Divalent paramagnetic counterions site binding in polyelectrolyte solutions. Analysis of the frequency dependence of the water protons magnetic relaxation and the characteristic parameters of “site binding”

Water in the formation of biogenic minerals: peeling away the hydration layers

Minerals of biogenic origin form and crystallize from aqueous environments at ambient temperatures and pressures. The in vivo environment either intracellular or intercellular, contains many components that modulate both the activity of the ions which associate to form the mineral, as well as the activity and structure of the crowded water. Most of the studies about the mechanism of mineralization, that is, the detailed pathways by which the mineral ions proceed from solution to crystal state, have been carried out in relatively dilute solutions and clean solutions. These studies have considered both thermodynamic and kinetic controls. Most have not considered the water itself. Is the water a passive bystander, or is it intimately a participant in the mineral ion densification reaction? A wide range of experiments show that the mineralization pathways proceed through a series of densification stages with intermediates, such as a "dense liquid" phase and the prenucleation clusters that form within it. This is in contrast to the idea of a single step phase transition, but consistent with the Gibbs concept of discontinuous phase transitions from supersaturated mother liquor to crystal. Further changes in the water structure at every surface and interface during densification guides the free energy trajectory leading to the crystalline state. In vertebrates, mineralization takes place in a hydrated collagen matrix, thus water must be considered as a direct participant. Although different in detail, the crystallization of calcium phosphates, as apatite, and calcium carbonates, as calcite, are mechanistically identical from the viewpoint of water.

Counterion condensation and shape within Poisson-Boltzmann theory

An analytical approximation to the nonlinear Poisson-Boltzmann (PB) equation is applied to charged macromolecules that possess one-dimensional symmetry and can be modeled by a plane, infinite cylinder, or sphere. A functional substitution allows the nonlinear PB equation subject to linear boundary conditions to be transformed into an approximate linear (Debye-Hückel-type) equation subject to nonlinear boundary conditions. A simple analytical result for the surface potential of such polyelectrolytes follows, leading to expressions for the amount of condensed (or renormalized) charge and the electrostatic Helmholtz energy for polyelectrolytes. Analytical high-charge/low-salt and low-charge/high-salt limits are shown to be similar to results obtained by others based on PB or counterion condensation theory. Several important general observations concerning polyelectrolytes treated within the context of PB theory can be made including: (1) all charged surfaces display some counterion condensation for finite electrolyte concentration, (2) the effect of surface geometry is described primarily by the sum of the Debye constant and the mean curvature of the surface, (3) two surfaces with the same surface charge density and mean curvature condense approximately identical fractions of counterions, (4) the amount of condensation is not determined by a predefined "condensation distance" although such a distance can be determined uniquely from it, and (5) substantial condensation occurs if the Debye constant of the electrolyte is much less than the mean curvature of a highly charged polyelectrolyte.

Quantitative similarity of zinc and calcium binding to heparin in excess salt solution

Zn2+ binding to the anticoagulant heparin was examined using a dye spectrophotometric method, with added NaCl concentrations of 0.005, 0.0075, 0.01, 0.02 and 0.04 mol/l. The results are shown as Scatchard plots and demonstrate the entropy-driven anticooperativity of Zn2+ binding to heparin. From these Scatchard plots, intrinsic binding constants are determined and are compared to our earlier data for Mg2+ and Ca2+ binding to heparin at similar ionic strengths (J. Mattai and J.C.T. Kwak, Biochim. Biophys. Acta 677 (1981) 303), and to Manning's two-variable theory (G.S. Manning, Q. Rev. Biophys. 2 (1978) 179) for a generalized system of polyelectrolyte + divalent cations + univalent cations. While Mg2+ binding to heparin is purely electrostatic (delocalized or territorial), Zn2+ and Ca2+ binding is much stronger and more specific. Binding constants for these two cations are identical, suggesting similar mechanisms for Zn2+ and Ca2+ binding to heparin.

Raman spectroscopic studies on the interaction between divalent counterion and polyion

The nature of the interaction between polyacrylate ion and several divalent cations, such as Cu2+, Mn2+, Zn2+, Ba2+ and Mg2+, was investigated using Raman spectroscopy. A specific Raman band characteristic of a carboxyl group is shifted upon addition of Cu2+, Zn2+ and Mn2+ to partially neutralized poly(acrylic acid). On the other hand, no frequency shift of the specific Raman band is observed on addition of Mg2+ and Ba2+, though the intensity of the specific Raman band decreases with concentration of MgCl2. It is concluded from these Raman data that the interaction between polyacrylate ion and Cu2+, Zn2+ or Mn2+ includes a specific interaction with bond formation, whereas in the case of Mg2+ and Ba2+, the electrostatic interaction is dominant.

Site binding as a local equilibrium

Mn2+ binding to poly(acrylic acid) at different degrees of ionization, alpha, has been studied from the frequency dependence of the water protons' relaxation rates T1(-1) and T2(-1). Site binding is treated as an equilibrium with the concentration of free ions at the immediate vicinity (CIV) of the polyion. The CIV is calculated as the solution of the Poisson-Boltzmann equation at the surface of the cylindrical polyion. A single value of K is shown to fit the results at all values of alpha. The amount of site binding is higher than the total amount of condensed divalent counterions predicted for a finite polyion concentration in the presence of monovalent counterions by Manning's theory.