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| − | <br>
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| − | <br>
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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>
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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 predictability across bacterial species. In order to achieve predictability, we identified a number of parameters that need to be addressed. For each of these parameters, we demonstrate through modeling how our system can account for all of these variables which have guided lab experiments.
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| − | To achieve a system that works predictably across bacterial species we took into account the following variables:
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| − | <div class="row">
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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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| − | <p>Promoters have different strengths in different organisms. Some promoters only work in a very narrow range of bacterial species. We, therefore, explored methods to overcome this variable by utilizing orthogonal transcription through the use of 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. </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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| − | <p> A ribosome binding site contains the Shine-Dalgarno sequence where the 16s rRNA of the Ribosome binds to. However, this sequence varies across species and often ribosome binding sites are extremely inefficient when applied in phylogenetically distant species. Our solution would thus require an approach independent on the efficiency of ribosomal binding sites.</p>
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| − | <img src = "https://static.igem.org/mediawiki/2019/d/d7/T--TUDelft--CDS.pdf" alt = "CDS SOBL" style = "width:85%;">
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| − | <p> Translation rates are dependent on both translation initiation and translation elongation. Translation elongation is largely dependent on codon usage <cite><a href="https://doi.org/10.1073/pnas.1719375115"><i>(Frumkin, Lajoie et al. 2018)</i></a></cite>. To achieve predictability across species this should thus be adressed. We developed a novel cross species codon harmonization tool that gives you a coding sequence with similar codon adaptation per organisms used. </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 wouldn't be possible or significantly more difficult if we couldn't use plasmids. However, plasmids need an 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. We, therefore, wanted to utilize an orthogonal replication system that would function in any bacterial host. To complement this approach we developed a genetic circuit independent of copy number to minimize the unpredictable nature when transferring between organisms.</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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| − | In our system, we exploit a commonly applied control system motif known as an Incoherent Feed-Forward Loop (iFFL), in which an input signal regulates both the activator and the repressor of the output of the system. An iFFL results in perfect adaptation when the negative regulation is uncooperative <cite><a href="https://www.nature.com/articles/nbt.4111"><i>(Sontag et al. (2018))</i></a></cite>. <br>
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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. This control 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 (source). The TALE protein has been engineered to bind to the promoter of a gene of interest and thus represses the expression of it. <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 further analyzed this system through the use of modeling, which revealed that it's insensitive to many other variables as well, which hasn't been explored yet.
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| − | Transferring genetic circuits between organisms yield large variation in most (if not all) of the parameters in the system, we exploited the robustness of this model to maintain predictability even when crossing species barriers.
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| − | <ul class="accordion">
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| − | <a class="toggle jump" href="javascript:void(0);" ><b>The kinetics</b></a>
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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 step-wise 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. <br> 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 $</il><br><br>
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| − | </ul>
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| − | <table id="tabletu">
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| − | <tr>
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| − | <th>Parameter</th>
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| − | <th>Explanation</th>
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| − | </tr>
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| − | <tr>
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| − | <td>$a_T$</td>
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| − | <td>Transcription rate TALE</td>
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| − | </tr>
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| − | <tr>
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| − | <td>c</td>
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| − | <td>copy number plasmid</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$y_m$</td>
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| − | <td>degradation rate mRNA</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$b_T$</td>
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| − | <td>Translation rate TALE</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$y_T$</td>
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| − | <td>Degradation rate TALE</td>
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| − | </tr>
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| − | <tr>
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| − | <td>n</td>
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| − | <td>Cooperativity of binding</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$k_{on} /k_{off}$</td>
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| − | <td>(un)Binding of TALE to promoter</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$a_{Gmax}/a_{Gmin}$</td>
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| − | <td>Maximum and minimum transcription of GFP</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$b_G$</td>
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| − | <td>Translation rate GFP</td>
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| − | </tr>
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| − | <tr>
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| − | <td>$y_G$</td>
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| − | <td>Degradation rate GFP</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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| − | <a class="toggle jump" href="javascript:void(0);" ><b>Full derivation</b></a>
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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 jump" 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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| − | </p>
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| − | <a class="toggle jump" href="javascript:void(0);" ><b>Transcriptional variation</b></a>
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| − | <a class="toggle jump" href="javascript:void(0);" ><b>Translational variation</b></a>
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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., et al. (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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| − | <a id="Segall-Shapiro" href="https://doi.org/10.1038/nbt.4111" target="_blank">
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| − | Segall-Shapiro, T. H., et al. (2018). "Engineered promoters enable constant gene expression at any copy number in bacteria." Nature Biotechnology 36: 352.
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