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| <h1 style="color: #ebebeb">Modeling</h1> | | <h1 style="color: #ebebeb">Modeling</h1> |
- | <p style="color: #ebebeb"></p> | + | <p style="color: #ebebeb">Click <a href="https://static.igem.org/mediawiki/2014/3/3d/Modeling-Everything_Ever.pdf" target="_blank" style="color:white;"><u>here</u></a> for full modeling file</p> |
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| <ul class="sub1"> | | <ul class="sub1"> |
| <li id="child1"><a href="https://igem.org/2014_Judging_Form?id=1343" target="_blank">Judging Form</a></li> | | <li id="child1"><a href="https://igem.org/2014_Judging_Form?id=1343" target="_blank">Judging Form</a></li> |
- | <li id="child1"><a href="https://2014.igem.org/Team:Technion-Israel/Judging#results">Results</a></li>
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| <li id="child1"><a href="https://2014.igem.org/Team:Technion-Israel/Judging#biobrick">BioBricks</a></li> | | <li id="child1"><a href="https://2014.igem.org/Team:Technion-Israel/Judging#biobrick">BioBricks</a></li> |
- | <li id="child1"><a href="https://2014.igem.org/Team:Technion-Israel/Judging#criteria">Judging Criteria</a></li> | + | <li id="child1"><a href="https://2014.igem.org/Team:Technion-Israel/Judging#results">Results</a></li> |
| </ul> | | </ul> |
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- | <p style="font-size: 1.1em;">It is clear from the goals of our system, that we want to have some sort of bi-stability in the result, when the term Gate I is small (see [2]). The answer to whether this condition is met, would obviously depend on the constants of the system for which we could not find a reliable source, but using a simple geometric analysis of the phase space (see [3]), we were able to produce a graph showing for which values of (v_A,v_B) we could configure the system (by changing the IPTG concentration and the OD) to show bi-stability:</p> | + | <p style="font-size: 1.1em;">It is clear from the goals of our system, that we want to have some sort of bi-stability in the result, when the term Gate I is small (see [2]). The answer to whether this condition is met, would obviously depend on the constants of the system for which we could not find a reliable source, but using a simple geometric analysis of the phase space (see [3]), we were able to produce a graph showing for which values of (v<sub>1</sub>,v<sub>2</sub>) we could configure the system (by changing the IPTG concentration and the OD) to show bi-stability:</p> |
| <p style="font-size: 1.1em;"> | | <p style="font-size: 1.1em;"> |
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| <h1 style="font-size: 2em;">Why Alpha System Should Fail – a stochastic model of alpha system</h1> | | <h1 style="font-size: 2em;">Why Alpha System Should Fail – a stochastic model of alpha system</h1> |
| <p>The above model assumes a low-noise system (as do all rate equation models), but especially when constructing a bi-stable network, it is important to consider the noise. To do this we need to create a stochastic model, which in our case, we based upon the commonly used Fokker Planck equation. Using the derivation found in [4] (Van Kampen "Stochastic Processes in Physics and Chemistry", Third Edition), we produced the Fokker Planck variant of the equation for the AHL concentration shown above</p> | | <p>The above model assumes a low-noise system (as do all rate equation models), but especially when constructing a bi-stable network, it is important to consider the noise. To do this we need to create a stochastic model, which in our case, we based upon the commonly used Fokker Planck equation. Using the derivation found in [4] (Van Kampen "Stochastic Processes in Physics and Chemistry", Third Edition), we produced the Fokker Planck variant of the equation for the AHL concentration shown above</p> |
- | <p>After analyzing this equation as explained in [5], we produced the following results (using a point on the (v_A,v_B) plane which the previous analysis showed would be bi-stable)</p> | + | <p>After analyzing this equation as explained in [5], we produced the following results (using a point on the (v<sub>1</sub>,v<sub>2</sub>) plane which the previous analysis showed would be bi-stable)</p> |
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- | <p style="color:#919499">We thought these changes would improve the bi-stability of the system (thereby reducing the odds of a false positive), because they enhance the non-linearity inherent in the system which has been shown to play a vital role in the bi-stability of the system ([9],[10]). When producing a similar analysis for the phase plane of this gate as we did for the phase plane of the original equation (see [7]), we found the values of (v_A,v_B) for which the system is bi-stable, and compared this analysis to the results of the analysis of the original analysis.</p> | + | <p style="color:#919499">We thought these changes would improve the bi-stability of the system (thereby reducing the odds of a false positive), because they enhance the non-linearity inherent in the system which has been shown to play a vital role in the bi-stability of the system ([9],[10]). When producing a similar analysis for the phase plane of this gate as we did for the phase plane of the original equation (see [7]), we found the values of (v<sub>1</sub>,v<sub>2</sub>) for which the system is bi-stable, and compared this analysis to the results of the analysis of the original analysis.</p> |
| <p style="color:#919499"> | | <p style="color:#919499"> |
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