Team:Slovenia/ModelingQuantitativeModel

From 2012.igem.org

(Difference between revisions)
 
(43 intermediate revisions not shown)
Line 3: Line 3:
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
 +
<!-- back to top -->
 +
<div style="position:fixed; bottom:45px; right:30px; width:100px; height:66px; background-color:transparent;">
 +
<a href="#topofthepage">
 +
<table style="background-color:transparent;" onclick="window.location = '#topofthepage'" class="invisible" style="height:100%;">
 +
<tr class="invisible" style="background-color:transparent;">
 +
<td class="invisible" style="background-color:transparent;" valign="center">
 +
<img width="100px" src ="https://static.igem.org/mediawiki/2012/1/14/Svn12_hp_btt.png"></img>
 +
</td></tr></table>
 +
</a>
 +
</div>
 +
 +
 +
<script type="text/javascript" src="http://igem2012.fri.uni-lj.si/scripts/inputcheck.js"></script>
<style type="text/css">
<style type="text/css">
Line 154: Line 167:
/* Tables */
/* Tables */
/* IE 6: http://webdesign.about.com/od/tables/qt/tiptablecenter.htm */
/* IE 6: http://webdesign.about.com/od/tables/qt/tiptablecenter.htm */
-
table.normal { border-collapse: collapse; margin: auto; width:70%; margin-bottom:15px; }
+
table.normal { border-collapse: collapse; margin: auto; width:80%; margin-bottom:15px; }
td.normal, th.normal { padding-left: 1.4em; padding-right: 1.4em; padding-top: 0.4em; padding-bottom: 0.4em; border: 1px #d8d8d8 solid; }
td.normal, th.normal { padding-left: 1.4em; padding-right: 1.4em; padding-top: 0.4em; padding-bottom: 0.4em; border: 1px #d8d8d8 solid; }
thead.normal{ background: #0C5DA5; color:#ffffff; border: 1px #d8d8d8 solid; }
thead.normal{ background: #0C5DA5; color:#ffffff; border: 1px #d8d8d8 solid; }
Line 169: Line 182:
/* invisible table */
/* invisible table */
-
table.invisible{ border-collapse: collapse; margin: auto; width:100%; margin-bottom:15px; }
+
table.invisible{ border-collapse: collapse; margin: auto; width:90%; margin-bottom:15px; }
-
td.invisible, th.invisible { padding-left: 1.4em; padding-right: 1.4em; padding-top: 0.4em; padding-bottom: 0.4em; border:none; }
+
td.invisible, th.invisible { padding-left: 1.4em; padding-right: 1.4em; padding-top: 0.4em; padding-bottom: 0.4em; border:none; text-align:left; }
thead.invisible{ background: #0C5DA5; color:#ffffff; border:none; }
thead.invisible{ background: #0C5DA5; color:#ffffff; border:none; }
tbody .invisible{ background: #fff; }
tbody .invisible{ background: #fff; }
 +
img.invisible{width:100%;}
 +
/* invisible2 table
 +
table.invisible2{ border-collapse: collapse; margin: auto; width:100%; margin-bottom:15px; }
 +
td.invisible2, th.invisible2 { padding-left: 1.4em; padding-right: 1.4em; padding-top: 0.4em; padding-bottom: 0.4em; border:none; }
 +
thead.invisible2{ background: #0C5DA5; color:#ffffff; border:none; }
 +
tbody .invisible2{ background: #fff; }
 +
*/
/* summary table */
/* summary table */
Line 208: Line 228:
#cssmenu ul li > ul li{display:block; list-style:inside none; padding:0; margin:0; position:relative;}  
#cssmenu ul li > ul li{display:block; list-style:inside none; padding:0; margin:0; position:relative;}  
#cssmenu ul li > ul li a{ outline:none; display:block; position:relative; margin:0; padding:8px 20px; font:10pt Arial, Helvetica, sans-serif; color:#fff; text-decoration:none; text-shadow:1px 1px 0 rgba(0,0,0, 0.5); }  
#cssmenu ul li > ul li a{ outline:none; display:block; position:relative; margin:0; padding:8px 20px; font:10pt Arial, Helvetica, sans-serif; color:#fff; text-decoration:none; text-shadow:1px 1px 0 rgba(0,0,0, 0.5); }  
 +
#cssmenu ul li > ul li a table tr td span{ outline:none; display:block; position:relative; margin:0; padding:0px 0px; font:10pt Arial, Helvetica, sans-serif; color:#fff; text-decoration:none; text-shadow:1px 1px 0 rgba(0,0,0, 0.5); }
#cssmenu, #cssmenu > ul > li > ul > li a:hover
#cssmenu, #cssmenu > ul > li > ul > li a:hover
{ background:#043A6B;  
{ background:#043A6B;  
Line 224: Line 245:
/* end CSS navigation menu (blue) */
/* end CSS navigation menu (blue) */
 +
/*new table start*/
 +
table.newtable {background-color:transparent;}
 +
td.newtable, th.newtable {background-color:transparent;}
 +
thead.newtable{ }
 +
tbody .newtable{}
 +
/*new table*/
ul {
ul {
Line 299: Line 326:
<body>
<body>
 +
<a name="topofthepage" style="background-color:transparent;"></a>
<div id="banner">
<div id="banner">
Line 323: Line 351:
<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>  
-
<li><a href='https://2012.igem.org/Team:Slovenia/TheSwitchPositiveFeedbackLoopSwitch'><span>Positive feedback loop switch</span></a></li>  
+
<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>
 +
    <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>
Line 331: Line 360:
<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>  
-
<li><a href='https://2012.igem.org/Team:Slovenia/SafetyMechanismsMicrocapsuleDegradation'><span>Microcapsule degradation</span></a></li>  
+
    <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>
Line 339: Line 368:
<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>  
 +
    <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>
Line 346: Line 376:
  <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>
-
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingPK'><span>Pharmacokinetics</span></a></li>
+
    <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>
-
<li><a href='https://2012.igem.org/Team:Slovenia/ModelingQuantitativeModel'><span>Quantitative and stability model</span></a></li>
+
<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>
 +
    <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>
Line 361: Line 392:
  <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>
-
<li><a href='https://2012.igem.org/Team:Slovenia/NotebookLablog'><span>Lablog</span></a></li>
+
    <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>
Line 370: Line 401:
<li><a href='https://2012.igem.org/Team:Slovenia/Society'><span>Human practice</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/Society'><span>Human practice</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyScientists'><span>Scientists</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyScientists'><span>Scientists</span></a></li>
-
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyMedicalDoctors'><span>Medical doctors</span></a></li>
+
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyMedicalDoctors'><span>Physicians</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyEthics'><span>Ethics, safety and regulations</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyEthics'><span>Ethics, safety and regulations</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyPatients'><span>Patients</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyPatients'><span>Patients</span></a></li>
-
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyMedia'><span>Media and general public</span></a></li>  
+
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyMedia'><span>Journalists and general public</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyOutreach'><span>Outreach</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyOutreach'><span>Outreach</span></a></li>
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyQuestionnaire'><span>Questionnaire</span></a></li>  
<li><a href='https://2012.igem.org/Team:Slovenia/SocietyQuestionnaire'><span>Questionnaire</span></a></li>  
Line 384: Line 415:
<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>
 +
<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>  
Line 391: Line 423:
</div>
</div>
<!-- end main menu -->
<!-- end main menu -->
 +
 +
</div> <!-- end menu -->
</div> <!-- end menu -->
Line 396: Line 430:
<div id="main">
<div id="main">
<br/>
<br/>
-
<h1>Quantitative model and stability analysis</h1>
+
<h1>Experimental model</h1>
-
<p>In order to be able to predict the quantitative behavior of <i>in vivo</i> application of the genetic switches, we set up a quantitative model of a Transcription-activator like effector (TAL) based bistable switches. We apply experimental measurements for individual parts and predict their behavior when applied into a single system. The essential characteristics of a switch are <i>responsiveness</i> (reaching a stable state with the introduction of the corresponding inducer), <i>stability</i> (not leaving the state it after inducer removal) and <i>robustness</i> (expressing equivalent qualitative behavior under a wide range of conditions). In the following subsections, modeling approaches for individual parts are described.</p>
+
<!-- dummy link na bannerju -->
 +
<a href="https://2012.igem.org/Main_Page">
 +
<div id="dummy" style="background-color:transparent; position:absolute; left:870px; top:25px; width:115px; height:80px; z-index:100; opacity:0.0;">
 +
</div>
 +
</a>
-
<p>A variety of well-established models in the literature were examined, which resulted in choosing ordinary differential Hill equations model, presented in (Tigges et al., 2009). The former work presents a tunable synthetic mammalian oscillator, whose model was readjusted to present a switch structure. On top of that, the host choice of mammalian cells and pristinamycin-based inducible system corresponds to our system.</p>
+
<table class="summary">
 +
<tbody class="summary">
 +
<tr class="summary">
 +
<td class="summary">
 +
<p><b>Question:</b> Are we able to somehow take advantage of the experimental measurements obtained
 +
from the wet lab? Does that allow us to predict the optimal input ratios of plasmids inserted?</p>
 +
<b>Answer:</b> Measurements were exploited in their full potential as we have developed a brand
 +
new modeling approach. As it turned out, it well describes the real behavior of the switch.  
 +
The results predicted bistable behavior for a range of input ratios. The optimal choice resulted
 +
to be the <b>p[B]_PMIN_TAL:KRAB</b> (repressors) plasmids being in around three times greater quantity
 +
than <b>p[B]_PMIN_TAL:VP16</b>  (activators).
 +
</td></tr></tbody></table>
-
<p>To get a better idea of the functioning of the model, an interactive web application was developed and is available <a href="https://2012.igem.org/Team:Slovenia/InteractiveSimulations">here</a>.</p>
 
-
<h2>Model description and parameter determination</h2>
+
<br/>
 +
<font style="">To get a better idea for the functioning of the Experimental model, we implemented it as a <b>web application.</b> Click here to
 +
<a id="displayText" href="javascript:toggle();" style="font-size:xx-large; color:orange;">show</a> the application. </font><br/><br/><br/>
-
<h3>TAL:KRAB repressor constructs</h3>
 
-
<p>For repressor constructs, the percentage of remaining transcription rate comparing to the unrepressed reporter plasmid was measured. Intuitively, the remaining rate was directly proportional to the repressor/reporter ratio, but not in a linear fashion. To approximate this relation for <i>TAL:KRAB</i> constructs, the following analytical function was fitted to the measurements:</p>
+
<div id="toggleText" style="display:none;">
 +
<form name="form1" action="http://igem2012.fri.uni-lj.si:443/cellulator/bistable_feedback_new"  method="GET" onsubmit="return validateForm(this)">
 +
      <input type="hidden" name="check_submit" value="1"/>
 +
   
 +
     
 +
     
 +
      <table style="border-radius: 30px;  background:cyan;  padding:10px 10px 10px 10px;">
 +
      <tr>
 +
     
 +
      <td width="700px" valign="top">
 +
     
 +
      <b>INPUT VECTORS DOSAGE</b> <br/>
 +
      <hr/>
 +
     
 +
      <table style="border-radius: 30px;  background:cyan;  padding:10px 10px 10px 10px;" >
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">The Switch</font></b></td><td></td></tr></th>
 +
      <th>
 +
        <tr><td>Construct</td><td>Dosage</td></tr>
 +
        </th>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/0/09/Svn12_qm_interactive_p0.png" width="300px"/></td><td> <input type="text" name="plasmid0" size="3" value="1" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/2/28/Svn12_qm_interactive_p1.png" width="200px"/><td> <input type="text" name="plasmid1" size="3" value="1" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/f/f0/Svn12_qm_interactive_p2.png" width="300px"/><td> <input type="text" name="plasmid2" size="3" value="1" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/7/70/Svn12_qm_interactive_p3.png" width="200px"/><td> <input type="text" name="plasmid3" size="3" value="1" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td>
 +
      <tr><td></td><td></td></tr>
 +
     
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">Inducible system</font></b></td><td></td></tr></th>
 +
      <th>
 +
        <tr><td>Construct</td><td>Dosage</td></tr>
 +
        </th>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/c/cf/Svn12_qm_interactive_p4.png" width="200px"/><td> <input type="text" name="plasmid4" size="3" value="5" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/f/f7/Svn12_qm_interactive_p5.png" width="200px"/><td> <input type="text" name="plasmid5" size="3" value="5" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/9/96/Svn12_qm_interactive_p6.png" width="200px"/><td> <input type="text" name="plasmid6" size="3" value="5" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/9/9f/Svn12_qm_interactive_p7.png" width="200px"/><td> <input type="text" name="plasmid7" size="3" value="5" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td></td><td></td></tr>
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">Pristinamycin/Erithromycin ind. proteins</font></b></td><td></td></tr></th>
 +
      <th>
 +
        <tr><td>Construct</td><td>Dosage</td></tr>
 +
        </th>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/6/6a/Svn12_qm_interactive_p8.png" width="200px"/><td> <input type="text" name="plasmid8" size="3" value="30" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/b/b1/Svn12_qm_interactive_p9.png" width="200px"/><td> <input type="text" name="plasmid9" size="3" value="30" onKeyPress="return numbersonly2(this, event)" maxlength="3"/> ng</td></tr>
 +
      </table>
 +
      <font color="blue">(Enter dosages for corresponding plasmids. <font color="black">To comply with the jetPEI® protocol, the sum of masses shall not exceed 1000 ng. </font>)</font><br /><br />
 +
     
 +
      </td>
 +
      <td valign="top">
 +
           
 +
      <b>INDUCERS</b> <br/>
 +
      <hr/>
 +
     
 +
      <table style="border-radius: 30px;  background:cyan;  padding:10px 10px 10px 10px;">
 +
        <th><tr><td  style="background: #0099FF;"><b><font color="white">Pristinamycin</font></b></td><td></td></tr></th>
 +
      <tr>
 +
        <td>Input times [min]</td>
 +
        <td><input type="text" name="pc_start1" size="5" value="200" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="pc_start2" size="5" value="5000" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="pc_start3" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="pc_start4" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
        <td><input type="text" name="pc_start5" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
      </tr>
 +
      <tr>
 +
        <td>Durations [min]</td>
 +
        <td><input type="text" name="pc_duration1" size="5" value="200" onKeyPress="return numbersonly(this, event)" maxlength="6"><br/></td>
 +
        <td><input type="text" name="pc_duration2" size="5" value="300" onKeyPress="return numbersonly(this, event)" maxlength="6"><br/></td>
 +
        <td><input type="text" name="pc_duration3" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"><br/></td>
 +
        <td><input type="text" name="pc_duration4" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"><br/></td>
 +
        <td><input type="text" name="pc_duration5" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"><br/></td>
 +
      </tr>
 +
      </table>
 +
 
 +
      <br/>
-
<center><img src="https://static.igem.org/mediawiki/2012/5/52/Svn12_qm_1eq_reptransfer.png" style="height:30px; width:auto;"/></center><br/>
+
      <table style="border-radius: 30px;  background:cyan;  padding:10px 10px 10px 10px;">
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">Erithromycin</font></b></td><td></td></tr></th>
 +
      <tr>
 +
        <td>Input times [min]</td>
 +
        <td><input type="text" name="rg_start1" size="5" value="1500" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="rg_start2" size="5" value="10000" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="rg_start3" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="rg_start4" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
        <td><input type="text" name="rg_start5" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"/></td>
 +
      </tr>
 +
      <tr>
 +
        <td>Durations [min]</td>
 +
        <td><input type="text" name="rg_duration1" size="5" value="2000" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
        <td><input type="text" name="rg_duration2" size="5" value="100" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
        <td><input type="text" name="rg_duration3" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
        <td><input type="text" name="rg_duration4" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
        <td><input type="text" name="rg_duration5" size="5" value="" onKeyPress="return numbersonly(this, event)" maxlength="6"></td>
 +
      </tr>
 +
      </table>
 +
     
 +
      <font color="blue">(For each input time of an inducer, enter its corresponding duration, i.e. after how many minutes the inducer will be removed. )</font><br />
-
<p>where <i>x</i> is repressor/reporter plasmid ratio, and <i>a, b, c</i> are parameters subject to least square error fitting. This produced decreasing function for remaining transcription rate <i>q</i>, depicted in Figure 1a. The achieved percentage of remaining transcription rate <i>q</i> was directly employed in repressed promoter rate equation. The dynamics were modeled using Hill equations for repression and activation (Alon, 2007). For example, the effect of a repressor on transcription rate is modeled as a factor in a rate equation:</p>
+
      <br />
 +
      <b>SIMULATION</b> <br/>
 +
      <hr />    
 +
      <input type="checkbox" name="noise" value="1" /> Apply measurement noise.
 +
      <br/>
 +
      <font color="blue">(Measured standard deviations will be applied in the calculations.)</font><br /> <br />
-
<p>Intuitively, the unrepressed transcription rate <i>r</i> is inversely proportional to the concentration of TAL-A:KRAB protein with non-linearity coefficient <i>n</i>. The remaining rate percentage <i>q</i> was used to determine the <i>s</i> constant, which determines the concentration at which half of the unrepressed rate is reached, after the concentration threshold <i>t</i> is crossed.</p>
 
 +
      Time: <input type="text" name="time" size="5" value="15000" onKeyPress="return numbersonly(this, event)" maxlength="7"/> min<br />
 +
      <font color="blue">(Simulation running time)</font><br /><br />
 +
     
 +
      <input type="submit" value="SIMULATE" /><br/>
 +
      <font color="blue">(The results will be shown in a new browser window/tab after few seconds.)</font>
 +
     
 +
      </td>
 +
      </tr>
 +
      </table>
 +
    </form>
 +
</div>
 +
<br/>
-
<h3>TAL:VP16 activator constructs </h3>
+
<p>
 +
<ul style="margin-left:15px;">
 +
<li><a href="#idea">Idea</a><br/></li>
 +
<li><a href="#modeldev">Model derivation</a><br/></li>
 +
<li><a href="#results">Results</a><br/></li>
 +
<li><a href="#source">Source code</a><br/></li>
 +
<li><a href="#references">References</a><br/></li>
 +
</ul>
 +
</p>
-
<p>Using a similar approach to that described above, we fitted the data achieved for activator constructs TAL-A:VP16 and <i>TAL-B:VP16</i>. As expected, the transcription rate increased proportionally with increasing activator/reporter ratio of plasmids transfected, again in a non-linear fashion. To approximate the behavior, the following increasing function was fitted:</p>
 
-
<p>where <i>x</i> is activator/reporter plasmid radio and <i>c, b</i> are parameters subject to least square error fitting. The plot of the function is shown in Figure 1b. The factor of activation <i>a</i> is again directly employed as a rate equation factor for activated promoter:</p>
+
<h2 ><a name="idea"></a>Idea</h2>
 +
<p>As we discovered throughout the project, the switch design is very sensible to the
 +
masses of the different plasmids (parts) used in the experiment.
 +
We thought, why not use the data we obtained for <i>individual constructs</i> and
 +
try to predict the switch behavior as they are combined into <i>a single system?</i>
 +
Thus, the data obtained from the wet lab was used to characterize each of the
 +
plasmid constructs in the positive feedback loop switch. The characterization
 +
was made in terms of how their products <i>regulate the transcription of the target genes.</i>
 +
That is the way how we connect the experimental work to the theory, as shown in Figure 1.</p>
-
<p>where <i>x</i> is activator/reporter plasmid radio and <i>c, b</i> are parameters subject to least square error fitting. The plot of the function is shown in Figure 1b. The factor of activation <i>a</i> is again directly employed as a rate equation factor for activated promoter:</b>
+
 +
<center>
 +
<div style="width:90%;">
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/6/67/Svn12_qm_splash.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 1.</b> Steps in connecting the experimental results to theoretical modeling. </p>
 +
</div>
 +
</center>
 +
 +
 +
<h2 ><a name="modeldev"></a>Model derivation</h2>
 +
<p>Ordinary differential equations (ODE) model was used as a module to build around.
 +
We made use of the two basic relations for transcriptional regulation.
 +
The activator and repressor function respectively, defined in (Alon, 2006), modify
 +
the basal transcription rate as follows:</p>
 +
<table>
 +
<tr>
 +
<td><img style="width:60%;" src="https://static.igem.org/mediawiki/2012/0/0d/Svn12_qm_acthill.png"></img></td>
 +
<td><font style="font-family:Times New Roman;">(1)</font></td>
 +
<td><img style="width:60%;" src="https://static.igem.org/mediawiki/2012/a/a6/Svn12_qm_rephill.png"></img></td>
 +
<td><font style="font-family:Times New Roman;">(2)</font></td>
 +
</tr>
 +
</table>
-
where the increasing concentration of TAL-B:VP16 protein reaches half the maximum activation rate <i>a</i> when crossing the concentration threshold <i>t</i>, with non-linearity exponent <i>n</i>.
+
<p>
 +
where <i>&beta;</i> is the basal transcription rate,
 +
<i>X*</i> is the quantity of active protein, <i>K</i>  
 +
is the activator/repressor coefficient and <i>n</i> is
 +
the Hill coefficient (which we neglect in this model
 +
to show that the switch can work without cooperativity).  
 +
</p>
   
   
-
<b>Figure 1</b>: Functions fitted to experimental data for repressor and activator constructs.  (a) Data measured for TAL-A:KRAB (blue) and TAL-B:KRAB (red) constructs and averaged afterwards (black). (b) Data measured for TAL-A:VP16 (blue) and TAL-B:VP16 (red) constructs and averaged afterwards (black).
 
-
<h3>Inducible system</h3>
+
<p>
 +
Since precisely defining transcription rates was not the primary goal of our project,
 +
their <i>absolute values</i> are not of central importance in the model.  Rather, we focus on
 +
the <i>relative changes</i> in transcription levels, caused by activators and repressors.
 +
Furthermore, concentration levels of reporters will also be presented <i>relative to each other</i>.
 +
This way, we avoid the use of <i>any units we did not measure</i>.
 +
</p>
-
<p>The inducible system in both switches is built upon two different inducer molecules. In the mutual repressor switch, we employ a <i>pristinamycin-inducible protein (PIP) with KRAB repressor domain</i>. After the introduction of <i>pristinamycin</i>, PIP:KRAB is inactivated and thus unbound from its binding site at the pCMV promoter. The concentration of active PIP:KRAB is hence inversely proportional to the pristinamycin concentration:</p>
+
<h3> Promoters </h3>
 +
As we use two different kinds of promoters, PCMV and PMIN, to account for the difference in
 +
<i>basal transcription rates</i>. Experiments have shown that relative luciferase units under
 +
PCMV promoter are 1000-fold greater than under PMIN (data not shown). Hence, <b>PCMV
 +
is assumed to have a 1000 times greater basal transcription rate than PMIN</b>.
-
<p>Consequently, the transcription rate of the corresponding promoter is proportional to the concentration of active PIP:KRAB :</p>
+
<h3> Transcriptional regulators </h3>  
-
<p>where k is the maximum transcription rate, f scaling factor and alpha the fraction of inactivated transcription rate. The increasing concentration of active PIP:KRAB causes the resulting rate r to approach the basal rate, with half the maximum rate concentration determined by the threshold K. In an analogue manner, the erythromycin and E:KRAB inducer system was modeled.</p>
+
<h4> Activators </h4>  
 +
<center>
 +
<div style="width:90%;">
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/c/cd/Svn_12_qm_actscheme.png"></img>
 +
</div>
 +
</center>
 +
<p>To characterize activators, <b>pPCMV_TALA:VP16</b> and <b>p[A]_PMIN_fLuc</b> plasmids were tested.
 +
Various ratios of input masses produced different levels of luciferase activity.
 +
Following equation (1), activators increase the transcription rate up to some maximum factor of
 +
<i>fold induction</i>. The former is derived by comparing the resulting luciferase activity with that
 +
of the <i>inactivated</i> <b>p[A]_PMIN_fLuc</b>. Gathering data for various input ratios (Figure 2), we fitted it to an
 +
analytical function (Figure 3), enabling us to predict the fold induction (A) for <i>arbitrary</i> input
 +
ratios of DNA for the two plasmids.</p>
 +
<p>Intuitively, more activator plasmids <i>increase</i> the maximum fold induction. On the other hand,
 +
more target plasmids <i>decrease it</i>. Relatively speaking, activator proteins thus have more plasmids
 +
to target. That leads to fold activation ratio being smaller from the <i>global point of view</i>.
 +
</p>
 +
<p>In an analogue manner <b>TAL-B:VP16</b> constructs were characterized.</p>
 +
 +
 +
<table>
 +
<tr>
 +
<td valign="top">
 +
<center>
 +
<div style="width:90%;">
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/5/5f/Svn_12_qm_actdata.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 2.</b> Fold induction rates, derived
 +
from relative luciferase activity for various ratios of
 +
<b>pPCMV_TALA:VP16</b> (activator) and <b>p[A]_PMIN_fLuc</b> (target) plasmids.  </p>
 +
</div>
 +
</center>
 +
</td>
 +
<td valign="top">
 +
<center>
 +
<div style="width:90%;">
 +
<img width="55%" src="https://static.igem.org/mediawiki/2012/2/22/Svn12_qm_acteq.png" align="middle"/><br />
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/5/5d/Svn_12_qm_actfit.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 3.</b> Plot of fold induction function for a continuous 
 +
range of activator and reporter.
 +
plasmid ratios, where <i>a</i> and <i>b</i> are parameters subject to least square
 +
error fitting.  </p>
 +
</div>
 +
</center>
 +
</td>
 +
</tr>
 +
</table>
 +
 +
 +
 +
 +
<h4> Repressors </h4>
-
<h2>Stability analysis</h2>
+
<center>
 +
<div style="width:90%;">
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/1/12/Svn_12_qm_repscheme.png"></img>
 +
</div>
 +
</center>
-
<p>For the purpose of stability analysis, the simulation was run multiple times with varying pairs of parameters and producing a two dimensional <i>parameter map</i>. For example, with varying plasmid input dosages (other things being equal), one or the other state might become not reachable. For an illustrative example, see Figure 2.</p>
+
<p>To characterize repressors, <b>pPCMV_TALA:KRAB </b> and <b>p[A]_PCMV_fLuc</b> plasmids were tested.
 +
Various ratios of input masses produced different levels of luciferase activity.
 +
Following equation (1), repressors <i>decrease</i> the basal transcription rate down to
 +
some minimum factor of <i>fold repression</i>. The former is derived by comparing the luciferase
 +
activity with that of the <i>unrepressed</i> <b>p[A]_PCMV_fLuc</b>, resulting in percentage of remaining
 +
transcription intensity. Gathering data for various input ratios (Figure 4), we fitted it to
 +
an analytical function (Figure 5). It enables us to predict the fold repression (Q) for arbitrary
 +
input rations of DNA.</p>
 +
<p>Intuitively, more repressor plasmids <i>increase</i> the maximum fold induction.
 +
On the other hand, more target plasmids <i>decrease it</i>. Relatively speaking,  
 +
repressor proteins thus have more plasmids to target. That leads to fold repression ratio
 +
being smaller from the <i>global point of view</i>.</p>
 +
<p>In an analogue manner <b>TAL-B:KRAB</b> constructs were characterized.</p>
-
<p>For every instance of the simulation (a colored point in Figure 2), the outcome results were examined. During the course of a simulation, a steady state is defined as a point in phase space (all possible pairs of the two reporter concentrations) where concentrations of <i>both reporter protein concentrations do not change</i>, i.e.:</p>
 
 +
<table>
 +
<tr>
 +
<td valign="top">
 +
<center>
 +
<div style="width:90%;">
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/5/5d/Svn_12_qm_repdata.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 4.</b> Fold repression rates, derived from relative luciferase activity for various ratios of
 +
<b>pPCMV_TALA:KRAB</b> (repressor) and p[A]_PCMV_fLuc (target) plasmids.
 +
</div>
 +
</center>
 +
</td>
 +
<td valign="top">
 +
<center>
 +
<div style="width:90%;">
 +
<img width="100%" src="https://static.igem.org/mediawiki/2012/8/87/Svn12_qm_repeq.png" align="middle"/><br />
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/d/db/Svn_12_qm_repfit.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 5.</b> Plot of fold induction function for a continuous range of repressor
 +
and reporter plasmid ratios, where a, b and c are parameters subject to least square error fitting.
 +
 +
</div>
 +
</center>
 +
</td>
 +
</tr>
 +
</table>
-
<p>The list of steady state points is achieved and analyzed for each instance of a simulation. A <i>valid state A</i> is defined when BFP concentration crosses a predefined threshold <i>th</i> while at the same time the mCitrine concentration is below <i>th</i>. <i>Valid state B</i> is defined analogously for mCitrine. If both stable states are reached during a simulation instance run, the system is labeled bistable.</p>
 
-
<p>If at any stable state points, both concentrations cross the threshold simultaneously or remain below threshold simultaneously, the state point and the system are defined ambiguous. In case no stable state points are found during the simulation, the system is labeled as not valid.</p>
+
 +
<h4> Inducible system </h4>  
-
<table class="summary" >
+
<center>
-
<tr class="summary">
+
<div style="width:90%;">
-
<td class="sumamry">
+
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/6/6e/Svn_12_qm_indscheme.png"></img>
-
<p>Summing up, five possible outcomes for each simulation instance were defined and placed on the parameter map (using separate colors to differentiate between them):</p>
+
</div>
-
<ul style="padding-left:30px;">
+
</center>
-
<li><font style="color:green;"><b>Bistable</b></font>; The system reached both stable states on a given time interval.</li>
+
 
-
<li><font style="color:blue;"><b>Monostable A;</b></font> The system reached expressed stable state A on a given time interval.</li>
+
<p>To characterize the erythromycin repressor induction system we measured relative luciferase
-
<li><font style="color:yellow;"><b>Monostable B;</b></font> The system only reached stable state B on a given time interval.</li>
+
activity for various ratios of <b>pPCMV_E:KRAB</b> (inducible protein), <b>pPCMV_[ETR]_TALA:KRAB</b> (repressor)
-
<li><font style="color:red;"><b>Ambigous;</b></font> The system expressed reached states simultaneously during a given time interval.</li>
+
and <b>p[A]_PCMV_fLuc </b> (target) plasmids (Figure 6). </p>
-
<li><font style="color:black;"><b>Not valid</b></font>; The system did not reach any stable states during a given time interval.</li>
+
<p>As E:KRAB gets stimulated by erythromycin, it unbinds from the [etr] binding site,
-
</ul>  
+
allowing the production of <b>TALA:KRAB</b>, which in turn represses the transcription of fLuc.
 +
By varying the ratios of the three input plasmids, we can observe the resulting difference in
 +
luciferase activity. That directly determines the fold repression of the inducible system <i>as a
 +
whole</i> (Figure 7).</p>
 +
<p>As inducible protein plasmids <i>increase</i>, the luciferase activity <i>increases</i> as well.
 +
The increasing masses of repressor and target plasmids both <i>decrease</i> the luciferase activity
 +
and consequently <i>decrease</i> the fold repression rate. </p>
 +
<p>In an analogue manner erithromycin activator, pristinamycin repressor and
 +
pristinamycin activator induction systems were characterized.</p>
 +
 +
<table>
 +
<tr>
 +
<td valign="top">
 +
<center>
 +
<div style="width:90%;">
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/9/97/Svn_12_qm_indrepdata.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 6.</b> Fold repression rates,
 +
derived from relative luciferase activity for various ratios of <b>pPCMV_E:KRAB (inducible protein)</b>,
 +
<b>pPCMV_[ETR]_TALA:KRAB</b> (repressor) and <b>p[A]_PCMV_fLuc</b> (target) plasmids.
 +
</div>
 +
</center>
 +
</td>
 +
<td valign="top">
 +
<center>
 +
<div style="width:90%;">
 +
<img width="100%" src="https://static.igem.org/mediawiki/2012/1/1f/Svn12_qm_indeq.png" align="middle"/><br />
 +
<img style="width:100%;" src="https://static.igem.org/mediawiki/2012/1/17/Svn_12_qm_indrepfit.png"></img>
 +
<p style="text-align:justify; width:100%;"><b>Figure 7.</b> Plot of fold
 +
induction function for a continuous  range of inducible protein, inducible system and target plasmid ratios,
 +
where a, b and c are parameters subject to least square error fitting
 +
</div>
 +
</center>
</td>
</td>
</tr>
</tr>
</table>
</table>
 +
 +
 +
<h3> Noise </h3>
 +
<p>Due to the noise in experimental measurements, we can directly apply it in the model as well.
 +
When determining fold repression ratios, <i>standard deviations</i> of up to 15 %  were observed. </p>
 +
 +
<h2 ><a name="results"></a>Results</h2>
-
<p>Figure 2: Parameter map of non-stimulated system (no inducer introduction) for parameters: [A]_pCMV_TAL-B:KRAB_NEPTUN dosage (x-axis) and [B]_pCMV_TAL-A:KRAB-mCitrine dosage (y-axis), on the interval 100-500 ng. Notice the red ambiguous states where both parameter values are equal.</p>
+
<table>
-
<h2>Mutual repressor switch model</h2>
+
<tr>
 +
<td valign="top">
 +
<table>
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">The Switch (top level)</font></b></td><td></td></tr></th>
 +
      <th>
 +
        </th>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/0/09/Svn12_qm_interactive_p0.png" width="300px"/></td><td><font style="font-family:Times New Roman;">p0</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/2/28/Svn12_qm_interactive_p1.png" width="200px"/></td><td><font style="font-family:Times New Roman;">p1</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/f/f0/Svn12_qm_interactive_p2.png" width="300px"/></td><td><font style="font-family:Times New Roman;">p2</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/7/70/Svn12_qm_interactive_p3.png" width="200px"/></td><td><font style="font-family:Times New Roman;">p3</font></td></tr>
 +
      <tr><td></td><td></td></tr>
 +
</table>
 +
</td>
-
Indexing of the constructs is described in List~1. The observed chemical species in the system are listed in Table~1, while the parameter values are found in Table~1. Ordinary diferential equations for the mutual repressor switch model are Eq. 1-22.
+
<td valign="top">
 +
<table>     
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">Inducible system (middle level)</font></b></td><td></td></tr></th>
 +
      <th>
 +
        </th>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/c/cf/Svn12_qm_interactive_p4.png" width="200px"/><td><font style="font-family:Times New Roman;">p4</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/f/f7/Svn12_qm_interactive_p5.png" width="200px"/><td><font style="font-family:Times New Roman;">p5</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/9/96/Svn12_qm_interactive_p6.png" width="200px"/><td><font style="font-family:Times New Roman;">p6</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/9/9f/Svn12_qm_interactive_p7.png" width="200px"/><td><font style="font-family:Times New Roman;">p7</font></td></tr>
 +
      <tr><td></td><td></td></tr>
 +
</table>  
 +
</td>
-
List 1: Used constructs and their indexes.
+
<td valign="top">
-
Table 1: Observed chemical species.
+
<table>
-
Table 2: Parameters, their initial values and source.
+
 
 +
      <th><tr><td  style="background: #0099FF;"><b><font color="white">Inducible proteins (bottom level)</font></b></td><td></td></tr></th>
 +
      <th>
 +
        </th>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/6/6a/Svn12_qm_interactive_p8.png" width="200px"/><td><font style="font-family:Times New Roman;">p8</font></td></tr>
 +
      <tr><td><img align="left" src="https://static.igem.org/mediawiki/2012/b/b1/Svn12_qm_interactive_p9.png" width="200px"/><td><font style="font-family:Times New Roman;">p9</font></td></tr>
 +
</table>
 +
</td>
 +
</tr>
 +
</table>
-
<h3>Model ordinary differential equations</h3>
+
<p>The main goal of this particular model was to help determine the input ratios for plasmids
-
<h4>Inducible system</h4>
+
that make up the switch system. The first confirmation was that if the masses of all
-
<h4>The Switch</h4>
+
plasmids will be equal, the switch will not be able to exhibit bistable behavior.<p>
-
<h4>Reporters</h4>
+
<p>We partition the whole system into levels, with the Switch being the top level
 +
and the Pristinamycin/Erithromycin inducible proteins the bottom level. It is obvious that
 +
a plasmid on a given level influences another level only in the direction bottom -&gt; top,
 +
so as we go downwards, the masses shall increase to have more influence on the targeted
 +
upper level. Hence the relation:<br/><br/>
 +
<center><font style="font-family:Times New Roman; font-size:large;">p0, p1, p2, p3 &lt; p4, p5, p6, p7 &lt; p8, p9</font></center><br/>
 +
Next, the ratio between repressor and activator constructs was examined. To preserve symmetry,
 +
we assume: <br/><br/>
 +
<center><font style="font-family:Times New Roman; font-size:large;">p0 = p2, p1 = p3, p4  = p6, p5 = p7, p8 = p9</font> </center><br/>
 +
All the following ratios will be given in the form p0 : p1 (repressor:activator).
 +
Testing began at the 1:1 ratio, and we gradually increased both the repressor and activator to observe the qualitative behavioral change. The Switch exhibited bistable behavior for all ratios between 10:1 until 1:5, as can be seen in Scroll Box 1.
 +
</p>
 +
<table class="invisible"><tr class="invisible"><td class="invisible"  >
 +
<img height="380px" src="https://static.igem.org/mediawiki/2012/5/5e/Svn_12_qm_results-04.png"></img>
 +
</td>
 +
<td class="invisible">
 +
<img width="800px" src="https://static.igem.org/mediawiki/2012/f/f0/Svn_12_qm_results-03-03.png"></img>
 +
<div style="height:380px;width:800px;border:1px solid #ccc;font:16px/26px Georgia, Garamond, Serif;overflow:auto;">
 +
<img src="https://static.igem.org/mediawiki/2012/3/31/Svn_12_qm_results-01.png"></img>
 +
</div>
 +
<img width="800px" src="https://static.igem.org/mediawiki/2012/c/c1/Svn_12_qm_results-02.png"></img>
 +
</td></tr></table>
 +
<b>Scroll Box 1. </b> Results for valid range of activator:repressor plasmid ratios.
-
<h2>The positive feedback loop switch model</h2>
+
<p>
 +
<br />
 +
The whole range in which the simulation reports bistable behaviour is thus:<br />
 +
<center><font style="font-family:Times New Roman; font-size:large;">[10:1, 9:1, 8:1, 7:1, 6:1, 5:1, 4:1, 3:1, 2:1, 1:1, 1:2, 1:3, 1:4, 1:5] </font></center><br />
-
Indexing of the constructs is described in List~2. The observed chemical species in the system are listed in Table~1, while the parameter values are found in Table~2. Ordinary diferential equations for the mutual repressor switch model are Eq. 23-47.
+
Taking the median of the above range, we conclude that
 +
the optimal ratio of input masses for wet lab experiments is at
 +
<b>around three to one in favour of the repressor plasmids</b>.
 +
</p>
 +
<h2 ><a name="source"></a>Source code</h2>
 +
All source code for the model and simulations described above can be found <a href ="https://2012.igem.org/Team:Slovenia/SourceCode">here</a>;
-
List 1: Used constructs and their indexes.
+
<br/>
-
Table 1: Observed chemical species.
+
<br/>
-
Table 2: Parameters, their initial values and source.
+
<h2 style="color:grey;" ><a name="references"></a>References</h2>
-
 
+
-
<h3>Model ordinary differential equations</h3>
+
-
<h4>Inducible system</h4>
+
-
<h4>The Switch</h4>
+
-
<h4>Reporters</h4>
+
-
 
+
-
<h2 style="color:grey;">References</h2>
+
<p style="color:grey;">
<p style="color:grey;">
-
Alon U. (2007), An introduction to systems biology: design principles of biological circuits. Chapman & Hall/CRC.
+
Alon, U. (2007) An introduction to systems biology: design principles of biological circuits. Chapman & Hall/CRC.
 +
<br/><br/>
 +
Batard, P., and Wurm, F. (2001) Transfer of high copy number plasmid into mammalian cells by calcium phosphate transfection. <i>Gene</i> <b>270</b>, 61-68.
<br/><br/>
<br/><br/>
-
Chatterjee A., Kaznessis Y., and Hu W. (2006) Tweaking biological switches through a better understanding of bistability behavior. Current opinion in biotechnology, 19(5):475-81.
+
Chatterjee, A., Kaznessis, Y., and Hu, W. (2006) Tweaking biological switches through a better understanding of bistability behavior. <i>Current opinion in biotechnology</i> <b>19</b>, 475-81.
<br/><br/>
<br/><br/>
-
Gardner T., Cantor C., and Collins J. (2000) Construction of a genetic toggle switch in Escherichia coli. Nature, 403(6767):339-42.
+
Gardner, T., Cantor, C., and Collins, J. (2000) Construction of a genetic toggle switch in Escherichia coli. <i>Nature</i> <b>403</b>, 339-42.
<br/><br/>
<br/><br/>
-
Batard P., and Wurm F. (2001) Transfer of high copy number plasmid into mammalian cells by calcium phosphate transfection. Gene: An international Journal on Genes and Genomes, 270:61-68.
+
Batard, P., and Wurm, F. (2001) Transfer of high copy number plasmid into mammalian cells by calcium phosphate transfection. <i>Gene</i> <b>270</b>, 61-68.
<br/><br/>
<br/><br/>
-
Malphettes L., and Fussenegger M. (2006) Impact of RNA interference on gene networks. Metabolic engineering, 8(6):672-83.
+
Malphettes, L., and Fussenegger, M. (2006) Impact of RNA interference on gene networks. <i>Metabolic engineering</i> <b>8</b>, 672-83.
<br/><br/>
<br/><br/>
-
Tigges M., Marquez-Lago T., Stelling J., and Fussenegger M. (2009) A tunable synthetic mammalian oscillator. Nature, 457(7227):309-12.
+
Tigges, M., Marquez-Lago, T., Stelling, J., and Fussenegger, M. (2009) A tunable synthetic mammalian oscillator. <i>Nature</i> <b>457</b>, 309-12.
<br/><br/>
<br/><br/>
-
Zakharova A., Kurths J., Vadivasova T., and Koseska A. (2011) Analysing dynamical behavior of cellular networks via stochastic bifurcations. PloS one, 6(5):e19696.
+
Zakharova, A., Kurths, J., Vadivasova, T., and Koseska, A. (2011) Analysing dynamical behavior of cellular networks via stochastic bifurcations. <i>PloS one</i> <b>6</b>, e19696.
</p>
</p>
Line 524: Line 913:
<hr>
<hr>
<b>
<b>
-
Next: <a href='https://2012.igem.org/Team:Slovenia/InteractiveSimulations'>Interactive Simulations >></a>
+
Next: <a href='https://2012.igem.org/Team:Slovenia/ModelingInteractiveSimulations'>Interactive Simulations >></a>
</b>
</b>

Latest revision as of 21:05, 26 October 2012


Experimental model

Question: Are we able to somehow take advantage of the experimental measurements obtained from the wet lab? Does that allow us to predict the optimal input ratios of plasmids inserted?

Answer: Measurements were exploited in their full potential as we have developed a brand new modeling approach. As it turned out, it well describes the real behavior of the switch. The results predicted bistable behavior for a range of input ratios. The optimal choice resulted to be the p[B]_PMIN_TAL:KRAB (repressors) plasmids being in around three times greater quantity than p[B]_PMIN_TAL:VP16 (activators).

To get a better idea for the functioning of the Experimental model, we implemented it as a web application. Click here to show the application.



Idea

As we discovered throughout the project, the switch design is very sensible to the masses of the different plasmids (parts) used in the experiment. We thought, why not use the data we obtained for individual constructs and try to predict the switch behavior as they are combined into a single system? Thus, the data obtained from the wet lab was used to characterize each of the plasmid constructs in the positive feedback loop switch. The characterization was made in terms of how their products regulate the transcription of the target genes. That is the way how we connect the experimental work to the theory, as shown in Figure 1.

Figure 1. Steps in connecting the experimental results to theoretical modeling.

Model derivation

Ordinary differential equations (ODE) model was used as a module to build around. We made use of the two basic relations for transcriptional regulation. The activator and repressor function respectively, defined in (Alon, 2006), modify the basal transcription rate as follows:

(1) (2)

where β is the basal transcription rate, X* is the quantity of active protein, K is the activator/repressor coefficient and n is the Hill coefficient (which we neglect in this model to show that the switch can work without cooperativity).

Since precisely defining transcription rates was not the primary goal of our project, their absolute values are not of central importance in the model. Rather, we focus on the relative changes in transcription levels, caused by activators and repressors. Furthermore, concentration levels of reporters will also be presented relative to each other. This way, we avoid the use of any units we did not measure.

Promoters

As we use two different kinds of promoters, PCMV and PMIN, to account for the difference in basal transcription rates. Experiments have shown that relative luciferase units under PCMV promoter are 1000-fold greater than under PMIN (data not shown). Hence, PCMV is assumed to have a 1000 times greater basal transcription rate than PMIN.

Transcriptional regulators

Activators

To characterize activators, pPCMV_TALA:VP16 and p[A]_PMIN_fLuc plasmids were tested. Various ratios of input masses produced different levels of luciferase activity. Following equation (1), activators increase the transcription rate up to some maximum factor of fold induction. The former is derived by comparing the resulting luciferase activity with that of the inactivated p[A]_PMIN_fLuc. Gathering data for various input ratios (Figure 2), we fitted it to an analytical function (Figure 3), enabling us to predict the fold induction (A) for arbitrary input ratios of DNA for the two plasmids.

Intuitively, more activator plasmids increase the maximum fold induction. On the other hand, more target plasmids decrease it. Relatively speaking, activator proteins thus have more plasmids to target. That leads to fold activation ratio being smaller from the global point of view.

In an analogue manner TAL-B:VP16 constructs were characterized.

Figure 2. Fold induction rates, derived from relative luciferase activity for various ratios of pPCMV_TALA:VP16 (activator) and p[A]_PMIN_fLuc (target) plasmids.


Figure 3. Plot of fold induction function for a continuous range of activator and reporter. plasmid ratios, where a and b are parameters subject to least square error fitting.

Repressors

To characterize repressors, pPCMV_TALA:KRAB and p[A]_PCMV_fLuc plasmids were tested. Various ratios of input masses produced different levels of luciferase activity. Following equation (1), repressors decrease the basal transcription rate down to some minimum factor of fold repression. The former is derived by comparing the luciferase activity with that of the unrepressed p[A]_PCMV_fLuc, resulting in percentage of remaining transcription intensity. Gathering data for various input ratios (Figure 4), we fitted it to an analytical function (Figure 5). It enables us to predict the fold repression (Q) for arbitrary input rations of DNA.

Intuitively, more repressor plasmids increase the maximum fold induction. On the other hand, more target plasmids decrease it. Relatively speaking, repressor proteins thus have more plasmids to target. That leads to fold repression ratio being smaller from the global point of view.

In an analogue manner TAL-B:KRAB constructs were characterized.

Figure 4. Fold repression rates, derived from relative luciferase activity for various ratios of pPCMV_TALA:KRAB (repressor) and p[A]_PCMV_fLuc (target) plasmids.


Figure 5. Plot of fold induction function for a continuous range of repressor and reporter plasmid ratios, where a, b and c are parameters subject to least square error fitting.

Inducible system

To characterize the erythromycin repressor induction system we measured relative luciferase activity for various ratios of pPCMV_E:KRAB (inducible protein), pPCMV_[ETR]_TALA:KRAB (repressor) and p[A]_PCMV_fLuc (target) plasmids (Figure 6).

As E:KRAB gets stimulated by erythromycin, it unbinds from the [etr] binding site, allowing the production of TALA:KRAB, which in turn represses the transcription of fLuc. By varying the ratios of the three input plasmids, we can observe the resulting difference in luciferase activity. That directly determines the fold repression of the inducible system as a whole (Figure 7).

As inducible protein plasmids increase, the luciferase activity increases as well. The increasing masses of repressor and target plasmids both decrease the luciferase activity and consequently decrease the fold repression rate.

In an analogue manner erithromycin activator, pristinamycin repressor and pristinamycin activator induction systems were characterized.

Figure 6. Fold repression rates, derived from relative luciferase activity for various ratios of pPCMV_E:KRAB (inducible protein), pPCMV_[ETR]_TALA:KRAB (repressor) and p[A]_PCMV_fLuc (target) plasmids.


Figure 7. Plot of fold induction function for a continuous range of inducible protein, inducible system and target plasmid ratios, where a, b and c are parameters subject to least square error fitting

Noise

Due to the noise in experimental measurements, we can directly apply it in the model as well. When determining fold repression ratios, standard deviations of up to 15 % were observed.

Results

The Switch (top level)
p0
p1
p2
p3
Inducible system (middle level)
p4
p5
p6
p7
Inducible proteins (bottom level)
p8
p9

The main goal of this particular model was to help determine the input ratios for plasmids that make up the switch system. The first confirmation was that if the masses of all plasmids will be equal, the switch will not be able to exhibit bistable behavior.

We partition the whole system into levels, with the Switch being the top level and the Pristinamycin/Erithromycin inducible proteins the bottom level. It is obvious that a plasmid on a given level influences another level only in the direction bottom -> top, so as we go downwards, the masses shall increase to have more influence on the targeted upper level. Hence the relation:

p0, p1, p2, p3 < p4, p5, p6, p7 < p8, p9

Next, the ratio between repressor and activator constructs was examined. To preserve symmetry, we assume:

p0 = p2, p1 = p3, p4 = p6, p5 = p7, p8 = p9

All the following ratios will be given in the form p0 : p1 (repressor:activator). Testing began at the 1:1 ratio, and we gradually increased both the repressor and activator to observe the qualitative behavioral change. The Switch exhibited bistable behavior for all ratios between 10:1 until 1:5, as can be seen in Scroll Box 1.

Scroll Box 1. Results for valid range of activator:repressor plasmid ratios.


The whole range in which the simulation reports bistable behaviour is thus:

[10:1, 9:1, 8:1, 7:1, 6:1, 5:1, 4:1, 3:1, 2:1, 1:1, 1:2, 1:3, 1:4, 1:5]

Taking the median of the above range, we conclude that the optimal ratio of input masses for wet lab experiments is at around three to one in favour of the repressor plasmids.

Source code

All source code for the model and simulations described above can be found here;

References

Alon, U. (2007) An introduction to systems biology: design principles of biological circuits. Chapman & Hall/CRC.

Batard, P., and Wurm, F. (2001) Transfer of high copy number plasmid into mammalian cells by calcium phosphate transfection. Gene 270, 61-68.

Chatterjee, A., Kaznessis, Y., and Hu, W. (2006) Tweaking biological switches through a better understanding of bistability behavior. Current opinion in biotechnology 19, 475-81.

Gardner, T., Cantor, C., and Collins, J. (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339-42.

Batard, P., and Wurm, F. (2001) Transfer of high copy number plasmid into mammalian cells by calcium phosphate transfection. Gene 270, 61-68.

Malphettes, L., and Fussenegger, M. (2006) Impact of RNA interference on gene networks. Metabolic engineering 8, 672-83.

Tigges, M., Marquez-Lago, T., Stelling, J., and Fussenegger, M. (2009) A tunable synthetic mammalian oscillator. Nature 457, 309-12.

Zakharova, A., Kurths, J., Vadivasova, T., and Koseska, A. (2011) Analysing dynamical behavior of cellular networks via stochastic bifurcations. PloS one 6, e19696.


Next: Interactive Simulations >>