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

 
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<h1> Modeling</h1>
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<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>
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<h3> Gold Medal Criterion #3</h3>
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Convince the judges that your project's design and/or implementation is based on insight you have gained from modeling. This could be either a new model you develop or the implementation of a model from a previous team. You must thoroughly document your model's contribution to your project on your team's wiki, including assumptions, relevant data, model results, and a clear explanation of your model that anyone can understand.  
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The model should impact your project design in a meaningful way. Modeling may include, but is not limited to, deterministic, exploratory, molecular dynamic, and stochastic models. Teams may also explore the physical modeling of a single component within a system or utilize mathematical modeling for predicting function of a more complex device.
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Please see the <a href="https://2018.igem.org/Judging/Medals"> 2018
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Medals Page</a> for more information.  
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<h3>Best Model Special Prize</h3>
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To compete for the <a href="https://2018.igem.org/Judging/Awards">Best Model prize</a>, please describe your work on this page  and also fill out the description on the <a href="https://2018.igem.org/Judging/Judging_Form">judging form</a>. Please note you can compete for both the gold medal criterion #3 and the best model prize with this page.
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You must also delete the message box on the top of this page to be eligible for the Best Model Prize.
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<h3> Inspiration </h3>
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Here are a few examples from previous teams:
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<li><a href="https://2016.igem.org/Team:Manchester/Model">2016 Manchester</a></li>
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<li><a href="https://2016.igem.org/Team:TU_Delft/Model">2016 TU Delft</li>
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<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">2014 ETH Zurich</a></li>
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<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">2014 Waterloo</a></li>
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        <h1>Modeling</h1>
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        <h2>Introduction</h2>
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        <p>Since the effectuality of our genetic-modified parts are highly depended on the copper concentration of the outside environment, so it is significant to test the optimal copper concentration for the use of our product. With the consideration that using waste water collected from a factory will bring unnecessary factors other than the copper concentration and disable us to conclude the relation to the parts. We rather undergo complex mathematical process to calculate the predicted optimal concentration with the experimental data.</p>
 +
        <p>We have carried out several testing experiments to investigate the maximum capacity of both our medium, the e.coli, and e.coli with PcopA encoded in a comparably severe environment. We measured the fluorescence every two hours of E.coli in different concentration of copper solution (Cupric Chloride) , then the data sheets of E.coli growth against time against Copper(II) ion concentration have been achieved.</p>
 +
        <p>The following analysis is highly based on the sheets that we have attached, aiming to analyze the correlations between these two independent variables and how much these variables could cause the e.coli to be more active and effective at working.</p>
 +
       
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        <h2>Variable justification</h2>
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        <img src="https://static.igem.org/mediawiki/2018/9/91/T--ASTWS-China--var_justification.png">
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        <h2>Model development </h2>
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        <h3>1. The correlation of E.coli fluorescence against time against copper concentration </h3>
 +
        <p>The data sheet we could obtain is shown below, which the side column represents the concentration of Cupric ion in a certain solution and the side row represents the time for e.coli bacteria placing in the solution. We have recorded 5 groups with one of them being the control group. And the result in this sheet will be analyzed in the following section. </p>
 +
        <img src="https://static.igem.org/mediawiki/2018/a/a1/T--ASTWS-China--Model1.png">
 +
        <p>Based on a common knowledge, both time and concentration will affect the bacterium’s growth, we had the first empirical equation, the two-variable linear function is then applied to test the simulation of these real-world data.</p>
 +
        <p style="text-align: center">E = a &#215; C + b &#215; H + d (a, b, d are constants)</p>
 +
        <p>By the regression in the Matlab, we have obtained the function of E = 17.4 &#215; C + 68.23 &#215; H + 1181 where R<sup>2</sup> = 0.782<br /></p>
 +
        <img src="https://static.igem.org/mediawiki/2018/7/7a/T--ASTWS-China--Model2.png">
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        <p>To increase the accuracy of this simulation, the trial with the assertion that the relations between these three factors may not be linear has been tested and applied.</p>
 +
        <p>In this equation, the R<sup>2</sup> has increased to 0.888 compared to the previous 0.782.</p>
 +
        <p  style="text-align: center">E = 13.02 &#215; C<sup>2</sup> + 1.504 &#215; H<sup>2</sup> + 37.23 &#215; C &#215; H - 237.2 &#215; C + 23.51 &#215; H +1500</p>
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        <img src="https://static.igem.org/mediawiki/2018/4/45/T--ASTWS-China--Model3.png">
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        <div class="clear extra_space"></div>
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        <div class="clear extra_space"></div>
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        <p>By seting the upper bound of time lasting (which is 10 hours), the best activation of the bacteria occurs when there is no copper ion in the solution. This is reasonable that the bacteria works best at the cultivating solution and this result also proves that there is no obvious abnormality in this model.</p>
 +
        <p>Compared to the average activation of e.coli which is 1630 fluorescence, generally, most experimental groups could stand their corresponding Cu concentration. And some bacteria would develop their suffering capacity as time lasts longer to against the harm of permeating in a dense copper solution. Therefore, we could conclude that e.coli itself could stand the copper concentration of 2.4 mg/L (which is the comparably high copper concentration (only solution counts) in agriculture factory or daily waste dump) and have certain degree of self-adjusting and self-repairing capacity.</p>
 +
       
 +
        <h3>2. The correlation of PcopA1 and PcopA2</h3>
 +
        <p>We have investigated two general groups of E.coli with PcopA1 and PcopA2 respectively. To test the accuracy of the data and avoid any abnormal data recorded to impact on the final result, we measured the correlation of these two groups.</p>
 +
        <img src="https://static.igem.org/mediawiki/2018/e/e5/T--ASTWS-China--Model4.png">
 +
        <p>Since they are encoded with the same gene with same effect towards the copper concentration, ideally, the result obtained should be linear. With linear regression in Matlab, the equation 3 could be acquired with a high R^2 which is 0.9916. It proves that data of these two experimental groups could be used in combination but qualified by the linear relationship. This solves the problem of having a few data for regression which may affect the overall accuracy. </p>
 +
        <p style="text-align: center">PcopA2 = 1.07 &#215; PcopA1 - 187.8</p>
 +
        <img src="https://static.igem.org/mediawiki/2018/0/08/T--ASTWS-China--Model5.png">
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        <h3>3. The correlation of PcopA against time against copper concentration</h3>
 +
        <img src="https://static.igem.org/mediawiki/2018/4/42/T--ASTWS-China--Model6.png">
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        <div class="clear extra_space"></div>
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        <p>By regression of binary linear function, we got the equation</p>
 +
        <p style="text-align: center">PcopA = 933.2 &#215; C + 814.7 &#215; H - 1951</p>
 +
        <img src="https://static.igem.org/mediawiki/2018/0/00/T--ASTWS-China--Model7.png">
 +
        <div class="clear extra_space"></div>
 +
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        <p>With non-linear regression, we got the regression function 5, and the graph has shown below. R<sup>2</sup>=0.9626 which shows a high improvement compared to the previous one.</p>
 +
        <p style="text-align: center">PcopA1 = -233.8 &#215; C<sup>2</sup> + 99.05 &#215; H<sup>2</sup> + 274.4 &#215; C &#215; H - 152.1 &#215; C - 703.1 &#215; H +2629</p>
 +
        <img src="https://static.igem.org/mediawiki/2018/4/45/T--ASTWS-China--Model3.png">
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        <div class="clear extra_space"></div>
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        <div class="clear extra_space"></div>
 +
       
 +
        <h3>4. The correlation of E.coli GFP fluorescence against time against copper concentration</h3>
 +
        <p>The further prediction and regression should be carried out when it comes to the GFP which is a type of protein that could be activated by certain effectual parts in the e.coli plasmid.</p>
 +
        <img src="https://static.igem.org/mediawiki/2018/3/3c/T--ASTWS-China--Model9.png">
 +
        <div class="clear extra_space"></div>
 +
        <div class="clear extra_space"></div>
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        <p>With binary non-linear regression, we obtained</p>
 +
        <p style="text-align: center">E = 0.000005209 &#215; C<sup>2</sup> - 0.001433 &#215; H<sup>2</sup> - 0.0001952 &#215; C &#215; H -0.004257 &#215; C + 0.1132 &#215; H + 0.6607</p>
 +
        <img src="https://static.igem.org/mediawiki/2018/9/93/T--ASTWS-China--Model10.png">
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        <div class="clear extra_space"></div>
 +
        <div class="clear extra_space"></div>
 +
        <p>Overall, the R<sup>2</sup>=0.71 which has improvement but still not high enough to conclude the correlation between these three factors when it applied its effect on GFP.</p>
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Latest revision as of 03:00, 18 October 2018

Modeling

Introduction

Since the effectuality of our genetic-modified parts are highly depended on the copper concentration of the outside environment, so it is significant to test the optimal copper concentration for the use of our product. With the consideration that using waste water collected from a factory will bring unnecessary factors other than the copper concentration and disable us to conclude the relation to the parts. We rather undergo complex mathematical process to calculate the predicted optimal concentration with the experimental data.

We have carried out several testing experiments to investigate the maximum capacity of both our medium, the e.coli, and e.coli with PcopA encoded in a comparably severe environment. We measured the fluorescence every two hours of E.coli in different concentration of copper solution (Cupric Chloride) , then the data sheets of E.coli growth against time against Copper(II) ion concentration have been achieved.

The following analysis is highly based on the sheets that we have attached, aiming to analyze the correlations between these two independent variables and how much these variables could cause the e.coli to be more active and effective at working.

Variable justification

Model development

1. The correlation of E.coli fluorescence against time against copper concentration

The data sheet we could obtain is shown below, which the side column represents the concentration of Cupric ion in a certain solution and the side row represents the time for e.coli bacteria placing in the solution. We have recorded 5 groups with one of them being the control group. And the result in this sheet will be analyzed in the following section.

Based on a common knowledge, both time and concentration will affect the bacterium’s growth, we had the first empirical equation, the two-variable linear function is then applied to test the simulation of these real-world data.

E = a × C + b × H + d (a, b, d are constants)

By the regression in the Matlab, we have obtained the function of E = 17.4 × C + 68.23 × H + 1181 where R2 = 0.782

To increase the accuracy of this simulation, the trial with the assertion that the relations between these three factors may not be linear has been tested and applied.

In this equation, the R2 has increased to 0.888 compared to the previous 0.782.

E = 13.02 × C2 + 1.504 × H2 + 37.23 × C × H - 237.2 × C + 23.51 × H +1500

By seting the upper bound of time lasting (which is 10 hours), the best activation of the bacteria occurs when there is no copper ion in the solution. This is reasonable that the bacteria works best at the cultivating solution and this result also proves that there is no obvious abnormality in this model.

Compared to the average activation of e.coli which is 1630 fluorescence, generally, most experimental groups could stand their corresponding Cu concentration. And some bacteria would develop their suffering capacity as time lasts longer to against the harm of permeating in a dense copper solution. Therefore, we could conclude that e.coli itself could stand the copper concentration of 2.4 mg/L (which is the comparably high copper concentration (only solution counts) in agriculture factory or daily waste dump) and have certain degree of self-adjusting and self-repairing capacity.

2. The correlation of PcopA1 and PcopA2

We have investigated two general groups of E.coli with PcopA1 and PcopA2 respectively. To test the accuracy of the data and avoid any abnormal data recorded to impact on the final result, we measured the correlation of these two groups.

Since they are encoded with the same gene with same effect towards the copper concentration, ideally, the result obtained should be linear. With linear regression in Matlab, the equation 3 could be acquired with a high R^2 which is 0.9916. It proves that data of these two experimental groups could be used in combination but qualified by the linear relationship. This solves the problem of having a few data for regression which may affect the overall accuracy.

PcopA2 = 1.07 × PcopA1 - 187.8

3. The correlation of PcopA against time against copper concentration

By regression of binary linear function, we got the equation

PcopA = 933.2 × C + 814.7 × H - 1951

With non-linear regression, we got the regression function 5, and the graph has shown below. R2=0.9626 which shows a high improvement compared to the previous one.

PcopA1 = -233.8 × C2 + 99.05 × H2 + 274.4 × C × H - 152.1 × C - 703.1 × H +2629

4. The correlation of E.coli GFP fluorescence against time against copper concentration

The further prediction and regression should be carried out when it comes to the GFP which is a type of protein that could be activated by certain effectual parts in the e.coli plasmid.

With binary non-linear regression, we obtained

E = 0.000005209 × C2 - 0.001433 × H2 - 0.0001952 × C × H -0.004257 × C + 0.1132 × H + 0.6607

Overall, the R2=0.71 which has improvement but still not high enough to conclude the correlation between these three factors when it applied its effect on GFP.

Copyright © 2018 Team:ASTWS-China All Rights Reserved.