Team:Tsinghua-A/Modeling/P1A

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<P><FONT COLOR="#000000"><FONT FACE="Times New Roman, serif"><SPAN LANG="en-US"><FONT FACE="Arial, sans-serif"><FONT SIZE=5 STYLE="font-size: 20pt"><SPAN LANG="en-US"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling">Modeling</A></SPAN></FONT></FONT></FONT><FONT FACE="Arial, sans-serif"><FONT SIZE=5 STYLE="font-size: 20pt"><SPAN LANG="en-US">::</SPAN></FONT></FONT><FONT COLOR="#666600"><FONT FACE="Arial, sans-serif"><FONT SIZE=5 STYLE="font-size: 20pt"><SPAN LANG="en-US">Quorum-sensing Effect</SPAN></FONT></FONT></FONT></SPAN></FONT></P><br>
 
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<p>What we have done insofar 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 amplitude of oscillation in this part.</p>
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<div style="position:relative;left:60px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling"><img src="https://static.igem.org/mediawiki/2011/2/2f/ThuA_A1.png" width="110px" height="105px"></A></div>
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<p>As we all know, no two things in this world are the same, so do cells. The major difference of individual cell that we take into considerations is twofold:</p>
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<P><B>●Each cell's activity of promoter is varied, so each cell has
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different rate to generate AHL.</B></P>
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<P><B>●The initial amount of AHL may be disproportionally distributed among
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cells.</B></P>
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<P>The rate of generating AHL is closely related to parameter m and n.
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Therefore, we introduce randomness to both parameters by letting them
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obey normal distribution, that is:
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</P>
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<P ALIGN=CENTER>m(i)= &mu;1+<I>N</I>(0,&sigma;1);</P>
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<P ALIGN=CENTER>n(i)= &mu;2+<I>N</I>(0,&sigma;2);</P>
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<P>&mu;1 and &mu;2 are the average ability of generating 30C6HSL and 3012CHSL,
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and normal distribution--(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.</P>
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<div style="position:relative;left:80px;display:inline"><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling/P1A"><img src="https://static.igem.org/mediawiki/2011/6/63/ThuA_B2.png" width="130px" height="120px"></A></div>
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<p align="center" style="text-intend:0em"><b>Figure 16 100 Cells Varied in parameter m and n</b></p>
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<p>The figures indicate that our system can oscillate synchronically being able to tolerate differences among a population of cells. Furthermore, the figures prove that different ability of generating AHLs of cells have nothing to do with the period and phase of the oscillation. We can also see that the oscillation amplitude of each cell is to a greater extent varied when the Variance of interruption is enlarged.</p>
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<p>Moreover, we test 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>
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<P ALIGN=CENTER>Initial(i)= <I>U</I>(0,20);</P>
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<p>The results would give evidence to prove that our system can start to oscillate synchronically given variant initial starting numbers.</p>
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<p>Based on this distribution restraining the initial AHL concentration in each cell, we simulated out a figure as follows.</p>
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<div style="position:relative;left:100px;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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<p align="center" style="text-intend:0em"><b>Figure 17 100 Cells Varied in initial AHL concentration</b></p>
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<p>The results demonstratively give evidence proving that our system can start to oscillate synchronically given variant initial starting numbers.</p>
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<div style="position:relative;left:120px;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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<table id="toc" class="toc">
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<div id="toctitle">
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<h2>Contents</h2>
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<ul>
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<li class="toclevel-1 tocsection-1"><a href="#Construction"><span class="tocnumber">1</span> <span class="toctext">Construction of ODE equation</span></a></li>
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<li class="toclevel-1 tocsection-2"><a href="#Parameters"><span class="tocnumber">2</span> <span class="toctext">Parameters</span></a></li>
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<li class="toclevel-1 tocsection-3"><a href="#Results"><span class="tocnumber">3</span> <span class="toctext">Results</span></a></li>
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<h1 id="Construction">Construction of ODE equation</h1><hr width="100%" size=2 color=gray>
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<p>At our first step, we wanted to describe the system thoroughly without leaving out any seemingly unimportant actions and factors. As a result, the description of the system contains every possible mass actions as well as some hill kinetics, Henri-Michaelis-Menten. We came up a set of ODEs with 19 equations.</p>
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<img style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/0/03/001.png" width = "430px" height="150px"/>
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<p class="cite">Figure 1 designed circuit of cell I</p>
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<img style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/2011/b/b0/002.png" width = "430px" height="150px" />
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<p class="cite">Figure 2 designed circuit of cell II</p>
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<p>Promoter 1 and promoter 2 preceding lasR and luxR genes respectively are constant promoters, which will transcribe and translate into protein PlasR and PluxR. LA1 is the binding association of lasR and 30C12HSL(A2C1) and it can affect the subsequent promoter 2 which can be described by Hill Equation. The same goes to LA2. Gene luxI will be translated into protein PluxI which would generate 30C6HSL(A1C1) through enzymatic reaction. The AHL will diffuse through the membrane to the environment(A1e) and finally enter into Cell 2(A1C2). Protein PtetR which is translated from gene tetR represses promoter 5 which is responsible for transcription of gene lasI. Promoter 6 is constant for translation of protein PlasI. 30C12HSL(A2C2) is generated from Protein PlasI through enzymatic reaction. 30C12HSL in the environment is called A2e which will diffuse to Cell 1. aTc is added manipulatively to change the phase of oscillation by binding the protein PTetR. Therefore, we have these following ODEs:<br><br></p>
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<p><img style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/igem.org/9/9a/ThuAModel_1_1.png" width = "707px" height="1115px" /><br></p>
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<h1 id="Parameters">Parameters</h1><hr width="100%" size=2 color=gray>
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<p>The parameters are inherent factors determining the behaviors, properties of a system. We selected the quantities thoughtfully from previous iGEM teams and some others were found from published papers.</p>
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<p align="center"><img style="border-color:#B2B2B2;"src="https://static.igem.org/mediawiki/igem.org/c/c8/ThuAModel_1_2.png" width = "746px" height="1794px" /><br></p>
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<p class="cite">Table 1 Parameters of ODEs</p>
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<br><br><br>
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<h1 id="Results">Results</h1><hr width="100%" size=2 color=gray>
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<p>We simulated this system by SIMBIOLOGY, a toolbox embedded in MATLAB. However, unaware of the key parameters to which the system is sensitive, we felt difficult to control or adjust properly, and the simulation result of the system came into a damped oscillation. We ascribed the inability of our model to the fact that the precise descriptions contain too many equations and parameters and we felt obliged to establish a simplified model in place of the precise one for simulation and further analysis.</p>
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Contents

Construction of ODE equation

At our first step, we wanted to describe the system thoroughly without leaving out any seemingly unimportant actions and factors. As a result, the description of the system contains every possible mass actions as well as some hill kinetics, Henri-Michaelis-Menten. We came up a set of ODEs with 19 equations.

Figure 1 designed circuit of cell I

Figure 2 designed circuit of cell II

Promoter 1 and promoter 2 preceding lasR and luxR genes respectively are constant promoters, which will transcribe and translate into protein PlasR and PluxR. LA1 is the binding association of lasR and 30C12HSL(A2C1) and it can affect the subsequent promoter 2 which can be described by Hill Equation. The same goes to LA2. Gene luxI will be translated into protein PluxI which would generate 30C6HSL(A1C1) through enzymatic reaction. The AHL will diffuse through the membrane to the environment(A1e) and finally enter into Cell 2(A1C2). Protein PtetR which is translated from gene tetR represses promoter 5 which is responsible for transcription of gene lasI. Promoter 6 is constant for translation of protein PlasI. 30C12HSL(A2C2) is generated from Protein PlasI through enzymatic reaction. 30C12HSL in the environment is called A2e which will diffuse to Cell 1. aTc is added manipulatively to change the phase of oscillation by binding the protein PTetR. Therefore, we have these following ODEs:


Parameters

The parameters are inherent factors determining the behaviors, properties of a system. We selected the quantities thoughtfully from previous iGEM teams and some others were found from published papers.


Table 1 Parameters of ODEs




Results

We simulated this system by SIMBIOLOGY, a toolbox embedded in MATLAB. However, unaware of the key parameters to which the system is sensitive, we felt difficult to control or adjust properly, and the simulation result of the system came into a damped oscillation. We ascribed the inability of our model to the fact that the precise descriptions contain too many equations and parameters and we felt obliged to establish a simplified model in place of the precise one for simulation and further analysis.




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