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| − | <br>
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| − | <br>
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| − | <img src = "https://static.igem.org/mediawiki/2019/0/03/T--TUDelft--Modeling_logo.png" alt="Modeling" style="width:60%";>
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| − | <div class= " centerjustify">
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| − | <h2>Overview</h2>
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| − | <p> The aim of our modeling was to apply a control systems approach to achieve stability across bacterial species. We modeled the kinetics of a genetic implementation of an incoherent feedforward loop. An analytical steady-state solution of this system showed complete independence of plasmid copy number and transcriptional and translational variations. We verified this analytical solution by the implementation of a full Ordinary Differential Equation (ODE) model..
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| − | Variables most often considered in the design of genetic circuits are plasmid copy number and transcriptional and translational rates. These variables play a major role in the steady-state levels of gene expression. However, when transfering genetic circuits between organisms these variables change in unpredictable ways:
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| − | <img src = "https://static.igem.org/mediawiki/2019/1/11/T--TUDelft--Promoter.png" alt="promoter SOBL" style="width:90%;">
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| − | </div>
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| − | <p>Promoters have different strengths in different organisms. Some promoters only work in a very narrow range of bacterial species (Yang, Liu et al. 2018). We, therefore, applied the concept of orthogonality, we approached the issue with the using T7 RNA polymerase. Although orthogonal transcription might behave differently when applied in varying biological contexts, we show through modeling that this won't influence gene expression levels, when our novel genetic circuit is implemented. </p>
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| − | <img src = "https://static.igem.org/mediawiki/2019/a/a6/T--TUDelft--RBS.png" alt="RBS SOBL" style="width:90%;">
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| − | </div>
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| − | <p> Ribosome binding sites contain the Shine-Dalgarno sequence where the 16s rRNA of the Ribosome binds. However, this sequence varies across species and often ribosome binding sites are extremely inefficient when applied in phylogenetically distant species (Damilola Omotajo 2015). Our model shows that similar expression levels across organisms can be maintained when all genes in our genetic circuit contain the same ribosome binding site, when our novel genetic circuit is implemented. However, this is assuming translation elongation is similar in these species. Codon usage has been shown to influence translation elongation. We, therefore, developed a software tool that provides the user with a coding sequence similar in codon usage across different species. Similar codon usage will ensure that any codon bias which would cause translation elongation differences, are minimized. </p>
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| − | <img src = "https://static.igem.org/mediawiki/2019/1/19/T--TUDelft--ORI.png" alt="Ori SOBL" style="width:90%;">
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| − | <p>Genetic engineering makes extensive use of plasmids. However, not all plasmids work in every organism as they require a different origin of replication. Although origins of replication have been heavily studied, we still lack the ability to easily transfer plasmids between prokaryotes and often they behave unpredictably (Jain and Srivastava 2013). Our system Sci-Phi29 makes use of the Phi29 replication system which is fully orthogonal. However, this might still result in varying copy number when transferring between organisms. Through modeling we show that the steady-state level of the gene of interest is independent of copy number when our genetic implementation of an incoherent feedforward loop is used. </p>
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| − | <h2>The core of our model - Incoherent feed forward loop </h2>
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| − | <p>
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| − | Our genetic circuit is a genetic implementation of an incoherent feedforward loop (iFFL). In an iFFL an input signal regulates both the activator and the repressor of the output of the system in the same way. An iFFL results in perfect adaptation to the input when the negative regulation is fully uncooperative (Segall-Shapiro, Sontag et al. 2018).
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| − | The input in our case is the copy number of the DNA template and the output is the steady-state expression of a gene of interest. The repression in our system is established through the expression of a Transcription activator-like effector (TALE) protein. TALE proteins recognize DNA by a simple DNA-binding mechanism and have been shown to bind fully uncooperative (Segall-Shapiro, Sontag et al. 2018). The promoter driving the gene of interest has been engineered to contain a binding site of a TALE protein. When the TALE protein is bound to the promoter the expression of the gene of interest is repressed.
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| − | <br>
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| − | </p>
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| − | <figure>
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| − | <img src="https://static.igem.org/mediawiki/2019/5/5a/T--TUDelft--iFFL.png" style="width:20%" class="center"
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| − | alt="iFFL" >
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| − | <figcaption class="center"><br>Figure 1: Scheme of incoherent Feed Forward Loop.</figcaption>
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| − | </figure>
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| − | <br>
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| − | We have extensively modeled the functioning of the genetic implementation of this system. An analytical steady-state solution of the system showed that the steady-state expression level of a gene of interest is completely independent of plasmid copy number and can be independent transcriptional and translational rates when the right design choices are made. After further verification through the implementation of a full ODE model we designed experiments to test the independence on these variables. Key design choices were identified by modeling. These consist of:
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| − | <ul>
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| − | <il>
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| − | The need for good insulation of the genes
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| − | </li>
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| − | <il>
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| − | The promoter strength of the TALE protein and of the gene of interest need to maintain the same ratio.
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| − | </li>
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| − | <il>
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| − | The ribosome binding site strength of the TALE protein and of the gene of interest need to maintain the same ratio.
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| − | </li>
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| − | </ul>
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| − | <br>
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| − | <p>More detail on how we modeled the output of our system and determined it is independent of copy number, transcriptional and translational variations, and how we came to these design choices can be found in the sections below. </p>
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| − | <br>
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| − | <ul class="accordion">
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| − | <li>
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| − | <a class="toggle " href="javascript:void(0);" ><b>The kinetics</b></a>
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| − | <div class="inner">
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| − | <p>
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| − | <h2>The kinetics</h2>
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| − | <p>In this section we explain the kinetics of our system and derive a system of ordinary differential equations to describe the interactions within the genetic circuit. From this, we will stepwise derive a steady-state solution and describe the properties of the system. In the other sections, we will use these properties to describe how we can utilize them to transfer genetic circuits between prokaryotes.
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| − | The following scheme depicts all interactions considered in our system. </p>
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| − | <figure>
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| − | <img src="https://static.igem.org/mediawiki/2019/8/85/T--TUDelft--TALE_system.png" style="width:70%" class="center"
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| − | alt="TALE system">
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| − | <figcaption class="center"><br>Figure 2: Scheme of genetic circuit interactions developed by <cite><a href="https://www.nature.com/articles/nbt.4111"><i>(Sontag et al. (2018))</i></a></cite></figcaption>
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| − | </figure>
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| − | <br>
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| − | <p>From these interactions we can derive the following system of ordinary differential equations: <br> </p>
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| − | <ul>
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| − | <il>${dm_T \over dt} = {c \cdot a_T - y_m \cdot m_T}$ </il> <br> <br>
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| − | <il> $\frac{dT}{dt} = b_T \cdot m_T - y_T \cdot T - n \cdot k_{on}\cdot T^n \cdot P_G + n \cdot k_{off} \cdot P_{G.T}$</il> <br><br>
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| − | <il>$\frac{dP_G}{dt} = k_{off} \cdot P_{G.T} - n \cdot k_{on} \cdot T^n \cdot P_G + n \cdot y_T \cdot P_{G.T}$</il><br><br>
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| − | <il>$\frac{dP_{G.T}}{dt} = n \cdot k_{on} \cdot T^n \cdot P_G - k_{off} \cdot P_{G.T} - n \cdot y_T \cdot P_{G.T} $ </il><br><br>
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| − | <il>$\frac{dm_G}{dt} = a_{Gmax} \cdot P_G + a_{Gmin} \cdot P_{G.T} - y_m \cdot m_G $</il> <br><br>
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| − | <il>$\frac{dm_G}{dt} = b_G \cdot m_G - y_G \cdot G $</il><br><br>
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| − | </ul>
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| − | <table id="tabletu">
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| − | <tr>
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| − | <th>Parameter</th>
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| − | <th> Value </th>
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| − | <th>Unit</th>
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| − | <th>Explanation</th>
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| − | <th> Source </th>
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| − | </tr>
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| − | <tr>
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| − | <td>$a_T$</td>
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| − | <td>1.03 </td>
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| − | <td> (nM/min) </td>
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| − | <td>Transcription rate TALE</td>
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| − | <td><cite><a href="2018.igem.org/Team:Thessaloniki"><i>2018 iGEM Thessaloniki</i></a></cite> </td>
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| − | </tr>
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| − | <tr>
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| − | <td>$y_m$</td>
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| − | <td>log(2)/5 </td>
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| − | <td>(1/min) </td>
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| − | <td>degradation rate mRNA</td>
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| − | <td><cite><a href="https://www.nature.com/articles/ncomms8832"><i>Kushwaha and Salis 2015</i></a></cite> </td>
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| − | <td>$b_T$</td>
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| − | <td> 0.44 </td>
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| − | <td> (1/min) </td>
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| − | <td>Translation rate TALE</td>
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| − | <td><cite><a href="2018.igem.org/Team:Thessaloniki"><i>2018 iGEM Thessaloniki</i></a></cite>. </td>
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| − | </tr>
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| − | <tr>
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| − | <td>$y_T$</td>
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| − | <td> 0.0347 </td>
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| − | <td> (1/min) </td>
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| − | <td>Degradation rate TALE</td>
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| − | <td> </td>
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| − | </tr>
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| − | <tr>
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| − | <td>n</td>
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| − | <td>1</td>
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| − | <td>-</td>
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| − | <td>Cooperativity of binding</td>
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| − | <td><cite><a href="https://www.ncbi.nlm.nih.gov/pubmed/29553576"><i>Segall-Shapiro, Sontag et al.</i></a></cite> </td>
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| − | </tr>
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| − | <tr>
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| − | <td>$k_{on}$</td>
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| − | <td>9.85 </td>
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| − | <td>(1/(nM*min)) </td>
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| − | <td>Binding of TALE to promoter</td>
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| − | <td><cite><a href="2018.igem.org/Team:Thessaloniki"><i>2018 iGEM Thessaloniki</i></a></cite>. </td>
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| − | </tr>
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| − | <tr>
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| − | <td>$k_{off}$</td>
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| − | <td>2.19</td>
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| − | <td>(1/(min))</td>
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| − | <td>Unbinding of TALE to promoter</td>
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| − | <td><cite><a href="2018.igem.org/Team:Thessaloniki"><i>2018 iGEM Thessaloniki</i></a></cite>. </td>
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| − | </tr>
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| − | <tr>
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| − | <td>$a_{Gmax}$</td>
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| − | <td> 3.78 </td>
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| − | <td>(1/(nM*Min)) </td>
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| − | <td>Maximum transcription of GFP</td>
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| − | <td><cite><a href="2018.igem.org/Team:Thessaloniki"><i>2018 iGEM Thessaloniki</i></a></cite> </td>
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| − | </tr>
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| − | <tr>
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| − | <tr>
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| − | <td>$a_{Gmin}$</td>
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| − | <td> 0 </td>
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| − | <td> (1/(nM*Min)) </td>
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| − | <td>Maximum transcription of GFP</td>
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| − | <td><cite><a href="https://www.ncbi.nlm.nih.gov/pubmed/29553576"><i>Segall-Shapiro, Sontag et al.</i></a></cite></td>
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| − | </tr>
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| − | <tr>
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| − | <td>$b_G$</td>
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| − | <td>3.65 </td>
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| − | <td> (1/Min)</td>
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| − | <td>Translation rate GFP</td>
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| − | <td><cite><a href="2018.igem.org/Team:Thessaloniki"><i>2018 iGEM Thessaloniki</i></a></cite></td>
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| − | </tr>
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| − | <tr>
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| − | <td>$y_G$</td>
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| − | <td> 0.0347 </td>
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| − | <td> 1/min </td>
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| − | <td>Degradation rate GFP</td>
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| − | <td> </td>
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| − | </tr>
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| − | </table>
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| − | <h4>Simplification of the system</h4>
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| − | <p>
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| − | This system can be simplified by making a few assumptions:</p>
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| − | <ol>
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| − | <li>Amount of TALE protein is much larger than binding sites for TALE</li>
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| − | <li>TALE binding and unbinding occurs much more rapidly than protein production and degradation</li>
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| − | <li>There is negligable expression when the promoter is repressed</li>
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| − | </ol>
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| − | <br>
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| − | This results in the following steady-state solution: <br> <br>
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| − | $$G = (\frac{c}{c^n}) (\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m})$$ <br>
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| − | <br>
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| − | <ul>
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| − | <a class="toggle " href="javascript:void(0);" ><b>Full derivation</b></a>
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| − | </ul>
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| − | <h3>Conclusion</h3>
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| − | <p>Our system yields a very simple dependency on only the transcription, translation and degradation rates for each gene involved in the genetic network. This allows us to design circuits where the output of our system is independent of these variables. We can use this to analyze how the system behaves when transferring between organisms.</p>
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| − | <a class="toggle " href="javascript:void(0);" ><b>Copy number independence</b></a>
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| − | <div class="inner">
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| − | <p>
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| − | <h2>Copy number</h2>
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| − | <p>A big factor in every genetic circuit is the copy number of the DNA template. Broad host range plasmids are often used when using different hosts however, they do not guarantee the same copy number in every organism <cite><a href="https://academic.oup.com/femsle/article/348/2/87/731695"><i>(Jain and Srivastava 2013)</i></a></cite>. In some organisms, it is not common practice to use a plasmid but rather insert into the genome. The need for consistent expression at a wide range of copy number is thus a desirable feature of any synthetic circuit. <br> Our model steady-state solution tells us that when our repressor binding is fully uncooperative we have complete independence of copy number:</p> <br>
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| − | $$G = (\frac{c}{c^n}) (\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m})$$
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| − | <p>We, therefore, have simulated this system from a range of 1 to 600 (genome integration to high-copy number plasmid). </p>
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| − | <img src="https://static.igem.org/mediawiki/2019/2/29/T--TUDelft--copynumber.png" style="width:70%" class="center"
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| − | alt="TALE system">
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| − | <figcaption class="center"> Steady-state GFP production for copy number 1 till 600 (genome integration till high copy number plasmid). </figcaption>
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| − | </div>
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| − | </li>
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| − | <a class="toggle " href="javascript:void(0);" ><b>Transcriptional variation</b></a>
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| − | <li>
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| − | <a class="toggle " href="javascript:void(0);" ><b>Translational variation</b></a>
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| − | <div class="inner">
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| − | </p>
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| − | <h3>References</h3>
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| − | <ol>
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| − | <a id="Frumkin" href="https://doi.org/10.1073/pnas.1719375115" target="_blank">
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| − | Frumkin, I., <i>et al.</i> (2018). "Codon usage of highly expressed genes affects proteome-wide translation efficiency." Proceedings of the National Academy of Sciences 115(21): E4940..
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| − | </a>
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