Team:CIDEB-UANL Mexico/Math-Graphics

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<p align="justify">The saturation values for mRNAs and proteins were calculated analytically; but since there are several variables, it becomes complicated to integrate by analytical methods, so we use methods of numerical integration in a computer program by called Simulink. The values of the parameters (rate of transcription, translation, degradation and dissociation) are the ones we have found so far, but we continue researching in order to improve and expand our model.</p></td></tr></table>

<p align="justify">The saturation values for mRNAs and proteins were calculated analytically; but since there are several variables, it becomes complicated to integrate by analytical methods, so we use methods of numerical integration in a computer program by called Simulink. The values of the parameters (rate of transcription, translation, degradation and dissociation) are the ones we have found so far, but we continue researching in order to improve and expand our model.</p></td></tr></table>

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<br>The graphs below shows the change in concentration with respect to time of all the proteins of our circuit in a cI inactive-active state. This simulations are showing our model in a temperature below 32ºC the first 200 minutes making the variables of cI protein production in their minimum value for this initial time, creating the possibility of Vip3Ca3 and GFP proteins to be processed in the bacteria at maximum capacity (maximum capacities shown in the parameter table). Past the half hour the temperature is higher of our ideal parameters of cI production (above 32ºC) allowing the transcription and translation of cI protein in a factor of 1 (represented in the equation number 5 showed above) this is the rise in the blue graph at the time 200 minutes, inhibiting the formation of the other two system parts: Vip3Ca3 and GFP proteins, simulated as the decrease of the purple and green graphics. Whose percents in the <i>E.Coli</i> bacterium drops to the minimum until the cI production stops again and the process restarts.</p></td>

<br>The graphs below shows the change in concentration with respect to time of all the proteins of our circuit in a cI inactive-active state. This simulations are showing our model in a temperature below 32ºC the first 200 minutes making the variables of cI protein production in their minimum value for this initial time, creating the possibility of Vip3Ca3 and GFP proteins to be processed in the bacteria at maximum capacity (maximum capacities shown in the parameter table). Past the half hour the temperature is higher of our ideal parameters of cI production (above 32ºC) allowing the transcription and translation of cI protein in a factor of 1 (represented in the equation number 5 showed above) this is the rise in the blue graph at the time 200 minutes, inhibiting the formation of the other two system parts: Vip3Ca3 and GFP proteins, simulated as the decrease of the purple and green graphics. Whose percents in the <i>E.Coli</i> bacterium drops to the minimum until the cI production stops again and the process restarts.</p></td>

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<td style="paddinng:12px;"><img src="https://static.igem.org/mediawiki/2013hs/0/05/Graphic_cI_on_off.png" height="300" width="400"></td>

<td style="paddinng:12px;"><img src="https://static.igem.org/mediawiki/2013hs/0/05/Graphic_cI_on_off.png" height="300" width="400"></td>

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The graphics that are shown represent the change of the concentration of each part in relation to time of all proteins in our cicuit, including all the parameters that we presented and the equation 5 (fRBS), where we represent the repression and activation of the riborswitch making the value of its function 0 or 1. The first graph simulation is showing our model in a temperature between 32 to 37ºC in the first 200 minutes. As you can see, in the graph of cI (c0051), it is active and produced constantly, repressing the Vip3Ca3 and GFP proteins, but when the temperature changes below than the 32 to 37ºC the cI it is now turning off allowing the transcription and translation of Vip3Ca3 and GFP so changes the graphic, but We can appreciate the GFP  is producing more than the Vip3Ca3, this because of the bigger base pair size of Vip3Ca3 than GFP that make it longer to be synthesis by the ribosome. This bp length of those proteins are 2412 and 876 respectively.</p>

The graphics that are shown represent the change of the concentration of each part in relation to time of all proteins in our cicuit, including all the parameters that we presented and the equation 5 (fRBS), where we represent the repression and activation of the riborswitch making the value of its function 0 or 1. The first graph simulation is showing our model in a temperature between 32 to 37ºC in the first 200 minutes. As you can see, in the graph of cI (c0051), it is active and produced constantly, repressing the Vip3Ca3 and GFP proteins, but when the temperature changes below than the 32 to 37ºC the cI it is now turning off allowing the transcription and translation of Vip3Ca3 and GFP so changes the graphic, but We can appreciate the GFP  is producing more than the Vip3Ca3, this because of the bigger base pair size of Vip3Ca3 than GFP that make it longer to be synthesis by the ribosome. This bp length of those proteins are 2412 and 876 respectively.</p>