Team:Slovenia/ModelingDerivation

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<a style="position:absolute; top:0px; left:490px;" href="https://2012.igem.org/Main_Page"><b>iGEM 2012</b></a>
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<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchDesignedTALregulators'><span>Designed TAL regulators</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchDesignedTALregulators'><span>Designed TAL regulators</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchMutualRepressorSwitch'><span>Mutual repressor switch</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchMutualRepressorSwitch'><span>Mutual repressor switch</span></a></li>  
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<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchPositiveFeedbackLoopSwitch'><span>Positive feedback loop switch</span></a></li>  
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<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchPositiveFeedbackLoopSwitch'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/TheSwitchPositiveFeedbackLoopSwitch';" class="newtable"><tr class="newtable"><td class="newtable"><span>Positive feedback loop switch</span></td><td class="newtable"><img style="margin-right:-15px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>
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    <li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchControls'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/TheSwitchControls';" class="newtable"><tr class="newtable"><td class="newtable"><span>Controls</span></td><td class="newtable"><img style="margin-right:-81px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>  
  </ul>
  </ul>
</li>
</li>
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<li><a href='https://2012.igem.org/Team:Slovenia/SafetyMechanismsEscapeTag'><span>Escape tag</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/SafetyMechanismsEscapeTag'><span>Escape tag</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/SafetyMechanismsTermination'><span>Termination</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/SafetyMechanismsTermination'><span>Termination</span></a></li>  
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<li><a href='https://2012.igem.org/Team:Slovenia/SafetyMechanismsMicrocapsuleDegradation'><span>Microcapsule degradation</span></a></li>  
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    <li><a href="https://2012.igem.org/Team:Slovenia/SafetyMechanismsMicrocapsuleDegradation"><table  onclick="window.location = 'https://2012.igem.org/Team:Slovenia/SafetyMechanismsMicrocapsuleDegradation';" class="newtable"><tr class="newtable"><td class="newtable"><span>Microcapsule degradation</span></td><td class="newtable"><img style="margin-right:-15px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>  
  </ul>
  </ul>
</li>
</li>
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<li><a href='https://2012.igem.org/Team:Slovenia/ImplementationHepatitisC'><span>Hepatitis C</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ImplementationHepatitisC'><span>Hepatitis C</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ImplementationIschaemicHeartDisease'><span>Ischaemic heart disease</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/ImplementationIschaemicHeartDisease'><span>Ischaemic heart disease</span></a></li>  
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    <li><a href='https://2012.igem.org/Team:Slovenia/ImplementationImpact'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/ImplementationImpact';" class="newtable"><tr class="newtable"><td class="newtable"><span>Impact</span></td><td class="newtable"><img style="margin-right:-86px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>
 
 
  </ul>
  </ul>
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  <ul>
  <ul>
<li><a href='https://2012.igem.org/Team:Slovenia/Modeling'><span>Overview</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/Modeling'><span>Overview</span></a></li>
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<li><a href='https://2012.igem.org/Team:Slovenia/ModelingPK'><span>Pharmacokinetics</span></a></li>
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    <li><a href='https://2012.igem.org/Team:Slovenia/ModelingPK'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/ModelingPK';" class="newtable"><tr class="newtable"><td class="newtable"><span>Pharmacokinetics</span></td><td class="newtable"><img style="margin-right:-15px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingMethods'><span>Modeling methods</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingMethods'><span>Modeling methods</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingMutualRepressorSwitch'><span>Mutual repressor switch</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingMutualRepressorSwitch'><span>Mutual repressor switch</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingPositiveFeedbackLoopSwitch'><span>Positive feedback loop switch</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingPositiveFeedbackLoopSwitch'><span>Positive feedback loop switch</span></a></li>
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<li><a href='https://2012.igem.org/Team:Slovenia/ModelingQuantitativeModel'><span>Quantitative and stability model</span></a></li>  
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<li><a href='https://2012.igem.org/Team:Slovenia/ModelingQuantitativeModel'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/ModelingQuantitativeModel';" class="newtable"><tr class="newtable"><td class="newtable"><span>Experimental model</span></td><td class="newtable"><img style="margin-right:-15px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>  
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<li><a href='https://2012.igem.org/Team:Slovenia/ModelingInteractiveSimulations'><span>Interactive simulations</span></a></li>
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    <li><a href='https://2012.igem.org/Team:Slovenia/ModelingInteractiveSimulations'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/ModelingInteractiveSimulations';" class="newtable"><tr class="newtable"><td class="newtable"><span>Interactive simulations</span></td><td class="newtable"><img style="margin-right:-15px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>
  </ul>
  </ul>
</li>
</li>
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  <ul>
  <ul>
<li><a href='https://2012.igem.org/Team:Slovenia/Notebook'><span>Experimental methods</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/Notebook'><span>Experimental methods</span></a></li>
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<li><a href='https://2012.igem.org/Team:Slovenia/NotebookLablog'><span>Lablog</span></a></li>
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    <li><a href='https://2012.igem.org/Team:Slovenia/NotebookLablog'><table onclick="window.location = 'https://2012.igem.org/Team:Slovenia/NotebookLablog';" class="newtable"><tr class="newtable"><td class="newtable"><span>Lablog</span></td><td class="newtable"><img style="margin-right:-90px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/NotebookLabSafety'><span>Lab safety</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/NotebookLabSafety'><span>Lab safety</span></a></li>  
  </ul>
  </ul>
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<li><a href='https://2012.igem.org/Team:Slovenia/Team'><span>Team members</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/Team'><span>Team members</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/TeamAttributions'><span>Attributions</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/TeamAttributions'><span>Attributions</span></a></li>
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<li><a href='https://2012.igem.org/Team:Slovenia/TeamCollaborations'><table  onclick="window.location = 'https://2012.igem.org/Team:Slovenia/TeamCollaborations';" class="newtable"><tr class="newtable"><td class="newtable"><span>Collaborations</span></td><td class="newtable"><img style="margin-right:-20px;" width="25px" src="https://static.igem.org/mediawiki/2012/e/ee/Svn12_hp_new.png"></img></td></tr></table></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/TeamGallery'><span>Gallery</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/TeamGallery'><span>Gallery</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/TeamSponsors'><span>Sponsors</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/TeamSponsors'><span>Sponsors</span></a></li>  
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<h1>Deterministic model derivation - genetic switch</h1>
<h1>Deterministic model derivation - genetic switch</h1>
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<p>Construct 1 promoter state transitioning is described by a reaction:<img src="https://static.igem.org/mediawiki/2012/f/ff/Svn12_derivation1_eq1.png"/>
<p>Construct 1 promoter state transitioning is described by a reaction:<img src="https://static.igem.org/mediawiki/2012/f/ff/Svn12_derivation1_eq1.png"/>
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<p>Assuming equilibrium of binding and unbinding, we can write:
<p>Assuming equilibrium of binding and unbinding, we can write:
<img src="https://static.igem.org/mediawiki/2012/f/f7/Svn12_derivation1_eq2.png"/>
<img src="https://static.igem.org/mediawiki/2012/f/f7/Svn12_derivation1_eq2.png"/>
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<p>
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The fractional occupancy of construct 1 promoter, f1, can be expressed as a ratio of active states to all states:
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The fractional occupancy of construct 1 promoter, f<sub>1</sub>, can be expressed as a ratio of active states to all states:
<img src="https://static.igem.org/mediawiki/2012/b/b7/Svn12_derivation1_eq3.png" />
<img src="https://static.igem.org/mediawiki/2012/b/b7/Svn12_derivation1_eq3.png" />
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<p>
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It follows that the fractional occupancy for construct 1 promoter is:
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Assuming equilibrium of binding and unbinding, it follows that the fractional occupancy for construct 1 promoter is:
<img src="https://static.igem.org/mediawiki/2012/b/ba/Svn12_derivation1_eq4.png" />
<img src="https://static.igem.org/mediawiki/2012/b/ba/Svn12_derivation1_eq4.png" />
</p>
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<p>To account for non-linearity, an exponent n1 was added, and the equation generalized to:
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<p>To account for non-linearity, an exponent n<sub>1</sub> was added, and the equation generalized to:
<img src="https://static.igem.org/mediawiki/2012/a/a9/Svn12_derivation1_eq5.png" />
<img src="https://static.igem.org/mediawiki/2012/a/a9/Svn12_derivation1_eq5.png" />
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K<sub>r</sub> is the amount of TAL-A:KRAB it takes for f1 to be equal to 50%.
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K<sub>r</sub> is the amount of TAL-A:KRAB it takes for f<sub>1</sub> to be equal to 50% when n<sub>1</sub>=k<sub>1</sub>=1.
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The positive feedback loop switch model was derived in a similar manner.
The positive feedback loop switch model was derived in a similar manner.
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<hr>
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<b>
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<a href='https://2012.igem.org/Team:Slovenia/ModelingMutualRepressorSwitch'>Deterministic model of the mutual repressor switch</a><br/>
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<a href='https://2012.igem.org/Team:Slovenia/ModelingPositiveFeedbackLoopSwitch'>Deterministic model of the positive feedback loop switch</a>
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Latest revision as of 18:02, 3 June 2013


Deterministic model derivation - genetic switch

The deterministic model for the mutual repressor switch was derived in the following way.

We assumed the following binding site states were possible:

Active promoter state is a state leading to gene expression.

Construct 1 promoter state transitioning is described by a reaction:

The fractional occupancy of construct 1 promoter, f1, can be expressed as a ratio of active states to all states:

The equations for other constructs take the same form.

Assuming equilibrium of binding and unbinding, it follows that the fractional occupancy for construct 1 promoter is:

To account for non-linearity, an exponent n1 was added, and the equation generalized to:

Kr is the amount of TAL-A:KRAB it takes for f1 to be equal to 50% when n1=k1=1.

Derivation for constructs 2, 3 and 4 was similar except for different transcription factor names.

Fractional occupancies were then used to construct a set of ordinary differential equations representing each protein production. Because each protein can be produced from different constructs, production rates (including leaky rates) were summed together. E.g., because TAL-B:KRAB is produced from both constructs 1 and 3, fractional occupancies f1 and f3 were used and corresponding terms summed to obtain:

Since construct 5 promoter has no binding sites and is active at all times, fractional occupancy of the promoter is equal to 1.

The positive feedback loop switch model was derived in a similar manner.


Deterministic model of the mutual repressor switch
Deterministic model of the positive feedback loop switch