Difference between revisions of "Team:KUAS Korea/DryLab/Conclusion"

 
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        <td class="align-middle text-center section-header"><h3>Modeling Results & Conclusion</h3></td>
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      <td class="align-middle text-center section-header"><h3>Modeling Results & Conclusion</h3></td>
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                <h4><strong>Modeling Equations</strong></h4>
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              <h4><strong>Modeling results</strong></h4>
                    <ol>Because we have to know about the relation of microbial growth rates in an aqueous environment with the concentration of a limiting nutrient, we used monod equation for design cheater and cooperators mathematical model. In our case, limiting nutrient will be cellobiose. Also, in our experiment we have to find out the quantificated information of the dependence of the growth rate on substance. Finally, we can compare the growth rates of two E.coli strains.<br><br>
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                    <ol>We coded python for our mathematical mode. We can change the parameter values.<br><br>
 
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<center><img src="https://static.igem.org/mediawiki/2018/b/ba/T--KUAS_Korea--code_epsilon.png" height="200px"  allowfullscreen>
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<center><img src="https://static.igem.org/mediawiki/2018/b/ba/T--KUAS_Korea--code_epsilon.png" height="600px"  allowfullscreen>
 
<br>[Fig 1] Python code</center><br><br>
 
<br>[Fig 1] Python code</center><br><br>
 
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This is basic monod Equation. S is glucose released from cellobiose by cooperators. S can be derived from multiplication of q, ρ, χ. q refers the glucose released from cellobiose by cooperators, ρ is the number of total cell density, and χ is the frequency of the cooperator.<br><br>
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We plotted graph by this python code, and these are results. We changed glucose capture efficiency value for each graph. In graph orange shows cheater's growth rate, and blue graph shows the cooperator's growth rate.<br><br>
 
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<center><img src="https://static.igem.org/mediawiki/2018/0/08/T--KUAS_Korea--epsilon.png" height="240px" align="center" allowfullscreen>
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<center><img src="https://static.igem.org/mediawiki/2018/0/08/T--KUAS_Korea--epsilon.png" height="350px" align="center" allowfullscreen>
 
<br>[Fig 2] curve of epsilon is 0.002<br><br></center>
 
<br>[Fig 2] curve of epsilon is 0.002<br><br></center>
 
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<center><img src="https://static.igem.org/mediawiki/2018/d/db/T--KUAS_Korea--epsilon_two.png" height="240px" align="center" allowfullscreen>
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<center><img src="https://static.igem.org/mediawiki/2018/d/db/T--KUAS_Korea--epsilon_two.png" height="350px" align="center" allowfullscreen>
 
<br>[Fig 3] Curve of epsilon = 0.2 <br><br><br></center>
 
<br>[Fig 3] Curve of epsilon = 0.2 <br><br><br></center>
 
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<center><img src="https://static.igem.org/mediawiki/2018/9/9c/T--KUAS_Korea--epsilon_eight.png" height="240px" align="center" allowfullscreen>
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<center><img src="https://static.igem.org/mediawiki/2018/9/9c/T--KUAS_Korea--epsilon_eight.png" height="350px" align="center" allowfullscreen>
 
<br>[Fig 4] Curve of epsilon = 0.8 <br><br><br></center>
 
<br>[Fig 4] Curve of epsilon = 0.8 <br><br><br></center>
 
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Then we changed the value of epsilon continuously.
 
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Then, we modified monod equation for Cooperator and Cheater. _𝜇_0_ is specific growth rate without glucose and c is the cost of the cooperation. Cost of the cooperation will decrease the growth rate of the cooperator. And 𝛿 is an advantage of cooperation. The cheater will not get the benefit of the cooperation. So we should minus from the cheater’s growth rate. And, we think that disadvantage comes from the glucose capture efficiency. Cheater could not catch efficiently like cooperator. So we give disadvantage to cheater by multiplying (1 – 𝜀) .
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<center><img src="https://static.igem.org/mediawiki/2018/4/45/T--KUAS_Korea--Expression_of_relative_fitness_of_cooperator.png" height="100px" align="center" allowfullscreen>
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<center><img src="https://static.igem.org/mediawiki/2018/b/b1/T--KUAS_Korea--code_rainbow.png" height="600px" align="center" allowfullscreen>
<br>[Fig 4] relative fitness</center>
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<br>[Fig 5] code which plot the rainbow curve</center>
 
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And we divided _𝜇_𝑐_ by _𝜇_𝐷_ to express the relative fitness of cooperator.
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If epsilon is 0, shows the blue cheater graph. And if epsilon is 1, shows the red cheater graph.
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<center><img src="https://static.igem.org/mediawiki/2018/0/0c/T--KUAS_Korea--epsilon_rainbow.png" height="350px" align="center" allowfullscreen>
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<br>[Fig 5] Graph of epsilon changing continuously</center><br><br>
 
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As a result, cheater growth is higher than value c. Also if glucose efficiency increase cheater need more cooperator to reach the maximum growth
 
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<h4><strong>Glucose Capture Efficiency</strong></h4>
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<strong>1.  Calculation of the flux of glucose into a cooperator cell</strong>
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• Measurement of displayed β-glucosidase per cell using whole-cell activity
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-  Vmax = 2.49 x 10^7 glucose·s-1 per cell
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-  The specific growth rate = 0.61 h-1 in 0.004% (w/v) glucose (5.16 x 10^5 cells·μL-1)
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-  Glucose creation rate = 2.40 x 10^7 glucose·s-1 per cell
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-  Glucose consumption = 2.59 x 10^8 glucose per cell
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• The resulting flux of glucose into a single cell
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= the growth rate x the number of glucose molecules per cell = 4.39 x 10^4 glucose ·s-1 per cell
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<center><img src="https://static.igem.org/mediawiki/2018/5/53/T--KUAS_Korea--GlucoseCapture_Efficiency.png" height="100px" align="center" allowfullscreen>
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<h4><strong>Conclusion</strong></h4>
<br>[Fig 5] glucose capture efficiency</center><br><br>
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We can change the value of the parameters. In our case we changed the epsilon value. Cheater is the dominant species in the co-culture environment. But epsilon value increases, cheater need more cooperators. But in the end, cheater and cooperator maintain certain concentration in co-culture. Because only cooperator can make glucose, which is the only essential substance for cheater and cooperator.
 
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And we esitmated the efficency of glucose capture with dividing glucose flux by glucose creation rate. We assumed that the glucose molecules produced by β-glucosidase directly diffuse into media because it is located in the outer membrane of E.coli. And this will cause temporary increase of glucose concentration by a local cloud of glucose at the surface. And this will benefit to influx rate of the glucose into the cell.
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Latest revision as of 01:42, 18 October 2018

Modeling Results & Conclusion

Modeling results

    We coded python for our mathematical mode. We can change the parameter values.

    ​ ​ ​

    [Fig 1] Python code


    ​ ​ We plotted graph by this python code, and these are results. We changed glucose capture efficiency value for each graph. In graph orange shows cheater's growth rate, and blue graph shows the cooperator's growth rate.

    ​ ​

    [Fig 2] curve of epsilon is 0.002

    ​ ​

    [Fig 3] Curve of epsilon = 0.2



    [Fig 4] Curve of epsilon = 0.8


    ​ Then we changed the value of epsilon continuously.



    [Fig 5] code which plot the rainbow curve


    ​ If epsilon is 0, shows the blue cheater graph. And if epsilon is 1, shows the red cheater graph.


    [Fig 5] Graph of epsilon changing continuously


​ As a result, cheater growth is higher than value c. Also if glucose efficiency increase cheater need more cooperator to reach the maximum growth ​ ​


Conclusion

​ We can change the value of the parameters. In our case we changed the epsilon value. Cheater is the dominant species in the co-culture environment. But epsilon value increases, cheater need more cooperators. But in the end, cheater and cooperator maintain certain concentration in co-culture. Because only cooperator can make glucose, which is the only essential substance for cheater and cooperator. ​

​ ​ ​ ​

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