Difference between revisions of "Team:Mingdao/Model"

 
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<img class="top-picture" src="https://static.igem.org/mediawiki/2018/3/36/T--Mingdao--phil39.png">
 
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      <img class="top-picture" src="https://static.igem.org/mediawiki/2018/1/14/T--Mingdao--modeling_top.jpg" style="width:100%">
 
 
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             <h1 id = "d-introduction">Modeling</h1>
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             <!-- <h1 id = "d-introduction">Modeling</h1> -->
 
<br />
 
<br />
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             <h2>Introduction</h2>
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 +
             <h2 id="d-introduction">Introduction</h2>
 
<br />
 
<br />
  
  
 
        
 
        
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<p>In our project, we want to calculate the bacteria concentration in the testers.  
+
<p>In our project, we want to calculate the bacteria concentration in the testing devices.  
 
<p>
 
<p>
 
<p>
 
<p>
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<p>
 
<p>
 
<p>
 
<p>
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What’s more, with the view to making sure our system works successfully, we need to make sure that testers can detect GFP in our devices. Since the GFP in mosquitoes take some time to be synthesized, we can detect the green fluorescence only few hours after the mosquitoes take in the tester’s blood. To prevent from the misleading of our devices and system, we should calculate the very beginning time that the testers can detect the green fluorescence in the devices.
+
What’s more, with the view to making sure our system works successfully, we need to make sure that GFP can be detected in our testing devices. Since the GFP in mosquitoes take some time to be synthesized, we can detect the green fluorescence only few hours after the mosquitoes draw the infected blood. To prevent from the misleading of our devices and system, we should calculate the very beginning time that the green fluorescence can be detected in the testing devices.  
 
</p>
 
</p>
 
<p>
 
<p>
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<p>
 
<p>
  
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                 <p>Since our devices can only detect the GFP intensity, we can only utilize GFP intensity to calculate E.coli concentration. After obtaining E.coli concentration, we will utilize it to calculate the very beginning time that testers can detect GFP. Finally, the two parameters will be demonstrated on our devices for the testers to take as reference.  
+
                 <p>Since our devices can only detect the GFP intensity, we can only utilize GFP intensity to calculate E. coli concentration. After obtaining E. coli concentration, we will utilize it to calculate the very beginning time that GFP can be detected in the testing devices. Finally, the two parameters will be demonstrated on our devices for the testing devices to take as reference.
−
</p>
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<p>
 
<p>
 
<p>
 
<p>
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<br />
 
<br />
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             <h2 id = "d-model1">Model 1: Calculating E.coli Concentration by GFP Intensity</h2>
+
             <h2 id = "d-model1">Model 1: Calculating E. coli Concentration by GFP Intensity</h2>
 
<br />
 
<br />
  
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<p>
 
<p>
 
<p>
 
<p>
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<p>To find the mathematical relationship between GFP and E.coli concentration, we measure the GFP growing curve with different MOI value every two hours. Then, perform a series of calculation and finally arrive at the mathematical relationship between GFP and E.coli concentration.</p>
+
<p>To find the mathematical relationship between GFP and E. coli concentration, we measure the GFP intensities with different MOI value every two hours. Then, perform a series of calculations and finally obtain the mathematical relationship between GFP intensity and E. coli concentration.</p>
 
<p>
 
<p>
 
<br />
 
<br />
 
<h3>Obtaining the Mathematical Relationship</h3>
 
<h3>Obtaining the Mathematical Relationship</h3>
 
<p>
 
<p>
−
<p>Table 1.0 shows the corresponding Fluorescence intensity with different MOI value. However, the units of E.coli we want should be transformed into another form.</p>
+
<p>Table 1.1 shows the relative fluorescence units (RFU) of GFP with different MOI values of E. coli.  First of all, we transformed the MOI to E. coli density.</p>
 +
<img class="center" src="https://static.igem.org/mediawiki/2018/d/d6/T--Mingdao--sam100-1.png"alt=" " style="width:35%" >
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<br /><br />
 +
<h3>Conversion of MOI to E. coli density</h3>
 
<p>
 
<p>
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<img class="center" src="https://static.igem.org/mediawiki/2018/f/fb/T--Mingdao--Modeling019.jpg"alt=" " style="width:35%" >
 
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<img class="center" src="https://static.igem.org/mediawiki/2018/1/12/T--Mingdao--Modeling017.jpg"alt=" " style="width:35%" >
 
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<br />
 
−
<h3>Conversion of MOI to E.coli density</h3>
 
 
<p>
 
<p>
−
<p>
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<p>The equation of E. coli density is shown below:
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<p>The equation of E.coli density is shown below:
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<p>
 
<p>
 
<img class="center" src="https://static.igem.org/mediawiki/2018/1/10/T--Mingdao--Modeling02.jpg"alt=" " style="width:70%" >
 
<img class="center" src="https://static.igem.org/mediawiki/2018/1/10/T--Mingdao--Modeling02.jpg"alt=" " style="width:70%" >
 
<p>
 
<p>
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Since the MOI value refers to the ratio of E.coli cells to mosquito cells, we can use the density of mosquito cells to calculate the E.coli density. Plus, the mosquito cells are seeded at the density of 1.8×〖10〗^5 cells/well, and the volume of each well is 100μL.  
+
Since the MOI value refers to the ratio of E. coli cells to mosquito cells, we can use the density of mosquito cells to calculate the E. coli density. Plus, the mosquito cells are seeded at the density of 1.8×10<sup>5</sup> cells/well, and the volume of each well is 100μL.  
 
<p>
 
<p>
 
Thus, the equation become
 
Thus, the equation become
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<img class="center" src="https://static.igem.org/mediawiki/2018/a/ac/T--Mingdao--Modeling03.jpg"alt=" " style="width:70%" >
 
<img class="center" src="https://static.igem.org/mediawiki/2018/a/ac/T--Mingdao--Modeling03.jpg"alt=" " style="width:70%" >
 
<p>
 
<p>
−
<p>Then, we will turn the MOI in Table 1.0 into E.coli density to form Table 1.1. Next, we will use Table 1.1 to keep figuring out the mathematical relationship between E.coli concentration and GFP intensity.</p>
+
<pFinally, we turned the MOIs into E. coli density to form Table 1.1 (the right column marked as red). In the following, we used the density of E. coli to calculate the mathematical relationship between E. coli concentration and GFP intensity.</p>
 
<br />
 
<br />
 
<h3>Forming the mathematical expression</h3>
 
<h3>Forming the mathematical expression</h3>
 
<p>
 
<p>
 
<p>
 
<p>
−
<p>Before we keep working on our calculation, it’s worth noticed that the GFP intensity has already existed while there is no E.coli . Thus, the intensity of GFP with no E.coli should be eliminated as discussing the relationship between E.coli concentration and GFP intensity, which means [GFP] should minus the [〖GFP〗_0] with no E.coli, and add it back in our final result.
+
<p>The cells transfected with DNA has basal levels of GFP before responding to the E. coli. Thus, the background intensity of GFP should be eliminated for the actual RFU to obtain the relationship between E. coli concentration and GFP intensity, which means [GFP] (i.e, RFU of GFP) should minus the [GFP<sub>0</sub>] of cells before the addition of E. coli (Table 1.2).
−
<p>
+
 
With that in mind, we form the Table 1.2
 
With that in mind, we form the Table 1.2
 
<p>
 
<p>
−
<img class="center" src="https://static.igem.org/mediawiki/2018/3/36/T--Mingdao--Modeling019r8.jpg"alt=" " style="width:35%">
+
<img class="center" src="https://static.igem.org/mediawiki/2018/d/d0/T--Mingdao--sam100-2.png"alt=" " style="width:50%">
 
<p>  
 
<p>  
 
Now we can begin with our data analyzing.
 
Now we can begin with our data analyzing.
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<p>
 
<p>
 
<p>
 
<p>
−
<P>Figure 2.0 shows the graphic expression between the [E.coli] and GFP intensity, the Exponential Function is shown below:<p>
+
<P>Figure 2.0 shows the graphic expression between the [E. coli] and GFP intensity [GFP], the Exponential Function is shown below:<p>
 
</p>
 
</p>
 
<p>
 
<p>
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<p>
 
<p>
 
<p>
 
<p>
−
<p>Next, we will bring in that [〖GFP〗_0 ]=813 to the Exponential Function and obtain the final graphic expression and function.</p>
+
<p>Next, we will bring in that [GFP<sub>0</sub>]=813 to the Exponential Function and obtain the final graphic expression and function.</p>
 
<p>
 
<p>
 
<img class="center" src="https://static.igem.org/mediawiki/2018/0/0a/T--Mingdao--Modeling08.jpg"  alt=" " style="width:70%">
 
<img class="center" src="https://static.igem.org/mediawiki/2018/0/0a/T--Mingdao--Modeling08.jpg"  alt=" " style="width:70%">
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<p>
 
<p>
 
<p>
 
<p>
−
<p>With the formula, we can now build a calculator to calculate the [E.coli] by GFP Intensity, and apply the formula to our devices to from a well-designed prototype. The devices will calculate the [E.coli] automatically based on the GFP intensity they detect. As a result, the testers will be able to know the [E.coli] in their blood through our devices.</p>
+
<p>With the formula, we can calculate the [E. coli] based on GFP Intensity, and apply the formula to our prototype design. </p>
−
<br />
+
 
−
<h3>Limitation</h3>
+
−
<p>
+
−
<p>
+
−
<p>However, there are some limitations to our Model 1. Not knowing when all the E.coli cells bind to the GAM 1 promoter, we can’t make sure when we can utilize the formula to conduct calculation.
+
−
<p>
+
−
Consequently, we will conduct Model 2 to figure out the limitation.</p>
+
 
<p>
 
<p>
  
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<br />
 
<br />
−
<h2 id="d-model2">Model 2: Number of E.coli Cells Binding to The GAM 1 Promoter Increase With Time</h2>
+
<h2 id="d-model2">Model 2: The GAM1 Promoter in Response to Number of E. coli Cells Increase With Time</h2>
 
<br />
 
<br />
 
<h3>Method</h3>
 
<h3>Method</h3>
 
<p>
 
<p>
 
<p>
 
<p>
−
<p>To know when all the E.coli cells bind to GAM 1 promoter, we measure the GFP growing curves with different MOI value every two hours, and differentiate the growing curves to find the time that the instant GFP transcription rate reaches the maximum, which is the time all the E.coli cells bind to GAM 1 promoter.
+
<p>To know how GAM1 promoter could be induced by E. coli concentration, we measure the GFP intensity with different MOI values every two hours. Then, we differentiate the curves, as are illustrated in Figure 3.0 - 3.4, to find the time that the instant GFP expression level reaches the maximum, which means the time E. coli cells begin to activate GAM1 promoter.
−
<p>
+
−
After the differentiation, we will be able to obtain the graphic expression between the binding time and the [E.coli]. By analyzing the graphic expression, the very beginning time that the testers can detect GFP can be calculated.
+
−
<p>
+
−
In addition, the limitation mentioned in Model 1 can also be quantified via the graphic expression we obtained in Model 2.
+
−
<p>
+
 
</p>
 
</p>
 
<br />
 
<br />
−
<h3>Standardization of GFP Growing Curve</h3>
+
<h3>Relative fluorescence units (RFU) of GFP intensity in different MOIs of E. coli</h3>
 
<p>
 
<p>
 
<p>
 
<p>
−
<p>Since we need to differentiate the GFP growing curve, the standardization is essential. Thus, we will digitize the GFP growing curve so that we can conduct the differentiation successfully. </p>
+
<p>The RFU of GFP intensities of GAM1 promoter activities induced by different E. coli concentrations were shown in Table 2. </p>
−
<br />
+
−
<h3>Raw Data</h3>
+
 
<p>
 
<p>
 +
<img class="center" src="https://static.igem.org/mediawiki/2018/5/52/T--Mingdao--Modelingnewphoto.jpg" alt=" " style="width:100%">
 
<p>
 
<p>
−
<p>
+
<p>The RFU curves in the function of time were illustrated by different MOIs of E. coli, as shown from Figure 3.0 to Figure 3.4
−
We perform two experiments respectively with different purposes.
+
−
<p>
+
−
The first one is to made for the blank so there is no DNA inside the well and no inducement of GAM 1 promoter, since the cells itself contribute to some absorbance, too.
+
−
<p>
+
−
The second one consists of E.coli with induced GAM 1 promoter. Both of the experiments are measured by our plate reader every two hours.
+
−
<p>
+
−
The Table 2.0 and Table 2.1 are shown below</p>
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−
<p>
+
−
<img class="center" src="https://static.igem.org/mediawiki/2018/b/b2/T--Mingdao--Modeling11.jpg" alt=" " style="width:100%">
+
−
<p>
+
−
<img class="center" src="https://static.igem.org/mediawiki/2018/3/37/T--Mingdao--Modeling12.jpg" alt=" " style="width:100%">
+
−
<br />
+
−
<h3>Absorbance of green fluorescence protein</h3>
+
−
<p>
+
−
<p>
+
−
<p>The actual absorbance of GFP is the absorbance of the E.coli cells with induced GAM 1 promoter minus the absorbance of E.coli cells without DNA and no inducement of GAM 1 promoter. After the calculation, the result are shown as Table 2.2</p>
+
−
<p>
+
−
<img class="center" src="https://static.igem.org/mediawiki/2018/2/22/T--Mingdao--Modeling13.jpg" alt=" " style="width:100%">
+
−
<br />
+
−
<h3>Standardization</h3>
+
−
<p>
+
−
<p>
+
−
<p>Then, we will illustrate the growing curves and find the formula of each growing curve so that we can differentiate them. It’s noticed that we don’t adopt the GFP growing curve without E.coli, since its GAM 1 promoter isn’t induced.
+
−
<p>
+
−
After analyzing, we find that cubic equation perfectly fits to our experiment data. Those cubic equations are shown as Figure 3.0 to Figure 3.4</p>
+
 
<p>
 
<p>
 
<img class="center" src="https://static.igem.org/mediawiki/2018/c/cb/T--Mingdao--Modeling002.jpg" alt=" " style="width:70%">
 
<img class="center" src="https://static.igem.org/mediawiki/2018/c/cb/T--Mingdao--Modeling002.jpg" alt=" " style="width:70%">
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<p>
 
<p>
 
<p>
 
<p>
−
<p>Also, the mathematical expressions of these cubic equations are shown as Table 3.0 and the graphic expressions are shown as Figure 4.0</p>
+
<p>Also, the mathematical expressions of these cubic equations were shown as Table 3.0 and the graphic expressions were shown as Figure 4.0</p>
 
<p>
 
<p>
 
<p>
 
<p>
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<img class="center" src="https://static.igem.org/mediawiki/2018/4/46/T--Mingdao--Modeling008.jpg" alt=" " style="width:70%">
 
<img class="center" src="https://static.igem.org/mediawiki/2018/4/46/T--Mingdao--Modeling008.jpg" alt=" " style="width:70%">
 
<br />
 
<br />
−
<h3><strong>Number of E.coli Cells Binding to GAM 1 Promoter</strong></h3>
 
 
<br />
 
<br />
−
<h3>Derivative of the green fluorescence growing curve<h3>
+
<h3>Derivative of the GFP Intensity Curve<h3>
 
<p>
 
<p>
 
<p>
 
<p>
−
<p>When all the E.coli cells bind to GAM 1 promoter, the instant GFP transcription rate will reach the maximum value. As a consequence, what we need to do is to differentiate the GFP growing curves at different MOI value, and find the maximum of the differentiated formulas as well as the corresponding time.
+
<p>We conducted the derivative of the mathematical formula in Table 3.0 and form Table 3.1
−
<p>
+
−
With that in mind, we conduct the derivative of the mathematical expressions in Table 3.0 and form Table 3.1
+
 
</p>
 
</p>
 
<p>
 
<p>
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<img class="center" src="https://static.igem.org/mediawiki/2018/9/99/T--Mingdao--Modeling009.jpg" alt=" " style="width:70%">
 
<img class="center" src="https://static.igem.org/mediawiki/2018/9/99/T--Mingdao--Modeling009.jpg" alt=" " style="width:70%">
 
<br />
 
<br />
−
<h3>Obtaining The Maximum and The Corresponding Time</h3>
+
<h3>The Responding Time to The Maximum of The Formula</h3>
 
<p>
 
<p>
 
<p>
 
<p>
−
<p>To calculate the maximum of the derivative of the green fluorescence growing curve, we need to conduct the second derivative and find the maximum and corresponding time. The result is shown as Table 3.2</p>
+
<p>To calculate the maximum of the derivative of the GFP intensity curve, we conducted the second derivative and found the maximum and responding time. The results were shown in Table 3.2</p>
 
<p>
 
<p>
−
<p>
+
<img class="center" src="https://static.igem.org/mediawiki/2018/0/0b/T--Mingdao--Modeling010.jpg" alt=" " style="width:70%">
−
<img class="center" src="https://2018.igem.org/File:T--Mingdao--Modeling010.jpg"alt=" " style="width:70%">
+
<p><p>
−
<p>
+
<p>The graphic expression of the relationship between time and E. coli density was shown in Table 3.3 and Figure 5.0</p>
−
<p>
+
−
<p>Then, we will turn the MOI value into E.coli density to form Table 3.3
+
−
Also, the graphic expression of the relationship between time and E.coli density is shown as Figure 5.0</p>
+
 
<p>
 
<p>
 
<p>
 
<p>
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<p>
 
<p>
 
<p>
 
<p>
−
<p>We also arrive at the equation between time and E.coli concentration</p>
+
<p>We also arrive at the equation between time and E. coli concentration</p>
 
<p>
 
<p>
 
<p>
 
<p>
 
<img class="center" src="https://static.igem.org/mediawiki/2018/d/d2/T--Mingdao--Modeling014.jpg" alt=" " style="width:70%">
 
<img class="center" src="https://static.igem.org/mediawiki/2018/d/d2/T--Mingdao--Modeling014.jpg" alt=" " style="width:70%">
−
<br />
 
−
<h3><strong>Conclusion</strong></h3>
 
 
<br />
 
<br />
 
<h3>Application</h3>
 
<h3>Application</h3>
 
<p>
 
<p>
 
<p>
 
<p>
−
<p>With the formula, we can utilize the [E.coli] calculated in Model 1 to calculate how long the testers should wait to detect green fluorescence in our devices and demonstrate it on our devices to inform the testers. Then, the formula will also be applied to our calculator as well.</p>
+
<p>With the formula, we can use the [E. coli] to calculate the responding time. Then, the formula will also be applied to our calculator and prototype, too.</p>
 
<p>
 
<p>
 
<p>
 
<p>
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−
 
+
<h2 style = "padding:0" id="d-calculator">CALCULATOR</h2>
 
                                  
 
                                  
  
 
                                         <div style = "border-style:solid; text-align:center; padding:20px" class="col-sm-12">
 
                                         <div style = "border-style:solid; text-align:center; padding:20px" class="col-sm-12">
 
                                     <div class="row">
 
                                     <div class="row">
−
                                    <h2 style = "padding:0">CALCULATOR</h2>
+
                                 
  
 
                                         <div class="col-sm-6">
 
                                         <div class="col-sm-6">
−
                                         <h3 style="padding:0"> E.coli Concentration Calculator</h3>
+
                                         <h3 style="padding:0"> E. coli Concentration Calculator</h3>
 
                                         <script>
 
                                         <script>
 
                                             function round(value, decimals) {
 
                                             function round(value, decimals) {
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                                             calculateee = function(){
 
                                             calculateee = function(){
 
                                                 var XInputLOCSP = document.getElementById("inputLOCS").value;
 
                                                 var XInputLOCSP = document.getElementById("inputLOCS").value;
−
                                                 var XCrystDamP =54.163*(2.7182<sup>(0.0024*(XInputLOCSP)</sup>)) ;
+
                                                 var XCrystDamP =54.163*Math.pow(2.7182,(0.0024*(XInputLOCSP))) ;
 
                                                  
 
                                                  
  
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                                         <span style="width:70%">Type in the value:</span><input id = "inputLOCS" type="text" style="width:30%">
 
                                         <span style="width:70%">Type in the value:</span><input id = "inputLOCS" type="text" style="width:30%">
  
−
                                         <br><span style="font-size:16px">          The calculator can calculate E.coli density based on the GFP intensity. </span>
+
                                         <br><span style="font-size:16px">          The calculator can calculate E. coli density based on the GFP intensity. </span>
 
                                         <br><button onclick = "calculateee()">Calculate!</button><br>
 
                                         <br><button onclick = "calculateee()">Calculate!</button><br>
 
                                         <br>
 
                                         <br>
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                                                 </tr>
 
                                                 </tr>
 
                                                 <tr>
 
                                                 <tr>
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                                                     <td>E.coli Concentration</td>
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                                                     <td>E. coli Concentration</td>
 
                                                     <td> <span id="XCrysDamPid">&nbsp;&nbsp;&nbsp; </span> Number of Cells Per uL</td>
 
                                                     <td> <span id="XCrysDamPid">&nbsp;&nbsp;&nbsp; </span> Number of Cells Per uL</td>
  
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                                         <span style="width:70%">Enter value:</span><input id = "inputLOCSTget" type="text" style="width:30%">
 
                                         <span style="width:70%">Enter value:</span><input id = "inputLOCSTget" type="text" style="width:30%">
  
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                                         <br><span style="font-size:16px">          The calculator can calculate responding time based on the E.coli concentration.</span>
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                                         <br><span style="font-size:16px">          The calculator can calculate responding time based on the E. coli concentration.</span>
 
                                         <br><button onclick = "calculateeeT()">Calculate!</button><br>
 
                                         <br><button onclick = "calculateeeT()">Calculate!</button><br>
 
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                                         <span style="font-size:26px">Calculation Results </span>
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                                         <span style="font-size:26px">Calculation Result </span>
  
 
                                         <table class="table table-hover fixed" style="font:16px">   
 
                                         <table class="table table-hover fixed" style="font:16px">   
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                                                     <td>E.coli Density</td>
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                                                     <td>E. coli Density</td>
 
                                                     <td> <span id="XInputLOCSTid">&nbsp;&nbsp;&nbsp;</span> Number of Cells  Per uL </td>
 
                                                     <td> <span id="XInputLOCSTid">&nbsp;&nbsp;&nbsp;</span> Number of Cells  Per uL </td>
  
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  <h2 id="d-conclusion">Conclusion</h2>
 
  <h2 id="d-conclusion">Conclusion</h2>
 
  <br />
 
  <br />
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<p>Our model not only help to build the formulaic system which applied to our devices, but also make us better understand our project. Because our devices can only detect the GFP intensity, our model is required to build a well-designed devices and system.
+
<p>Our model not only builds the mathematical system which could be applied to our devices, but also makes us better understand our project. Because our device can only detect the GFP intensity, our model is required for a well-established devices and system. In our model 1, we obtain the formula which allows us to calculate [E. coli] from GFP intensity. While in model 2, we obtain the formula which allows us to calculate how long the device should take to get the result of the testing in response to a known concentration of bacteria. To sum up, our model obtain the significant parameters for our prototype design and provides information of the device limitation.</p>
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In our model 1, we obtain the formula which allows us to calculate [E.coli] from GFP intensity. While in model 2, we obtain the formula which allows us to calculate how long the testers should wait to get the result of the test based on the [E.coli] calculated in mode 1. For [E.coli] and the time interval, they will be demonstrated on our devices to show them to the testers.  
+
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To sum up, Our model act as a bridge between our devices and the testers, and quantifies the significant parameters in our project, which allow the masses to simply get the result of the test without complex calculations.</p>
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       <img class="center" src="https://static.igem.org/mediawiki/2017/5/52/T--CSMU_NCHU_Taiwan--top.png" alt="">
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       <img class="center" src="https://static.igem.org/mediawiki/2018/5/58/T--Mingdao--go_to_top.jpg" alt="">
 
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     $("#d-introduction-btn").click(function() {
 
     $("#d-introduction-btn").click(function() {
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             d_introduction_pos = $("#d-introduction").offset().top -100
 
             d_introduction_pos = $("#d-introduction").offset().top -100
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                 $("#d-model2-btn").css('background-color', '#385e66');}
 
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             // conclusion
 
             // conclusion

Latest revision as of 01:56, 15 October 2018

HOME
Description

Introduction


In our project, we want to calculate the bacteria concentration in the testing devices.

However, our devices can only detect GFP intensity, so we can only utilize GFP intensity to calculate bacteria concentration.

What’s more, with the view to making sure our system works successfully, we need to make sure that GFP can be detected in our testing devices. Since the GFP in mosquitoes take some time to be synthesized, we can detect the green fluorescence only few hours after the mosquitoes draw the infected blood. To prevent from the misleading of our devices and system, we should calculate the very beginning time that the green fluorescence can be detected in the testing devices.


Guiding Questions

1. How many bacteria can be tested in our model ? (Model 1)

2. How long do our devices take to send out signal ? (Model 2)


Focus on Our Model

Since our devices can only detect the GFP intensity, we can only utilize GFP intensity to calculate E. coli concentration. After obtaining E. coli concentration, we will utilize it to calculate the very beginning time that GFP can be detected in the testing devices. Finally, the two parameters will be demonstrated on our devices for the testing devices to take as reference.


Model 1: Calculating E. coli Concentration by GFP Intensity


Method

To find the mathematical relationship between GFP and E. coli concentration, we measure the GFP intensities with different MOI value every two hours. Then, perform a series of calculations and finally obtain the mathematical relationship between GFP intensity and E. coli concentration.


Obtaining the Mathematical Relationship

Table 1.1 shows the relative fluorescence units (RFU) of GFP with different MOI values of E. coli. First of all, we transformed the MOI to E. coli density.



Conversion of MOI to E. coli density

The equation of E. coli density is shown below:

Since the MOI value refers to the ratio of E. coli cells to mosquito cells, we can use the density of mosquito cells to calculate the E. coli density. Plus, the mosquito cells are seeded at the density of 1.8×105 cells/well, and the volume of each well is 100μL.

Thus, the equation become


Forming the mathematical expression

The cells transfected with DNA has basal levels of GFP before responding to the E. coli. Thus, the background intensity of GFP should be eliminated for the actual RFU to obtain the relationship between E. coli concentration and GFP intensity, which means [GFP] (i.e, RFU of GFP) should minus the [GFP0] of cells before the addition of E. coli (Table 1.2). With that in mind, we form the Table 1.2

Now we can begin with our data analyzing.


Data Analyzing

Figure 2.0 shows the graphic expression between the [E. coli] and GFP intensity [GFP], the Exponential Function is shown below:

Next, we will bring in that [GFP0]=813 to the Exponential Function and obtain the final graphic expression and function.

Combining the constants, we arrive at


Conclusion


Application

With the formula, we can calculate the [E. coli] based on GFP Intensity, and apply the formula to our prototype design.


Model 2: The GAM1 Promoter in Response to Number of E. coli Cells Increase With Time


Method

To know how GAM1 promoter could be induced by E. coli concentration, we measure the GFP intensity with different MOI values every two hours. Then, we differentiate the curves, as are illustrated in Figure 3.0 - 3.4, to find the time that the instant GFP expression level reaches the maximum, which means the time E. coli cells begin to activate GAM1 promoter.


Relative fluorescence units (RFU) of GFP intensity in different MOIs of E. coli

The RFU of GFP intensities of GAM1 promoter activities induced by different E. coli concentrations were shown in Table 2.

The RFU curves in the function of time were illustrated by different MOIs of E. coli, as shown from Figure 3.0 to Figure 3.4

Also, the mathematical expressions of these cubic equations were shown as Table 3.0 and the graphic expressions were shown as Figure 4.0



Derivative of the GFP Intensity Curve

We conducted the derivative of the mathematical formula in Table 3.0 and form Table 3.1


The Responding Time to The Maximum of The Formula

To calculate the maximum of the derivative of the GFP intensity curve, we conducted the second derivative and found the maximum and responding time. The results were shown in Table 3.2

The graphic expression of the relationship between time and E. coli density was shown in Table 3.3 and Figure 5.0

We also arrive at the equation between time and E. coli concentration


Application

With the formula, we can use the [E. coli] to calculate the responding time. Then, the formula will also be applied to our calculator and prototype, too.


CALCULATOR

E. coli Concentration Calculator

Type in the value:
The calculator can calculate E. coli density based on the GFP intensity.


Calculation Result
Variable Value Source
GFP Intensity     RFU
E. coli Concentration     Number of Cells Per uL Model 1

Responding Time Calculator

Enter value:
The calculator can calculate responding time based on the E. coli concentration.


Calculation Result
Variable Value Source
E. coli Density     Number of Cells Per uL
Responding Time       Hr Model 2

Conclusion


Our model not only builds the mathematical system which could be applied to our devices, but also makes us better understand our project. Because our device can only detect the GFP intensity, our model is required for a well-established devices and system. In our model 1, we obtain the formula which allows us to calculate [E. coli] from GFP intensity. While in model 2, we obtain the formula which allows us to calculate how long the device should take to get the result of the testing in response to a known concentration of bacteria. To sum up, our model obtain the significant parameters for our prototype design and provides information of the device limitation.

Introduction

Model 1

Model 2

Conclusion