Difference between revisions of "Team:NKU CHINA/Model"

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     <h1 class="text-center" style="font-size: 80px;font-weight: normal;color: white;padding-bottom: 0;margin-bottom: 20px; font-family: myTitle;margin-top: 30px;padding-top: 0;">Model</h3>
 
     <h1 class="text-center" style="font-size: 80px;font-weight: normal;color: white;padding-bottom: 0;margin-bottom: 20px; font-family: myTitle;margin-top: 30px;padding-top: 0;">Model</h3>
 
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             <h2 class="model_header">Abstract</h4>
 
             <h2 class="model_header">Abstract</h4>
             <p class="model_content">PopQC, which is the abbreviation for population quality control, is a new approach designed for biosynthesis production enhancement based on the non-genetic cell-to-cell variation. Because of some nongenetic differences, different cells in a single colony will have considerable variations in protein and metabolite concentrations. Based on this, PopQC was designed as a plasmid-based gene circuit, which continuously selects high-producers to increase production.</p>
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             <p class="model_content" style="margin-top: 20px;">PopQC, which is the abbreviation for population quality control, is a new approach designed for biosynthesis production enhancement based on the non-genetic cell-to-cell variation. Because of some nongenetic differences, different cells in a single colony will have considerable variations in protein and metabolite concentrations. Based on this, PopQC was designed as a plasmid-based gene circuit, which continuously selects high-producers to increase production.</p>
 
             <p class="model_content">We first use ODEs to explain why the concentration of glutamate can vary in a wide range and stay stable. We then use biophysical model to explain the biosynthetic performance of our system based on the inhibition effect of promoter&#39;s occupation by RNA polymerase. Finally, we use our model to predict initial condition to get the maximum production, and test our systems&#39; efficiency and accuracy.</p>
 
             <p class="model_content">We first use ODEs to explain why the concentration of glutamate can vary in a wide range and stay stable. We then use biophysical model to explain the biosynthetic performance of our system based on the inhibition effect of promoter&#39;s occupation by RNA polymerase. Finally, we use our model to predict initial condition to get the maximum production, and test our systems&#39; efficiency and accuracy.</p>
 
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       <h3 class="content_header">Glutamate and GltC Concerntration</h3>
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       <h3 class="content_header">Glutamate and GltC Concentration</h3>
 
       <img src="https://static.igem.org/mediawiki/2018/1/1a/T--NKU_CHINA--part3.png" class="img-responsive center-block" style="background-color: white;border-radius: 5px;">
 
       <img src="https://static.igem.org/mediawiki/2018/1/1a/T--NKU_CHINA--part3.png" class="img-responsive center-block" style="background-color: white;border-radius: 5px;">
 
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       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 1: Pattern diagram of PopQC based on our design</p></div>
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       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 1: Pattern diagram of PopQC based on our design</p></div>
 
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       <p class="model_content">In our project, <i>Bacillus amyloliquefaciens</i> LL3 was selected as the engineered strain introduced into the PopQC plasmid. In <i>Bacillus amyloliquefaciens</i> LL3, the intracellular glutamate concentration varies from 20 mM to 200 mM based on some nongenetic differences, which is from the result of our lab&#39;s previous work. We hope in the presence of PopQC, high glutamate strains can stay alive while low glutamate strains are unable to survive.</p>
 
       <p class="model_content">In our project, <i>Bacillus amyloliquefaciens</i> LL3 was selected as the engineered strain introduced into the PopQC plasmid. In <i>Bacillus amyloliquefaciens</i> LL3, the intracellular glutamate concentration varies from 20 mM to 200 mM based on some nongenetic differences, which is from the result of our lab&#39;s previous work. We hope in the presence of PopQC, high glutamate strains can stay alive while low glutamate strains are unable to survive.</p>
       <p class="model_content">GltC combines with glutamate to form GltC-Glu complex. And it&#39;s suggested that in the case of <i>Bacillus amyloliquefaciens</i> RNAP, glutamate inhibits GltC-dependent transcription of <i>gltAB</i> mostly by GltC-Glu complex&#39; additional non-specific inhibitory effect on RNAP for binding on <i>gltAB</i> promoter that form unstable open complexes<sup>[1]</sup>. <i>gltAB</i> operon encodes glutamate synthase<sup>[2]</sup>, so it forms a feedback suppression network by GltC-Glu complex. Meanwhile, GltC-Glu complex also has an inhibitory effect on <i>gltC</i> promoter, which forms a self-negative feedback network. These feedback suppression networks work together to keep intracellular glutamate pool stable. See Figure 2:</p>
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       <p class="model_content">GltC combines with glutamate to form GltC-Glu complex. And it &#39;s suggested that in the case of <i>Bacillus amyloliquefaciens</i> RNAP, glutamate inhibits GltC-dependent transcription of <i>gltAB</i> mostly by GltC-Glu complex &#39;s additional non-specific inhibitory effect on RNAP for binding on <i>gltAB</i> promoter<sup>[1]</sup>. <i>gltAB</i> operon encodes glutamate synthase<sup>[2]</sup>, so it forms a feedback suppression network by GltC-Glu complex. Meanwhile, GltC-Glu complex also has an inhibitory effect on <i>gltC</i> promoter, which forms a self-negative feedback network. These feedback suppression networks work together to keep intracellular glutamate pool stable. See Figure 2:</p>
 
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       <img src="https://static.igem.org/mediawiki/2018/d/d7/T--NKU_CHINA--model2.jpg" class="img-responsive center-block" style="border-radius: 5px;">
 
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       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 2: Feedback suppression networks based on GltC-Glu complex</p></div>
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       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 2: Feedback suppression networks based on GltC-Glu complex</p></div>
 
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       <p class="model_content">We use ordinary differential equations (Table 1) to describe this progress, the fitting result is shown as Figure 3:</p>
 
       <p class="model_content">We use ordinary differential equations (Table 1) to describe this progress, the fitting result is shown as Figure 3:</p>
 
       <p style="color: white;font-size: 20px;margin-top: 5px;text-align: justify;">Table 1: Ordinary differential equations that describes feedback suppression networks based on GltC-Glu complex. We have estimated the parameters and the result are: k1=0.81, k2=2.15&#215;10<sup>4</sup>, k3=49, k4=0.96, k5=0.84, k6=1.6&#215;10<sup>-4</sup>, k7=5.0&#215;10<sup>6</sup>, k8=0.47, k9=1.7&#215;10<sup>6</sup>,k10=9.7&#215;10<sup>4</sup>. &#946; represents gene leakage rate, const=1.</p>
 
       <p style="color: white;font-size: 20px;margin-top: 5px;text-align: justify;">Table 1: Ordinary differential equations that describes feedback suppression networks based on GltC-Glu complex. We have estimated the parameters and the result are: k1=0.81, k2=2.15&#215;10<sup>4</sup>, k3=49, k4=0.96, k5=0.84, k6=1.6&#215;10<sup>-4</sup>, k7=5.0&#215;10<sup>6</sup>, k8=0.47, k9=1.7&#215;10<sup>6</sup>,k10=9.7&#215;10<sup>4</sup>. &#946; represents gene leakage rate, const=1.</p>
       <img src="https://static.igem.org/mediawiki/2018/6/6f/T--NKU_CHINA--model1_15.png" class="img-responsive center-block" style="border-radius: 4px;">
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       <img src="https://static.igem.org/mediawiki/2018/6/6f/T--NKU_CHINA--model1_15.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 500px;">
 
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       <div class="col-xs-6"><img src="https://static.igem.org/mediawiki/2018/1/12/T--NKU_CHINA--model3-1.png" class="img-responsive center-block" style="border-radius: 5px;margin-top: 20px;height: 400px;width: auto;"></div>
 
       <div class="col-xs-6"><img src="https://static.igem.org/mediawiki/2018/1/12/T--NKU_CHINA--model3-1.png" class="img-responsive center-block" style="border-radius: 5px;margin-top: 20px;height: 400px;width: auto;"></div>
 
       <div class="col-xs-6"><img src="https://static.igem.org/mediawiki/2018/3/32/T--NKU_CHINA--model3-2.png" class="img-responsive center-block" style="border-radius: 5px;margin-top: 20px;height: 400px;width: auto;"></div>
 
       <div class="col-xs-6"><img src="https://static.igem.org/mediawiki/2018/3/32/T--NKU_CHINA--model3-2.png" class="img-responsive center-block" style="border-radius: 5px;margin-top: 20px;height: 400px;width: auto;"></div>
       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 3: Simulated glutamate and GltC production</p></div>
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       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 3: (a) Simulated glutamate production process. (b) Simulated GltC production process</p></div>
 
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       <p class="model_content">Accroding to Figure 3, it can be seen that the time evolutions are smooth and that no oscillations are present, and eventually the concentration of Glutamate and GltC is stable, which is necessary for bacteria. We have also found that even small changes in mRNA degradation rate or mRNA copy number may result in large differences in intracellular glutamate concentrations. This result demonstrates why the concentration of glutamate can vary in a wide range and stay stable, which provides a theoretical basis for our experiment.</p>
+
       <p class="model_content">Accroding to Figure 3, it can be seen that the time evolutions are smooth and that no oscillations are present, and eventually the concentration of Glutamate and GltC are stable, which is necessary for bacteria. We have also found that even small changes in mRNA degradation rates or mRNA copy numbers may result in large differences in intracellular glutamate concentrations. This result demonstrates why the concentration of glutamate can vary in a wide range and stay stable, which provides a theoretical basis for our experiment.</p>
       <p class="model_content">However, the intracellular GltC concentration is basically stable in different cells because of its self-negative feedback network. So is reasonable to assume that the concentration of GltC-Glu complex is only affected by different intracellular glutamate concentrations. The reaction equilibrium constant in Equation (9) is <img src="https://static.igem.org/mediawiki/2018/9/91/T--NKU_CHINA--duangluo1.png" style="border-radius: 2px;height: 60px;width: auto;">, so the concentration of GltC-Glu complex is proportional to glutamate concentration. Define its proportional coefficient <img src="https://static.igem.org/mediawiki/2018/6/6f/T--NKU_CHINA--duangluo2.png" style="border-radius: 2px;height: 40px;width: auto;">.</p>
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       <p class="model_content">However, we find that the intracellular GltC concentration is basically equivalent in different cells because of its self-negative feedback network. So is reasonable to assume that the concentration of GltC-Glu complex is only affected by different intracellular glutamate concentrations. The reaction equilibrium constant in Equation (9) is <img src="https://static.igem.org/mediawiki/2018/9/91/T--NKU_CHINA--duangluo1.png" style="border-radius: 2px;height: 60px;width: auto;">, so the concentration of GltC-Glu complex is proportional to glutamate concentration. Define its proportional coefficient <img src="https://static.igem.org/mediawiki/2018/6/6f/T--NKU_CHINA--duangluo2.png" style="border-radius: 2px;height: 40px;width: auto;">.</p>
 
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       <img src="https://static.igem.org/mediawiki/2018/9/97/T--NKU_CHINA--model4.png" class="img-responsive center-block" style="border-radius: 5px;">
 
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       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 4: Using 50,000 cells to simulate the normally distribution</p></div>     
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       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 4: Using 50,000 cells to simulate the normally distribution</p></div>     
 
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       <p class="model_content">The complex GltC-Glu achieves transcriptional regulation by altering the probability of RNA polymerase binding to the P<sub><i>gltAB</i></sub> promoter. We model this process and assume that the probability of binding of RNA polymerase to the <i>tetA</i> promoter is linear to the <i>tetA</i> mRNA transcription level.</p>
 
       <p class="model_content">The complex GltC-Glu achieves transcriptional regulation by altering the probability of RNA polymerase binding to the P<sub><i>gltAB</i></sub> promoter. We model this process and assume that the probability of binding of RNA polymerase to the <i>tetA</i> promoter is linear to the <i>tetA</i> mRNA transcription level.</p>
 
       <p class="model_content">Total partition function:</p>
 
       <p class="model_content">Total partition function:</p>
       <img src="https://static.igem.org/mediawiki/2018/e/e2/T--NKU_CHINA--gongshi16.png" class="img-responsive center-block" style="border-radius: 5px;height: 50px;width: auto;">
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       <p class="model_content">(16)<img src="https://static.igem.org/mediawiki/2018/e/e2/T--NKU_CHINA--gongshi16.png" class="img-responsive center-block" style="border-radius: 5px;height: 50px;width: auto;"></p>
 
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       <p class="model_content">where Z(P, R; N<sub>NS</sub>) refers to the partition function of P polymerase and R complex GltC-Glu binding to N<sub>NS</sub> non-specific sites (Dividing DNA sites into promoters and non-specific binding sites,which is approximately equal to 4&#215;10<sup>6</sup> in <i>Bacillus amyloliquefaciens</i>.) &#946;=K<sub>B</sub>T. Here we assume that RNA polymerase is randomly collided onto DNA. Therefore, the probability of a promoter occupied by RNA polymerase is:</p>
 
       <p class="model_content">where Z(P, R; N<sub>NS</sub>) refers to the partition function of P polymerase and R complex GltC-Glu binding to N<sub>NS</sub> non-specific sites (Dividing DNA sites into promoters and non-specific binding sites,which is approximately equal to 4&#215;10<sup>6</sup> in <i>Bacillus amyloliquefaciens</i>.) &#946;=K<sub>B</sub>T. Here we assume that RNA polymerase is randomly collided onto DNA. Therefore, the probability of a promoter occupied by RNA polymerase is:</p>
       <img src="https://static.igem.org/mediawiki/2018/6/67/T--NKU_CHINA--gongshi17.png" class="img-responsive center-block" style="border-radius: 4px;width: 500px;height: auto;">
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       <p class="model_content">(17)<img src="https://static.igem.org/mediawiki/2018/6/67/T--NKU_CHINA--gongshi17.png" class="img-responsive center-block" style="border-radius: 4px;width: 500px;height: auto;"></p>
 
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       <p class="model_content">Because the number of polymerase and GltC-Glu complexes is negligible relative to the number of effective binding sites, so:</p>
 
       <p class="model_content">Because the number of polymerase and GltC-Glu complexes is negligible relative to the number of effective binding sites, so:</p>
       <img src="https://static.igem.org/mediawiki/2018/0/08/T--NKU_CHINA--gongshi18.png" class="img-responsive center-block" style="border-radius: 4px;width: 500px;height: auto;">
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       <p class="model_content">(18)<img src="https://static.igem.org/mediawiki/2018/0/08/T--NKU_CHINA--gongshi18.png" class="img-responsive center-block" style="border-radius: 4px;width: 500px;height: auto;"></p>
 
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       <p class="model_content">Substituting Equation (3) into Equation (4):</p>
 
       <p class="model_content">Substituting Equation (3) into Equation (4):</p>
       <img src="https://static.igem.org/mediawiki/2018/7/7e/T--NKU_CHINA--gongshi19.png" class="img-responsive center-block" style="border-radius: 4px;width: 600px;height: auto;">
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       <p class="model_content">(19)<img src="https://static.igem.org/mediawiki/2018/7/7e/T--NKU_CHINA--gongshi19.png" class="img-responsive center-block" style="border-radius: 4px;width: 600px;height: auto;"></p>
 
       <p class="model_content">We define the degree of deterrence(D) as the ratio of the probability that the promoter is occupied by RNA polymerase in the absence of a complex GltC-Glu to the probability of having a complex GltC-Glu:</p>
 
       <p class="model_content">We define the degree of deterrence(D) as the ratio of the probability that the promoter is occupied by RNA polymerase in the absence of a complex GltC-Glu to the probability of having a complex GltC-Glu:</p>
       <img src="https://static.igem.org/mediawiki/2018/3/32/T--NKU_CHINA--gongshi20.png" class="img-responsive center-block" style="border-radius: 4px;width: 600px;height: auto;">
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       <p class="model_content">(20)<img src="https://static.igem.org/mediawiki/2018/3/32/T--NKU_CHINA--gongshi20.png" class="img-responsive center-block" style="border-radius: 4px;width: 600px;height: auto;"></p>
 
       <p class="model_content">For weak promotors:</p>
 
       <p class="model_content">For weak promotors:</p>
       <img src="https://static.igem.org/mediawiki/2018/8/85/T--NKU_CHINA--gongshi21.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 300px;">
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       <p class="model_content">(21)<img src="https://static.igem.org/mediawiki/2018/8/85/T--NKU_CHINA--gongshi21.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 300px;"></p>
 
       <p class="model_content">Define the expression level of P<sub><i>gltAB</i></sub> as 1 when glutamate concentration is 0, so the relative expression level of P<sub><i>gltAB</i></sub> is:</p>
 
       <p class="model_content">Define the expression level of P<sub><i>gltAB</i></sub> as 1 when glutamate concentration is 0, so the relative expression level of P<sub><i>gltAB</i></sub> is:</p>
       <img src="https://static.igem.org/mediawiki/2018/a/ab/T--NKU_CHINA--gongshi22.png" class="img-responsive center-block" style="border-radius: 4px;width: 600px;height: auto;">
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       <p class="model_content">(22)<img src="https://static.igem.org/mediawiki/2018/a/ab/T--NKU_CHINA--gongshi22.png" class="img-responsive center-block" style="border-radius: 4px;width: 600px;height: auto;"></p>
       <p class="model_content">According to the in vitro experimental data <sup>[1]</sup> as in Figure 2(a), we can find the parameter in  equation (8):<img src="https://static.igem.org/mediawiki/2018/6/65/T--NKU_CHINA--duangluo3.png" style="border-radius: 4px;width: 350px;height: auto;">, which is shown as Figure 2(b):</p>
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       <p class="model_content">According to the in vitro experimental data <sup>[1]</sup> as in Figure 5(a), we can find the parameter in  equation (8) as:<img src="https://static.igem.org/mediawiki/2018/6/65/T--NKU_CHINA--duangluo3.png" style="border-radius: 4px;width: 350px;height: auto;"> and get a fitting result, which is shown in Figure 5(b):</p>
 
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       <img src="https://static.igem.org/mediawiki/2018/1/1a/T--NKU_CHINA--model5b.png" class="img-responsive center-block" style="border-radius: 5px;margin-top: 20px;height: 400px;width: auto;">
 
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       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 5: Use in vitro experimental data to describe the relationship between P<sub><i>gltAB</i></sub> transcriptional level and glutamate concentrantion</p></div>
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       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 5: Use in vitro experimental data to describe the relationship between P<sub><i>gltAB</i></sub> transcriptional level and glutamate concentration (a) The in vitro experimental data <sup>[1]</sup>. (b) Fitting result of the relationship between glutamate concentration and <i>gltAB</i> expression level</p></div>
 
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       <p class="model_content">According to the above formulas and glutamate distribution, we can get the distribution of P<sub><i>gltAB</i></sub> expression in the cells, and since the P<sub><i>gltAB</i></sub> promoter is linked to the LacI protein, which can also be considered as the distribution of intracellular <i>lacI</i> in Figure 6:</p>
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       <p class="model_content">According to the above formulas and glutamate distribution, we can get the distribution of <i>gltAB</i> expression in the cells, and since the P<sub><i>gltAB<i></sub> promoter is linked to LacI protein, which can also be considered as the distribution of intracellular LacI in Figure 6:</p>
 
       <img src="https://static.igem.org/mediawiki/2018/7/7e/T--NKU_CHINA--model6.png" class="img-responsive center-block" style="border-radius: 5px;">
 
       <img src="https://static.igem.org/mediawiki/2018/7/7e/T--NKU_CHINA--model6.png" class="img-responsive center-block" style="border-radius: 5px;">
 
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       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 6: The distribution of intracellular <i>lacI</i></p></div>  
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       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 6: The distribution of intracellular LacI</p></div>  
 
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       <p class="model_content">LacI protein achieves transcriptional regulation by altering the probability of RNA polymerase binding to the <i>tetA</i> gene promoter, which is similar to the complex GltC-Glu alters the the probability of RNA polymerase binding to the P<sub><i>gltAB</i></sub> promoter. So similarly we can get the total partition function:</p>
 
       <p class="model_content">LacI protein achieves transcriptional regulation by altering the probability of RNA polymerase binding to the <i>tetA</i> gene promoter, which is similar to the complex GltC-Glu alters the the probability of RNA polymerase binding to the P<sub><i>gltAB</i></sub> promoter. So similarly we can get the total partition function:</p>
       <img src="https://static.igem.org/mediawiki/2018/6/62/T--NKU_CHINA--gongshi23.png" class="img-responsive center-block" style="border-radius: 4px;height: 50px;width: auto;">
+
       <p class="model_content">(23)<img src="https://static.igem.org/mediawiki/2018/6/62/T--NKU_CHINA--gongshi23.png" class="img-responsive center-block" style="border-radius: 4px;height: 50px;width: auto;"></p>
 
       <p class="model_content">where Z(P, R; N<sub>NS</sub>) refers to the partition function of P polymerase and R LacI proteins binding to N<sub>NS</sub> non-specific sites. Then:</p>
 
       <p class="model_content">where Z(P, R; N<sub>NS</sub>) refers to the partition function of P polymerase and R LacI proteins binding to N<sub>NS</sub> non-specific sites. Then:</p>
       <img src="https://static.igem.org/mediawiki/2018/2/25/T--NKU_CHINA--gongshi24.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 300px;"><br>
+
       <p class="model_content">(24)<img src="https://static.igem.org/mediawiki/2018/2/25/T--NKU_CHINA--gongshi24.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 300px;"><br>
       <img src="https://static.igem.org/mediawiki/2018/5/53/T--NKU_CHINA--gongshi25.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 300px;">
+
       (25)<img src="https://static.igem.org/mediawiki/2018/5/53/T--NKU_CHINA--gongshi25.png" class="img-responsive center-block" style="border-radius: 4px;height: auto;width: 300px;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
Line 263: Line 263:
 
       <img src="https://static.igem.org/mediawiki/2018/c/ce/T--NKU_CHINA--model7c.png" class="img-responsive center-block" style="border-radius: 5px;height: 400px;width: auto;margin-top: 10px;">
 
       <img src="https://static.igem.org/mediawiki/2018/c/ce/T--NKU_CHINA--model7c.png" class="img-responsive center-block" style="border-radius: 5px;height: 400px;width: auto;margin-top: 10px;">
 
       </div>
 
       </div>
       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 7: (a) Experimental data obtained by our team and the fitting result (normalized). (b) The relationship between <i>tetA</i> expression and lacI. (c) The distribution of <i>tetA</i> mRNA in different cells</p></div>
+
       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 7: (a) Experimental data obtained by our team and the fitting result (normalized). (b) The relationship between <i>tetA</i> expression and lacI. (c) The distribution of <i>tetA</i> mRNA in different cells</p></div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">It can be seen that in the same community, the mRNA distribution of <i>tetA</i> is significantly different, and the system has high sensitivity, so tetracycline can be used to achieve separation of high-producers and low-producers.</p>
 
       <p class="model_content">It can be seen that in the same community, the mRNA distribution of <i>tetA</i> is significantly different, and the system has high sensitivity, so tetracycline can be used to achieve separation of high-producers and low-producers.</p>
Line 275: Line 275:
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
       <p class="model_content">When tetracycline is added to the medium, it is assumed that the bacteria whose mRNA expression is at a certain threshold can survive (that is, the amount of glutamate expressed at a certain threshold), and we hope to predict the threshold for maximizing the total production. The specific model is: set this threshold to m, and the bacteria can survive when the intracellular glutamate concentration is greater than m. And since the difference in the expression of glutamate is non-genetic, it can be considered that the glutamate remains normal distribution between 20 mM to 200 mM in the offspring after the bacterial division. Among these bacteria, also only the intracellular glutamate concentration is greater than m can survive. Define &#969; as the ratio of the number of bacteria with intracellular glutamate concentration greater than m devide by the total number of bacteria:</p>
+
       <p class="model_content">When tetracycline is added to the medium, we assume that the bacteria whose <i>tetA</i> mRNA expression is at a certain threshold can survive (that is, the intracellular glutamate concentration is at a certain threshold), and we hope to predict the threshold for maximizing the total production. The specific model is: set this threshold to m, and the bacteria can survive when the intracellular glutamate concentration is greater than m. And since the difference in the expression of glutamate is non-genetic, it can be considered that the glutamate remains normal distribution between 20 mM to 200 mM in the offspring after the bacterial division. Among these bacteria, also only the intracellular glutamate concentration is greater than m can survive. Define &#969; as the ratio of the number of bacteria with intracellular glutamate concentration greater than m devide by the total number of bacteria:</p>
       <img src="https://static.igem.org/mediawiki/2018/e/ed/T--NKU_CHINA--gongshi26.png" class="img-responsive center-block" style="border-radius: 4px;height: 90px;width: auto;">
+
       <p class="model_content">(26)<img src="https://static.igem.org/mediawiki/2018/e/ed/T--NKU_CHINA--gongshi26.png" class="img-responsive center-block" style="border-radius: 4px;height: 90px;width: auto;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">The average glutamate concentration in these strains is:</p>
 
       <p class="model_content">The average glutamate concentration in these strains is:</p>
       <img src="https://static.igem.org/mediawiki/2018/0/0c/T--NKU_CHINA--gongshi27.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;">
+
       <p class="model_content">(27)<img src="https://static.igem.org/mediawiki/2018/0/0c/T--NKU_CHINA--gongshi27.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">Assume that the production of &#947;-polyglutamic acid is proportional to the intracellular glutamate content, that is:</p>
 
       <p class="model_content">Assume that the production of &#947;-polyglutamic acid is proportional to the intracellular glutamate content, that is:</p>
       <img src="https://static.igem.org/mediawiki/2018/c/c6/T--NKU_CHINA--gongshi28.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;">
+
       <p class="model_content">(28)<img src="https://static.igem.org/mediawiki/2018/c/c6/T--NKU_CHINA--gongshi28.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
       <p class="model_content">Substituting equation (14) into the Logistic formula, and assume that tetracycline only affects the population growth rate and the initial bacterial number without changing the environmental capacity, that is, after adding a certain amount of tetracycline:</p>
+
       <p class="model_content">Substituting equation (28) into the Logistic formula, and assume that tetracycline only affects the population growth rate and the initial bacterial number without changing the environmental capacity, that is, after adding a certain amount of tetracycline:</p>
       <img src="https://static.igem.org/mediawiki/2018/0/0a/T--NKU_CHINA--gongshi29.png" class="img-responsive center-block" style="border-radius: 4px;height: 40px;width: auto;">
+
       <p class="model_content">(29)<img src="https://static.igem.org/mediawiki/2018/0/0a/T--NKU_CHINA--gongshi29.png" class="img-responsive center-block" style="border-radius: 4px;height: 40px;width: auto;"></p>
       <img src="https://static.igem.org/mediawiki/2018/c/c4/T--NKU_CHINA--gongshi30.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;margin-top: 10px;">
+
       <p class="model_content">(30)<img src="https://static.igem.org/mediawiki/2018/c/c4/T--NKU_CHINA--gongshi30.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;margin-top: 10px;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">Simplified:</p>
 
       <p class="model_content">Simplified:</p>
       <img src="https://static.igem.org/mediawiki/2018/a/a2/T--NKU_CHINA--gongshi31.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;">
+
       <p class="model_content">(31)<img src="https://static.igem.org/mediawiki/2018/a/a2/T--NKU_CHINA--gongshi31.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">The total &#947;-polyglutamic acid concentration is:</p>
 
       <p class="model_content">The total &#947;-polyglutamic acid concentration is:</p>
       <img src="https://static.igem.org/mediawiki/2018/4/49/T--NKU_CHINA--gongshi32.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;">
+
       <p class="model_content">(32)<img src="https://static.igem.org/mediawiki/2018/4/49/T--NKU_CHINA--gongshi32.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;"></p>
 
       </div>   
 
       </div>   
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">Polyglutamic acid is a growth-coupled product in <i>B. amyloliquefaciens</i> LL3 <sup>[3]</sup>. For the growth coupled product, the Luedeking-Pieret formula which describes product synthes kinetics is:</p>
 
       <p class="model_content">Polyglutamic acid is a growth-coupled product in <i>B. amyloliquefaciens</i> LL3 <sup>[3]</sup>. For the growth coupled product, the Luedeking-Pieret formula which describes product synthes kinetics is:</p>
       <img src="https://static.igem.org/mediawiki/2018/5/56/T--NKU_CHINA--gongshi33.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;">
+
       <p class="model_content">(33)<img src="https://static.igem.org/mediawiki/2018/5/56/T--NKU_CHINA--gongshi33.png" class="img-responsive center-block" style="border-radius: 4px;height: 100px;width: auto;"></p>
 
       </div>
 
       </div>
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
       <p class="model_content">Since X<sub>0</sub> is negligible, equation (18) has a consistent form with the predicted total &#947;-polyglutamic acid production equation (19), which confirms the correctness of the established model. The fitting result for total &#947;-polyglutamic acid production is shown in Figure 8:</p>
+
       <p class="model_content">Since X<sub>0</sub> is negligible, Equation (33) has a consistent form with the predicted total &#947;-polyglutamic acid production Equation (32), which confirms the correctness of the established model. The fitting result for total &#947;-polyglutamic acid production is shown in Figure 8:</p>
 
       <img src="https://static.igem.org/mediawiki/2018/9/9f/T--NKU_CHINA--model8.png" class="img-responsive center-block" style="border-radius: 5px;">
 
       <img src="https://static.igem.org/mediawiki/2018/9/9f/T--NKU_CHINA--model8.png" class="img-responsive center-block" style="border-radius: 5px;">
       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 8: Total &#947;-polyglutamic acid production. Colorbar indicats that m changes from 20 mM to 200 mM (interval is 3 mM)</p></div>
+
       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 8: Total &#947;-polyglutamic acid production. The Color bar indicates that m changes from 20 mM to 200 mM (interval is 3 mM). According to our experimental data, the time of one fermentation is 32h, and the time to reach the maximum population density is about 10h.</p></div>
 
       </div>  
 
       </div>  
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
       <p class="model_content">It can be seen from the figure that the concentration of &#947;-polyglutamic acid increases first and then decreases with increasing m at a certain point in time (eg, t=70h). When m is small, the total concentration is small due to the presence of low production cells; and when m is large, the total concentration of &#947;-polyglutamic acid is small because the tetracycline has a strong inhibitory effect and the total number of cells is small. It can be seen that when the concentration of tetracycline is too high, the bacteria hardly grow, which is also consistent with the observed results.</p>
+
       <p class="model_content">It can be seen from Figure 8 that the concentration of &#947;-polyglutamic acid increases first and then decreases with increasing m at a certain point in time (e.g. t=32h). When m is too small, the total concentration is small due to the presence of low production cells; and when m is too large, the total concentration of &#947;-polyglutamic acid is small because the tetracycline has a strong inhibitory effect and the total number of cells is small. When the concentration of tetracycline is too high, the bacteria hardly grow, which is also consistent with the observed results.</p>
       <p class="model_content">We chose t=70h as the time of one fermentation. The m value when &#947;-polyglutamic acid production is the highest at t=70h was 119 mM, which is shown in Figure 6. This result demonstrates we need to adjust the concentration of tetracycline to make the strains whose intracellular glutamate concentration below 119 mM to die, and the strains whose intracellular glutamate concentration is above this threshold can continue to survive. In that case, the maximum expected increase in production can achieve 34.8%.</p>
+
       <p class="model_content">We chose t=32 h as the time of one fermentation. When &#947;-polyglutamic acid production reachs the highest at t=32 h, m equals to 112 mM, which is shown in Figure 9. This result demonstrates we need to adjust the concentration of tetracycline to make the strains whose intracellular glutamate concentration below 112 mM to die, and the strains whose intracellular glutamate concentration is above this threshold can continue to survive. In that case, the maximum production increase is about 35%. We can also find the fact that production will drop quickly after its increase reaches the peak, which indicates that precise regulation of tetracycline is needed near the critical point in industrial production.</p>
 
       <img src="https://static.igem.org/mediawiki/2018/7/7b/T--NKU_CHINA--model9.png" class="img-responsive center-block" style="border-radius: 5px;">
 
       <img src="https://static.igem.org/mediawiki/2018/7/7b/T--NKU_CHINA--model9.png" class="img-responsive center-block" style="border-radius: 5px;">
       <div class="col-xs-12"><p class="text-center" style="color: white;font-size: 20px;margin-top: 5px;">Figure 9: Relationship between &#947;-polyglutamic acid production and threshold m, at t=70h</p></div>
+
       <div class="col-xs-12"><p style="color: white;font-size: 20px;margin-top: 5px;text-align: center;">Figure 9: Relationship between &#947;-polyglutamic acid production and threshold m, at t=70h</p></div>
 
       </div>           
 
       </div>           
 
       </div>
 
       </div>
Line 323: Line 323:
 
       <div class="col-xs-12">
 
       <div class="col-xs-12">
 
       <p class="model_content">[1] Silvia Picossi, Boris R. Belitsky, and Abraham L. Sonenshein (2007). Molecular mechanism of the regulation of <i>Bacillus subtilis</i> <i>gltAB</i> expression by GltC. J Mol Biol, 365(5): 1298–1313.</p>
 
       <p class="model_content">[1] Silvia Picossi, Boris R. Belitsky, and Abraham L. Sonenshein (2007). Molecular mechanism of the regulation of <i>Bacillus subtilis</i> <i>gltAB</i> expression by GltC. J Mol Biol, 365(5): 1298–1313.</p>
       <p class="model_content">[2] Katrin Gunka and Fabian M. Commichau<sup>*</sup>.Control of glutamate homeostasis in <i>Bacillus subtilis</i>: a complex interplay between ammonium assimilation, glutamate biosynthesis and degradation.Molecular Microbiology (2012) 85(2), 213–224.</p>
+
       <p class="model_content">[2] Katrin Gunka and Fabian M. Commichau<sup>*</sup>. Control of glutamate homeostasis in <i>Bacillus subtilis</i>: a complex interplay between ammonium assimilation, glutamate biosynthesis and degradation. Molecular Microbiology (2012) 85(2), 213–224.</p>
 
       <p class="model_content">[3] Mingfeng Cao, Weitao Geng, Li Liu, Cunjiang Song, Hui Xie, Wenbin Guo, Yinghong Jin, Shufang Wang (2011). Glutamic acid independent production of poly-c-glutamic acid by <i>Bacillus amyloliquefaciens</i> LL3 and cloning of <i>pgsBCA</i> genes. Bioresource Technology 102 (2011) 4251-4257.</p>
 
       <p class="model_content">[3] Mingfeng Cao, Weitao Geng, Li Liu, Cunjiang Song, Hui Xie, Wenbin Guo, Yinghong Jin, Shufang Wang (2011). Glutamic acid independent production of poly-c-glutamic acid by <i>Bacillus amyloliquefaciens</i> LL3 and cloning of <i>pgsBCA</i> genes. Bioresource Technology 102 (2011) 4251-4257.</p>
 
       </div>
 
       </div>

Revision as of 06:04, 17 October 2018

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Model

Abstract

PopQC, which is the abbreviation for population quality control, is a new approach designed for biosynthesis production enhancement based on the non-genetic cell-to-cell variation. Because of some nongenetic differences, different cells in a single colony will have considerable variations in protein and metabolite concentrations. Based on this, PopQC was designed as a plasmid-based gene circuit, which continuously selects high-producers to increase production.

We first use ODEs to explain why the concentration of glutamate can vary in a wide range and stay stable. We then use biophysical model to explain the biosynthetic performance of our system based on the inhibition effect of promoter's occupation by RNA polymerase. Finally, we use our model to predict initial condition to get the maximum production, and test our systems' efficiency and accuracy.

Glutamate and GltC Concentration

Figure 1: Pattern diagram of PopQC based on our design

In our project, Bacillus amyloliquefaciens LL3 was selected as the engineered strain introduced into the PopQC plasmid. In Bacillus amyloliquefaciens LL3, the intracellular glutamate concentration varies from 20 mM to 200 mM based on some nongenetic differences, which is from the result of our lab's previous work. We hope in the presence of PopQC, high glutamate strains can stay alive while low glutamate strains are unable to survive.

GltC combines with glutamate to form GltC-Glu complex. And it 's suggested that in the case of Bacillus amyloliquefaciens RNAP, glutamate inhibits GltC-dependent transcription of gltAB mostly by GltC-Glu complex 's additional non-specific inhibitory effect on RNAP for binding on gltAB promoter[1]. gltAB operon encodes glutamate synthase[2], so it forms a feedback suppression network by GltC-Glu complex. Meanwhile, GltC-Glu complex also has an inhibitory effect on gltC promoter, which forms a self-negative feedback network. These feedback suppression networks work together to keep intracellular glutamate pool stable. See Figure 2:

Figure 2: Feedback suppression networks based on GltC-Glu complex

We use ordinary differential equations (Table 1) to describe this progress, the fitting result is shown as Figure 3:

Table 1: Ordinary differential equations that describes feedback suppression networks based on GltC-Glu complex. We have estimated the parameters and the result are: k1=0.81, k2=2.15×104, k3=49, k4=0.96, k5=0.84, k6=1.6×10-4, k7=5.0×106, k8=0.47, k9=1.7×106,k10=9.7×104. β represents gene leakage rate, const=1.

Figure 3: (a) Simulated glutamate production process. (b) Simulated GltC production process

Accroding to Figure 3, it can be seen that the time evolutions are smooth and that no oscillations are present, and eventually the concentration of Glutamate and GltC are stable, which is necessary for bacteria. We have also found that even small changes in mRNA degradation rates or mRNA copy numbers may result in large differences in intracellular glutamate concentrations. This result demonstrates why the concentration of glutamate can vary in a wide range and stay stable, which provides a theoretical basis for our experiment.

However, we find that the intracellular GltC concentration is basically equivalent in different cells because of its self-negative feedback network. So is reasonable to assume that the concentration of GltC-Glu complex is only affected by different intracellular glutamate concentrations. The reaction equilibrium constant in Equation (9) is , so the concentration of GltC-Glu complex is proportional to glutamate concentration. Define its proportional coefficient .

Biophysical Model

We assume that the intracellular glutamate concentration is normally distributed between 20'200 mM, which is from the result of our lab's previous work. See Figure 4:

Figure 4: Using 50,000 cells to simulate the normally distribution

The complex GltC-Glu achieves transcriptional regulation by altering the probability of RNA polymerase binding to the PgltAB promoter. We model this process and assume that the probability of binding of RNA polymerase to the tetA promoter is linear to the tetA mRNA transcription level.

Total partition function:

(16)

where Z(P, R; NNS) refers to the partition function of P polymerase and R complex GltC-Glu binding to NNS non-specific sites (Dividing DNA sites into promoters and non-specific binding sites,which is approximately equal to 4×106 in Bacillus amyloliquefaciens.) β=KBT. Here we assume that RNA polymerase is randomly collided onto DNA. Therefore, the probability of a promoter occupied by RNA polymerase is:

(17)

Because the number of polymerase and GltC-Glu complexes is negligible relative to the number of effective binding sites, so:

(18)

Substituting Equation (3) into Equation (4):

(19)

We define the degree of deterrence(D) as the ratio of the probability that the promoter is occupied by RNA polymerase in the absence of a complex GltC-Glu to the probability of having a complex GltC-Glu:

(20)

For weak promotors:

(21)

Define the expression level of PgltAB as 1 when glutamate concentration is 0, so the relative expression level of PgltAB is:

(22)

According to the in vitro experimental data [1] as in Figure 5(a), we can find the parameter in equation (8) as: and get a fitting result, which is shown in Figure 5(b):

Figure 5: Use in vitro experimental data to describe the relationship between PgltAB transcriptional level and glutamate concentration (a) The in vitro experimental data [1]. (b) Fitting result of the relationship between glutamate concentration and gltAB expression level

According to the above formulas and glutamate distribution, we can get the distribution of gltAB expression in the cells, and since the PgltAB promoter is linked to LacI protein, which can also be considered as the distribution of intracellular LacI in Figure 6:

Figure 6: The distribution of intracellular LacI

LacI protein achieves transcriptional regulation by altering the probability of RNA polymerase binding to the tetA gene promoter, which is similar to the complex GltC-Glu alters the the probability of RNA polymerase binding to the PgltAB promoter. So similarly we can get the total partition function:

(23)

where Z(P, R; NNS) refers to the partition function of P polymerase and R LacI proteins binding to NNS non-specific sites. Then:

(24)
(25)

Figure 7(a) shows the experimental data obtained by our team and the fitting result according to equation (11). Therefore we can get the relationship between tetA expression and lacI as Figure 7(b). The distribution of tetA mRNA in cells can also be obtained as Figure 7(c):

Figure 7: (a) Experimental data obtained by our team and the fitting result (normalized). (b) The relationship between tetA expression and lacI. (c) The distribution of tetA mRNA in different cells

It can be seen that in the same community, the mRNA distribution of tetA is significantly different, and the system has high sensitivity, so tetracycline can be used to achieve separation of high-producers and low-producers.

Optimization Initial Condition

When tetracycline is added to the medium, we assume that the bacteria whose tetA mRNA expression is at a certain threshold can survive (that is, the intracellular glutamate concentration is at a certain threshold), and we hope to predict the threshold for maximizing the total production. The specific model is: set this threshold to m, and the bacteria can survive when the intracellular glutamate concentration is greater than m. And since the difference in the expression of glutamate is non-genetic, it can be considered that the glutamate remains normal distribution between 20 mM to 200 mM in the offspring after the bacterial division. Among these bacteria, also only the intracellular glutamate concentration is greater than m can survive. Define ω as the ratio of the number of bacteria with intracellular glutamate concentration greater than m devide by the total number of bacteria:

(26)

The average glutamate concentration in these strains is:

(27)

Assume that the production of γ-polyglutamic acid is proportional to the intracellular glutamate content, that is:

(28)

Substituting equation (28) into the Logistic formula, and assume that tetracycline only affects the population growth rate and the initial bacterial number without changing the environmental capacity, that is, after adding a certain amount of tetracycline:

(29)

(30)

Simplified:

(31)

The total γ-polyglutamic acid concentration is:

(32)

Polyglutamic acid is a growth-coupled product in B. amyloliquefaciens LL3 [3]. For the growth coupled product, the Luedeking-Pieret formula which describes product synthes kinetics is:

(33)

Since X0 is negligible, Equation (33) has a consistent form with the predicted total γ-polyglutamic acid production Equation (32), which confirms the correctness of the established model. The fitting result for total γ-polyglutamic acid production is shown in Figure 8:

Figure 8: Total γ-polyglutamic acid production. The Color bar indicates that m changes from 20 mM to 200 mM (interval is 3 mM). According to our experimental data, the time of one fermentation is 32h, and the time to reach the maximum population density is about 10h.

It can be seen from Figure 8 that the concentration of γ-polyglutamic acid increases first and then decreases with increasing m at a certain point in time (e.g. t=32h). When m is too small, the total concentration is small due to the presence of low production cells; and when m is too large, the total concentration of γ-polyglutamic acid is small because the tetracycline has a strong inhibitory effect and the total number of cells is small. When the concentration of tetracycline is too high, the bacteria hardly grow, which is also consistent with the observed results.

We chose t=32 h as the time of one fermentation. When γ-polyglutamic acid production reachs the highest at t=32 h, m equals to 112 mM, which is shown in Figure 9. This result demonstrates we need to adjust the concentration of tetracycline to make the strains whose intracellular glutamate concentration below 112 mM to die, and the strains whose intracellular glutamate concentration is above this threshold can continue to survive. In that case, the maximum production increase is about 35%. We can also find the fact that production will drop quickly after its increase reaches the peak, which indicates that precise regulation of tetracycline is needed near the critical point in industrial production.

Figure 9: Relationship between γ-polyglutamic acid production and threshold m, at t=70h

References:

[1] Silvia Picossi, Boris R. Belitsky, and Abraham L. Sonenshein (2007). Molecular mechanism of the regulation of Bacillus subtilis gltAB expression by GltC. J Mol Biol, 365(5): 1298–1313.

[2] Katrin Gunka and Fabian M. Commichau*. Control of glutamate homeostasis in Bacillus subtilis: a complex interplay between ammonium assimilation, glutamate biosynthesis and degradation. Molecular Microbiology (2012) 85(2), 213–224.

[3] Mingfeng Cao, Weitao Geng, Li Liu, Cunjiang Song, Hui Xie, Wenbin Guo, Yinghong Jin, Shufang Wang (2011). Glutamic acid independent production of poly-c-glutamic acid by Bacillus amyloliquefaciens LL3 and cloning of pgsBCA genes. Bioresource Technology 102 (2011) 4251-4257.

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