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| + | <td class="t1">Modeling</td> | ||
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| + | <tr> | ||
| + | <td class="t2"><strong>Introduction</storng></td> | ||
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| + | <td class="t2"> Our biological system connects the biosensors and the reporters. The different concentration of antibiotics can result in different intension of fluorescences.So if we can predict the concentration with the detected intension of fluorescences. The problem is how to get the relationship of them in math.<br> | ||
| + | In addition, noise exits in the system and the electronic device. That is the reason we make the amplifier and the controller. Through those parts, we can get the value of prediction more accurately.<br> | ||
| + | What’s more, on the condition that the intension of fluorescence is constant, to make sure our system can adjust to different standard of concentration, we can predict the IPTG which needs adding based on our model. In other word, we can give a value of IPTG which needs adding to decide if the antibiotics is superscalar in any standards.</td> | ||
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| + | <td class="t2"><strong>Calculation</strong></td> | ||
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| + | <td class="t2"> In this part, we list our calculating progress. Because of the same principle, we only take the tetracycline part as an example.<br> | ||
| + | At first, let’s look at our tetracycline biosensor:<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/8/8c/BIT_Modeling1.jpg"><br> | ||
| + | We use Df represent the concentration of DNA that does not combine with tetR protein; and X－D represent the concentration of DNA bonded by tetR protein; Dt represent the total concentration of promoter of DNA; X represent the concentration of tetR protein.<br> | ||
| + | According to law of conservation of mass:</br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/8/8b/BIT_Modeling2.jpg"><br> | ||
| + | Among them, kon represent the compound X－D generation rate and koff represent the compound X－D dissociation rate.<br> | ||
| + | If<img src="https://static.igem.org/mediawiki/2013/0/0c/BIT_Modeling3.jpg"<br> | ||
| + | Then:<img src="https://static.igem.org/mediawiki/2013/b/b8/BIT_Modeling4.jpg" <br><br> | ||
| + | When location of D is free, the RNA polymerase could combine with promoter PltetO1, and start transcription. The transcription rate of free promoter PltetO1 can described by the biggest transcription rate β. As we know, β is changed along with the changes of DNA sequence, the location of RNA combine to and other facts.<br> | ||
| + | The activity of promoter=<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/f/f2/BIT_Modeling5.jpg"><br> | ||
| + | Now, let’s look at tetracycline. Just as our PPT shows, tetracycline is an inducer.<br> | ||
| + | X－Tx represent the concentration of X bonded with Tx, and Tx is the concentration of inducer-tetracycline. Xt is the total concentration of tetR protein.<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/8/81/BIT_Modeling6.jpg"><br> | ||
| + | And if we use X* represent the tetR protein not bond with tetracycline<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/e/e0/BIT_Modeling7.jpg"><br> | ||
| + | But in fact, there is a tetR dimer that will prohibit the gene GFP.<br> | ||
| + | So, we should change equation (1.1.6) into the following equation:<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/d/dd/BIT_Modeling8.jpg"><br> | ||
| + | Similarly, by the Hill equation:<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/e/e4/BIT_Modeling9.jpg"><br> | ||
| + | Considering the more specific model, we use the Monod-Changeux model. And L represents the bigger probability X present than X*.<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/0/05/BIT_Modeling10.jpg"><br> | ||
| + | So far, we can write the equation of transcription:<br> | ||
| + | At this point, the input function describe transcription rate as input function of the concentration of inducer Tx<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/0/0b/BIT_Modeling11.jpg"><br> | ||
| + | Now, it’s time to quantify the expression of GFP. G is the concentration of GFP protein, α represent the depression coefficient.<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/2/20/BIT_Modeling12.jpg"><br> | ||
| + | Here, Tx =0.5 Txout, Xt>>Kd, because tetracycline is a kind of fat soluble antibiotic, it should diffuse freely until the concentrations between the intracellular and extracellular cell are equal.<br> | ||
| + | Equation (1.1.15) can be roughly write to (1.1.17) :<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/6/64/BIT_Modeling13.jpg"><br> | ||
| + | Because Xt, Kd are about constant, we make K’=Xt/Kd,<br> | ||
| + | So,<img src="https://static.igem.org/mediawiki/2013/1/1f/BIT_Modeling14.jpg"><br> | ||
| + | At the same time, we can make M=β/K’ because both of β、K’ are constants.<br> | ||
| + | So:<img src="https://static.igem.org/mediawiki/2013/4/4b/BIT_Modeling15.jpg"><br> | ||
| + | If Tx is far smaller than Kx,<br> | ||
| + | then<img src="https://static.igem.org/mediawiki/2013/6/66/BIT_Modeling16.jpg"><br> | ||
| + | So<img src="https://static.igem.org/mediawiki/2013/b/b5/BIT_Modeling17.jpg"><br> | ||
| + | So, when C→0, or α is big enough,<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/1/1b/BIT_Modeling18.jpg"><br> | ||
| + | If Tx is far bigger than Kx, with the same method, we can easily get the following equation: G=P’*Txout^n<br> | ||
| + | As we know, n=2,<br> | ||
| + | So<img src="https://static.igem.org/mediawiki/2013/2/25/BIT_Modeling19.jpg"><br> | ||
| + | As you can see, the relationship between the expression intensity and the concentration of Tetracycline does obey equation (1.1.22)firstly, then obey equation(1.1.23).<br> | ||
| + | Here is the result:<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/9/99/BIT_Modeling20.jpg"><br> | ||
| + | Compared to our experiment data:<br> | ||
| + | <img src="https://static.igem.org/mediawiki/2013/9/9f/BIT_Modeling21.jpg"><br> | ||
| + | So combined with equations(1.1.22) and(1.1.23), our model is suitable for our biosensor!<br> | ||
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Latest revision as of 07:30, 28 October 2013
| Modeling |
| Introduction |
| Our biological system connects the biosensors and the reporters. The different concentration of antibiotics can result in different intension of fluorescences.So if we can predict the concentration with the detected intension of fluorescences. The problem is how to get the relationship of them in math. In addition, noise exits in the system and the electronic device. That is the reason we make the amplifier and the controller. Through those parts, we can get the value of prediction more accurately. What’s more, on the condition that the intension of fluorescence is constant, to make sure our system can adjust to different standard of concentration, we can predict the IPTG which needs adding based on our model. In other word, we can give a value of IPTG which needs adding to decide if the antibiotics is superscalar in any standards. |
| Calculation |
| In this part, we list our calculating progress. Because of the same principle, we only take the tetracycline part as an example. At first, let’s look at our tetracycline biosensor:  We use Df represent the concentration of DNA that does not combine with tetR protein; and X－D represent the concentration of DNA bonded by tetR protein; Dt represent the total concentration of promoter of DNA; X represent the concentration of tetR protein. According to law of conservation of mass:  Among them, kon represent the compound X－D generation rate and koff represent the compound X－D dissociation rate. If 
Then: When location of D is free, the RNA polymerase could combine with promoter PltetO1, and start transcription. The transcription rate of free promoter PltetO1 can described by the biggest transcription rate β. As we know, β is changed along with the changes of DNA sequence, the location of RNA combine to and other facts. The activity of promoter=  Now, let’s look at tetracycline. Just as our PPT shows, tetracycline is an inducer. X－Tx represent the concentration of X bonded with Tx, and Tx is the concentration of inducer-tetracycline. Xt is the total concentration of tetR protein.  And if we use X* represent the tetR protein not bond with tetracycline  But in fact, there is a tetR dimer that will prohibit the gene GFP. So, we should change equation (1.1.6) into the following equation:  Similarly, by the Hill equation:  Considering the more specific model, we use the Monod-Changeux model. And L represents the bigger probability X present than X*.  So far, we can write the equation of transcription: At this point, the input function describe transcription rate as input function of the concentration of inducer Tx  Now, it’s time to quantify the expression of GFP. G is the concentration of GFP protein, α represent the depression coefficient.  Here, Tx =0.5 Txout, Xt>>Kd, because tetracycline is a kind of fat soluble antibiotic, it should diffuse freely until the concentrations between the intracellular and extracellular cell are equal. Equation (1.1.15) can be roughly write to (1.1.17) :  Because Xt, Kd are about constant, we make K’=Xt/Kd, So,  At the same time, we can make M=β/K’ because both of β、K’ are constants. So:  If Tx is far smaller than Kx, then  So  So, when C→0, or α is big enough,  If Tx is far bigger than Kx, with the same method, we can easily get the following equation: G=P’*Txout^n As we know, n=2, So  As you can see, the relationship between the expression intensity and the concentration of Tetracycline does obey equation (1.1.22)firstly, then obey equation(1.1.23). Here is the result:  Compared to our experiment data:  So combined with equations(1.1.22) and(1.1.23), our model is suitable for our biosensor! |
