The mathematical modelling of cheese ripening

Abstract

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening. References

• D. Dawson and J. Feagan, Bacteriology of cheddar cheese: A study of starter organisms in manufacture and maturing. J. Dairy Res. 24, 210–224, 1957.
• M.A. Drake, R.E. Miracle and D.J. McMahon, Impact of fat reduction on flavor and flavor chemistry of Cheddar cheeses. Journal of Dairy Science 93, 5069–5081, 2010.
• M. Fenelon and T. Guinee, Primary proteolysis and textural changes during ripening in cheddar cheeses manufactured to different fat contents. Int. Dairy J. 10, 151–158, 2000.
• R. Hutkins and N. Nannen, pH homeostasis in lactic acid bacteria. J. Dairy Sci. 76, 2354–2365, 1992.
• M. Johnson, Cheese pH–-what's behind the rise and fall? Technical Report 14, Wisconsin Center for Dairy Research, December 2002.
• J.K. Kim, K. Starzak, G.W. Preckshot, R. Marshall and R.K. Bajpai, Critical reactions in ripening of cheeses–-a kinetic analysis. Appl. Biochem. Biotech. 45, 51–68, 1994.
• B.A. Law and A.S. Wigmore, Microbial proteinases as agents for accelerated cheese ripening. Int. J. Dairy Tech. 35, 75–76, 2007.
• R. Lawrence, L. Creamer, and J. Gilles, Texture development during cheese ripening. J. Dairy Sci. 70, 1748–1760, 1987.
• R. Marsili, Monitoring chemical changes in cheddar cheese during aging by high performance liquid chromatography and gas chromatography techniques. Journal of Dairy Science 68, 3155–3161, 1985.
• K. Presser, D. Ratkowsky, and T. Ross, Modelling the growth rate of Escherichia coli as a function of pH and lactic acid concentration. Appl. Environ. Microbiol. 63, 2355–2360, 1997.
• S. Rehman, D. Waldron, and P. Fox, Effect of modifying lactose concentration in cheese curd on proteolysis and in quality of Cheddar cheese. Int. Dairy J. 14, 591–597, 2004.
• T. Singh, M. Drake, and K. Cadwallader, Flavour of cheddar cheese: A chemical and sensory perspective. Compr. Rev. Food Sci. F. 2, 166–189, 2003.
• S. Toelstede and T. Hofmann, Kokumi-active glutamyl peptides in cheeses and their biogeneration by Penicillium roquefortii. Agric. Food Chem. 13, 3738–3748, 2009.