Difference between revisions of "Team:ZJUT-China/Model"

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              Team
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              <a href="https://2018.igem.org/Team:ZJUT-China/Design">Design</a>
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 +
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+
 
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            <a href="https://2018.igem.org/Team:ZJUT-China/Model"> Modeling</a>
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+
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          </div>
 
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     <br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
+
   <div class="col-10">
 +
     <h1>Abstract</h1>
 +
    <p>
 +
      In order to ensure that our system will be used better by the researchers who want to clean the arg after experiment, we developed a model to Calculate when all args will be cleaned and the bacterial will suicide. We get some data of our parts and built some rate equations. We then used those rate equations to simulate how our system work and find a better ratio of the vector’s copy number.
 +
    </p>
 +
    <h1>System modeling Var1.0</h1>
 +
    <div class="modelingmath">
 +
            d[express-cas]/dt=[vector]*vm/(1+[light_signal])
 +
      <br> d[cut off]/dt=kf*[sg]*[cas9]*[arg]/(km+[arg])
 +
    </div>
 +
    <div class="note2">
 +
        Our ODE model of the light control arg cutting system var1.0. We assume the express rate proportional to the copy number of the vector, vm means the mixture rate of one vector express the cas9, [light signal] we use is a dimensionless parameter here, and the cut off rate of cas9 conform Michaelis-Menten equation.
 +
    </div>
 +
    <h1>Result</h1>
 +
    <p>
 +
      This is the result we get by the ODE model of the light control arg cutting system var1.0
 +
    </p>
 +
    <div class="modelingimg">
 +
      <img src="https://static.igem.org/mediawiki/2018/6/6c/T--ZJUT-China--modeling1.png" alt="">
 +
    </div>
 +
    <h1>System modeling Var3.0</h1>
 +
    <p>
 +
      This presents an issue for researchers and factors who wish to make use of our system of the arg killing parts in a more complex environment. In order to address this issue, we decided to develop a mathematical model of how light signal effects influence the time of cut off all args and suicide of bacterial by our arg killing system.
 +
      In the light control arg cutting system var3.0 we want add 3 repressors, one more sgRNA and a lysin gene to let our cells can cut off all the args and suicide by the time order we designed.
 +
    <br>
 +
    </p>
 +
    <div class="modelingmath">
 +
      d[express_r1]/t=kf*[vector_1]/(vm+[light signal])
 +
      <br>d[degrade_r1]/t=vm*[repressor_1]/([repressor_1]+km)
 +
      <br>d[express_r2]/t=kf*[vector_2]
 +
      <br>d[degrade_r2]/t=vm*[repressor_2]/([repressor_2]+km)
 +
      <br>d[express_r3]/t=kf*[vector_1]
 +
      <br>d[degrade_r3]/t=vm*[repressor_3]/([repressor_3]+km)
 +
      <br>d[express_cas]/t=kf*[vector_1]*(vm-[repressor_1])
 +
      <br>d[express_sg1]/t=0
 +
      <br>d[express_sg2]/t=kf*[vector_2]*(vm-[repressor_2])
 +
      <br>d[express_ly]/t=kf*[chromosome]*(vm-[repressor_3])
 +
      <br>d[cut off_1]/t=kf*[arg_1]*[sg_1]*[cas9]/(km+[arg_1])
 +
      <br>d[cut off_2]/t=kf*[arg_2]*[sg_2]*[cas9]/(km+[arg_2])
 +
    </div>
 +
    <div class="note2">
 +
      Our ODE model of the light control arg cutting system var3.0. In this model we considered the express and degrade rate of the repressor and the effect of the copy number of 2vectors.
 +
    </div>
 +
    <p>
 +
      Through change the copy number of two vectors in our system model, we can get a ratio of the copy number let our system do nothing before we give the light signal, while has a faster react rate when we want it work.
 +
    </p>
 +
    <h1>Result</h1>
 +
    <div class="modelingimg">
 +
      <img src="https://static.igem.org/mediawiki/2018/4/4c/T--ZJUT-China--modeling3.png" alt="">
 +
    </div>
 +
    <div class="note">
 +
      Figure 1:when Time>=1t the strength of light signal=0.1,it use 12.5t to cut off all antibiotic resistance gene.
 +
    </div>
 +
    <div class="modelingimg">
 +
      <img src="https://static.igem.org/mediawiki/2018/4/4a/T--ZJUT-China--modeling4.png" alt="">
 +
    </div>
 +
    <div class="note">
 +
      Figure 2:when Time>=1t the strength of light signal=1,it use 12t to cut off all antibiotic resistance gene.
 +
    </div>
 +
    <div class="modelingimg">
 +
      <img src="https://static.igem.org/mediawiki/2018/f/fa/T--ZJUT-China--modeling5.png" alt="">
 +
    </div>
 +
    <div class="note">
 +
      Figure 3:when Time>=1t the strength of light signal=1, and shutdown when Time=2, it use 12t to cut off.
 +
    </div>
 +
    <h1>
 +
      Discussion
 +
    </h1>
 +
    <p>
 +
      Our modeling and analysis was focused to achieve a better theoretical grounding of forecasting how our system work after we give the light signal.
 +
      From the test of our ODE model of the light control arg cutting system var3.0, we find give a short pulse light signal can make almost same effect as we constant light signal, so we can find a plan to just give a short pulse light signal but make our system till response as fast as it, and save energy used to give the light signal.
 +
    </p>
 +
    <div class="note1">
 +
      [1]Quantitative approaches to the study of bistability in the lac operon of Escherichia coli  J R Soc Interface. 2008 Aug 6; 5(Suppl 1): S29–S39.
 +
      Published online 2008 Apr 15. doi:  10.1098/rsif.2008.0086.focus
 +
      [2]Combinatorial transcriptional control of the lactose operon of Escherichia coli
 +
      Thomas Kuhlman, Zhongge Zhang, Milton H. Saier, Jr., Terence Hwa
 +
      Proc Natl Acad Sci U S A. 2007 Apr 3; 104(14): 6043–6048. Published online 2007 Mar 21. doi: 10.1073/pnas.0606717104
 +
    </div>
 
   </div>
 
   </div>
 
</div>
 
</div>

Revision as of 11:25, 13 October 2018

Team:ZJUT-China - 2018.igem.org

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Team:ZJUT-China

Abstract

In order to ensure that our system will be used better by the researchers who want to clean the arg after experiment, we developed a model to Calculate when all args will be cleaned and the bacterial will suicide. We get some data of our parts and built some rate equations. We then used those rate equations to simulate how our system work and find a better ratio of the vector’s copy number.

System modeling Var1.0

d[express-cas]/dt=[vector]*vm/(1+[light_signal])
d[cut off]/dt=kf*[sg]*[cas9]*[arg]/(km+[arg])
Our ODE model of the light control arg cutting system var1.0. We assume the express rate proportional to the copy number of the vector, vm means the mixture rate of one vector express the cas9, [light signal] we use is a dimensionless parameter here, and the cut off rate of cas9 conform Michaelis-Menten equation.

Result

This is the result we get by the ODE model of the light control arg cutting system var1.0

System modeling Var3.0

This presents an issue for researchers and factors who wish to make use of our system of the arg killing parts in a more complex environment. In order to address this issue, we decided to develop a mathematical model of how light signal effects influence the time of cut off all args and suicide of bacterial by our arg killing system. In the light control arg cutting system var3.0 we want add 3 repressors, one more sgRNA and a lysin gene to let our cells can cut off all the args and suicide by the time order we designed.

d[express_r1]/t=kf*[vector_1]/(vm+[light signal])
d[degrade_r1]/t=vm*[repressor_1]/([repressor_1]+km)
d[express_r2]/t=kf*[vector_2]
d[degrade_r2]/t=vm*[repressor_2]/([repressor_2]+km)
d[express_r3]/t=kf*[vector_1]
d[degrade_r3]/t=vm*[repressor_3]/([repressor_3]+km)
d[express_cas]/t=kf*[vector_1]*(vm-[repressor_1])
d[express_sg1]/t=0
d[express_sg2]/t=kf*[vector_2]*(vm-[repressor_2])
d[express_ly]/t=kf*[chromosome]*(vm-[repressor_3])
d[cut off_1]/t=kf*[arg_1]*[sg_1]*[cas9]/(km+[arg_1])
d[cut off_2]/t=kf*[arg_2]*[sg_2]*[cas9]/(km+[arg_2])
Our ODE model of the light control arg cutting system var3.0. In this model we considered the express and degrade rate of the repressor and the effect of the copy number of 2vectors.

Through change the copy number of two vectors in our system model, we can get a ratio of the copy number let our system do nothing before we give the light signal, while has a faster react rate when we want it work.

Result

Figure 1:when Time>=1t the strength of light signal=0.1,it use 12.5t to cut off all antibiotic resistance gene.
Figure 2:when Time>=1t the strength of light signal=1,it use 12t to cut off all antibiotic resistance gene.
Figure 3:when Time>=1t the strength of light signal=1, and shutdown when Time=2, it use 12t to cut off.

Discussion

Our modeling and analysis was focused to achieve a better theoretical grounding of forecasting how our system work after we give the light signal. From the test of our ODE model of the light control arg cutting system var3.0, we find give a short pulse light signal can make almost same effect as we constant light signal, so we can find a plan to just give a short pulse light signal but make our system till response as fast as it, and save energy used to give the light signal.

[1]Quantitative approaches to the study of bistability in the lac operon of Escherichia coli J R Soc Interface. 2008 Aug 6; 5(Suppl 1): S29–S39. Published online 2008 Apr 15. doi:  10.1098/rsif.2008.0086.focus [2]Combinatorial transcriptional control of the lactose operon of Escherichia coli Thomas Kuhlman, Zhongge Zhang, Milton H. Saier, Jr., Terence Hwa Proc Natl Acad Sci U S A. 2007 Apr 3; 104(14): 6043–6048. Published online 2007 Mar 21. doi: 10.1073/pnas.0606717104