Advertisement

European Biophysics Journal

, Volume 33, Issue 5, pp 421–434 | Cite as

An equilibrium thermodynamic model of the sequestration of calcium phosphate by casein micelles and its application to the calculation of the partition of salts in milk

  • Carl HoltEmail author
Article

Abstract

An equilibrium thermodynamic model of the interaction of calcium, phosphate and casein in milk is described in which the micellar calcium phosphate is assumed to be in the form of calcium phosphate nanoclusters. A generalized empirical formula for the nanocluster is used to define the molar ratios of small ions (Ca, Mg, Pi and citrate) to a casein phosphorylated sequence (phosphate centre, PC). From this model, a method of calculating the partition of milk salts into diffusible and non-diffusible fractions is obtained. No arbitrary assumptions are made, no fitting of adjustable parameters is done and the PCs in the caseins are defined by inspection of their primary structures. In addition to the salt partition, the mole fractions of the individual caseins not complexed to the calcium phosphate through one or more of their PCs are computed and a generic stability rule for milks is derived. The use of the model is illustrated by calculations of the partition of salts in a standard milk and by comparison with experimental data on the partition of salts in the milk of individual cows. The generic stability rule is applied to the individual milks to determine whether the micellar calcium phosphate is thermodynamically stable. According to the calculations, compositions that might lead to pathological calcification in the lumen of the mammary gland were seldom found in primiparous healthy cows in early or mid lactation but occurred more often in multiparous animals, in late lactation and during mastitic infection.

Keywords

Calcification Calcium phosphate Casein Milk Salt partition 

Abbreviations

ACP

amorphous calcium phosphate

Cit

citrate

CN

casein

CPN

calcium phosphate nanocluster

DCPD

dicalcium phosphate dihydrate

HA

hydroxyapatite

IAP

ion activity product

MCP

micellar calcium phosphate

MWCO

molecular weight cut-off

OCP

octacalcium phosphate

PC

phosphate centre

TCC

tricalcium citrate

Notes

Acknowledgements

The author is grateful to Drs. D.T. Davies, A.J.R. Law and J.C.D. White for allowing use of their original compositional data on cows’ milk.

References

  1. Ailamo MH, Kumosinski TF, Farrell HM Jr (1996) High resolution solid state NMR of milk products. J Magn Reson Anal 2:267–274Google Scholar
  2. Andrews AT, Alichanidis E (1983) Proteolysis of caseins and the proteose-peptone fraction of bovine milk. J Dairy Res 50:275–290Google Scholar
  3. Aoki T, Umeda T, Kako Y (1992) The least number of phosphate groups for crosslinking of casein by non-diffusible calcium phosphate. J Dairy Sci 75:971–975PubMedGoogle Scholar
  4. Bak M, Rasmussen LK, Petersen TE, Nielsen NC (2001). Non-diffusible calcium phosphate in casein micelles studied by slow-speed spinning 31P magic angle spinning solid state nuclear magnetic resonance, J Dairy Sci 84:1310–1319Google Scholar
  5. Chaplin LC (1984) Studies of micellar calcium phosphate: composition and apparent solubility product in milk over a wide pH range. J Dairy Res 51:251–257Google Scholar
  6. Chaplin LC, Lyster RLJ (1988) Effect of temperature on the pH of skim milk. J Dairy Res 55:277–280Google Scholar
  7. Creamer LK, Berry GP, Mills OE (1977) A study of the dissociation of β-casein from the bovine casein micelle at low temperature. NZ J Dairy Sci Technol 12:58–66Google Scholar
  8. Dalgleish DG, Law AJR (1988) pH-induced dissociation of bovine casein micelles. I. Analysis of liberated caseins. J Dairy Res 55:529–538Google Scholar
  9. Dalgleish DG, Law AJR (1989) pH-induced dissociation of bovine casein micelles. II. Mineral solubilization and its relation to casein release. J Dairy Res 56:727–735Google Scholar
  10. Davies DT, Law AJR (1977) The composition of whole casein from the milk of Ayrshire cows. J Dairy Res 44:447–454Google Scholar
  11. Davies DT, Law AJR (1983) Variation in the protein composition of bovine casein micelles and serum casein in relation to micellar size and milk temperature. J Dairy Res 50:67–75Google Scholar
  12. Davies DT, Law AJR (1987) Quantitative fractionation of casein mixtures by fast protein liquid chromatography. J Dairy Res 54:369–376Google Scholar
  13. Davies DT, White JCD (1960). The use of ultrafiltration and dialysis in isolating the aqueous phase of milk and in determining the partition of milk constituents between the aqueous and disperse phases. J Dairy Res 27:171–190Google Scholar
  14. De Kruif CG, Holt C (2003) Structure, functions and interactions of casein micelles. In: Fox PF, McSweeney P (eds) Advanced dairy chemistry, vol 1: proteins, 3rd edn. Kluwer/Plenum, New York, pp 233–276Google Scholar
  15. Fox PF (1992) Indigenous enzymes of milk. 3. Proteinases. In: Fox PF (ed) Advanced dairy chemistry, vol 1: proteins. Elsevier, Barking, UKGoogle Scholar
  16. Hansen S, Bauer R, Lomholt SB, Bruun Qvist K, Pedersen JS, Mortensen K (1996) Structure of casein micelles studied by small-angle neutron scattering. Eur Biophys J 24:143–147Google Scholar
  17. Holt C (1982) The inorganic constituents of milk. III. The non-diffusible calcium phosphate of cow milk. J Dairy Res 49:29–38PubMedGoogle Scholar
  18. Holt C (1993) Interrelationships of the concentrations of some ionic constituents of human milk and comparison with cow and goat milks. Comp Biochem Physiol A 104:5–41CrossRefGoogle Scholar
  19. Holt C (1997) The milk salts and their interaction with casein. In: Fox PF (ed) Advanced dairy chemistry, vol 3: lactose, water, salts and vitamins. Chapman and Hall, London, pp 233–254Google Scholar
  20. Holt C (1998) Casein micelle substructure and calcium phosphate interactions studied by sephacryl column chromatography. J Dairy Sci 81:2994–3003Google Scholar
  21. Holt C (2001) Calcium phosphate nanoclusters and their applications. UK Pat Appl 0030634.0; PCT Appl PCT/GB00/04827Google Scholar
  22. Holt C, Hukins DWL (1991) Structural analysis of the environment of Ca ions in crystalline and amorphous calcium phosphates by X-ray absorption spectroscopy and a hypothesis concerning the biological function of the casein micelle. Int Dairy J 1:151–165CrossRefGoogle Scholar
  23. Holt C, Dalgleish DG, Jenness R (1981) Calculation of the ion equilibria in milk diffusate and comparison with experiment. Anal Biochem 113:154–163PubMedGoogle Scholar
  24. Holt C, Hasnain SS, Hukins DWL (1982) Structure of bovine milk calcium phosphate determined by X-ray absorption spectroscopy. Biochim Biophys Acta 719:299–303CrossRefPubMedGoogle Scholar
  25. Holt C, Davies DT, Law AJR (1986) The effects of non-diffusible calcium phosphate content and milk serum free Ca ion concentration on the dissociation of bovine casein micelles. J Dairy Res 53:557–572Google Scholar
  26. Holt C, van Kemenade MJJM, Nelson LS Jr, Sawyer L, Harries JE, Bailey RT, Hukins DWL (1989) Composition and structure of micellar calcium phosphate. J Dairy Res 56:411–416Google Scholar
  27. Holt C, Wahlgren NM, Drakenberg T (1996) Ability of a β-casein phosphopeptide to modulate the precipitation of calcium phosphate by forming amorphous dicalcium phosphate nanoclusters. Biochem J 314:1035–1039PubMedGoogle Scholar
  28. Holt C, Timmins PA, Errington N, Leaver J (1998) A core-shell model of calcium phosphate nanoclusters derived from sedimentation equilibrium and small angle X-ray and neutron scattering measurements. Eur J Biochem 252:73–78CrossRefPubMedGoogle Scholar
  29. Holt C, de Kruif CG, Tuinier R, Timmins PE (2003) Substructure of bovine casein micelles by small-angle X-ray and neutron scattering. Colloids Surf 213:275–284CrossRefGoogle Scholar
  30. Kent JC, Arthur PG, Hartmann PE (1998) Citrate, calcium, phosphate and magnesium in sow’s milk at initiation of lactation. J Dairy Res 65:55–68CrossRefPubMedGoogle Scholar
  31. Knoop A-M, Knoop E, Wiechen A (1979) Sub-structure of synthetic casein micelles. J Dairy Res 46:347–350PubMedGoogle Scholar
  32. Kolar ZI, Verburga TG, van Dijk HJM (2002) Three kinetically different inorganic phosphate entities in bovine casein micelles revealed by isotopic exchange method and compartmental analysis. J Inorg Biochem 90:61–66CrossRefPubMedGoogle Scholar
  33. Le Bars D, Gripon JC (1989) Specificity of plasmin towards αs2-casein. J Dairy Res 56:817–821PubMedGoogle Scholar
  34. Little EM, Holt C (2004) An equilibrium thermodynamic model of the sequestration of calcium phosphate by casein phosphopeptides. Eur Biophys J (in press)Google Scholar
  35. Lyster RLJ, Mann S, Parker SB, Williams RJP (1984) Nature of micellar calcium phosphate in cow’s milk as studied by high resolution electron microscopy. Biochim Biophys Acta 801:315–317CrossRefPubMedGoogle Scholar
  36. Mayer JL, Eanes ED (1978) A thermodynamic analysis of the amorphous to crystalline calcium phosphate transformation. Calcif Tiss Int 25:59–68Google Scholar
  37. McGann TCA, Pyne GT (1960) The non-diffusible phosphate of milk. III. Nature of its association with casein. J Dairy Res 27: 403–417Google Scholar
  38. McGann TCA, Buchheim W, Kearney RD, Richardson T (1983a) Composition and ultrastructure of calcium phosphate–citrate complexes in bovine milk systems. Biochim Biophys Acta 760:415–420CrossRefPubMedGoogle Scholar
  39. McGann TCA, Kearney RD, Buchheim W, Posner AS, Betts F, Blumenthal NC (1983b) Amorphous calcium phosphate in casein micelles of bovine milk. Calcif Tiss Int 35:821–823Google Scholar
  40. McMahon DJ, McManus WR (1998) Rethinking casein micelle structure using electron microscopy. J Dairy Sci 81:2985–2993Google Scholar
  41. Niewold TA, Murphy CL, Hulskamp-Koch CAM, Tooten CJ, Gruys E (1999) Casein related amyloid, characterisation of a new and unique amyloid protein isolated from bovine corpora amylacea. Int J Exp Clin Invest 6:244–249Google Scholar
  42. Ono T, Ohotawa T, Takagi Y (1994) Complexes of casein phosphopeptide and calcium phosphate prepared from casein micelles by tryptic digestion. Biosci Biotechnol Biochem 58:1376–1380Google Scholar
  43. Pierre A, Brulé G, Fauquant J (1983) Etude de la mobilité du Ca dans le lait à l’aide du Ca 45. Lait 63:473–489Google Scholar
  44. Pyne GT (1934) The non-diffusible phosphate of milk. Biochem J 28:940–948Google Scholar
  45. Pyne GT (1962) Some aspects of the physical chemistry of the salts in milk. J Dairy Res 29:101–130Google Scholar
  46. Pyne GT, McGann TCA (1960) The non-diffusible phosphate of milk. II. Influence of citrate. J Dairy Res 27:9–17Google Scholar
  47. Pyne GT, Ryan JJ (1932) Non-diffusible calcium phosphate of milk. Sci Proc R Dublin Soc 20:471–476Google Scholar
  48. Rasmussen LK, Sørensen ES, Petersen TE, Nielsen NC, Thomsen JK (1997) Characterization of phosphate sites in native ovine, caprine and bovine casein micelles and their caseinomacropeptides: a solid-state phosphorus-31 nuclear magnetic resonance and sequence and mass spectrometric study. J Dairy Sci 80:607–614PubMedGoogle Scholar
  49. Schmidt DG (1982) Association of caseins and casein micelle structure. In: Fox PF (ed) Developments in dairy chemistry. Applied Science, Barking, UK, pp 61–86Google Scholar
  50. Shennan DB, Peaker M (2000) Transport of milk constituents by the mammary gland. Physiol Rev 80:925–951PubMedGoogle Scholar
  51. Stothart PH (1989) Subunit structure of casein micelles from small-angle neutron scattering. J Mol Biol 208:635–638PubMedGoogle Scholar
  52. Stothart PH, Cebula DJ (1982) Small-angle neutron scattering study of bovine casein micelles and sub-micelles. J Mol Biol 160:391–395PubMedGoogle Scholar
  53. Thomsen JK, Jakobsen HJ, Nielsen NC, Petersen TE, Rasmussen LK (1995) Solid state magic angle spinning 31P NMR studies of native casein micelles. Eur J Biochem 230:454–459PubMedGoogle Scholar
  54. van Dijk HJM (1990a) The properties of casein micelles. 1. Formation and degradation of the micellar calcium phosphate. Neth Milk Dairy J 44:111–124Google Scholar
  55. van Dijk HJM (1990b) The properties of casein micelles. 2. The nature of the micellar calcium phosphate. Neth Milk Dairy J 44:65–81Google Scholar
  56. van Dijk HJM (1991) The properties of casein micelles. 4. The effect of the addition of NaCl, MgCl2, or NaOH on the partition of Ca, Mg and PO4 in cows’ milk. Neth Milk Dairy J 45:241–251Google Scholar
  57. van Dijk HJM, Hersevoort A (1992) The properties of casein micelles. 5. The determination of heat-induced calcium phosphate precipitations in milk. Neth Milk Dairy J 46:69–76Google Scholar
  58. van Kemenade MJJM, de Bruyn PL (1989a) The influence of casein on the kinetics of hydroxyapatite precipitation. J Colloid Interface Sci 129:1-14Google Scholar
  59. van Kemenade MJJM, de Bruyn PL (1989b) The influence of casein on the precipitation of brushite and octacalcium phosphate. Colloids Surf 36:359–368CrossRefGoogle Scholar
  60. Wahlgren M, Dejmek P, Drakenberg T (1990) A 43Ca and 31P NMR study of the Ca and phosphate equilibria in heated milk solutions. J Dairy Res 57:355–364Google Scholar
  61. Walstra P (1999) Casein sub-micelles: do they exist? Int Dairy J 9:189–192CrossRefGoogle Scholar
  62. White JCD, Davies DT (1958) The relation between the chemical composition of milk and the stability of the caseinate complex. 1. General introduction, description of samples, methods and chemical composition of samples. J Dairy Res 25:236–255Google Scholar
  63. White JCD, Davies DT (1963) The determination of citric acid in milk and milk sera. J Dairy Res 30:171–189Google Scholar
  64. Yamauchi K, Yoneda Y (1977) Effect of some treatments of milk on the exchangeability of non-diffusible Ca in milk with soluble calcium. Agric Biol Chem 41:2395–2399Google Scholar
  65. Yamauchi K, Yoneda Y, Koga Y, Tsugo T (1969) Exchangeability of non-diffusible Ca in milk with soluble calcium. Agric Biol Chem 33:907–914Google Scholar
  66. Zhang PZ, Aoki T (1996) Behaviour of Ca and phosphate in bovine casein micelles. Int Dairy J 6:769–78CrossRefGoogle Scholar

Copyright information

© EBSA 2004

Authors and Affiliations

  1. 1.Hannah Research InstituteAyrUK

Personalised recommendations