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− | <p class="low-rise-padding">We collaborated with the <b>Columbia University iGEM Team</b> to help them model the collateral cleavage activity of Cas13a, an enzyme used to cleave RNA in CRISPR technology. Our team provided the system of equations and resulting graphs.</p> | + | <p class="low-rise-padding">We collaborated with the <b>Columbia University iGEM Team</b> to help them model the collateral cleavage activity of Cas13a, an enzyme used to cleave RNA in CRISPR technology. Our team provided the base system of equations and simulated the equations. <a id="bodyLink" href="https://2018.igem.org/Team:CUNY_Kingsborough/CRISPR-Cas13a">See the details here.</a></p> |
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− | <h3 class="low-rise-padding">What is CRISPR?</h3>
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− | <p class="low-rise-padding">CRISPRs, or Clustered Regularly Interspaced Short Palindromic Repeats, are DNA sequences commonly found in bacteria and archaea that serve as a defense mechanism. They originate from pathogens that previously infected the host are are used to detect said pathogens when they try to re-infect the host.</p>
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− | <h3 class="low-rise-padding">A Nuclease Defends - Its Mechanism of Action</h2>
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− | <p class="low-rise-padding">When pathogens that have previously infected the host try to re-invade, host nucleases use CRISPR sequences to detect the RNA sequences of the pathogen. A nuclease is an enzyme the cleaves nucleic acids in DNA or RNA. In CRISPR derived technology, the nuclease is lead by a guid RNA (gRNA) - a sequence of nucleotides complementary to a target strand area - to the CRISPR originating from the pathogen, and cleaves it. Here, Cas13a is the nuclease.</p>
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− | <h3 class="low-rise-padding">The Model</h3>
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− | <p class="low-rise-padding">We based our model and parameter values on the <a id="bodyLink" href="https://2017.igem.org/Team:Munich/Model">2017 Munich iGEM team's model</a>. For values which could not be found in literature, values can be populated based on the desired system behavior. We created a slide tool in Mathematica using the built-in ManipulatePlot function to do this (see image below).</p>
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− | <ol>
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− | <li>\(\frac{d[Cas13a_{M}]}{dt} = k_1 - \beta \cdot [Cas13a_{M}]-k_2 \cdot [Cas13a_{M}]\)</li>
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− | <li>\(\frac{d[crRNA]}{dt} = k_1- \beta \cdot [crRNA] - k_3 \cdot [crRNA]\)</li>
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− | <li>\(\frac{d[Cas13a]}{dt} = k_2 \cdot [Cas13a_{M}] - \beta \cdot [Cas13a] - k_2 \cdot [Cas13a] [crRNA]\)</li>
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− | <li>\(\frac{d[Cas13a_{crRNA}]}{dt} = k_3 \cdot [Cas13a][crRNA] - k_4 \cdot [Target][Cas13a_{crRNA}]\)</li>
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− | <li>\(\frac{d[Target]}{dt} = -k_4 \cdot [Target][Cas13a_{crRNA}] - \beta \cdot [Target]\)</li>
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− | <li>\(\frac{d[Cas13a_{crRNA/Target}]}{dt} = k_4 \cdot [Target][Cas13a_{crRNA}]\)</li>
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− | <li>\(\frac{d[RNA]}{dt} = -k_{col} \cdot \frac{[Cas13a_{crRNA/Target}][RNA]}{k_M+[RNA]}-\beta \cdot [RNA]\)</li>
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− | </ol>
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− | | + | |
− | <center>
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− | <table id="param-table">
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− | <thead>
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− | <th><span>Constant/Parameter</span></th>
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− | <th><span>Value</span></th>
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− | <th><span>Description</span></th>
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− | </thead>
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− | <tbody>
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− | <tr>
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− | <td>\(k_{col}\)</td>
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− | <td>\(10 \frac{1}{min}\)</td>
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− | <td></td>
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− | </tr>
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− | <tr>
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− | <td>\(k_M\)</td>
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− | <td>\(500 nM\)</td>
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− | <td></td>
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− | </tr>
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− | <tr>
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− | <td>\(k_1\)</td>
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− | <td>Determined by speculation</td>
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− | <td>Constitutive expression of \(Cas13a_M\), crRNA (coupled)</td>
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− | </tr>
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− | <tr>
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− | <td>\(k_2\)</td>
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− | <td>Determined by speculation</td>
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− | <td>Transcription of \(Cas13a_M\)</td>
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− | </tr>
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− | <tr>
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− | <td>\(k_3\)</td>
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− | <td>\(1 \frac{1}{min}\)</td>
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− | <td>Equivalent to \(k_{cr}\) in Munich 2017's model</td>
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− | </tr>
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− | <tr>
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− | <td>\(k_4\)</td>
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− | <td>\(0.001 \frac{1}{min}\)</td>
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− | <td>Equivalent to \(k_{t}\) in Munich 2017's model</td>
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− | <tr>
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− | <td>\(\beta\)</td>
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− | <td>Determined by speculation</td>
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− | <td>Degradation factor</td>
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− | </tr>
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− | </tbody>
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− | </table>
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− | </center>
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− | <center>
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− | <figure>
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− | <img src="https://static.igem.org/mediawiki/2018/8/84/T--CUNY_Kingsborough--slideplot.jpeg
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− | " width="300">
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− | <figcaption>
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− | <small>Mathematica slide plot used to determine arbitrary values for \(k_1\), \(k_2\), \(\beta\)</small>
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− | </figcaption>
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− | </figure>
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− | </center>
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| <hr> | | <hr> |
We want our standard curve to be able to predict concentrations from varying levels of pixel intensity. In order to do so, we needed a larger and more diverse dataset. So we asked iGEM teams to perform the following task: dilute 1 uL of DNA of an unknown concentration into 9 uL EtBr (1 ng/uL), photograph the samples under UV light, and send us the images. Using ImageJ®, we compared the pixel intensity of the sample with a known DNA concentration to the predicted pixel intensity based on our standard curve. Special thanks to HD Resolution from the US and Tec de Monterrey_Gdl from Mexico!