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	Image:CBD Koutsoumanis Step Model.png|Koutsoumanis		Image:CBD Koutsoumanis Step Model.png|Koutsoumanis
	Image:CBD Giannuzzi 1998 Model.PNG|Gianuzzi		Image:CBD Giannuzzi 1998 Model.PNG|Gianuzzi

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Revision as of 15:55, 25 October 2007

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Cell by Date: Modelling

Modelling the spoilage of Aerobically Stored Ground Hamburger Meat

Koutsoumanis

Gianuzzi

Previous work has been carried out to model the spoilage of ground beef by living organisms. Above in figure 1 is is a model developed by Koutsoumanis ¹which colesly fit the behaviour of the spoilage organism we are interested in, Pseudomonas, under dynamic temperature conditions. One of the Key conclusions drawn from this model is the almost instantaneous repsone time of the Pseudomonas' growth parameter. The result of this is that our system needs to have a quick respone time to correclty report the temperature history of the beef.

Koutsoumanis' model, and also one Giannuzzi developed ² are both based on the Gompertz model. This model allows some insight into the mechanisms of ground beef spoilage. In particular through manipulation of the Gompertz Parameters and assuming a Arrhenius type relationship between Pseudomonas' growth parameter and temperature we can infer the Activation energy of the spoilage reaction. ³ This is shown in figure 2 in which a stongly linear behaviour allows us to continue with our Arrhenius assumption and extract that Activatoin energy of the spoilge reaction. As given in our specifications the Activation energy for ground meat seem to be around 30kJ/mol. The result of this as per Leak's work is that our system needs to have a similar activation energy. I hope to determine our system activation energy in the same way Giannuzzi determined Pseudomonas'.

Modelling our system :energy-limited constitutive expression by pTET-mut3BGFP

Jaroslaw This second ODE should read d[E]/dt = .... Also, dont forget to include energy-cost of gene transcription - i.e. αi k1 - rate constant for pTET *KE - Half Saturation Coefficient for Energy Hill function *n - Positive Cooperativity Coefficient : here n = 2 *δGFP - Decay constant of mut3BGFP : here δGFP = 0.0005

With some understanding of how Pseuodmonas spoils aerobically stored ground beef it is really important for us to gain some understanding of how our sytem behaves in similar scenarios to the models developed by Koutsoumanis and Giannuzi in order to extract the same parameters. For Isothermal conditions we have been able to devlope some simple models of the gene expression of our sytem with a strong dependance on energy depletion as will feel this is the major limiting factor of our system. As seen above in figures 3 and 4 with energy depletion as our major limiting factor we expect the concentration of our reporter gene to increase to a peak and then as energy runs out expressoin is curbed and decay of our reporter takes over giving an exponential like decay.

M Files used to make the above plots

Plot of time evolution of GFP expression and Energy depletion ODE function for energy-limited constitutive expression by pTET

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References

1. [http://iufost.edpsciences.org/index.php?option=article&access=standard&Itemid=129&url=/articles/iufost/pdf/2006/01/iufost06000765.pdf Koutsoumanis K, Stamatiou A, Skandamis P, Nychas GJ. Development of a Microbial Model for the Combined Effect of Temperature and pH on Spoilage of Ground Meat, and Validation of the Model under Dynamic Temperature Conditions. Appl Environ Microbiol. 2006 Jan;72(1):124-34.]
2. [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T7K-3S3M25D-B&_user=217827&_coverDate=01%2F06%2F1998&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000011279&_version=1&_urlVersion=0&_userid=217827&md5=80630ba21fbc6869b9f5179d334734da Giannuzzi L, Pinotti A, Zaritzky N. Mathematical modelling of microbial growth in packaged refrigerated beef stored at different temperatures. Int J Food Microbiol. 1998 Jan 6;39(1-2):101-10.]
3. [http://66.102.1.104/scholar?hl=en&lr=&q=cache:thi6BTIW1YMJ:www.vitsab.com/PDF/V507.pdf+TTI+Beef+Activation+Energy Leak, F.W. (2000): Quality changes in Ground beef during distribution and storage, and determination of Time- Temperature-Indicator (TTI) charakteristic of ground beef University of Florida Institute of food and Agricultural Sciences Internet: www.vitsab.com, Stand: April 2003]
4. [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T7K-4CP14B0-2&_user=217827&_coverDate=11%2F15%2F2004&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000011279&_version=1&_urlVersion=0&_userid=217827&md5=cf92d0ca2566b940589f521601b36eca Lopez, 2004 : Critique of Gompertz Model]
   
5. [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T7K-485PCG5-3&_user=217827&_coverDate=11%2F01%2F2003&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000011279&_version=1&_urlVersion=0&_userid=217827&md5=608c478638b6d194576d0f151be2223f Huang, 2003 Simulation of a Similar Problem using Gompertz Model]