Difference between revisions of "Team:HKUST-Rice/Modeling"

 
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<div class= "project_superrow">
 
<div class= "project_superrow">
 
<div id= "page_title"><h1>Modeling</h1></div>
 
<div id= "page_title"><h1>Modeling</h1></div>
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<p style="color:#5570b0; font-size: 130%"> Phosphate sensor </p></a>
 
<p style="color:#5570b0; font-size: 130%"> Phosphate sensor </p></a>
 
</div>
 
</div>
 +
 
<div class="project_content">
 
<div class="project_content">
 
<div class="project_row">
 
<div class="project_row">
 +
<h1>Introduction</h1>
 +
<p>To fully appreciate the mechanism of our biosensor and its behavior in an ideal situation, we explored the structure and dynamics
 +
of our system by creating a mathematical model of the reaction kinetics. We studied the dynamics of the Kdp system using a <i>P<sub>KdpF</sub></i>
 +
- GFP generator (BBa_E0240) in pSB3K3 backbone in a DH10B <i>E. coli</i> strain. Ordinary differential equations were derived to demonstrate how
 +
potassium ions concentration interact with the endogenous Kdp system, thus affecting the GFP expression of the cell.
 +
Modeling was done using MATLAB R2015a.</p>
 +
<p>In addition, by using the prediction model, users of our potassium biosensor can estimate the potassium concentration
 +
of cultures and mediums by obtaining fluorescence intensity per cell using flow cytometry.</p>
 +
</div>
 +
 +
<div class="project_row">
 +
<hr class="para">
 +
<h1>Prediction Model</h1>
 +
<div class="project_image">
 +
<img src="https://static.igem.org/mediawiki/2015/f/fb/HKUST-Rice_2015_Modeling_20.jpg" alt="image caption">
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        </div>
 +
                </div>   
 +
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<div class="project_row">
 +
<hr class="para">
 
<h1>Model's Assumption</h1>
 
<h1>Model's Assumption</h1>
−
<p>The effect of the endogenous Kdp system of E.coli was neglected.<br><br>
+
<p class="subTitle">The effect of the endogenous Kdp system of <i>E. coli</i> was neglected.</p>
−
In our engineered E.coli, it contains the inserted plasmid of PKdpF plus green fluorescence protein generator (BBa_E0240) in pSB3K3 backbone as well as the endogenous Kdp operon, and both operons have the same promoter, PKdpF. As a matter of fact, titration by the endogenous kdp operon of the transcription inducer, phosphorylated KdpE which binds to PKdpF was expected initially. And the titration of phosphorylated KdpE is anticipated to lower the expression of GFP. However, when the DNA copy number of both endogenous and the inserted operons were determined, it was found that the number of endogenous kdp operon is 10 times smaller than that of the inserted one:
+
<p>In our engineered <i>E. coli</i>, titration by the endogenous <i>kdp</i> operon of the transcription regulator, phosphorylated KdpE which binds to <i>P<sub>KdpF</sub></i>, was expected initially. This titration of phosphorylated KdpE is anticipated to lower  
−
</p>
+
the expression of GFP. However, since the native DNA copy number is only an 11<sup>th</sup> of the pSB3K3 plasmid copy number, the effect
 +
of endogenous Kdp system was neglected.
 +
</p>
  
 +
<!--<div class="project_image">
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<p>This implied that the number of endogenous promoter PKdpF is ten times smaller than that of the inserted operon and accounts only 8.33% of the total number of promoter PKdpF in the engineered E.coli. Therefore, the titration effect of phosphorylated KdpE becomes insignificant. As a result, the effect of endogenous Kdp system was negligible.
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<div class="project_image">
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<br><br>
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<img id="copyNumber" src="https://static.igem.org/mediawiki/2015/4/44/HKUST-Rice_15_Modeling_1c.png" alt="image caption">
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Level of KdpD, KdpE and KdpF were assumed to be constant
+
</div>-->
−
<br><br>
+
−
In accordance to [Kremling A. 04], in the potassium ions concentration range which we were studying, from 0mM to 0.02 mM, the fluctuation of the concentration KdpF as well as KdpD and KdpE was only within 10 µM and 3 µM respectively. Due to the small fluctuation range compared to the gene expression of GFP reporter, it was reasonable to assume the concentration of KdpD, KdpE and KdpF to be constant in the model.
+
<!--<p>This implied that the number of endogenous promoter P<sub>KdpF</sub> is ten times smaller than that of the inserted operon and accounts only 8.33% of the total number of promoter P<sub>KdpF</sub> in the engineered <i>E. coli</i>. Therefore, the titration effect of phosphorylated KdpE becomes insignificant. As a result, the effect of endogenous Kdp system was negligible.
−
<br><br>It was assumed that the initial concentration of mRNA for GFP, immature GFP and mature GFP equal to zero.
+
</p>-->
−
<br><br>
+
<p class="subTitle">Level of KdpD, KdpE and KdpF were assumed to be constant.</p>
−
It was assumed that all reactions below were in steady state such that:
+
−
<div class="project_image">
+
<p>In accordance to [Kremling A. 04], for the potassium ion concentration range which we were studying- 0 mM to 0.02 mM, the fluctuation of the concentration of KdpF as well as KdpD and KdpE was only within 10 μM and 3 μM respectively. Due to the small fluctuation range compared to the gene expression of GFP reporter, it was reasonable that KdpD, KdpE and KdpF concentrations were assumed to be constant in the model.
−
<img src="https://static.igem.org/mediawiki/2015/c/c1/Team_HKUST-Rice_2015_Modelling_2.PNG" alt="image caption">
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</p>
 +
<p>It was assumed that the initial concentration of mRNA for GFP, immature GFP and mature GFP was zero.</p>
 +
 +
<p>It was assumed that all reactions below were in steady state such that:</p>
 +
<div class="project_image">
 +
<img src="https://static.igem.org/mediawiki/2015/c/c1/Team_HKUST-Rice_2015_Modelling_2.PNG" alt="image caption">
 
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</div>
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                 </div>
 
                 </div>
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                 <div class="project_row">
 
                 <div class="project_row">
 
<hr class="para">
 
<hr class="para">
 
<h1>Equations of the Model:</h1>
 
<h1>Equations of the Model:</h1>
−
             <p><b>Phosphorylation of KdpD:</b></p>
+
             <p class="subTitle"><b>Phosphorylation of KdpD:</b></p>
 
             <div class="project_image">
 
             <div class="project_image">
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<img src="https://static.igem.org/mediawiki/2015/1/14/HKUST-Rice_2015_1a.png" alt="image caption">
 
</div>
 
</div>
  
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  <p><b>Phosphyl-group Transfer:</b></p>
+
  <p class="subTitle"><b>Phosphyl-group Transfer:</b></p>
 
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             <div class="project_image">
 
<img src="https://static.igem.org/mediawiki/2015/0/0a/Team_HKUST-Rice_2015_Modelling_4.PNG" alt="image caption">
 
<img src="https://static.igem.org/mediawiki/2015/0/0a/Team_HKUST-Rice_2015_Modelling_4.PNG" alt="image caption">
 
</div>
 
</div>
 
 
−
<p><b>Binding of KdpE to promoter PkdpF:</b></p>
+
<p class="subTitle"><b>Binding of KdpE to promoter PkdpF:</b></p>
 
             <div class="project_image">
 
             <div class="project_image">
 
<img src="https://static.igem.org/mediawiki/2015/8/8c/Team_HKUST-Rice_2015_Modelling_5.PNG" alt="image caption">
 
<img src="https://static.igem.org/mediawiki/2015/8/8c/Team_HKUST-Rice_2015_Modelling_5.PNG" alt="image caption">
 
</div>
 
</div>
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<p><b>Transcription:</b></p>
+
<p class="subTitle"><b>Transcription:</b></p>
 
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             <div class="project_image">
 
<img src="https://static.igem.org/mediawiki/2015/4/48/Team_HKUST-Rice_2015_Modelling_6.PNG" alt="image caption">
 
<img src="https://static.igem.org/mediawiki/2015/4/48/Team_HKUST-Rice_2015_Modelling_6.PNG" alt="image caption">
 
</div>
 
</div>
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<p><b>Translation:</b></p>
+
<p class="subTitle"><b>Translation:</b></p>
 
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             <div class="project_image">
 
<img src="https://static.igem.org/mediawiki/2015/a/af/Team_HKUST-Rice_2015_Modelling_7.PNG" alt="image caption">
 
<img src="https://static.igem.org/mediawiki/2015/a/af/Team_HKUST-Rice_2015_Modelling_7.PNG" alt="image caption">
 
</div>
 
</div>
−
<p><b>Green Fluorescent Protein maturation:</b></p>
+
<p class="subTitle"><b>Green Fluorescent Protein maturation:</b></p>
 
             <div class="project_image">
 
             <div class="project_image">
 
<img src="https://static.igem.org/mediawiki/2015/9/9e/Team_HKUST-Rice_2015_Modelling_8.PNG" alt="image caption">
 
<img src="https://static.igem.org/mediawiki/2015/9/9e/Team_HKUST-Rice_2015_Modelling_8.PNG" alt="image caption">
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</div>
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</div>
 +
<p> For parameters and variables, please click <a href="https://static.igem.org/mediawiki/2015/4/4e/Team_HKUST-Rice_2015_Parameters_and_Variables_list.pdf" target="_blank">here</a></p>
 
</div>
 
</div>
−
                    <div class="project_row">
 
−
<hr class="para">
 
−
<h1>Data point fitting to the model:</h1>
 
−
<p>The experimental data from FACS were used to fit in the prediction model; then we adapt the unit conversion from [Caitlin C, Jeniffer B 13] to convert GFP per cell fluorescence intensity to concentration of GFP per cell:<p>
 
−
<div class="project_image">
 
−
<img src="https://static.igem.org/mediawiki/2015/a/a8/Team_HKUST-Rice_2015_Modelling_9.PNG" alt="image caption">
 
−
</div>
 
  
 +
                             
 +
                    <!--<div class="project_row">
 
<hr class="para">
 
<hr class="para">
−
<h1>Prediction model:</h1>
+
<h1>Data Point Fitting to the Model:</h1>
−
<div class="project_image">
+
<p>The experimental data from FACS were used to fit in the prediction model; then we adapt the unit conversion from [Caitlin C, Jeniffer B 13] to convert GFP per cell fluorescence intensity to concentration of GFP per cell:<p>
−
<img src="https://static.igem.org/mediawiki/2015/f/f9/Team_HKUST-Rice_2015_Modelling_20.PNG" alt="image caption">
+
<div class="project_image">
 +
<img src="https://static.igem.org/mediawiki/2015/a/a8/Team_HKUST-Rice_2015_Modelling_9.PNG" alt="image caption">
 
</div>
 
</div>
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</div>
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</div>-->
  
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                     <!--<div class="project_row">
 
<hr class="para">
 
<hr class="para">
−
<h1>Parameters and Variables list</h1>
+
<h1>Parameters and Variables List</h1>
 
<center><table id="parameters">
 
<center><table id="parameters">
 
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes; '>
 
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes; '>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 
  mso-fareast-language:ZH-CN'>0.00087 1/&micro;M <span  >hr</span><o:p></o:p></span></p>
 
  mso-fareast-language:ZH-CN'>0.00087 1/&micro;M <span  >hr</span><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:4; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
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  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'>&alpha;: Adjustable proportionality coefficient of ATP</span></p>
 +
  </td>
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  <td  valign=top style='width:50%;border-top:none;border-left:
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  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
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  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
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  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'>0.001223</span></p>
 +
  </td>
 +
</tr> <tr style='mso-yfti-irow:4; '>
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  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
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  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
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  padding:0cm 5.4pt 0cm 5.4pt; '>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&beta;: Adjustable proportionality coefficient of ADP</span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
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  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
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  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.001223</span></p>
 
  </td>
 
  </td>
 
</tr>
 
</tr>
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<table id="variables">
 
<table id="variables">
 
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
 
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
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  <td style="border-top:1px solid">Variables<o:p></o:p></td>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'>Variables<o:p></o:p></span></p>
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  </td>
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  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'><o:p>&nbsp;</o:p></span></p>
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  mso-fareast-language:ZH-CN'>-</span></p>
 
  </td>
 
  </td>
 
</tr>
 
</tr>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'><o:p>&nbsp;</o:p></span></p>
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  mso-fareast-language:ZH-CN'>Adjustable parameter</span></p>
 
  </td>
 
  </td>
 
  <td  valign=top style='width:50%;border-top:none;border-left:
 
  <td  valign=top style='width:50%;border-top:none;border-left:
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'><o:p>&nbsp;</o:p></span></p>
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  mso-fareast-language:ZH-CN'>-</span></p>
 
  </td>
 
  </td>
 
</tr>
 
</tr>
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  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
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  mso-fareast-language:ZH-CN'><o:p>&nbsp;</o:p></span></p>
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  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 
  </td>
 
  </td>
 
</tr>
 
</tr>
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<p class="PICdiscription">Table 3. Variables list. </p>
 
<p class="PICdiscription">Table 3. Variables list. </p>
 
 
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<hr class="para">
−
<h1>Reference:</h1>
+
<h2>References</h2>
−
<p><br>Heermann R, Zigann K, Gayer S, Rodriguez-Fernandez M, Banga JR, et al. (2014) Dynamics of an Interactive Network Composed of a Bacterial Two- Component System, a Transporter and K+ as Mediator. PLoS ONE 9(2): e89671. doi:10.1371/journal.pone.0089671  
+
                                <p style="font-size:125%">Heermann R, Zigann K, Gayer S, Rodriguez-Fernandez M, Banga JR, et al. (2014) Dynamics of an Interactive Network Composed of a Bacterial Two- Component System, a Transporter and K+ as Mediator. PLoS ONE 9(2): e89671. doi:10.1371/journal.pone.0089671  
 
<br><br>Brewster RC, Jones DL, Phillips R (2012) Tuning Promoter Strength through RNA Polymerase Binding Site Design in Escherichia coli. PLoS Comput Biol 8(12): e1002811. doi:10.1371/journal.pcbi.1002811  
 
<br><br>Brewster RC, Jones DL, Phillips R (2012) Tuning Promoter Strength through RNA Polymerase Binding Site Design in Escherichia coli. PLoS Comput Biol 8(12): e1002811. doi:10.1371/journal.pcbi.1002811  
−
<br><br>Modeling, Simulation and Identification of the Dynamics of K Uptake in E. coli. (2014). Universitätsbibliothek der TU München.
+
<br><br>Modeling, Simulation and Identification of the Dynamics of K Uptake in E. coli. (2014). Universitatsbibliothek der TU Munchen.
 
<br><br>Kelly, Jason et al. “Measuring the activity of BioBrick promoters using an in vivo reference standard.” Journal of Biological Engineering 3.1 (2009): 4.
 
<br><br>Kelly, Jason et al. “Measuring the activity of BioBrick promoters using an in vivo reference standard.” Journal of Biological Engineering 3.1 (2009): 4.
  
−
<br><br>J. Gayer, Stefan. "Modeling, Simulation and Identification of the Dynamics of K Uptake in E. Coli." Technische Universität München Fachgebiet Für Systembiotechnologie (2013). Print.
+
<br><br>J. Gayer, Stefan. "Modeling, Simulation and Identification of the Dynamics of K Uptake in E. Coli." Technische Universitat Munchen Fachgebiet Fur Systembiotechnologie (2013). Print.
  
 
<br><br>Kremling, A., Heermann, R., Centler, F., & Gilles, E. (2004). Analysis of two-component signal transduction by mathematical modeling using the KdpD/KdpE system of Escherichia coli.
 
<br><br>Kremling, A., Heermann, R., Centler, F., & Gilles, E. (2004). Analysis of two-component signal transduction by mathematical modeling using the KdpD/KdpE system of Escherichia coli.
  
 
<br><br>Conboy, C., & Braff, J. (2013, May 29). Molecules of Equivalent GFP. Retrieved from http://openwetware.org/wiki/MEG
 
<br><br>Conboy, C., & Braff, J. (2013, May 29). Molecules of Equivalent GFP. Retrieved from http://openwetware.org/wiki/MEG
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<br><br>Epstein W (2003) The roles and regulation of potassium in bacteria. Prog Nucleic Acid Res Mol Biol 75: 293–320.
 
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Latest revision as of 14:55, 18 September 2015

Modeling

Introduction

To fully appreciate the mechanism of our biosensor and its behavior in an ideal situation, we explored the structure and dynamics of our system by creating a mathematical model of the reaction kinetics. We studied the dynamics of the Kdp system using a PKdpF - GFP generator (BBa_E0240) in pSB3K3 backbone in a DH10B E. coli strain. Ordinary differential equations were derived to demonstrate how potassium ions concentration interact with the endogenous Kdp system, thus affecting the GFP expression of the cell. Modeling was done using MATLAB R2015a.

In addition, by using the prediction model, users of our potassium biosensor can estimate the potassium concentration of cultures and mediums by obtaining fluorescence intensity per cell using flow cytometry.

Prediction Model

image caption

Model's Assumption

The effect of the endogenous Kdp system of E. coli was neglected.

In our engineered E. coli, titration by the endogenous kdp operon of the transcription regulator, phosphorylated KdpE which binds to PKdpF, was expected initially. This titration of phosphorylated KdpE is anticipated to lower the expression of GFP. However, since the native DNA copy number is only an 11th of the pSB3K3 plasmid copy number, the effect of endogenous Kdp system was neglected.

Level of KdpD, KdpE and KdpF were assumed to be constant.

In accordance to [Kremling A. 04], for the potassium ion concentration range which we were studying- 0 mM to 0.02 mM, the fluctuation of the concentration of KdpF as well as KdpD and KdpE was only within 10 μM and 3 μM respectively. Due to the small fluctuation range compared to the gene expression of GFP reporter, it was reasonable that KdpD, KdpE and KdpF concentrations were assumed to be constant in the model.

It was assumed that the initial concentration of mRNA for GFP, immature GFP and mature GFP was zero.

It was assumed that all reactions below were in steady state such that:

image caption

Equations of the Model:

Phosphorylation of KdpD:

image caption

Phosphyl-group Transfer:

image caption

Binding of KdpE to promoter PkdpF:

image caption

Transcription:

image caption

Translation:

image caption

Green Fluorescent Protein maturation:

image caption

For parameters and variables, please click here

References

Heermann R, Zigann K, Gayer S, Rodriguez-Fernandez M, Banga JR, et al. (2014) Dynamics of an Interactive Network Composed of a Bacterial Two- Component System, a Transporter and K+ as Mediator. PLoS ONE 9(2): e89671. doi:10.1371/journal.pone.0089671

Brewster RC, Jones DL, Phillips R (2012) Tuning Promoter Strength through RNA Polymerase Binding Site Design in Escherichia coli. PLoS Comput Biol 8(12): e1002811. doi:10.1371/journal.pcbi.1002811

Modeling, Simulation and Identification of the Dynamics of K Uptake in E. coli. (2014). Universitatsbibliothek der TU Munchen.

Kelly, Jason et al. “Measuring the activity of BioBrick promoters using an in vivo reference standard.” Journal of Biological Engineering 3.1 (2009): 4.

J. Gayer, Stefan. "Modeling, Simulation and Identification of the Dynamics of K Uptake in E. Coli." Technische Universitat Munchen Fachgebiet Fur Systembiotechnologie (2013). Print.

Kremling, A., Heermann, R., Centler, F., & Gilles, E. (2004). Analysis of two-component signal transduction by mathematical modeling using the KdpD/KdpE system of Escherichia coli.

Conboy, C., & Braff, J. (2013, May 29). Molecules of Equivalent GFP. Retrieved from http://openwetware.org/wiki/MEG

Epstein W (2003) The roles and regulation of potassium in bacteria. Prog Nucleic Acid Res Mol Biol 75: 293–320.