Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-02T19:59:59.090Z Has data issue: false hasContentIssue false
  • English
  • Français

A mathematical model for the description of chymosin action on casein micelles

Published online by Cambridge University Press:  01 June 2009

Uzi Merin ,
Hovav Talpaz  and
Svetlana Fishman
Uzi Merin
Affiliation:
Department of Food Science and Department Of Statistics and Experimental Design Agricultural Research Organization, The Volcani Center, PO Box 6 Bet Dagan 50250, Israel
Hovav Talpaz
Affiliation:
Department Of Statistics and Experimental Design Agricultural Research Organization, The Volcani Center, PO Box 6 Bet Dagan 50250, Israel
Svetlana Fishman
Affiliation:
Department Of Statistics and Experimental Design Agricultural Research Organization, The Volcani Center, PO Box 6 Bet Dagan 50250, Israel
Get access Rights & Permissions [Opens in a new window]

Summary

A mathematical model for chymosin action on casein micelles is presented in a two-stage equation which results in a single curve demonstrating the lag time from enzyme addition to the end of coagulum firming. The model uses the Michaelis–Menten enzyme kinetics equation for the first reaction followed by an nth order reaction for the casein micelles agglomeration stage. The computer output using these equations shows that lag time is elongated as enzyme concentration is lowered. Regression analysis of time of gelation against l/E0 shows good correlation. Viscosity of the milk drops at the beginning of the κ-casein hydrolysis and increases thereafter, when the coagulum is being formed.

Type
Original Articles
Information
Journal of Dairy Research , Volume 56 , Issue 1 , February 1989 , pp. 79 - 86
Copyright
Copyright © Proprietors of Journal of Dairy Research 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bringe, N. A. & Kinsella, J. E. 1986 Use of Platelet Aggregometer to monitor the chymosin-initiated coagulation of casein micelles. Journal of Dairy Research 53 359–370CrossRefGoogle Scholar
Brown, R. J. & Ernstrom, C. A 1984 Use of computers in the cheese industry: modelling milk coagulation. In Engineering and Food, Vol. 2, Processing and Applications (Ed. McKenna, B. M.) London: Elsevier Applied Science.Google Scholar
Carlson, A. 1985 Kinetics of gel forming in enzyme coagulated milk. Biotechnology Progress 1 46–52CrossRefGoogle ScholarPubMed
Carlson, A., Hill, C. G. & Olson, N. F. 1987 a Kinetics of milk coagulation. II. Kinetics of the secondary phase: micelle flocculation. Biotechnology and Bioengineering 29 590–600CrossRefGoogle ScholarPubMed
Carlson, A., Hill, C. G. & Olson, N. F. 1987 b Kinetics of milk coagulation. III. Mathematical modeling of the kinetics of curd formation following enzymatic hydrolysis of κ-casein – parameter estimation. Biotechnology and Bioengineering 29 601–611CrossRefGoogle ScholarPubMed
Carlson, A., Hill, C. G. & Olson, N. F. 1987 c The kinetics of milk coagulation. IV. The kinetics of the gel-firming process. Biotechnology and Bioengineering 29 612–624CrossRefGoogle ScholarPubMed
Dalgleish, D. G. 1979 Proteolysis and aggregation of casein micelles treated with immobilized or soluble chymosin. Journal of Dairy Research 46 653–661CrossRefGoogle Scholar
Dalgleish, D. G. 1980 A mechanism for the chymosin-induced flocculation of casein micelles. Biophysical Chemistry 11 147–155CrossRefGoogle ScholarPubMed
Darling, D. F. & Van Hooydonk, A. C. M. 1981 Derivation of a mathematical model for the mechanism of casein micelle coagulation by rennet. Journal of Dairy Research 48 189–200CrossRefGoogle Scholar
Ernstrom, C. A. 1974 Milk-clotting enzymes and their action. In Fundamentals of Dairy Chemistry, 2nd edn, pp. 662–718, (Eds Webb, B. H., Johnson, A. H. and Alford, J. A..) Westport, CT: Avi Publishing Co.Google Scholar
Gordin, S. & Rosenthal, I. 1978 Efficacy of chicken pepsin as a milk clotting enzyme. Journal of food Protection 41 684–688CrossRefGoogle ScholarPubMed
Guthy, Kl. & Novak, G. 1977 Observations on the primary phase of milk coagulation by rennet under standardized conditions. Journal of Dairy Research 44 363–366CrossRefGoogle Scholar
Johnston, D. E. 1984 Application of polymer cross-linking theory to rennet-induced milk gels. Journal of Dairy Research 51 91–101CrossRefGoogle Scholar
Krongauz, V. A., Fishman, S. N. & Goldburt, E. S. 1978 Quasi-crystals. Growth from photochromic spiropyrans on irradiation in a constant electric field. Journal of Physical Chemistry 82 2469–2474CrossRefGoogle Scholar
Lindqvist, B. 1963 Casein and the action of rennin. Part II. Dairy Science Abstracts 25 299–308.Google Scholar
McMahon, D. J. & Brown, R. J. 1982 Evaluation of Formagraph for comparing rennet solutions. Journal of Dairy Science 65 1639–1642Google Scholar
McMahon, D. J. & Brown, R. J. 1984 Composition, structure, and integrity of casein micelles: a review. Journal of Dairy Science 67 499–512CrossRefGoogle Scholar
McMahon, D. J., Brown, R. J. & Ernstrom, C. A. 1984 Enzymic coagulation of milk casein micelles. Journal of Dairy Science 67 745–748CrossRefGoogle Scholar
Murtagh, B. A. & Saunders, M. A. 1983 MINOS 5·0 User's Guide, TR SOL 83–20, Stanford, CA: Stanford UniversityCrossRefGoogle Scholar
Payens, T. A. J. 1976 On the enzyme-triggered clotting of casein; a preliminary account. Netherlands Milk and Dairy Journal 30 55–59Google Scholar
Payens, T. A. J. 1978 On different modes of casein clotting; the kinetics of enzymatic and non-enzymatic coagulation compared. Netherlands Milk and Dairy Journal 32 170–183Google Scholar
Payens, T. A. J. 1982 Stable and unstable casein micelles. Journal of Dairy Science 65 1863–1873CrossRefGoogle ScholarPubMed
Payens, T. A. J., Wiersma, A. K. & Brinkhuis, J. 1977 On enzymatic clotting processes 1. Kinetics of enzyme-triggered coagulation reactions. Biophysical Chemistry 6 253–261CrossRefGoogle Scholar
Ptitsyn, O. B. & Eizner, Ye. Ye. 1965 Theory of globule to coil transitions in macromolecules. Biophysics 10 3–7Google Scholar
Pyne, G. T. 1955 The chemistry of casein: a review of the literature. Dairy Science Abstracts 17 531–554Google Scholar
Schmidt, D. G. 1982 Association of caseins and casein micelle structure. In Developments in Dairy Chemistry-1. Proteins, pp. 61–86, (Ed. Fox, P. F.) London: Applied Science PublishersGoogle Scholar
Scott Blair, G. W. 1971 A simple model to describe the kinetics of the coagulation of casein (milk) and fibrin (blood). Rheologica Acta 10 316–318Google Scholar
Scott Blair, G. W. & Oosthuizen, J. C. 1961 A viscometric study of the breakdown of casein in milk by rennin and rennet. Journal of Dairy Research 28 165–173CrossRefGoogle Scholar
Talpaz, H., Da Roza, G. D. & Hearn, A. B. 1987 Parameter estimation and calibration of simulation models as a nonlinear optimization problem. Agricultural Systems 23 107–116Google Scholar
Tuszyński, W. B. 1971 A kinetic model of the clotting of casein by rennet. Journal of Dairy Research 38 115–125CrossRefGoogle Scholar
Van Hooydonk, A. C. M., Hagedoorn, H. G. & Boerrigter, I. J. 1986 pH-induced physico-chemical changes of casein micelles in milk and their effect on renneting. I. Effect of acidification on physico-chemical properties. Netherlands Milk and Dairy Journal 40 281–296Google Scholar