Team:Tsinghua-A/Modeling

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<div style="position:relative;left:30px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling"><img src="https://static.igem.org/mediawiki/2011/b/b7/ThuA_A2.png" width="150px" height="100px"></A></div>
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<P ALIGN=CENTER><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Team/mem"><FONT COLOR="#99284c"><FONT FACE="Arial, sans-serif"><FONT SIZE=4 STYLE="font-size: 15pt"><SPAN LANG="en-US">Members</SPAN></FONT></FONT></FONT><FONT COLOR="#6b4794"><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US">
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</SPAN></FONT></FONT></A><FONT COLOR="#6b4794"><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US">
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<div style="position:relative;left:50px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P1A"><img src="https://static.igem.org/mediawiki/2011/0/0d/ThuA_B1.png" width="110px" height="100px"></A></div>
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  </SPAN></FONT></FONT><FONT COLOR="#6b4794"><FONT FACE="Arial, sans-serif"><FONT SIZE=4 STYLE="font-size: 15pt"><SPAN LANG="en-US">|
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  </SPAN></FONT></FONT></FONT><A HREF="https://2011.igem.org/Team:Tsinghua-A/Team/gal"><FONT COLOR="#800000"><FONT FACE="Arial, sans-serif"><FONT SIZE=4 STYLE="font-size: 15pt"><SPAN LANG="en-US">Gallery
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<div style="position:relative;left:70px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P2A"><img src="https://static.igem.org/mediawiki/2011/b/b6/ThuA_C1.png" width="110px" height="60px"></A></div>
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</SPAN></FONT></FONT></FONT></A><FONT COLOR="#99284c"><FONT FACE="Arial, sans-serif"><FONT SIZE=4 STYLE="font-size: 15pt"><SPAN LANG="en-US">
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  |    </SPAN></FONT></FONT></FONT><A HREF="https://2011.igem.org/Team:Tsinghua-A/Team/ack"><FONT COLOR="#800000"><FONT FACE="Arial, sans-serif"><FONT SIZE=4 STYLE="font-size: 15pt"><SPAN LANG="en-US">Attributions</SPAN></FONT></FONT></FONT></A></SPAN></FONT></P><br><br>
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<div style="position:relative;left:90px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P3A"><img src="https://static.igem.org/mediawiki/2011/6/6e/ThuA_D1.png" width="110px" height="60px"></A></div>
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<P ALIGN=LEFT><BR><BR>
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<div style="position:relative;left:110px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P4"><img src="https://static.igem.org/mediawiki/2011/6/6a/ThuA_E1.png" width="110px" height="120px"></A></div>
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<div class="slider" style="padding-buttom:20px">
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<p><IMG SRC="https://static.igem.org/mediawiki/2011/1/13/ModelBack.jpg" ALIGN=bottom WIDTH=750 HEIGHT=175 BORDER=0 ISMAP></div>
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<div class="nav">
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<table id="toc" class="toc">
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<td>
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<div id="toctitle">
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<h2>Contents</h2>
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</div>
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<ul>
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<li class="toclevel-1 tocsection-1"><a href="#Introduction"><span class="tocnumber">1</span> <span class="toctext">Introduction to Model</span></a></li>
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<li class="toclevel-1 tocsection-2"><a href="#Original Full Model"><span class="tocnumber">2</span> <span class="toctext">Original Full Model</span></a></li>
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<li class="toclevel-1 tocsection-3"><a href="#Simplified DDE Model"><span class="tocnumber">3</span> <span class="toctext">Simplified DDE Model</span></a></li>
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<li class="toclevel-1 tocsection-4"><a href="#Dimensionless Model"><span class="tocnumber">4</span> <span class="toctext">Dimensionless Model</span></a></li>
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<li class="toclevel-1 tocsection-5"><a href="#Quorum Sensing"><span class="tocnumber">5</span> <span class="toctext">Quorum Sensing Effect</span></a></li>
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<li class="toclevel-1 tocsection-6"><a href="#References"><span class="tocnumber">6</span> <span class="toctext">References</span></a></li>
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</ul>
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</td>
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</tr>
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</table>
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<br>
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<div class="slider">
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<p><IMG SRC="https://static.igem.org/mediawiki/2011/2/2b/000.png" NAME="graph1" ALIGN=bottom WIDTH=20 HEIGHT=20 BORDER=0 ISMAP><A HREF="https://static.igem.org/mediawiki/2011/9/9a/Modeling_Wiki.pdf"><U><I>Download the full text </I></U></A><IMG SRC="https://static.igem.org/mediawiki/2011/0/08/Thu_matlab.png" NAME="graph2" ALIGN=BOTTOM WIDTH=20 HEIGHT=20 BORDER=0 ISMAP><A HREF="https://static.igem.org/mediawiki/2011/c/c6/Thu_A_Matlab_Code.zip"><U><I>Download the source code package(Matlab)</I></U></A></P></div>
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<h1 id="Introduction">Introduction to Model</h1><hr width="100%" size=2 color=gray>
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<div class="imgbox">
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/0/03/001.png" width = "430px" height="148px"/>
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/b/b0/002.png" width = "430px" height="148px" />
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<p class="cite">Designed gene circuit in cell A and cell B</p>
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</div>
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<p>In our project, we designed a quorum-sensing oscillator which consists of two types of cells. The expression of the reporter genes (GFP of one cell type and GFP of another) of the cells of the same type can fluctuate synchronously and certain designs were made to adjust the phase and the period of oscillation. To understand the property of our system, we built a mathematical model based on ODEs (Ordinary Differential Equations) and DDEs (Delayed Differential Equations) to model and characterize this system. The simulation results helped us to deepen into further characteristics of the system.
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</p>
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<br><br>
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<div class="slider">
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<p><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P1A"><U><I>Read
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more</I></U></A></P>
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</div>
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<P id="Original Full Model"><h1>Original Full Model</h1></P>
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<hr width="100%" size=2 color=gray>
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<P>Firstly we
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described the system thoroughly without leaving out any
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seemingly unimportant actions and factors. As a result, the
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description of the system contains every possible mass actions as
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well as some hill kinetics, Henri-Michaelis-Menten kinetics, and the
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parameters were got from literature. The model was represented and
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simulated in the Matlab toolbox SIMBIOLOGY, but too many parameters make
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it difficult to do further analyses, So here we only listed all 19 ODEs
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and a reletive parameter table( see <A HREF="https://static.igem.org/mediawiki/2011/9/9a/Modeling_Wiki.pdf">attached pdf file</A>).
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</P>
</P>
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<P ALIGN=CENTER><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US"><FONT FACE="Arial, sans-serif"><FONT SIZE=4><SPAN LANG="en-US">Tsinghua-A
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<br>
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2011 iGEM Team consists of 8 undergraduates, together
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<div class="slider">
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with professors on biology and information acting as advisors.</SPAN></FONT></FONT></SPAN></FONT></P>
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<p><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P2A"><U><I>Read
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<P ALIGN=CENTER><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US"><FONT FACE="Arial, sans-serif"><FONT SIZE=4><SPAN LANG="en-US">The
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more</I></U></A></P>
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letter &lsquo;</SPAN></FONT></FONT><FONT FACE="Arial, sans-serif"><FONT SIZE=4><SPAN LANG="en-US">A</SPAN></FONT></FONT><FONT FACE="Arial, sans-serif"><FONT SIZE=4><SPAN LANG="en-US">&rsquo;
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</div>
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stands for &lsquo;Automation&rsquo;, for that most of our teammates
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<P id="Simplified DDE Model"><h1>Simplified DDE</h1></P>
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come from Department of Automation, School of Information Science and
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<hr width="100%" size=2 color=gray>
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Technology. With the background of EECS, we determine to achieve a
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harmonious combination of biology and information science in a
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<div class="imgbox">
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special and innovative perspective.</SPAN></FONT></FONT></SPAN></FONT></P>
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/b/b0/003.png" width = "440px" height="310px"/>
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<P ALIGN=CENTER><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US"><FONT FACE="Arial, sans-serif"><FONT SIZE=4><SPAN LANG="en-US">This
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<p class="cite">Simplified DDEs</p>
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is our first year participating in iGEM. We will do our uttermost!</SPAN></FONT></FONT></SPAN></FONT></P>
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</div>
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<P ALIGN=LEFT><BR><BR>
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<P>
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original model contains too many factors for analyzing the general
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property of system. To understand the essential characters of the
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oscillator, we simplify the original model according to certain
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appropriate assumptions, like Quasi-equilibrium
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for fast reactions.</P>
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<P>After series of derivation based on those assumptions, we came
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up with the following set of DDEs (Delay Differential Equations)
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which contains only 6 equations, see the figure right. And it
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would be much more convenient for us to do some neccessary analyses
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and research into the mathematical essence of our model.
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</P>
</P>
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<P ALIGN=Center><img src="http://bioinfo.au.tsinghua.edu.cn/member/IGEM/foto_mem/111.jpg"></P>
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<P ALIGN=CENTER><FONT COLOR="#333333"><FONT FACE="Arial, sans-serif"><FONT SIZE=2><SPAN LANG="en-US"><B>In
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the back(from left):</B> Junyu Chen, Qi Sang, Silu Yang, Lei Wei ,
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Weixi Liao, Pei Xie, Jian Wen, Zhirong Wu, Honglei Liu, Ying
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Liu(researcher at the same lab)</SPAN></FONT></FONT></FONT></P>
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<P ALIGN=CENTER><FONT COLOR="#333333"><FONT FACE="Arial, sans-serif"><FONT SIZE=2><SPAN LANG="en-US"><B>In
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the front(from left):</B> Dr Chen, Dr Wang</SPAN></FONT></FONT></FONT></P>
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<div class="imgbox2">
 
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/d/d5/004.png" width = "440px" height="310px"/>
 
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<p class="cite">Figure shows all variables are oscillating</p>
 
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</div>
 
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<P>We
 
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coded the system by DDE description in MATLAB and did simulation
 
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analysis accordingly. The result showed that the system could
 
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oscillate under certain parameters.</P>
 
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<P>To
 
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further understand what parameters could make the system oscillate,
 
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we did bifurcation analysis on the Hill parameters. What we had to do
 
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was find the critical points where the system can nearly oscillate
 
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but a little disruption may lead to a steady state.</P>
 
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<P>Depicting
 
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all those critical points, as shown in the figure, the system could
 
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oscillate when cellB's Hill parameters were located in the
 
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area named <FONT COLOR="#00b0f0"></FONT><FONT COLOR="#00b0f0"><I><B>Bistable</B></I></FONT><FONT COLOR="#00b0f0"></B></I>.</P>
 
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<div class="imgbox3">
 
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/2/20/005.png" width = "540px" height="300px"/>
 
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<p class="cite">The figure right is the phase trajectory of two signal molecules in environment,
 
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the more it looks like a circle, the more steadily our system will oscillate.</p>
 
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</div>
 
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<div class="imgbox4">
 
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/1/18/006.png" width = "370px" height="300px"/>
 
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<p class="cite">Our system oscillates when parameters were selected in the area named 'Bistable'</p>
 
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</div>
 
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<div class="imgbox5">
 
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<img class="border" style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/e/e8/007.png" width = "370px" height="280px"/>
 
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</div>
 
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<br><br>
 
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<div class="temp"><P>By
 
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adjusting certain parameters, we saw that the oscillation&rsquo;s
 
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period and phase could be controlled properly, which is the most
 
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impressive character of our system. Here we present a figure that the
 
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oscillation phase was adjusted by adding araC, which could induce the
 
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pBad promoter, in cell type B. After adding araC to our system at
 
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certain time, the oscillation was interrupted at beginning, but could
 
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gradually recover and finally, the phase was changed.</P></div>
 
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<br><br><br><br><br><br>
 
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<div class="slider">
 
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<p><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P3A"><U><I>Read
 
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more</I></U></A></P>
 
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<P id="Dimensionless Model"><h1>Dimensionless Model</h1></P>
 
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<hr width="100%" size=2 color=gray>
 
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<P>In
 
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order to make a further analysis on stability of the system, and
 
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sensitivity of parameters, we further simplified the model to make
 
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them dimensionless. In addition, we tried to introduce feedback to
 
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our system and made a brief analysis on different types of
 
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feedback we introduced. Some analyses were similar to the simplified
 
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DDE model, and you can see more details by clicking
 
-
<A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P4">read
 
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more</A></P>
 
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<br>
 
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<div class="slider">
 
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<p><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P4"><U><I>Read
 
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more</I></U></A></P>
 
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<P id="Quorum Sensing"><h1>Quorum Sensing Effect</h1></P>
 
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<hr width="100%" size=2 color=gray>
 
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<P>What
 
-
we have analyzed so far is focused on two-cell oscillation.
 
-
Quorum-sensing oscillator is not
 
-
simply a matter of expansion in magnitude, but a matter of robustness
 
-
in allowing difference of each individual cell. Moreover, we test the
 
-
adjustment of phase and period of oscillation in this part.</P>
 
-
<P>As
 
-
we all know, no two things in this world are exactly the same, so do
 
-
cells. The major differences between individual cells that we take
 
-
into consideration include:</P>
 
-
<P><B>●Each cell's activity of promoter is varied, so each cell has
 
-
different rate to generate AHL.</B></P>
 
-
<P><B>●The initial amount of AHL may be disproportionally distributed among
 
-
cells.</B></P>
 
-
<P>The rate of generating AHL is closely related to parameter m and n.
 
-
Therefore, we introduce randomness to both parameters by letting them
 
-
obey normal distribution, that is:
 
-
</P>
 
-
<P ALIGN=CENTER style="text-intent:0em">m(i)= &mu;1+<I>N</I>(0,&sigma;1);</P>
 
-
<P ALIGN=CENTER style="text-intent:0em">n(i)= &mu;2+<I>N</I>(0,&sigma;2);</P>
 
-
<P ALIGN=LEFT><A NAME="OLE_LINK63"></A><A NAME="OLE_LINK62"></A>&mu;<SPAN LANG="en-US">1
 
-
and &mu;2 are the average ability of generating 30C6HSL and 3012CHSL,
 
-
and normal distribution-- </SPAN><SPAN LANG="en-US"><I>N</I></SPAN><SPAN LANG="en-US">(0,&sigma;)--describes
 
-
the fluctuations of AHL generating rate in individual cell. We then
 
-
expanded our equations from 2 cells to a population of cells. Each
 
-
cell share a mutual environment in which we assume that AHL in
 
-
environment is proportionally distributed.</SPAN></SPAN></P>
 
-
<P ALIGN="center" style="text-intent:0em"><IMG SRC="https://static.igem.org/mediawiki/2011/1/17/008.png" WIDTH=800 HEIGHT=600 BORDER=0></P>
 
-
<P>The
 
-
figures indicate that our system can oscillate synchronically being
 
-
able to tolerate differences at certain range among a population of
 
-
cells.</P>
 
-
<P>We
 
-
also tested whether the oscillation is dependent on initial
 
-
distribution of AHL by changing the initial amount drastically by
 
-
letting them follow uniform distribution. That is:</P>
 
-
<P ALIGN="center" style="text-intent:0em">Initial(i)= <I>U</I>(0,20);</P>
 
-
<P>Based
 
-
on this distribution restraining the initial AHL concentration in
 
-
each cell, we simulated out a figure as follows.</P>
 
-
<P ALIGN="center" style="text-intent:0em"><IMG SRC="https://static.igem.org/mediawiki/2011/d/d2/009.png" WIDTH=800 HEIGHT=600 BORDER=0></P>
 
-
<P>The
 
-
results demonstratively give evidence proving that our system can
 
-
start to oscillate synchronically given variant initial starting
 
-
status.</P>
 
-
<br>
 
-
 
-
<P id="References"><h1>References</h1></P>
 
-
<hr width="100%" size=2 color=gray>
 
-
<P>[1]
 
-
Uri Alon, (2007). Network motifs: theory and experimental approaches.
 
-
Nature.</P>
 
-
<P>[2]
 
-
Chunbo Lou, Xili Liu, Ming Ni, et al. (2010). Synthesizing a novel
 
-
genetic sequential logic circuit: a push-on push-off switch.
 
-
Molecular Systems Biology.</P>
 
-
<P>[3]
 
-
Tal Danino, Octavio Mondragon-Palomino, Lev Tsimring &amp; Jeff Hasty
 
-
(2010). A synchronized quorum of genetic clocks. Nature.</P>
 
-
<P>[4]
 
-
Marcel Tigges, Tatiana T. Marquez-Lago, Jorg Stelling &amp; Martin
 
-
Fussenegger (2009). A tunable synthetic mammalian oscillator. Nature.</P>
 
-
<P>[5]
 
-
Sergi Regot, Javio Macia el al. (2010). Distributed biological
 
-
computation with multicellular engineered networks. Nature.</P>
 
-
<P>[6]
 
-
Martin Fussenegger, (2010). Synchronized bacterial clocks. Nature.</P>
 
-
<P>[7]
 
-
Andrew H Babiskin and Christina D Smolke, (2011). A synthetic library
 
-
of RNA control modules for predictable tuning of gene expression in
 
-
yeast. Molecular Systems Biology.</P>
 
-
<P>[8]
 
-
Santhosh Palani and Casim A Sarkar, (2011). Synthetic conversion of a
 
-
graded receptor signal into a tunable, reversible switch. Molecular
 
-
Systems Biology.</P>
 
-
<P>[9]
 
-
Nancy Kopell, (2002). Synchronizing genetic relaxation oscillation by
 
-
intercell signaling. PNS</P>
 
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Tsinghua-A 2011 iGEM Team consists of 8 undergraduates, together with professors on biology and information acting as advisors.

The letter ‘A’ stands for ‘Automation’, for that most of our teammates come from Department of Automation, School of Information Science and Technology. With the background of EECS, we determine to achieve a harmonious combination of biology and information science in a special and innovative perspective.

This is our first year participating in iGEM. We will do our uttermost!



In the back(from left): Junyu Chen, Qi Sang, Silu Yang, Lei Wei , Weixi Liao, Pei Xie, Jian Wen, Zhirong Wu, Honglei Liu, Ying Liu(researcher at the same lab)

In the front(from left): Dr Chen, Dr Wang

 

 

 





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