Team:Tokyo Tech/Modeling/Analysis of C4HSL-dependent Switch

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	       <h2 class="title">Modeling</h2>
             <span class="meta">Analysis of C4HSL-dependent Switch </span>
             <div class="entry-long">
               <p>&nbsp;</p>
                <div id="gototop"><a href="#"><img src="https://static.igem.org/mediawiki/2014/5/55/Tokyo_Tech_Go-to-top-icon.png" height="50" /></a></div>

               <p align="center"><span class="title-small">Content</span></p>
               		  <p align="left" class="info-24"><a href="#1">1. Motivation </a></p>			  
	          		  <p align="left" class="info-24"><a href="#2">2. Analysis </a></p>
					  <p align="left" class="info-18"><a href="#2.1">2.1. Problem definition </a></p>
					  <p align="left" class="info-18"><a href="#2.2">2.2. Nullclines and stable state</a></p>
                      <div class="title" style="clear: both;">&nbsp;</div>
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                   <td width="890" class="entry-long"><a name="1" id="1"></td>
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                   <td>&nbsp;</td>
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                   <td><h2>1. Motivation</h2></td>
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                   <td><p class="info-18">In our story, Bank has to  change its state from collection state to distribution state, and vice versa  depending on the concentration of C4HSL.</p></td>
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                   <td><p class="info-18">We analyzed the parameter  range which can realize the mechanism.  </p></td>
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                   <td>&nbsp;</td>
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                   <td class="entry-long">&nbsp;<a name="2" id="2"></td>
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                   <td>&nbsp;</td>
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                   <td><h2>2. Analysis</h2><a name="2.1" id="2.1"></td>
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                   <td><h1>2.1. Problem definition</h1></td>
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                   <td><p class="info-18">The main components of Bank  circuit are shown below.</p></td>
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                   <td><div align="center"><a href="https://2014.igem.org/File:Tokyo_Tech_C4HSL_dependent.png"><img src="https://static.igem.org/mediawiki/2014/a/a8/Tokyo_Tech_C4HSL_dependent.png"  width="600"/></a></div></td>
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                   <td><div align="center"><strong>Fig. 4-3-2-1.</strong> C4HSL dependent switch</div></td>
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                   <td>&nbsp;</td>
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                   <td><p class="info-18">The equations for the components  are described in Fig. 4-3-2-2. RhlR is ignored in the equations because it is  constantly expressed in the cell. Also, AiiA and RhlI are ignored because it is  not related to the following analysis.</p></td>
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                   <td>&nbsp;</td>
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                   <td><div align="center"><a href="https://2014.igem.org/File:Tokyo_Tech_Equations_for_C4HSL.jpg"><img src="https://static.igem.org/mediawiki/2014/a/aa/Tokyo_Tech_Equations_for_C4HSL.jpg"  width="700"/></a></div></td>
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                   <td><div align="center"><strong>Fig. 4-3-2-2.</strong> equations for C4HSL dependent switch</div></td>
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                   <td>&nbsp;</td>
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                   <td><p class="head">What we want to achieve is</p></td>
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                   <td><p class="info-18">1. In the high concentration of C4HSL, Bank circuit is  stably in collection state. TetR expresses highly and LacI doesn’t express  much.</p></td>
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                   <td><p class="info-18">2. In the low concentration of C4HSL, Bank circuit is stably  in the distribution state. LacI expresses highly and TetR doesn’t express much.</p></td>
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                   <td>&nbsp;<a name="2.2" id="2.2"></td>
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                   <td><h2>2.2 Nullclines and stable state</h2></td>
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                   <td><p class="info-18">Since our aim is to estimate  stable state, nullclines for each equation play crucial role. Equations for  nullclines of each protein are described below.</p></td>
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                   <td>&nbsp;</td>
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                   <td><div align="center"><a href="https://2014.igem.org/File:Tokyo_Tech_Nullcline_equations.jpg"><img src="https://static.igem.org/mediawiki/2014/1/18/Tokyo_Tech_Nullcline_equations.jpg"  width="700"/></a></div></td>
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                   <td><div align="center"><strong>Fig. 4-3-2-3.</strong> nullcline equations for LacI and  TetR</div></td>
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                   <td>&nbsp;</td>
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                   <td><p class="head">In terms of these equations,  our aim is translated as follows.</p></td>
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                   <td><p class="info-18">When the value of [C4] is high, these nullclines  have to have one intersection which has high value on [TetR] and low value on  [LacI]. </p></td>
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                   <td>&nbsp;</td>
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                   <td><div align="center"><a href="https://2014.igem.org/File:Tokyo_Tech_Two_nullclines_intersect.jpg"><img src="https://static.igem.org/mediawiki/2014/d/df/Tokyo_Tech_Two_nullclines_intersect.jpg"  width="500"/></a></div></td>
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                   <td><div align="center"><strong>Fig. 4-3-2-4.</strong> Two nullclines intersect on the  point which is on high TetR concentration and low LacI concentration. Green  line shows the equation (1) and blue line shows the equation (2).</div></td>
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                   <td>&nbsp;</td>
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                   <td><p class="info-18">To meet this requirement, we have to make the  maximum expression rate of Prhl/lac should be high enough to make the nullclines  have only one intersection.</p></td>
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                   <td><p class="info-18">When the value of [C4] is low, these nullclines  have to have one intersection which has low value on [TetR] and high value on  [LacI]</p></td>
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                   <td>&nbsp;</td>
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                   <td><div align="center"><a href="https://2014.igem.org/File:Tokyo_Tech_Two_nullclines_intersect_2.jpg"><img src="https://static.igem.org/mediawiki/2014/0/03/Tokyo_Tech_Two_nullclines_intersect_2.jpg"  width="500"/></a></div></td>
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                   <td><div align="center"><strong>Fig. 4-3-2-5.</strong> Two nullclines  intersect on the point which is on low TetR concentration and high LacI  concentration. Green line shows the equation (1) and blue line shows the  equation (2).</div></td>
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                   <td>&nbsp;</td>
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                   <td><p class="info-18">This condition can be satisfied with any parameter  values because the C4HSL concentration can be 0. This make the intersection of  the two nullclines to have one intersection with any parameter values.</p></td>
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                   <td><p class="info-18">With the optimized parameter values, the system was  confirmed to work as we expected.</p></td>
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                   <td>&nbsp;</td>
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                   <td><div align="center"><a href="https://2014.igem.org/File:Tokyo_Tech_LacI_concentration.png"><img src="https://static.igem.org/mediawiki/2014/6/6a/Tokyo_Tech_LacI_concentration.png"  width="500"/></a></div></td>
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                   <td><div align="center"><strong>Fig. 4-3-2-6.</strong> LacI concentration depending on  C4HSL</div></td>
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                   <td>&nbsp;</td>
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                   <td><p class="info-18">When the C4HSL concentration gradually decreases, LacI will be expressed following the green line as shown in Fig. 4-3-2-6. On the other hand, when the C4HSL concentration increases, LacI will be expressed following the blue line as shown in Fig. 4-3-2-6. </p></td>
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