Team:Stockholm/Modelling/Final eq

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=== Which model? ===
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=== A new gene and protein? ===
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Here we will introduce the model proposed by [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002] a brief introduction to their model, then we will try to simplify it, declare some of our assumptions, apply our assumptions and continue with our gene expression model in bacteria as final stage.
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After having the gene expressed in ''E. Coli'' the model that we came up with after studying extensively the articles [1]-[7] is as eq. 1 and eq. 2; where eq. 1 represents the dynamics for mRNA and eq. 2 represents the dynamics of protein translated from mRNA. These two equations are not complete though.
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=== Yildirim N et al model ===
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[[image:SU_final_equation.png|580px]]
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In a series of 5 equations, They proposed dynamics for mRNA production, <VAR>&beta;</VAR>-galactosidase production, Allolactose, Lactose for Lac operon. In their model they also considered transcriptional and translational delays (ie. <VAR>&beta;</VAR>-galactosidase and <VAR>&beta;</VAR>-galactoside permease production from mRNA is not instant and takes time).
 
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<img src="https://static.igem.org/mediawiki/2010/f/f8/SU_yildirim_equations.png" alt="http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002" />
 
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Here, eq. (2) is the dynamics for mRNA, eq. (3) is dynamics for <VAR>&beta;</VAR>-galactosidase, eq. 4 is dynamics of allolactose, eq. (5) is dynamics of Lactose, and finally eq. (6) is the equation for premease. For more detailed explanation for the terms look in: [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002].
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In these equations there are variables that need to be defined and values found. The description to how to find the values are as below:
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Until this point we have the same assumption as [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002].
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=== Simplified model ===
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*<VAR>&Gamma;<sub>0</sub></VAR>: This spontaneous rate of mRNA production through translation. This variable can be *:calculated from Bremer H. et al. 1996 (mRNA elongation rate). In this case this means that sometimes ''lacI'' *:unbinds and lets the RNAP to bind and start translation. However RNAP binding strength needed to be discussed, which *:we will talk more about on discussion
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*<VAR>&gamma;<sub>M<sub>P</sub></sub></VAR> and <VAR>&alpha;<sub>M<sub>P</sub></sub></VAR>: for this case our approach is same as Yildirim et. al. 2003. We solve a system of equations for A = 0 and A <VAR>&rarr;&infin;</VAR>, in which when A = 0  we have no induction, and A <VAR>&rarr;&infin;</VAR> means high induction. At A <VAR>&rarr;&infin;</VAR>, we can assume that ,depending on the bacteria growth factor, mRNA production is increased at least 500folds (This is very dependent on the number of plasmids inside bacteria, environment and growth factor). So from these information one can calculate <VAR>&gamma;<sub>M<sub>P</sub></sub></VAR> and <VAR>&alpha;<sub>M<sub>P</sub></sub></VAR>.
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*<VAR>&gamma;<sub>P</sub></VAR> and <VAR>&alpha;<sub>P</sub></VAR>: Unfortunately we couldn't find a reliable source for making scientific guess about degradation and production rate. However, one can from put forward reasonable values for these variables based on number of active ribosomes, growth factor, environment and translation elongation rate. These can be found in Bremer H. et al 1996.
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So as a final model, we propose equations 1 and 2, and equations 7.1 to 7.4e from "Proposing the model" section as the toy model for protein production prediction for our genes.
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This model can be simplified. Ahmadzadeh et al. 2005 proposed a simplified model of [http://www.ncbi.nlm.nih.gov/pubmed/12719218 Yildirim N et al 2002], where they ignored time delays for transcription and translation. For more simplification they also assumed that β-galactosidase and β-galactoside permease reach their steady state values instantly, ending up with 3 equations just for mRNA, Lactose and Allolactose dynamics. Full description of the assumptions behind this simplification can be found at Ahmadzadeh et al. 2005 .
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<img src="https://static.igem.org/mediawiki/2010/6/60/Su_team_simplified_equation_sets.png" alt="eq. 3.1: mRNA dynamics eq." />
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{{Stockholm/Footer}}
{{Stockholm/Footer}}

Latest revision as of 19:42, 27 October 2010

Home Project Idea Lab Work Results Modelling Team       Follow us on and        2010.igem.org

↳   Introduction Suitable Model Proposing the Models Final Model Discussion


SU modelling Icon.gif  

A new gene and protein?

After having the gene expressed in E. Coli the model that we came up with after studying extensively the articles [1]-[7] is as eq. 1 and eq. 2; where eq. 1 represents the dynamics for mRNA and eq. 2 represents the dynamics of protein translated from mRNA. These two equations are not complete though.

SU final equation.png


In these equations there are variables that need to be defined and values found. The description to how to find the values are as below:

  • Γ0: This spontaneous rate of mRNA production through translation. This variable can be *:calculated from Bremer H. et al. 1996 (mRNA elongation rate). In this case this means that sometimes lacI *:unbinds and lets the RNAP to bind and start translation. However RNAP binding strength needed to be discussed, which *:we will talk more about on discussion
  • γMP and αMP: for this case our approach is same as Yildirim et. al. 2003. We solve a system of equations for A = 0 and A →∞, in which when A = 0 we have no induction, and A →∞ means high induction. At A →∞, we can assume that ,depending on the bacteria growth factor, mRNA production is increased at least 500folds (This is very dependent on the number of plasmids inside bacteria, environment and growth factor). So from these information one can calculate γMP and αMP.
  • γP and αP: Unfortunately we couldn't find a reliable source for making scientific guess about degradation and production rate. However, one can from put forward reasonable values for these variables based on number of active ribosomes, growth factor, environment and translation elongation rate. These can be found in Bremer H. et al 1996.

So as a final model, we propose equations 1 and 2, and equations 7.1 to 7.4e from "Proposing the model" section as the toy model for protein production prediction for our genes.





The Faculty of Science at Stockholm University Swedish Vitiligo association (Svenska Vitiligoförbundet) Geneious Fermentas/ Sigma-Aldrich/

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