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

 
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     <h1>Abstract</h1>
 
     <h1>Abstract</h1>
 
     <p>
 
     <p>
−
       In order to ensure that our system will be used better by the researchers who want to clean the antibiotic resistance gene(arg) after experiment, we developed a model to calculate when all args will be cut off and cause bacteria auto-lysis. 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.
+
       In order to improve the feasibility of our system utilized by other researchers , we have tried our best to develop a model to predict the time point when the all antibiotic resistance genes(ARGs) are cut off and the cell auto-lysis is going to begin. This model is made up of some rate equations which are based on experimental data of our system. Then we are able to simulate the operation of our system and gain the information we need from the analog results.
 
     </p>
 
     </p>
 
     <h1>System modeling Ver1.0</h1>
 
     <h1>System modeling Ver1.0</h1>
 +
    For the purpose of calculating the time point when the all ARGs are cut off and the cell auto-lysis is going to begin,we have tried to construct a model used by the following equations.
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/3/31/T--ZJUT-China--modeling11.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/9/9a/T--ZJUT-China--modeling10181.png" alt="">
−
    </div>
+
−
    <div class="note2">
+
−
      Our ODE model of the light control arg cutting system ver1.0. 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>
 
     </div>
 +
    <div class="note3">Our ODE model of the light control ARG cutting system ver1.0.
 +
        <br>[Cas9]: The relative number of Cas9 protein
 +
        <br>[vector]: The relative copy number of the vector
 +
        <br>[light signal]: The relative light strength
 +
      <br>  [ARG]: The relative number of ARGs
 +
        <br>[sg]: The relative number of sgRNA
 +
      </div>
 
     <h1>Result</h1>
 
     <h1>Result</h1>
 
     <p>
 
     <p>
−
       This is the result we got by the ODE model of the light-controlled ARG cutting system ver1.0
+
       The result that we gain from the system modeling ver1.0 is shown below.
 
     </p>
 
     </p>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/a/ae/T--ZJUT-China--modeli19.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/3/31/T--ZJUT-China--modeling10182.png" alt="">
 
     </div>
 
     </div>
 
     <h1>System modeling Ver1.1</h1>
 
     <h1>System modeling Ver1.1</h1>
−
    <p>This model is built to predict the growth curve. And to test whether our system model ver1.0 can fit the data of our wet lab. This model concern more about the growth of cell, and the death
+
      <p>
−
    </p>
+
        Our system modeling ver1.0 is limited by problems that we are unable to verify the validity of the model through the experiments.Because the quantization of cas9 protein and ARGs is difficult.Therefore,we have tried to build up another model which is named as System modeling Ver1.1. This model can be used to predict the time point which is same as the System modeling Ver1.0 by growth curve. We are able to verify our model by experiments because the growth curve is easily gained by experiments.In addition,we can also prove the validity of system model ver1.0 for the reason that the equations of this model is based on the system model ver1.0.
−
    <h1>Result</h1>
+
      </p>
 +
      <div class="modelingimg">
 +
        <img src="https://static.igem.org/mediawiki/2018/0/0a/T--ZJUT-China--modeling10183.png" alt="">
 +
      </div>
 +
      <div class="note3">
 +
        Our ODE model of the light control ARG cutting system ver1.1.(the experimental group with the system and ARG)
 +
        <br>[Cas9]: The relative number of Cas9 protein
 +
        <br>[vector]: The relative copy number of the vector
 +
        <br>[ara]: The concentration of arabinose used to induced expression
 +
        <br>[ARG]: The relative number of ARGs
 +
        <br>[sg]: The relative number of sgRNA
 +
        <br>[cell]: The OD600 of viable cell
 +
      </div>
 +
      <div class="modelingimg">
 +
        <img src="https://static.igem.org/mediawiki/2018/8/8c/T--ZJUT-China--modeling10184.png" alt="">
 +
      </div>
 +
        <div class="note3">
 +
          Our ODE model of the light control ARG cutting system ver1.1.(the control group with ARG but without the system)
 +
          <br>[cell-c]: The OD600 of viable cell
 +
        </div>
 +
      <h1>Result</h1>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
 
       <img src="https://static.igem.org/mediawiki/2018/b/bd/T--ZJUT-China--modeli20.png" alt="">
 
       <img src="https://static.igem.org/mediawiki/2018/b/bd/T--ZJUT-China--modeli20.png" alt="">
 
     </div>
 
     </div>
−
     <div class="note2">
+
     <div class="note">
 
       When time=5h we put in different concentrations of Arabinose in the medium.
 
       When time=5h we put in different concentrations of Arabinose in the medium.
−
    <br>The points are the data get tested by wet lab and the lines are the data simulated by computer.
+
      <br>The points are the data get tested by wet lab and the lines are the data simulated by computer.
 
     </div>
 
     </div>
 +
    <p>Our ODE model after fit data:</p>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/e/e0/T--ZJUT-China--modeling13.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/c/c8/T--ZJUT-China--modeling10186.png" alt="">
 
     </div>
 
     </div>
−
     <div class="note2">
+
     <div class="note3">
−
       The first 3 equations are built to show the how the E.coli with our system ver1.0 growth, and the last one is the growth equation of control group.
+
       Our ODE model of the light control ARG cutting system ver1.1.(the experimental group)
 +
    <br>  [Cas9]: The relative number of Cas9 protein
 +
    <br>  [vector]: The relative copy number of the vector
 +
    <br>  [ara]: The concentration of arabinose used to induced expression
 +
    <br>  [ARG]: The relative number of ARGs
 +
    <br>  [sg]: The relative number of sgRNA
 +
    <br>  [cell]: The OD600 of viable cell
 +
    </div>
 +
    <div class="modelingimg">
 +
      <img src="https://static.igem.org/mediawiki/2018/1/18/T--ZJUT-China--modeling10187.png" alt="">
 +
    </div>
 +
    <div class="note3">
 +
      Our ODE model of the light control ARG cutting system ver1.1.(the control group)
 +
      <br>[cell]: The OD600 of viable cell
 
     </div>
 
     </div>
−
    <h1>System modeling Ver2.0</h1>
 
 
     <p>
 
     <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.
+
       By fitting the experimental data, we find that our system is feasible to predict the completion time of all the ARGs cleavage.Furthermore, we determine some constants based on experimental data which further improves our system and meets the requirements of the construction of the next model.
−
      In the light control arg cutting system ver2.0 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.
+
    </p>
 +
        <h1>System modeling Ver2.0</h1>
 +
    <p>
 +
      However, if researchers would like to use our system in the complex environment,System modeling Ver1.1 can not meet their requirements. In order to address this issue, we have managed to develop a mathematical model considering the influence of light signal and some other factors.In other words,we regard the factors which include the influence of three repressors, sgRNA and lysin as parameters of system modeling ver2.0 .
 
     </p>
 
     </p>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/2/2e/T--ZJUT-China--modeli14.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/c/c5/T--ZJUT-China--modeling10188.png" alt="">
−
    </div>
+
−
    <div class="note2">
+
−
      Our ODE model of the light control arg cutting system ver2.0. In this model we considered the express and degrade rate of the repressors and the effect of the copy number of 2vectors.
+
 
     </div>
 
     </div>
 +
    <div class="note3">
 +
      Our ODE model of the light control ARG cutting system ver2.0. In this model we considered the express and degrade rate of the Repressors and the effect of the copy number of 2vectors.
 +
    <br>  [Repressor-1]: The relative number of the first Repressor protein we used in the system
 +
    <br>  [Repressor-2]: The relative number of the second Repressor protein we used in the system
 +
    <br>  [Repressor-3]: The relative number of the third Repressor protein we used in the system
 +
    <br>  [vector-1]: The relative copy number of the vector with the light-controlled promoter, repressor gene-2, cas9 gene, sgRNA gene-1, ARG-2, repressor gene-3 on it
 +
    <br>  [vector-2]: The relative copy number of the vector with ARG-1, repressor gene-2 on it
 +
    <br>  [chromosome]: The relative copy number of the chromosome
 +
    <br>  [Cas9]: The relative number of Cas9 protein
 +
    <br>  [sg-1]: The relative number of the first sgRNA
 +
    <br>  [sg-2]: The relative number of the second sgRNA
 +
    <br>  [ARG-1]: The relative number of the first ARG
 +
    <br>  [ARG-2]: The relative number of the second ARG
 +
    <br>  [lysin]: The relative number of the lysin protein
 +
    <br>  [cell]: The OD600 of viable cell
 +
        </div>
 
     <p>
 
     <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.
 
       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.
Line 1,069: Line 1,131:
 
     <h1>Result</h1>
 
     <h1>Result</h1>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/f/f1/T--ZJUT-China--modeli21.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/1/1f/T--ZJUT-China--modeling10189.png" alt="">
 
     </div>
 
     </div>
−
     <div class="note">Figure 1：when Time>=1t the strength of light signal=0.1,it use 9t to cut off all antibiotic resistance gene.
+
     <div class="note">Our system spend 9t on cutting off all the ARGs and 23t for lysis, when time no less than 1t and the strength of light signal is 0.1.
 
     </div>
 
     </div>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/d/d2/T--ZJUT-China--modeli22.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/0/07/T--ZJUT-China--modeling101810.png" alt="">
 
     </div>
 
     </div>
−
     <div class="note">Figure 2：when Time>=1t the strength of light signal=1,it use 8t to cut off all antibiotic resistance gene.</div>
+
     <div class="note">Our system spend 8t on cutting off all the ARGs and 21t for lysis, when time no less than 1t and the strength of light signal is 1.</div>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/2/2d/T--ZJUT-China--modeli23.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/e/e8/T--ZJUT-China--modeling101811.png" alt="">
 
     </div>
 
     </div>
−
     <div class="note">Figure 3：when Time>=1t the strength of light signal=1, and shutdown when Time=2, it use 11t to cut off.
+
     <div class="note">Our system spend 11t on cutting off all the ARGs and 23t for lysis, when time no less than 1t , the strength of light signal is 1 and the time of stopping lighting is 2t.
 
     </div>
 
     </div>
 
     <div class="modelingimg">
 
     <div class="modelingimg">
−
       <img src="https://static.igem.org/mediawiki/2018/b/b9/T--ZJUT-China--modeli24.png" alt="">
+
       <img src="https://static.igem.org/mediawiki/2018/4/47/T--ZJUT-China--modeling101812.png" alt="">
 
     </div>
 
     </div>
−
     <div class="note">Figure 4：when Time>=1t the strength of light signal=0.01, and shutdown when Time=2, it use 11t to cut off.
+
     <div class="note">Our system spend 11t on cutting off all the ARGs and 28t for lysis, when time no less than 1t , the strength of light signal is 0.01 and the time of stopping lighting is 2t.
 
     </div>
 
     </div>
 
     <p>
 
     <p>
−
       It’s obverse that final system will react faster when under a very strength light signal. However, just a very weak plased light signal is enough to start our system. So our system is very safe even if some bacteria equipped with our system we don’t treat it seriously, it will finally cut off all args it has and lysis automaticly.
+
       From the above results,we can clearly see that our system react faster under a very strength light signal.What’ more,we find that just a quite weak pulsed light signal is enough to start the operation of our system. According to this conclusion,our system is safe because the accidental leakage of bacteria will cut off all the ARGs and autolysis for the natural light.
 
     </p>
 
     </p>
 
     <h1>Discussion</h1>
 
     <h1>Discussion</h1>
 
     <p>
 
     <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 system modeling ver2.0, we find that the effect of giving a short pulsed light signal is almost same as a constant light signal.Therefore, we decide to give a short pulsed light signal for energy conservation.All in all, our modeling and analysis was focused to achieve a better theoretical grounding of forecasting how our system works after giving the light signal.
−
    </p><p>  From the test of our ODE model of the light control arg cutting system ver2.0, 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>
 
     </p>
 
     <div class="note1">
 
     <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.
 
       [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
 
       Published online 2008 Apr 15. doi:  10.1098/rsif.2008.0086.focus
−
       <br>[2]Combinatorial transcriptional control of the lactose operon of Escherichia coli
+
       <br>[2]Combinatorial transcriptional control of the lactose operon of <i>Escherichia coli</i>
 
       Thomas Kuhlman, Zhongge Zhang, Milton H. Saier, Jr., Terence Hwa
 
       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
 
       Proc Natl Acad Sci U S A. 2007 Apr 3; 104(14): 6043–6048. Published online 2007 Mar 21. doi: 10.1073/pnas.0606717104

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Abstract

In order to improve the feasibility of our system utilized by other researchers , we have tried our best to develop a model to predict the time point when the all antibiotic resistance genes(ARGs) are cut off and the cell auto-lysis is going to begin. This model is made up of some rate equations which are based on experimental data of our system. Then we are able to simulate the operation of our system and gain the information we need from the analog results.

System modeling Ver1.0

For the purpose of calculating the time point when the all ARGs are cut off and the cell auto-lysis is going to begin,we have tried to construct a model used by the following equations.
Our ODE model of the light control ARG cutting system ver1.0.
[Cas9]: The relative number of Cas9 protein
[vector]: The relative copy number of the vector
[light signal]: The relative light strength
[ARG]: The relative number of ARGs
[sg]: The relative number of sgRNA

Result

The result that we gain from the system modeling ver1.0 is shown below.

System modeling Ver1.1

Our system modeling ver1.0 is limited by problems that we are unable to verify the validity of the model through the experiments.Because the quantization of cas9 protein and ARGs is difficult.Therefore,we have tried to build up another model which is named as System modeling Ver1.1. This model can be used to predict the time point which is same as the System modeling Ver1.0 by growth curve. We are able to verify our model by experiments because the growth curve is easily gained by experiments.In addition,we can also prove the validity of system model ver1.0 for the reason that the equations of this model is based on the system model ver1.0.

Our ODE model of the light control ARG cutting system ver1.1.(the experimental group with the system and ARG)
[Cas9]: The relative number of Cas9 protein
[vector]: The relative copy number of the vector
[ara]: The concentration of arabinose used to induced expression
[ARG]: The relative number of ARGs
[sg]: The relative number of sgRNA
[cell]: The OD600 of viable cell
Our ODE model of the light control ARG cutting system ver1.1.(the control group with ARG but without the system)
[cell-c]: The OD600 of viable cell

Result

When time=5h we put in different concentrations of Arabinose in the medium.
The points are the data get tested by wet lab and the lines are the data simulated by computer.

Our ODE model after fit data:

Our ODE model of the light control ARG cutting system ver1.1.(the experimental group)
[Cas9]: The relative number of Cas9 protein
[vector]: The relative copy number of the vector
[ara]: The concentration of arabinose used to induced expression
[ARG]: The relative number of ARGs
[sg]: The relative number of sgRNA
[cell]: The OD600 of viable cell
Our ODE model of the light control ARG cutting system ver1.1.(the control group)
[cell]: The OD600 of viable cell

By fitting the experimental data, we find that our system is feasible to predict the completion time of all the ARGs cleavage.Furthermore, we determine some constants based on experimental data which further improves our system and meets the requirements of the construction of the next model.

System modeling Ver2.0

However, if researchers would like to use our system in the complex environment,System modeling Ver1.1 can not meet their requirements. In order to address this issue, we have managed to develop a mathematical model considering the influence of light signal and some other factors.In other words,we regard the factors which include the influence of three repressors, sgRNA and lysin as parameters of system modeling ver2.0 .

Our ODE model of the light control ARG cutting system ver2.0. In this model we considered the express and degrade rate of the Repressors and the effect of the copy number of 2vectors.
[Repressor-1]: The relative number of the first Repressor protein we used in the system
[Repressor-2]: The relative number of the second Repressor protein we used in the system
[Repressor-3]: The relative number of the third Repressor protein we used in the system
[vector-1]: The relative copy number of the vector with the light-controlled promoter, repressor gene-2, cas9 gene, sgRNA gene-1, ARG-2, repressor gene-3 on it
[vector-2]: The relative copy number of the vector with ARG-1, repressor gene-2 on it
[chromosome]: The relative copy number of the chromosome
[Cas9]: The relative number of Cas9 protein
[sg-1]: The relative number of the first sgRNA
[sg-2]: The relative number of the second sgRNA
[ARG-1]: The relative number of the first ARG
[ARG-2]: The relative number of the second ARG
[lysin]: The relative number of the lysin protein
[cell]: The OD600 of viable cell

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

Our system spend 9t on cutting off all the ARGs and 23t for lysis, when time no less than 1t and the strength of light signal is 0.1.
Our system spend 8t on cutting off all the ARGs and 21t for lysis, when time no less than 1t and the strength of light signal is 1.
Our system spend 11t on cutting off all the ARGs and 23t for lysis, when time no less than 1t , the strength of light signal is 1 and the time of stopping lighting is 2t.
Our system spend 11t on cutting off all the ARGs and 28t for lysis, when time no less than 1t , the strength of light signal is 0.01 and the time of stopping lighting is 2t.

From the above results,we can clearly see that our system react faster under a very strength light signal.What’ more,we find that just a quite weak pulsed light signal is enough to start the operation of our system. According to this conclusion,our system is safe because the accidental leakage of bacteria will cut off all the ARGs and autolysis for the natural light.

Discussion

From the test of system modeling ver2.0, we find that the effect of giving a short pulsed light signal is almost same as a constant light signal.Therefore, we decide to give a short pulsed light signal for energy conservation.All in all, our modeling and analysis was focused to achieve a better theoretical grounding of forecasting how our system works after giving 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
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College of Biotechnology and Bioengineering

Zhejiang University of Technology

Chaowang Rd. 18, 310014, Hangzhou, China

E-mail: cbb@zjut.edu.cn Tel: +86-571-88320391

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