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 beta-lactoglobulin and lysozyme amyloid networks, this approach provides the correct scaling of elasticity versus both concentration (G similar to c(2.2) and G similar to c(2.5) for semiflexible and rigid fibrils, respectively) and ionic strength (G similar to I-4.4 and G similar to I-3.8 for beta-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.