Polyelectrolyte gels formed by filamentous biopolymers: Dependence of crosslinking efficiency on the chemical softness of divalent cations

Filamentous anionic polyelectrolytes are common in biological materials. Some examples are the cytoskeletal filaments that assemble into networks and bundled structures to give the cell mechanical resistance and that act as surfaces on which enzymes and other molecules can dock. Some viruses, especially bacteriophages are also long thin polyelectrolytes, and their bending stiffness is similar to those of the intermediate filament class of cytoskeletal polymers. These relatively stiff, thin, and long polyelectrolytes have charge densities similar to those of more flexible polyelectrolytes such as DNA, hyaluronic acid, and polyacrylates, and they can form interpenetrating networks and viscoelastic gels at volume fractions far below those at which more flexible polymers form hydrogels. In this report, we examine how different types of divalent and multivalent counterions interact with two biochemically different but physically similar filamentous polyelectrolytes: Pf1 virus and vimentin intermediate filaments (VIF). Different divalent cations aggregate both polyelectrolytes similarly, but transition metal ions are more efficient than alkaline earth ions and their efficiency increases with increasing atomic weight. Comparison of these two different types of polyelectrolyte filaments enables identification of general effects of counterions with polyelectrolytes and can identify cases where the interaction of the counterions and the filaments exhibits stronger and more specific interactions than those of counterion condensation.