Cation binding to β-casein. a comparison of electrostatic models

The binding of cations of β-casein at pH 6.6 was considered previously. Available for three sodium concentiations, I = 0.04, 0.08, or 0.16 M are: [1] proton releases between I and [2] for each I, as calcium activity is increased, correlated sequences of monomer net charge, proton release, site bound calcium and protein Solvation- Models for ion binding are examined. Critical considerations are the intrinsic binding constants between hydrogen[H], calcium[Ca] and sodium[Na] ions and phosphate[P] and caiboxyIate[C] sites, and the effects of electrostatic interaction between sites as influenced by spatial fixed charge distribution, ionic strength and dielectric constant [D]. Anticipated intrinsic binding constants are k_H,P^o = 3 × 10⁶, k_Ca,P^o = 120, k_Na,P^o = 1, k_H,C^o = 7 × 10⁴ and k_Ca,C^o = 5.6. Distributed charge models, either surface or volume, are inadequate since any reasonable monomer size yields fixed charge densities requiring k_H,P^o and k_Ca,C^o which are too low when the maximum in D is 75. Also, with increasing calcium binding, calculated proton release is only 0.4 to 0.5 of that observed. Discrete charge models accept anticipated k^o and yield calculated sequences of calcium binding and proton release which are in good agreement with those observed provided that: (1) using the known amino acid sequence of the phosphate-containing acidic peptide portion of the molecule, pep tide fixed charge is distributed at the lowest I so as to minimize electrostatic free energy; (2) in the region of fixed charge, D is approximately 5; (3) the distances between peptide fixed charges decrease with increasing ionic strength or calcium binding and (4) while protein is in solution, the acidic peptide and the remainder of the molecule are essentially electrostatically independent.