Team:LCG-UNAM-Mexico/Modeling

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

<img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /> </a>Reactions You can click on the next image to see a table of our reactions with their kinetics. <img src="http://2008.igem.org/wiki/images/1/12/Bichem_react_table.PNG" alt="Table of biochemical reactions" width="581" height="279" border="0"></a> * The equations are numbered like this because those we had initially defined evolved into this final list throughout the  summer. We didn't want to change all references made to these equations so we just adjusted the numbering. <img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a> <img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /> </a>Ordinary Differential Equations We are taking into account the following set of ODEs, based on the biochemical reactions above. This set accurately and completely describes our model. Please click on the image to see a higher resolution. <img src="http://2008.igem.org/wiki/images/6/63/Equationa.PNG" alt="Set of ODEs" border="0"></a> <img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a> <img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /> </a>Assumptions of the model <ol> <li> Once there is nickel in the medium, RcnR no longer participates in the pump’s regulation. If there’s nickel in the medium, we can assume that RcnR is always coupled with a Ni molecule, so it will not be capable of repressing  RcnA (The few RcnR molecules in the cell will cause noise, but this  will be indistinguishable from the pump’s normal behavior).1 </li> <li> Cell membrane permeability to AHL is not considered inside the model. The model assumes all AHL enters the cell, however the concentration needed in the model to obtain the desired results is changed by us  accordingly. 2                </li> <li> All decrease in AHL concentration is due to AiiA. We consider the natural degradation of AHL to be unimportant given the time taken to make the analysis (AHL half-life is long, from 3 to 24  hours). 3                </li> <li> The change in the transcription of cI* is dependent only on AHL concentration. There’s a basal production of cI*, however the change will always be due to the AHL concentration given that production of LuxR is  constitutive. </li> <li> It is a homogeneous system. This means that the coefficients of the equations are constant (so we don’t have compartmentalization). </li> <li> The quantity of nickel used by the cell is negligible compared to the concentrations in and out of the cell. This means we don’t need to include an equation describing the change in the Ni concentration due to cell consumption in the time used by the  experiment.1 </li> <li> The production of RcnR, LuxR and AiiA is constitutive and their  concentrations have reached the steady state at the beginning of the  experiment. </li> <li> NikABCDE will not play a role in our model. NikABCDE serves to import nickel to the cell, however it only works in anaerobic conditions and our experiment will be made in aerobic  conditions. This therefore implies that the nickel import will only take place by the unknown mechanism, which nonetheless is constant and  constitutive.1 </li> </ol> <img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a> <img src="http://2008.igem.org/wiki/images/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /> References 1.      Iwig JS, Rowe JL and Chivers PT (2006) Nickel homeostasis in Escherichia coli – the rcnR-rcnA efflux pathway and its linkage to NikR function  Mol Microbiol 62 (1), 252–262. 2.     Tian T and Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch Proc Natl Acad Sci 103 (22):8372-8377. 3.    Imperial College Team, iGEM 2006 WIKI. The I. CoLi Reporter (http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207</a>) </a><img src="http://2008.igem.org/wiki/images/c/cd/Boton_back.jpg" alt="Back to top" border="0"></a><img src="http://2008.igem.org/wiki/images/f/fd/Model2ae.jpg" alt="Parameters&amp;Kinetics" width="190" height="31" border="0"></a><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" /> <td valign="top" class="bodyText">