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">
 +
        </div>
 +
                </div>   
 +
 +
<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">
 +
<img id="copyNumber" src="https://static.igem.org/mediawiki/2015/1/14/HKUST-Rice_2015_1a.png" alt="image caption">
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</div>
 
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<div class="project_image">
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<img id="copyNumber" src="https://static.igem.org/mediawiki/2015/5/5f/HKUST-Rice_15_Modeling_1b.png" alt="image caption">
 
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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.
+
<div class="project_image">
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<br><br>
+
<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">
+
</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">
 
</div>
 
</div>
−
 
 
                 </div>
 
                 </div>
 +
 
                 <div class="project_row">
 
                 <div class="project_row">
 +
<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">
−
<img src="https://static.igem.org/mediawiki/2015/2/22/Team_HKUST-Rice_2015_Modelling_2%3D3.PNG" alt="image caption">
+
<img src="https://static.igem.org/mediawiki/2015/1/14/HKUST-Rice_2015_1a.png" alt="image caption">
 
</div>
 
</div>
  
−
  <p><b>Phosphyl-group Transfer:</b></p>
+
  <p class="subTitle"><b>Phosphyl-group Transfer:</b></p>
 
             <div class="project_image">
 
             <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>
−
<p><b>Transcription:</b></p>
+
<p class="subTitle"><b>Transcription:</b></p>
 
             <div class="project_image">
 
             <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>
−
<p><b>Translation:</b></p>
+
<p class="subTitle"><b>Translation:</b></p>
 
             <div class="project_image">
 
             <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">
−
</div>
 
−
</div>
 
−
                    <div class="project_row">
 
−
<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>
−
<h1>Prediction model:</h1>
+
<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 class="project_image">
+
</div>
−
<img src="https://static.igem.org/mediawiki/2015/f/f9/Team_HKUST-Rice_2015_Modelling_20.PNG" alt="image caption">
+
 
 +
                             
 +
                    <!--<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>
−
<p style="font-size:120%">Reference:
+
</div>-->
−
<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  
+
 
 +
                    <!--<div class="project_row">
 +
<hr class="para">
 +
<h1>Parameters and Variables List</h1>
 +
<center><table id="parameters">
 +
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Parameters:<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
 +
  solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Values:<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:1; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>k<sub>1</sub>: Rate constant of forward
 +
  auto-phosphorylation<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.23 1/&micro;M <span  >hr</span><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:2; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>k<sub>-1</sub>:<sub> </sub>Rate constant of
 +
  backward auto-phosphorylation<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.0000051 1/&micro;M <span  >hr</span><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:3; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>k<sub>2</sub>: Rate constant of forward <span
 +
  >phosphyl</span>-group transfer<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.00227 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;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>k<sub>-2</sub>: Rate constant of backward <span
 +
  >phosphyl</span>-group transfer<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <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>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:4; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&alpha;: Adjustable proportionality coefficient of ATP</span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <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>
 +
</tr> <tr style='mso-yfti-irow:4; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <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:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <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>
 +
</tr>
 +
<tr style='mso-yfti-irow:5; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>K<sub>b</sub>: Dissociation constant (<span
 +
  ><i style='mso-bidi-font-style:normal'>KdpE</i></span>-DNA)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.0532 1/&micro;M<sup><o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:6; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>K<sub>h</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: Dissociation constant (<span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpF</i>-KdpE</span> <span  >dephosphorylation</span>
 +
  system)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.0532 &micro;M (adjustable)<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:7; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>k<sup>0</sup><sub>h</sub>: Reference <span
 +
  >k<sub>h</sub></span> value<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.00023 1/&micro;M <span  >hr</span>
 +
  (adjustable)<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:8; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>C<sup>0</sup><sub>K+</sub>: Reference
 +
  concentration of potassium ions <o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.02mM<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:9; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>tr</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: transcription rate constant<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>10600 hr<sup>-1</sup><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:10; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>z</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: mRNA degradation rate of <span  >kdpFABC</span>
 +
  and <span  >kdpDE</span> coding region<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>21.74 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:11; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>d</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: degradation rate of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpDE</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.2 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:12; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>d,F</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: degradation of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpF</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>4.8 hr<sup>-1</sup><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:13; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>tlD</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: translation rate constant of <span
 +
  ><i style='mso-bidi-font-style:normal'>KdpD</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>160 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:14; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>tlE</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: translation rate constant of <span
 +
  ><i style='mso-bidi-font-style:normal'>KdpE</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>8100 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:15; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>k<sub>tlF</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>: translation rate constant of <span
 +
  ><i style='mso-bidi-font-style:normal'>KdpF</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>5.4 hr<sup>-1</sup><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:16; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>u: growth rate of the cell (in K minimal medium,
 +
  2<sup>nd</sup> order)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-font-family:""Helvetica Neue", Helvetica, sans-serif";color:black;mso-fareast-language:
 +
  EN-US'>0.275466667 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:#660066;mso-fareast-language:ZH-CN'>(exp. obtained)<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:17; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>Ψ: basal activity of the promoter</span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.0017<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:18; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;color:black;mso-fareast-language:ZH-CN'>k<sub>deg,GFP,mRNA</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>: GFP mRNA degradation rate (1<sup>st</sup>
 +
  order)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.0048s<sup>-1 </sup><o:p></o:p></span></p>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>=17.28 /<span  >hr</span><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:19; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;color:black;mso-fareast-language:ZH-CN'>γ<sub>I</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>: Immature GFP degradation rate</span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.7 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:20; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;color:black;mso-fareast-language:ZH-CN'>γ<sub>m</sub></span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>: Mature GFP degradation rate<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.021 hr<sup>-1<o:p></o:p></sup></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:21; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>ρ: Immature GFP synthesis rate (</span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-themecolor:text1;mso-fareast-language:ZH-CN'>trans rate</span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>, 1<sup>st</sup> order)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-themecolor:text1;mso-fareast-language:ZH-CN'>1440 protein/<span
 +
  >hr</span>/mRNA (0.4protein/s/mRNA) <o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:22;mso-yfti-lastrow:yes; '>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  color:black;mso-fareast-language:ZH-CN'>w: GFP maturation rate (1<sup>st</sup>
 +
  order)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt; '>
 +
  <p  style='margin-right:-15.25pt'><span 
 +
  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:
 +
  ZH-CN'>6.48 hr<sup>-1</sup> <o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
</table>
 +
</center>
 +
<p class="PICdiscription">Table 1. Parameters list 1. </p>
 +
 +
<center>
 +
<table id="parameters">
 +
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Parameters<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
 +
  solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Values<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:1'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>ADP concentration<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.305 <span  >mM</span><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:2'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>ATP concentration<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>3.05 <span  >mM</span><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:3'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Initial concentration of mRNA (GFP)<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0/cell<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;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpF</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>10 &micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:5'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpE</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>2.6 &micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:6'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpD</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>2.6 &micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:7'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of inserted plasmid<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0.0183 &micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:8;mso-yfti-lastrow:yes'>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
 +
  padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Initial concentration of immature and mature GFP<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>0 /cell<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
</table>
 +
</center>
 +
<p class="PICdiscription">Table 2. Parameters list 2. </p>
 +
 
 +
<center>
 +
<table id="variables">
 +
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
 +
  <td style="border-top:1px solid">Variables<o:p></o:p></td>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
 +
  solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Denotation<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border:solid windowtext 1.0pt;
 +
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
 +
  solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Unit<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:1'>
 +
  <td>[kdpD]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpD</i></span><i style='mso-bidi-font-style:
 +
  normal'> </i><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:2'>
 +
  <td>[kdpD<sup>P</sup>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of phosphorylated <span
 +
  ><i style='mso-bidi-font-style:normal'>KdpD</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:3'>
 +
  <td>[kdpE<sup>P</sup>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of phosphorylated <span
 +
  ><i style='mso-bidi-font-style:normal'>KdpE</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:4'>
 +
  <td>[ADP]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of ADP molecules<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>mM</span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:5'>
 +
  <td>[ATP]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of ATP molecules<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>mM</span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:6'>
 +
  <td>[kdpF]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpF</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:7'>
 +
  <td>k<sub>3</sub></td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Rate constant of <span  >dephosphorylation</span>
 +
  of <span  ><i style='mso-bidi-font-style:normal'>KdpE</i></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>-</span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:8'>
 +
  <td>k<sub>h</sub></td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Adjustable parameter</span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>-</span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:9'>
 +
  <td>c<sub>K<sup>+</sup></sub></td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of potassium ions<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  ><span  style='font-size:14.0pt;
 +
  font-family:""Helvetica Neue", Helvetica, sans-serif",serif;mso-fareast-language:ZH-CN'>mM</span></span><span
 +
style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:10'>
 +
  <td>[kdpE - DNA]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of <span  ><i
 +
  style='mso-bidi-font-style:normal'>KdpE</i></span> bound promoter <span
 +
  >P<sub>kdpF</sub></span><sub><o:p></o:p></sub></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<sub><o:p></o:p></sub></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:11'>
 +
  <td>[DNA<sub>f</sub>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of Unbound promoter <span
 +
  >P<sub>kdpF</sub></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:12'>
 +
  <td>[DNA<sub>0</sub>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Total concentration of promoter <span
 +
  >P<sub>kdpF</sub></span><o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:13'>
 +
  <td>[mRNA<sub>GFP</sub>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of mRNA molecules for green
 +
  fluorescence protein<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:14'>
 +
  <td>[GFP<sub>I</sub>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of immature green fluorescent
 +
  protein<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
<tr style='mso-yfti-irow:15;mso-yfti-lastrow:yes'>
 +
  <td>[GFP<sub>M</sub>]</td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>Concentration of mature green fluorescent protein<o:p></o:p></span></p>
 +
  </td>
 +
  <td  valign=top style='width:50%;border-top:none;border-left:
 +
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
 +
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
 +
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
 +
  <p  ><span  style='font-size:14.0pt;font-family:""Helvetica Neue", Helvetica, sans-serif",serif;
 +
  mso-fareast-language:ZH-CN'>&micro;M<o:p></o:p></span></p>
 +
  </td>
 +
</tr>
 +
</table>
 +
</center>
 +
<p class="PICdiscription">Table 3. Variables list. </p>
 +
 +
</div>-->
 +
 
 +
                    <div class="project_row">
 +
<hr class="para">
 +
<h2>References</h2>
 +
                                <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
 +
<br><br>Epstein W (2003) The roles and regulation of potassium in bacteria. Prog Nucleic Acid Res Mol Biol 75: 293–320.
 
</p>
 
</p>
  
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{{HKUST-Rice Directory}}
  
 
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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:

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Translation:

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Green Fluorescent Protein maturation:

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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.