Imperial/Cell by Date/Modelling

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==Modelling the spoilage of  Aerobically Stored Ground Hamburger Meat==
==Modelling the spoilage of  Aerobically Stored Ground Hamburger Meat==
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[[Image:CBD Koutsoumanis Step Model.png|Koutsoumanis Step Model 5 to 20 C]]
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[[Image:CBDKoutsoumanisModel.jpg]]
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[[Image:CBD Giannuzzi 1998 Model.PNG|Giannuzzi Arrhenius Plot]] <br clear = "all" >
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Previous work has been carried out to model the spoilage of ground beef by living organisms. 
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Above in figure 1 is is a model developed by Koutsoumanis <sup>[[#References|1]]</sup>which 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.
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Koutsoumanis' model, and also one Giannuzzi developed <sup>[[#References|2]]</sup> 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. <sup>[[#References|3]]</sup> 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'.
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A substantial body of work already exists on the topic of spoilage of ground beef by living organisms. The above figure shows the results of a model developed by Koutsoumanis (1) to simulate the spoilage under dynamic temperature conditions of meat by Pseudomonas, - an organism responsible for spoiling refrigerated packaged beef.<br><br> 
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An important property was the almost instantaneous response time of the Pseudomonas' growth parameter.  To report accurately our system should therefore also share this property.<br><br>
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Koutsoumanis' model, along with Giannuzzi ‘s (2) are both based on the larger class of Gompertz model. A remarkable feature of such models is that 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)(See figure below).<br><br>
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==Modelling our system :energy-limited constitutive expression by pTET-mut3BGFP==
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[[Image:CBDModellingGianuzziAndEquations.png]]<br clear = "all">
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[[Image:CBDFPconcmodel.jpg|400px]][[Image:CBDEnergyDepletionModel.jpg|400px]]<br clear ="all">
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Above we can see an arrhenius plot (the log version of the arrhenius equation) of the certain interesting combinations of the parameters in the modifired Gompertz equation such as the Lag Phase Duration (LPD). Doing such a plot allows us to calculate the activation energy of the spoilage reaction.
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As given in our specifications the Activation energy for ground meat seem to be around 30kJ/mol. Again to report accurately our system needs to have a similar activation energy.<br><br><br clear = "all">
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{|
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==Modelling our system: Energy-limited constitutive expression by pTET-mut3BGFP==
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[[Image:CBDFPconcmodel.jpg|thumb|left|420px]][[Image:CBDEnergyDepletionModel.jpg|thumb|right|420px]]<br clear="all">
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[[Image: CBDModel.png|thumb|left|382px|Energy-dependent model for CBD]]
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{|align right class="wikitable" border="1" cellspacing="0" cellpadding="2" style="text-align:right; margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
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! Parameter                   
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! Description
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|-
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| [[Image:CBDmodelling-1.png]]<br>
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| k<sub>1</sub>
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[[Image:CBDmodelling-2.png]] <br>
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| Maximal constitutive transcription by pTET
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[[User: Jjk105| Jaroslaw]] <font color=red>This second ODE should read d[E]/dt = ....</font>
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|-
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*k<sub>1</sub> - rate constant for pTET <br>*K<sub>E</sub> - Half Saturation Coefficient for Energy Hill function <br>*n - Positive Cooperativity Coefficient : here n = 2 <br>*&delta;<sub>GFP</sub> - Decay constant of mut3BGFP : here &delta;<sub>GFP</sub> = 0.0005<br>
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|K<sub>E</sub>
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|Half-Saturation Coefficient for Energy Hill function  
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|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.<br><br>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.
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|-
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|n
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|Positive Cooperativity Coefficient (Hill-coefficient)
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|-
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|&delta;<sub>GFP</sub>
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|Decay constant of mut3BGFP  
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==M Files used to make the above plots==
 
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'''here''' ''&delta;<sub>GFP</sub> = 0.0005<br>''
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<br clear ="all">
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In order to use the previous results on how Pseuodmonas spoils aerobically stored ground beef  we need to understand how our sytem behaves in similar scenarios to the models developed by Koutsoumanis and Giannuzi.<br><br>
 +
 +
For isothermal conditions we have been able to develop a simple model of the gene expression in a cell free extract (see chassis characterisation [[Imperial/Cell-Free/Whatis|Cell Free Systems]]) .
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An important feature of the model was the introduction of a resource dependent term that curbs the synthesis if the system is depleted. <br><br>
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The m-files used in the following simulations can be accessed on our [[Imperial/Dry_Lab/Software#Download CBD Simulations| Software]] page.
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[[Image:CBD Energy General.m |Plot of time evolution of GFP expression and Energy depletion]]
 
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[[Image:CBD Energy ode.m |ODE function for energy-limited constitutive expression by pTET]]
 
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<br>
 
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==Navigation==
 
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==References==
==References==
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# [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.]
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# [http://aem.asm.org/cgi/content/abstract/72/1/124 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.]
# [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.]
# [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.]
# [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]
# [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]
#[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]<br>
#[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]<br>
#[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]<br>
#[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]<br>

Latest revision as of 03:28, 27 October 2007



Cell by Date: Modelling

Modelling the spoilage of Aerobically Stored Ground Hamburger Meat

CBDKoutsoumanisModel.jpg


A substantial body of work already exists on the topic of spoilage of ground beef by living organisms. The above figure shows the results of a model developed by Koutsoumanis (1) to simulate the spoilage under dynamic temperature conditions of meat by Pseudomonas, - an organism responsible for spoiling refrigerated packaged beef.

An important property was the almost instantaneous response time of the Pseudomonas' growth parameter. To report accurately our system should therefore also share this property.

Koutsoumanis' model, along with Giannuzzi ‘s (2) are both based on the larger class of Gompertz model. A remarkable feature of such models is that 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)(See figure below).

CBDModellingGianuzziAndEquations.png

Above we can see an arrhenius plot (the log version of the arrhenius equation) of the certain interesting combinations of the parameters in the modifired Gompertz equation such as the Lag Phase Duration (LPD). Doing such a plot allows us to calculate the activation energy of the spoilage reaction.

As given in our specifications the Activation energy for ground meat seem to be around 30kJ/mol. Again to report accurately our system needs to have a similar activation energy.



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

CBDFPconcmodel.jpg
CBDEnergyDepletionModel.jpg


Energy-dependent model for CBD
Parameter Description
k1 Maximal constitutive transcription by pTET
KE Half-Saturation Coefficient for Energy Hill function
n Positive Cooperativity Coefficient (Hill-coefficient)
δGFP Decay constant of mut3BGFP


here δGFP = 0.0005

In order to use the previous results on how Pseuodmonas spoils aerobically stored ground beef we need to understand how our sytem behaves in similar scenarios to the models developed by Koutsoumanis and Giannuzi.

For isothermal conditions we have been able to develop a simple model of the gene expression in a cell free extract (see chassis characterisation Cell Free Systems) . An important feature of the model was the introduction of a resource dependent term that curbs the synthesis if the system is depleted.


The m-files used in the following simulations can be accessed on our Software page.



<< Design | Modelling | Implementation >>

References

  1. [http://aem.asm.org/cgi/content/abstract/72/1/124 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]
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