Gelation of semiflexible polyelectrolytes by multivalent counterions

Abstract

Filamentous polyelectrolytes in aqueous solution aggregate into bundles by interactions with multivalent counterions. These effects are well documented by experiment and theory. Theories also predict a gel phase in isotropic rodlike polyelectrolyte solutions caused by multivalent counterion concentrations much lower than those required for filament bundling. We report here the gelation of Pf1 virus, a model semiflexible polyelectrolyte, by the counterions Mg2+, Mn2+ and spermine4+. Gelation can occur at 0.04% Pf1 volume fraction, which is far below the isotropic-nematic transition of 0.7% for Pf1 in monovalent salt. Unlike strongly crosslinked gels of semiflexible polymers, which stiffen at large strains, Pf1 gels reversibly soften at high strain. The onset strain for softening depends on the strength of interaction between counterions and the polyelectrolyte. Simulations show that the elasticity of counterion crosslinked gels is consistent with a model of semiflexible filaments held by weak crosslinks that reversibly rupture at a critical force.

Polyelectrolyte properties of filamentous biopolymers and their consequences in biological fluids

“…Comparison of experiments in which Pf1 gels such as those in Figure 4 were strained until the value of G′ abruptly decreased, presumably because of crosslink failure, with computer simulations to estimate the average force per crosslink at the breaking point, suggest a value of <0.4 pN as the critical breaking force, consistent with lower dielectric constant of the virus which would decrease α 12 . In contrast, actin crosslinking proteins such as filamin or alpha actinin have rupture forces on the order of 40 pN 86 .…”

“…Pf1 is 2 microns long, 6 nm in diameter, and in the absence of multivalent counterions remains isotropic at concentrations above 5 mg/ml. Divalent ions at concentrations well below those needed to form Pf1 bundles (Figure 3) induce the formation of elastic networks 12 with relatively low mechanical loss and Young’s moduli (Figure 4) very close to those of vimentin networks stabilized by Mg 2+ . Just as Mn 2+ is a stronger bundling agent than Mg 2+ (Figure 2), it is also a stronger gelation agent than Mg 2+ for Pf1 (Figure 4) and the concentrations of divalent counterions needed for gelation are slightly affected but not eliminated in solutions of physiological ionic strength 12 .…”

“…Divalent ions at concentrations well below those needed to form Pf1 bundles (Figure 3) induce the formation of elastic networks 12 with relatively low mechanical loss and Young’s moduli (Figure 4) very close to those of vimentin networks stabilized by Mg 2+ . Just as Mn 2+ is a stronger bundling agent than Mg 2+ (Figure 2), it is also a stronger gelation agent than Mg 2+ for Pf1 (Figure 4) and the concentrations of divalent counterions needed for gelation are slightly affected but not eliminated in solutions of physiological ionic strength 12 . Since Pf1 has a relatively simple structure formed by a single coat protein with a short sequence of acidic amino acids at the virus surface 53 , it seems unlikely that the virus has specific binding sites with different affinities for Mg 2+ and Mn 2+ , and therefore the possibility that gelation is caused by generic electrostatic effects rather than specific binding seems probable.…”

“…As a result, networks of rigid or semiflexible polymers crosslinked only by counterions are not strain-stiffening, as they are when tightly crosslinked, but rather the networks soften at moderate strains, but rapidly reform when the stress generated by the deformation is relieved 12 . An estimate of the counterion crosslink strength has been obtained by comparing experiments of Pf1 virus with simulations 12 , and these strengths are consistent with an analytic theory developed by Shklovskii et al 7, 83 .…”

Magnetic wire-based sensors for the microrheology of complex fluids

“…With the development of microfluidics systems in the last decade [1], rapid advances were made in the field of µ-rheology. Standard experimental protocols and data treatment softwares are now available and implemented on a regular and controlled basis [2][3][4][5][6][7]. The correspondence between µ-and macro-rheology is nowadays well established.…”