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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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        <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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            <br>
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            <br>
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            <br>
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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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                <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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            <div class="column right">
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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.</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> 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 of 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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            </div>
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            <div class="column right">
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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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            </div>
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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 which 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 repress 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:10%" 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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        <br>
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        <br>
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        <ul>
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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 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:60%" 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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                    <br>
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                            <a class="toggle" 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" href="javascript:void(0);" ><b>Copy number independence</b></a>
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                    <p>
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                          <h2>Copy number</h2>
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                          <p>The amount of DNA template inlfuences the output of any genetic circuit.  </p>
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                <a class="toggle" href="javascript:void(0);" ><b>Transcriptional variation</b></a>
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                <a class="toggle" href="javascript:void(0);" ><b>Translational variation</b></a>
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Latest revision as of 17:33, 20 October 2019

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