Effect of the free energies of formation of the core and shell and of the density of the casein phosphate centres on the
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Effect of the free energies of formation of the core and shell and of the density of the casein phosphate centres on the thermodynamic stability of calcium phosphate nanoclusters Carl Holt Hannah Research Institute Ayr KA6 5HL UK ABSTRACT Calcium phosphate is sparingly soluble at neutral pH but the milk of nearly all species contains many times the concentrations of calcium and phosphate that this solubility allows. The explanation for this apparent paradox is that milk calcium is mainly present in the form of thermodynamically stable nanoclusters formed from casein phosphoproteins and amorphous calcium phosphate. A simplified model system comprising the main milk salts and a hydrophilic N-terminal phosphopeptide from β-casein, at or about neutral pH, forms complexes called calcium phosphate nanoclusters. It is shown that two constants, KS and y, together with the empirical chemical formula of the nanoclusters allow the concentrations of all the important chemical species in this model system to be calculated. The method has been extended successfully to the more complex problem of calculating all the important chemical species in milk. It is suggested, on the basis of a simple analysis of the thermodynamics of the formation of nanoclusters, that their size and stability is determined principally by three factors. These are the relatively low free energy of formation of the amorphous core material, the particular pattern of phosphorylation of seryl residues in the caseins that gives a large chelate effect during the sequestration of the calcium phosphate and the unfolded conformation of the caseins that allows a high density of phosphate centres on the core surface. INTRODUCTION The white appearance of skim milk is due to the light scattered by colloidal particles called casein micelles formed from casein phosphoproteins and about 7% by dry weight of micellar calcium phosphate [1]. When cow’s milk is partitioned by ultrafiltration through a low molecular weight cut-off membrane a straw coloured ultrafiltrate is obtained containing about one third of the total calcium, half the inorganic phosphorus (Pi) two thirds the magnesium and about 90% of the citrate. The ultrafiltrate is a simple salt and lactose solution for which all the ion equilibria can be calculated relatively easily. In all milks that have been examined in sufficient detail [2], there is a constant value for an ion activity product of KS = {Ca2+}{HPO42-}y{PO43-}(2-2y)/3, where the curly brackets signify an ion activity and 0.6 ≤ y ≤ 1.0. In a two-phase system at equilibrium, such an invariant ion activity product would indicate a phase equilibrium between a saturated solution and a solid phase with the empirical formula Ca(HPO42-)y(PO43-)(2-2y)/3. Attempts to describe the ion equilibria in milk as a two-phase system at equilibrium have not meet with success because the measured composition of the colloidal calcium phosphate is incompatible with the ion activity product. To resolve the difficulty it was proposed that the phosphate moieties of the
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