Difference between revisions of "Team:BIT/Model"

 
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                <h1>Model</h1>
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                <p>
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                    The modeling work is ahead of experimental work to provide the necessary guidance for the success of our subsequent experiments and is roughly divided into two parts. Part 1 aims to provide the theoretical basis for the proof of the sensing line and the verification of the inverse line. Based on the Hill equation and preliminary experimental data, we guarantee the input signal was further linear amplified by the ratio of green fluorescent signal. And Part 2 is designed for the proof of scheme 2. We construct the analog reaction line to verify the correctness of the experimental circuit as well as provide detection limits for the reaction. The final result shows that the gene line of scheme 1 feasible and gives the result prediction of scheme 1,2.
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                        <a class="third-menu-item" href="javascript:void(0);" onclick="jump(1)">Assumption</a>
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                        <a class="third-menu-item" href="javascript:void(0);" onclick="jump(2)">Part1-1</a>
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                        <a class="third-menu-item" href="javascript:void(0);" onclick="jump(3)">Part1-2</a>
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                        <a class="third-menu-item" href="javascript:void(0);" onclick="jump(4)">Part2</a>
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                        <h2>Assumption</h2>
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                        <p>
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                            In the modeling process, we made the following assumptions:<br>
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                            1)the promoter sequence unchanged after the inhibition of protein binding to the promoter.<br>
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                            2)the terminator can completely terminate the promoter.<br>
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                            3)when the inhibitory protein is absent, the promoter can stably express green fluorescent protein (GFP)<br>
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                            4)not considering the expression of the leakage of gene lines.
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                    </div>
  
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                    <div class="mid">
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                        <h2>Part 1-1</h2>
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                        <p>
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<div class="clear"></div>
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                            The part 1 aims to give stable theoretical basis for scheme 1 as well as predict some of the experiment data of the first gene line.
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                            <p>
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<h1> Modeling</h1>
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                                First, according to the gene figure of the above figure, the expression of the following genes and the equation of the degradation process can be obtained. Among them, k(1) is the rate of production of mRNA lacI, k(-1) is the degradation rate of mRNA lacI, k(2) is the rate of proteinlacI production, and k(-2) is the degradation rate of proteinlacI:
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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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                            <img src="https://static.igem.org/mediawiki/2018/a/a6/T--BIT--iGEM_BIT2018_MODEL_6.png">
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                        </div><br>
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                        <div class="shadow">
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                            <p>
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                                The Hill's equation was then used to construct a promoter expression formula. 11 is the maximum start-up ability of the promoter (generally set to 1), M1 is the amount of leakage of the promoter, SluxR is the amount of regulatory factor, and kd is the value of SluxR when the trend of the model changes:
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                            </p>
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                            <img src="https://static.igem.org/mediawiki/2018/e/ef/T--BIT--iGEM_BIT2018_MODEL_7.png">
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                        </div><br>
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                        <div class="shadow">
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                            <p>
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                                Finally, according to the differential equation, the expression transcription and degradation process of the whole gene are expressed:
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                            </p>
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                            <img src="https://static.igem.org/mediawiki/2018/5/57/T--BIT--iGEM_BIT2018_MODEL_8.png">
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                        </div><br>
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                        <div class="shadow">
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                            <p>
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                                According to our genetic map, the amount of proteinlacI can be approximated as the amount of proteinGFP (green fluorescence). therefore:
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                            </p>
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                            <img src="https://static.igem.org/mediawiki/2018/thumb/e/eb/T--BIT--iGEM_BIT2018_MODEL_9.png/800px-T--BIT--iGEM_BIT2018_MODEL_9.png">
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                        </div>
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                        <p>
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                            Among them, according to the database of igem official website, we can know the value of some parameters among them: the maximum starting ability of the promoter is β1=0.6; the leakage amount of the promoter is M1=0; n1=2.
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                            So we take these known parameters and put the values of kd equally spaced 50, 100, 150, 200, and draw a rough image:
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                        </p>
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                        <div class="shadow">
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                            <img src="https://static.igem.org/mediawiki/2018/thumb/2/29/T--BIT--iGEM_BIT2018_MODEL_3.png/783px-T--BIT--iGEM_BIT2018_MODEL_3.png">
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                            <span>Figure 2 relationship between gene expression rate and regulation factor under different kd</span>
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                        </div>
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                        <p>
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                            From this differential equation, combined with the gene figure of the whole expression group, we can model the expression rate of green fluorescent protein, and obtain: the higher the concentration of SAM from the upstream, the higher the survival rate of E. coli, the fluorescence of GFP. The conclusion that the intensity will be greater. This is also consistent with the original intention of the expression group members to design this circuit diagram, which proves the feasibility of this genetic line.
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                        </p>
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                    </div>
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                    <div class="mid">
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                        <h2>Part 1-2</h2>
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                        <div class="shadow">
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                            <img src="https://static.igem.org/mediawiki/2018/thumb/c/ca/T--BIT--iGEM_BIT2018_MODEL_4.png/800px-T--BIT--iGEM_BIT2018_MODEL_4.png">
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                            <span>Figure 3 inverse gene line of scheme 1</span>
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                        </div>
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                        <p>
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                            From this differential equation, combined with the gene figure of the whole expression group, we can model the expression rate of green fluorescent protein, and obtain: the higher the concentration of SAM from the upstream, the higher the survival rate of E. coli, the fluorescence of GFP. The conclusion that the intensity will be greater. This is also consistent with the original intention of the expression group members to design this circuit diagram, which proves the feasibility of this genetic line.
 +
                        </p>
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                        <p>
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                            This gene line uses the combination of SAM and riboswitch to inhibit subsequent GFP expression. The content of SAM and GFP is inversely related.<br>
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                            Test data from the test of the SAM riboswitch is as follows:
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                        </p>
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                        <div class="shadow">
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                            <img src="https://static.igem.org/mediawiki/2018/thumb/7/79/T--BIT--iGEM_BIT2018_MODEL_5.png/800px-T--BIT--iGEM_BIT2018_MODEL_5.png">
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                            <span>Figure 4 fluorescence under different concentration of SAM</span>
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                        </div>
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                        <p>
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                            We can get the inhibition of the riboswitch by SAM. Moreover, since the expression of GFP is controlled by the riboswitch, the expression of the final amount of fluorescence is affected. Here we use the function fitting form of a/(x+b)+c model to substitute the data measured in the previous stage, and then obtain the prediction relationship between SAM and fluorescence (as shown below).
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                        </p>
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                        <div class="shadow">
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                            <img src="https://static.igem.org/mediawiki/2018/1/16/T--BIT--iGEM_BIT2018_MODEL_1.png">
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                            <span>Figure 5 the relationship between fluorescence and SAM concentration</span>
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                        </div>
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                        <p>
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                            By observing the graph, we can conclude that the content of SAM is inversely proportional to the amount of fluorescence expressed, and during the reaction, the inhibition of SAM is gradually strengthened and finally stabilized. This verifies the feasibility of the experimental line 2 in principle. And through this data, we can calculate the final expression of green fluorescent protein content according to the content of SAM, and achieve the effect of predicting experimental results.
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                        </p>
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                        <p><b>Conclusion</b><br>
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                            According to the modeling work of Part 1, we could guarantee that the feasibility verification of gene line. Based on the modeling of two parts, we can also get this conclusion: The input signal was further linear amplified by the ratio of green fluorescent signal. So we succeeded in part 1, providing theoretical basis for the expression group as well as providing theoretical support for the purpose of our team's final testing. Further, we provide the necessary guidance for the success of their subsequent experiments.
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                        </p>
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                    </div>
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                    <div class="mid">
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                        <h2>Part 2</h2>
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                        <p>
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                            The second part of the modeling mainly uses the construction simulation gene lines of scheme 2. The concentration of the reaction chain is changed under the condition of constant protein concentration, and the concentration of the product and the reactants are finally determined by the intermediate product and the reaction coefficient. This chart is ultimately used as a function of the overall response to time and applied.
 +
                        </p>
 +
                        <p>
 +
                            Based on the Michaelis-Menten equation, we constructed the competitive experimental route of the second scheme. The amount of the protein was fixed and the amount of the reaction chain was changed to determine the relationship between the target product and the target product. The relationship between the target product and the reaction chain under different reaction conditions was determined by limiting the reaction constants of the two steps of the reaction.
 +
                        </p>
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                        <div class="shadow">
 +
                            <img src="https://static.igem.org/mediawiki/2018/0/07/T--BIT--iGEM_BIT2018_Modeling_Fig_1.png">
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                            <span>Figure 6 the relationship between reaction chain and the target product</span>
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                        </div>
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                        <p>
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                            Given more time, we could make this piece of result play a bigger role among the whole project. Since we have got the relationship between the product and reactant, the next step is to give predictions of the following experiments including the amount of GFP, etc.
 +
                        </p>
 +
                        <p><b>Conclusion</b><br>
 +
                            According to the modeling work of Part 2, we could get the conclusion that the gene line of scheme 2 is feasible, while also we can get a relationship between product and reactant. Furthermore, we give mathematical proof of gene line of scheme 2, provide a stable theoretical basis for the lab group. If given more time in the future, we can also get a precise relationship between the product we add and theoretical values for subsequent experiments.
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                        </p>
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                    </div>
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                </div>
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            <a href="javascript:void(0);" onclick="toTop()"><img src="https://static.igem.org/mediawiki/2018/0/0f/T--BIT--top.png"></a>
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<h3> Gold Medal Criterion #3</h3>
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<script src="https://2018.igem.org/Template:BIT/js/third?action=raw&ctype=text/javascript"></script>
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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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<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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Latest revision as of 22:56, 17 October 2018

<!DOCTYPE html> Model

Model

The modeling work is ahead of experimental work to provide the necessary guidance for the success of our subsequent experiments and is roughly divided into two parts. Part 1 aims to provide the theoretical basis for the proof of the sensing line and the verification of the inverse line. Based on the Hill equation and preliminary experimental data, we guarantee the input signal was further linear amplified by the ratio of green fluorescent signal. And Part 2 is designed for the proof of scheme 2. We construct the analog reaction line to verify the correctness of the experimental circuit as well as provide detection limits for the reaction. The final result shows that the gene line of scheme 1 feasible and gives the result prediction of scheme 1,2.

Assumption

In the modeling process, we made the following assumptions:
1)the promoter sequence unchanged after the inhibition of protein binding to the promoter.
2)the terminator can completely terminate the promoter.
3)when the inhibitory protein is absent, the promoter can stably express green fluorescent protein (GFP)
4)not considering the expression of the leakage of gene lines.

Part 1-1

The part 1 aims to give stable theoretical basis for scheme 1 as well as predict some of the experiment data of the first gene line.

First, according to the gene figure of the above figure, the expression of the following genes and the equation of the degradation process can be obtained. Among them, k(1) is the rate of production of mRNA lacI, k(-1) is the degradation rate of mRNA lacI, k(2) is the rate of proteinlacI production, and k(-2) is the degradation rate of proteinlacI:


The Hill's equation was then used to construct a promoter expression formula. 11 is the maximum start-up ability of the promoter (generally set to 1), M1 is the amount of leakage of the promoter, SluxR is the amount of regulatory factor, and kd is the value of SluxR when the trend of the model changes:


Finally, according to the differential equation, the expression transcription and degradation process of the whole gene are expressed:


According to our genetic map, the amount of proteinlacI can be approximated as the amount of proteinGFP (green fluorescence). therefore:

Among them, according to the database of igem official website, we can know the value of some parameters among them: the maximum starting ability of the promoter is β1=0.6; the leakage amount of the promoter is M1=0; n1=2. So we take these known parameters and put the values of kd equally spaced 50, 100, 150, 200, and draw a rough image:

Figure 2 relationship between gene expression rate and regulation factor under different kd

From this differential equation, combined with the gene figure of the whole expression group, we can model the expression rate of green fluorescent protein, and obtain: the higher the concentration of SAM from the upstream, the higher the survival rate of E. coli, the fluorescence of GFP. The conclusion that the intensity will be greater. This is also consistent with the original intention of the expression group members to design this circuit diagram, which proves the feasibility of this genetic line.

Part 1-2

Figure 3 inverse gene line of scheme 1

From this differential equation, combined with the gene figure of the whole expression group, we can model the expression rate of green fluorescent protein, and obtain: the higher the concentration of SAM from the upstream, the higher the survival rate of E. coli, the fluorescence of GFP. The conclusion that the intensity will be greater. This is also consistent with the original intention of the expression group members to design this circuit diagram, which proves the feasibility of this genetic line.

This gene line uses the combination of SAM and riboswitch to inhibit subsequent GFP expression. The content of SAM and GFP is inversely related.
Test data from the test of the SAM riboswitch is as follows:

Figure 4 fluorescence under different concentration of SAM

We can get the inhibition of the riboswitch by SAM. Moreover, since the expression of GFP is controlled by the riboswitch, the expression of the final amount of fluorescence is affected. Here we use the function fitting form of a/(x+b)+c model to substitute the data measured in the previous stage, and then obtain the prediction relationship between SAM and fluorescence (as shown below).

Figure 5 the relationship between fluorescence and SAM concentration

By observing the graph, we can conclude that the content of SAM is inversely proportional to the amount of fluorescence expressed, and during the reaction, the inhibition of SAM is gradually strengthened and finally stabilized. This verifies the feasibility of the experimental line 2 in principle. And through this data, we can calculate the final expression of green fluorescent protein content according to the content of SAM, and achieve the effect of predicting experimental results.

Conclusion
According to the modeling work of Part 1, we could guarantee that the feasibility verification of gene line. Based on the modeling of two parts, we can also get this conclusion: The input signal was further linear amplified by the ratio of green fluorescent signal. So we succeeded in part 1, providing theoretical basis for the expression group as well as providing theoretical support for the purpose of our team's final testing. Further, we provide the necessary guidance for the success of their subsequent experiments.

Part 2

The second part of the modeling mainly uses the construction simulation gene lines of scheme 2. The concentration of the reaction chain is changed under the condition of constant protein concentration, and the concentration of the product and the reactants are finally determined by the intermediate product and the reaction coefficient. This chart is ultimately used as a function of the overall response to time and applied.

Based on the Michaelis-Menten equation, we constructed the competitive experimental route of the second scheme. The amount of the protein was fixed and the amount of the reaction chain was changed to determine the relationship between the target product and the target product. The relationship between the target product and the reaction chain under different reaction conditions was determined by limiting the reaction constants of the two steps of the reaction.

Figure 6 the relationship between reaction chain and the target product

Given more time, we could make this piece of result play a bigger role among the whole project. Since we have got the relationship between the product and reactant, the next step is to give predictions of the following experiments including the amount of GFP, etc.

Conclusion
According to the modeling work of Part 2, we could get the conclusion that the gene line of scheme 2 is feasible, while also we can get a relationship between product and reactant. Furthermore, we give mathematical proof of gene line of scheme 2, provide a stable theoretical basis for the lab group. If given more time in the future, we can also get a precise relationship between the product we add and theoretical values for subsequent experiments.