http://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&feed=atom&action=historyEdinburgh/DivisionPopper/Modelling - Revision history2024-03-28T13:46:48ZRevision history for this page on the wikiMediaWiki 1.16.5http://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=49096&oldid=prevLuca.Gerosa: /* CTMC (stochastic and discrete) */2007-12-17T17:27:29Z<p><span class="autocomment">CTMC (stochastic and discrete)</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>NB: This approach can be used to model more complex systems (pathways and gene networks for examples). A graphical notation used as human interface to process algebra, the theoretical background, guidelines and case studies of this approach are the Master Dissertation topic of one of the team member ([https://2007.igem.org/User:Luca.Gerosa Luca Gerosa]). [https://static.igem.org/mediawiki/2007/0/0d/DissertationLucaGerosa.pdf The Dissertation PDF can be viewed or downloaded from here].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>NB: This approach can be used to model more complex systems (pathways and gene networks for examples). A graphical notation used as human interface to process algebra, the theoretical background, guidelines and case studies of this approach are the Master Dissertation topic of one of the team member ([https://2007.igem.org/User:Luca.Gerosa Luca Gerosa]). [https://static.igem.org/mediawiki/2007/0/0d/DissertationLucaGerosa.pdf The Dissertation PDF can be viewed or downloaded from here].</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">will be uploaded after graduation (December 2007).</del></div></td><td colspan="2"> </td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=49095&oldid=prevLuca.Gerosa: /* CTMC (stochastic and discrete) */2007-12-17T17:26:54Z<p><span class="autocomment">CTMC (stochastic and discrete)</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>on a longer run that consider more than one division.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>on a longer run that consider more than one division.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>NB: This approach can be used to model more complex systems (pathways and gene networks for examples). A graphical notation used as human interface to process algebra, the theoretical background, guidelines and case studies of this approach are the Master Dissertation topic of one of the team member ([https://2007.igem.org/User:Luca.Gerosa Luca Gerosa]). The <del class="diffchange diffchange-inline">document </del>will be uploaded after graduation (December 2007).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>NB: This approach can be used to model more complex systems (pathways and gene networks for examples). A graphical notation used as human interface to process algebra, the theoretical background, guidelines and case studies of this approach are the Master Dissertation topic of one of the team member ([https://2007.igem.org/User:Luca.Gerosa Luca Gerosa]). <ins class="diffchange diffchange-inline"> [https://static.igem.org/mediawiki/2007/0/0d/DissertationLucaGerosa.pdf </ins>The <ins class="diffchange diffchange-inline">Dissertation PDF can be viewed or downloaded from here].</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>will be uploaded after graduation (December 2007).</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=46381&oldid=prevLuca.Gerosa: /* ODEs (deterministic and continuous) */2007-10-27T00:50:58Z<p><span class="autocomment">ODEs (deterministic and continuous)</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====ODEs (deterministic and continuous)====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====ODEs (deterministic and continuous)====</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We define a set of ordinary differential equations that represents the behaviour of a individual cell during time. First, we define a set of equations for each one of the three phases (''Forward'', ''Flipping'', ''Backward'') and then we construct a unified set of equations by using two support functions. The concentrations in which we are interested are obviously GFP and <del class="diffchange diffchange-inline">RFP </del>concentrations.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We define a set of ordinary differential equations that represents the behaviour of a individual cell during time. First, we define a set of equations for each one of the three phases (''Forward'', ''Flipping'', ''Backward'') and then we construct a unified set of equations by using two support functions. The concentrations in which we are interested are obviously GFP and <ins class="diffchange diffchange-inline">YFP </ins>concentrations.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The biological mechanisms (or processes) we need to represent are: gene expression of proteins and degradation of proteins.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The biological mechanisms (or processes) we need to represent are: gene expression of proteins and degradation of proteins.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We assume gene expression of a protein to be in on or off state and, when in the on state, to be expressed at a constant rate.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We assume gene expression of a protein to be in on or off state and, when in the on state, to be expressed at a constant rate.</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43827&oldid=prevLuca.Gerosa: /* With reporter protein */2007-10-26T19:12:15Z<p><span class="autocomment">With reporter protein</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[PoPS]= (1-(1/(1+e^(-[CLambdaR+SP]))) * PoPSmax</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[PoPS]= (1-(1/(1+e^(-[CLambdaR+SP]))) * PoPSmax</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>d[YFP]/dt = [PoPS] - YFPdeg * [YFP] </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>d[YFP]/dt = [PoPS] - YFPdeg * [YFP] </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|-</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|-</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43679&oldid=prevLuca.Gerosa: /* ODEs (deterministic and continuous) */2007-10-26T18:49:19Z<p><span class="autocomment">ODEs (deterministic and continuous)</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>([https://2006.igem.org/wiki/index.php/ETH_Zurich_2005#Abstract ETH device]) implements a quite complex biological mechanisim in order to count how many peaks the PoPS input signal has. We replicated the PoPS output signal of Division PoPper in a MATLAB format and we passed it as input file for the Counter MATLAB program made by ETH Zurich</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>([https://2006.igem.org/wiki/index.php/ETH_Zurich_2005#Abstract ETH device]) implements a quite complex biological mechanisim in order to count how many peaks the PoPS input signal has. We replicated the PoPS output signal of Division PoPper in a MATLAB format and we passed it as input file for the Counter MATLAB program made by ETH Zurich</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(we made some changes to Zurich code in order to allow full compatibility). In the input file we had to amplify <del class="diffchange diffchange-inline">the size of </del>the PoPS signal.. In modelling this is not a problem. In <del class="diffchange diffchange-inline">realliy </del>this can probably be done by one of the device that will be competing this year (<del class="diffchange diffchange-inline">a </del>amplifier).. We do love compositionality, because solves problems for you before you encounter them! :P.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>(we made some changes to Zurich code in order to allow full compatibility). In the input file we had to amplify <ins class="diffchange diffchange-inline">a bit </ins>the PoPS signal.. In modelling this is not a problem. In <ins class="diffchange diffchange-inline">reality </ins>this can probably be done by one of the device that will be competing this year (<ins class="diffchange diffchange-inline">an </ins>amplifier<ins class="diffchange diffchange-inline">, if we are not wrong</ins>).. We do love compositionality, because solves problems for you before you encounter them! :P.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>What follow is the prediction made by ETH Zurich model code on our PoPS output signal (input for the Counter).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>What follow is the prediction made by ETH Zurich model code on our PoPS output signal (input for the Counter).</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43655&oldid=prevLuca.Gerosa: /* Results */2007-10-26T18:45:34Z<p><span class="autocomment">Results</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Looking at the modelled behaviour of the device composed by the Division PoPper and the Counter is possible to see that compatibility is theoretical possible from a qualitative and quantitative point of view. The PoPS signal generate from the Division PopPer, through biological mechanism implemented into the ETH Counter device, is able to cause the rise of R2 at each first peak (thus counting to one) and to rise of R4 at each second following peak (thus counting to two).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Looking at the modelled behaviour of the device composed by the Division PoPper and the Counter is possible to see that compatibility is theoretical possible from a qualitative and quantitative point of view. The PoPS signal generate from the Division PopPer, through biological mechanism implemented into the ETH Counter device, is able to cause the rise of R2 at each first peak (thus counting to one) and to rise of R4 at each second following peak (thus counting to two)<ins class="diffchange diffchange-inline">. To confirm that the Counter is working on the PoPS signal, it is possible to see how:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">* R1 senses (by going high) the first pulse front</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">* R2 senses (by going high) the descending front</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">* R3 senses (by going high) the next pulse front.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">* R4 senses (by going high) the next descending front and so on</ins>.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43616&oldid=prevLuca.Gerosa: /* Results */2007-10-26T18:35:58Z<p><span class="autocomment">Results</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Looking at the modelled behaviour of the device composed by the Division PoPper and the Counter is possible to see that compatibility is theoretical possible from a qualitative and quantitative point of view. The PoPS signal generate from the Division PopPer, through biological mechanism implemented into the ETH Counter device, is able to cause the rise of R2 at each first peak (thus counting to one) and to rise of R4 at each second peak (thus counting to two).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Looking at the modelled behaviour of the device composed by the Division PoPper and the Counter is possible to see that compatibility is theoretical possible from a qualitative and quantitative point of view. The PoPS signal generate from the Division PopPer, through biological mechanism implemented into the ETH Counter device, is able to cause the rise of R2 at each first peak (thus counting to one) and to rise of R4 at each second <ins class="diffchange diffchange-inline">following </ins>peak (thus counting to two).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43599&oldid=prevLuca.Gerosa: /* Results */2007-10-26T18:33:01Z<p><span class="autocomment">Results</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Looking at the modelled behaviour of the device composed by the Division PoPper and the Counter is possible to see that compatibility is theoretical possible from a qualitative and quantitative point of view. The PoPS signal generate from the Division PopPer, through biological mechanism implemented into the ETH Counter device, is able to cause the rise of R2 at each first peak (thus counting to one) and to rise of R4 at each second peak (thus counting to two).</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43489&oldid=prevLuca.Gerosa: /* ODEs (deterministic and continuous) */2007-10-26T18:23:09Z<p><span class="autocomment">ODEs (deterministic and continuous)</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====ODEs (deterministic and continuous)====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====ODEs (deterministic and continuous)====</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>([https://2006.igem.org/wiki/index.php/ETH_Zurich_2005#Abstract ETH device]) implements a quite complex biological mechanisim in order to count how many peaks the PoPS input signal has. We replicated the PoPS output signal of Division PoPper in a MATLAB format and we passed it as input file for the Counter MATLAB program made by ETH Zurich. In the input file we had to amplify the size of the PoPS signal.. <del class="diffchange diffchange-inline">This </del>can probably be done by one of the device that will be competing this year.. We do love compositionality, because solves problems for you before you encounter them! :P.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>([https://2006.igem.org/wiki/index.php/ETH_Zurich_2005#Abstract ETH device]) implements a quite complex biological mechanisim in order to count how many peaks the PoPS input signal has. We replicated the PoPS output signal of Division PoPper in a MATLAB format and we passed it as input file for the Counter MATLAB program made by ETH Zurich</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">(we made some changes to Zurich code in order to allow full compatibility)</ins>. In the input file we had to amplify the size of the PoPS signal.. <ins class="diffchange diffchange-inline">In modelling this is not a problem. In realliy this </ins>can probably be done by one of the device that will be competing this year <ins class="diffchange diffchange-inline">(a amplifier)</ins>.. We do love compositionality, because solves problems for you before you encounter them! :P.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>What follow is the prediction made by ETH Zurich model code on our PoPS output signal (input for the Counter).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>What follow is the prediction made by ETH Zurich model code on our PoPS output signal (input for the Counter).</div></td></tr>
</table>Luca.Gerosahttp://2007.igem.org/wiki/index.php?title=Edinburgh/DivisionPopper/Modelling&diff=43471&oldid=prevLuca.Gerosa: /* ODEs (deterministic and continuous) */2007-10-26T18:21:19Z<p><span class="autocomment">ODEs (deterministic and continuous)</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 18:21, 26 October 2007</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>What follow is the prediction made by ETH Zurich model code on our PoPS output signal (input for the Counter).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>What follow is the prediction made by ETH Zurich model code on our PoPS output signal (input for the Counter).</div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Image:PoPperAndCounter.jpg]]</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====Results====</div></td></tr>
</table>Luca.Gerosa