G∼c^{2.5} for semiflexible and rigid fibrils, respectively) and ionic strength (G∼I^{4.4} and G∼I^{3.8} for β-lactoglobulin and lysozyme, independent from fibril flexibility). The pivotal role played by the screening salt is to reduce the electrostatic barrier among amyloid fibrils, converting labile physical entanglements into long-lived cross-links. This gives a power-law behavior of G with I having exponents significantly larger than in other semiflexible polymer networks (e.g., actin) and carrying DLVO traits specific to the individual amyloid fibrils.