Team:LCG-UNAM-Mexico/Parameters

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   </a><img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" />

2. Complex formation and dissociation between AHL and LuxR 2.1. </a>Dimer formation and dissociation between AHL:LuxR complexes 3.1. CI synthesis induced by AHL and LuxR complexes dimer </a>3.2. Constitutive CI synthesis </a>4. Natural degradation of CI                </a>4.1. </a>Dimer formation and dissociation between  CI molecules </a>6. RcnA production 7. Nickel efflux by RcnA </a>8. Natural degradation of RcnA 9. Nickel import by unknown channel NOTE: The average volume of an E. coli cell is 10-15 liters. <img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a> <img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /> </a>Defining the initial state of the system The initial concentrations of the constitutive proteins (AiiA, LuxR, CI -constitutive synthesis- and CI:CI -due to constitutive  synthesis-) were estimated based on the efficiency rate of their  promoters, number of promoters per cell, degradation rate of their  mRNAs, translation efficiency and degradation rate of the proteins. Initial concentrations of AHL:LuxR complex, the dimer of complexes, CI and CI:CI due to complex activation were set to 0, given these  are all due to the action of AHL. Number of copies of both cI and rcnA promoters are 10 based on plasmid copy number. RcnA and Unk were estimated experimentally and set consistent to the observed rate. Concentration of AHL and nickel is determined by us to obtain the desired results. AHL: It’s an arbitrary and adjustable value. Different outcomes can be observed manipulating this initial value</a>. Nickel (total): It’s an arbitrary and adjustable value. Different outcomes can be observed manipulating this initial value</a>. Unk: Both the Unk concentration and its rate constant are unknown. They are arbitrarily defined in such a way that it is consistent with the desired flux.</a> [Unk] = 3,315 molecules ρ and ρCI: Their concentration is defined by the copy number of the plasmids that contain them. [ρ] = 10 molecules [ρcI] = 10 molecules </a>CI and CI:CI: Given the constitutive synthesis</a> and degradation</a> rate of CI, as well as its dimerization constant</a>, CI and CI:CI concentrations are estimated in absence of AHL. [CI] = 138 molecules [CI:CI] = 19 molecules RcnA: Given the synthesis</a> and degradation</a> rate of RcnA, as well as the <a href="#ciciconstitutive">constitutive concentration of CI:CI</a>, RcnA concentration is estimated in absence of AHL. [RcnA] = 33150 molecules AiiA: The constant concentration of AiiA is calculated taking into account the following parameters retrieved from literature: -      pLac average transcription rate12:           0.003 s-1 -      mRNA average degradation rate13:         0.00766 s-1 -      Average translation rate13:                     0.31333 s-1 -      AiiA degration rate:                               0.00012 s-1 The half life of RcnA with LVA tail is approximately 2 minutes14; Andersen JB et al. found that this tail reduces the half life of GFP forty-eight times.9 Therefore the half life of wildtype AiiA can be estimated to 96 minutes. [AiiA] = 10000 molecules LuxR: The constant concentration of LuxR is calculated taking into account the following parameters retrieved from literature: -      pTet average transcription rate12,15:        0.003 s-1 -      mRNA average degradation rate13:         0.00766 s-1 -      LuxR translation rate16:                          0.556 s-1 -      LuxR degration rate16:                           9.627E-5 s-1 [LuxR] = 22000 molecules <a href="#top"><img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a> <img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /> References 1.    Wang LH et al. (2004) Specificity and Enzyme Kinetics of the Quorum-quenching N- Acyl Homoserine Lactone Lactonase (AHL-Lactonase). J Biol Chem 279: 4, 13645-13651. 2.    Hee Kim et al. (2005) The molecular structure and catalytic mechanism of a quorum-quenching N-acyl-L-homoserine lactone hydrolase. Proc Natl Acad Sci USA 102:49, 17606-17611. 3.    Goryachev AB, Toh DJ, Lee T (2006). Systems analysis of a quorum sensing network: Design constraints imposed by the  functional requirements, network topology and kinetic constants. Biosystems 83, 178-187. 4.    Babic AC, Little JW (2007) Cooperative binding by CI repressor is dispensable in a phage  λ  variant. Proc Natl Acad Sci USA 104: 17741-17746. 5.    Ackers GK, Johnson AD, Shea MA (1982). Quantitative model for gene regulation by λ  phage repressor. Proc Natl Acad Sci USA 79: 1129-1133. 6.    Reinitz J, Vaisnys JR (1990) Theoretical and Experimental Analysis of the Phage Lambda Genetic Switch Implies Missing Levels of Co-operativity. J Theor Biol 145: 295-318. 7.    Iadevaia S, Mantzaris NV (2006) Genetic Network Driven Control of PHBV Copolymer Composition. J Biotechnol 122: 99-121. 8.    Elowitz MB &amp; Leibler S (2000). A synthetic oscillatory network of transcriptional regulators. Nature 403 335-338. 9.    Andersen JB et al (1998). New Unstable of Green Fluorescent Protein for Studies of Transient Gene Expression in Bacteria. Appl Environ Microbiol 64,6: 2240-2246. 10.  Kenneth S.  Koblan and Gary K. Ackers (1991) Energetics of Subunit Dimerization in Bacteriophage  λ  cI  Repressor: Linkage to    Protons, Temperature, and KCl. Biochemistry 1991, 30, 7817-7821.

11.  M. Santillán and M. C. Mackey (2004). Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon. Biophys J. 86: 1282-1292 12.  Malan, T. P., A. Kolb, H. Buc, and W. R. McClure (1984). Mechanism of CRP-cAMP activation of lac operon transcription initiation activation of the P1 promoter. J. Mol. Biol. 180:881–909.            13.   Kennell, D., and H. Riezman (1977). Transcription and translation initiation frequencies of the Escherichia coli lac operon. J. Mol. Biol. 114:1–21.            14.   Christopher Batten. Modeling the Lux/AiiA Relaxation Oscillator. Unpublished (<a href="http://www.mit.edu/%7Ecbatten/work/ssbc04/modeling-ssbc04.pdf">http://www.mit.edu/~cbatten/work/ssbc04/modeling-ssbc04.pdf</a>). 15.  Bologna Cesena Campus, iGEM 2007 WIKI. ( <a href="http://2007.igem.org/Bologna">http://2007.igem.org/Bologna</a> ) 16.  KULeuven team, iGEM 2008 WIKI. Dr. Coli, the bacterial drug delivery system. (<a href="http://2008.igem.org/Team:KULeuven/Model/CellDeath" target="_blank">http://2008.igem.org/Team:KULeuven/Model/CellDeath</a>) </a><a href="#top"><img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" width="190" height="31" border="0"></a><a href="http://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling"><img src="http://2008.igem.org/wiki/images/5/5b/Model1a.jpg" alt="Modeling the system" width="190" height="31" border="0"></a><a href="http://2008.igem.org/Team:LCG-UNAM-Mexico/Simulation"><img src="http://2008.igem.org/wiki/images/7/7f/Model3.jpg" alt="Simulation&amp;Analysis" width="190" height="31" border="0"></a> <img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" />