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<p class="introduction"> | <p class="introduction"> | ||
Modelling in Biosciences is a powerful tool that allows us to get a deeper understanding | Modelling in Biosciences is a powerful tool that allows us to get a deeper understanding | ||
− | of our system. It guided and assisted the design of our detection system which helped us saving a lot of time by avoiding dead-end designs. We used simple models to simulate the kinetics of our enzyme cascade to develop intuition for the design of experiments. We then used our models to optimize the design of our reaction cascades for an improved detection limit and | + | of our system. It guided and assisted the design of our detection system which helped us saving a lot of time by avoiding dead-end designs. We used simple models to simulate the kinetics of our enzyme cascade to develop intuition for the design of experiments. We then used our models to optimize the design of our reaction cascades for an improved detection limit and optimal lysis times. Our scripts can be found on our <a class='myLink' href='https://github.com/igemsoftware2017/igem_munich_2017/tree/master/Modelling'>GitHub repository</a>. |
</p> | </p> | ||
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detection can actually be performed. Since we wanted our method to be non-invasive, one concern that we needed to | detection can actually be performed. Since we wanted our method to be non-invasive, one concern that we needed to | ||
deal with is the concentration of pathogens and thus detectable RNA in the patients mucus or other non-invasive sample. First approximations from different papers already showed that virological samples show concentrations no higher than low pM and can even go as low as aM. | deal with is the concentration of pathogens and thus detectable RNA in the patients mucus or other non-invasive sample. First approximations from different papers already showed that virological samples show concentrations no higher than low pM and can even go as low as aM. | ||
− | + | </p> | |
+ | <p> | ||
Our <a class='myLink' href=https://2017.igem.org/Team:Munich/Cas13a>wetlab experiments</a> indicated that the detection limit of the Cas13a RNase activity is in the range of 10 nM. | Our <a class='myLink' href=https://2017.igem.org/Team:Munich/Cas13a>wetlab experiments</a> indicated that the detection limit of the Cas13a RNase activity is in the range of 10 nM. | ||
− | Using our kinetic data, we estimated the rate constants for the different reactions to create a simple ODE model | + | Using our kinetic data, we estimated the rate constants for the different reactions to create a simple ODE model. |
− | + | <br>The chemical and differential equations for the model are shown below: | |
− | + | </p> | |
− | + | ||
− | The chemical and differential equations for the model are shown below: | + | |
<div class="captionPicture"> | <div class="captionPicture"> | ||
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</p> | </p> | ||
</div> | </div> | ||
+ | |||
+ | <tr class="lastRow"><td colspan=6 align=center valign=center> | ||
+ | <table class="myTable" width=100%> | ||
+ | <th class="leftAligned">rate constant</th> | ||
+ | <th class=”leftAligned”>value</th> | ||
+ | <th class="leftAligned">reference or rationale</th> | ||
+ | <tr> | ||
+ | <td class="leftAligned">k<sub>cr</sub></td> | ||
+ | <td class="leftAligned">1 [1/min]</td> | ||
+ | <td class="leftAligned">Mekler et al. (2016) Nucleic Acids Resarch</td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td class="leftAligned">k<sub>t</sub></td> | ||
+ | <td class="leftAligned">0.001 [1/min]</td> | ||
+ | <td class="leftAligned">Estimated to be slow in comparison to k<sub>cr</sub></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td class="leftAligned">k<sub>col</sub></td> | ||
+ | <td class="leftAligned">10 [1/min]</td> | ||
+ | <td class="leftAligned">Estimated to be fast in comparison to k<sub>cr</sub> </td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td class="leftAligned">k<sub>RT-RPA-Tx</sub></td> | ||
+ | <td class="leftAligned">0.4 [1/min]</td> | ||
+ | <td class="leftAligned">Estimated from RPA-Tx amplification experiments</td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td class="leftAligned">K<sub>M</sub></td> | ||
+ | <td class="leftAligned">500 [nM]</td> | ||
+ | <td class="leftAligned">Weitz et al. (2014) Nature Chemistry</td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | |||
+ | <br> | ||
+ | <br> | ||
+ | <p> | ||
+ | As shown in <b>Figure 1</b>, our simulations are able to reproduce the behavior observed experimentally. | ||
+ | </p> | ||
<div class="captionPicture"> | <div class="captionPicture"> | ||
− | <img alt="LightbringerReal" src="https://static.igem.org/mediawiki/2017/8/87/T--Munich--ModellingPagePicture_kinetics_Cas13a_only.png" width=" | + | <img alt="LightbringerReal" src="https://static.igem.org/mediawiki/2017/8/87/T--Munich--ModellingPagePicture_kinetics_Cas13a_only.png" width="700"> |
<p> | <p> | ||
− | Figure | + | Figure 1: Kinetics of Cas13a using 1 nM Cas13a and 10 nM crRNA at different target concentrations. |
</p> | </p> | ||
</div> | </div> | ||
+ | |||
+ | <p> | ||
+ | Next, we analysed the amount of readout RNA that was cleaved after 30 minutes for varying target concentrations. As shown in <b>Figure 2</b>, the curve follows a sigmoidal behavior and suggests a detection limit in the range of 10 nM. Due to this result, our initial design of applying the lysed and purified RNA sample directly on the detection paper strip had to be discarded. Since it is known from literature that Cas proteins show activity independent of their activation mechanism at high concentrations, we could not increase the concentration of Cas13a to improve the sensitivity. Instead, we explored amplification methods upstream in the detection process. | ||
</p> | </p> | ||
+ | |||
<div class="captionPicture"> | <div class="captionPicture"> | ||
− | <img alt="LightbringerReal" src="https://static.igem.org/mediawiki/2017/ | + | <img alt="LightbringerReal" src="https://static.igem.org/mediawiki/2017/b/b8/T--Munich--ModellingPagePicture_CascAID.png" width="600"> |
<p> | <p> | ||
− | Figure | + | Figure 2: Estimated detection limit determined for the Cas13a system using 1 nM Cas13a and 10 nM crRNA. |
</p> | </p> | ||
</div> | </div> | ||
+ | |||
+ | |||
+ | <h3>Improved Reaction Cascade</h3> | ||
+ | <p> | ||
+ | |||
+ | |||
+ | In collaboration with our wetlab team we developed a reaction cascade for sample pre-amplification by coupling reverse transcription to isothermal recombinase polymerase amplification and transcription (RT-RPA-TX), resulting in auto-catalysis of target RNA <b>(Figure 3)</b>.</p> | ||
+ | |||
<div class="captionPicture"> | <div class="captionPicture"> | ||
− | <img | + | <img width=600 src="https://static.igem.org/mediawiki/2017/d/dc/T--Munich--ModellingPagePicture_RT-RPA-TX_scheme.svg" alt="RT-RPA-TX_scheme"> |
<p> | <p> | ||
− | Figure | + | Figure 3: Scheme for the RT-RPA-TX amplification system. |
</p> | </p> | ||
</div> | </div> | ||
<p> | <p> | ||
− | + | In order to compare the detection limit of the Cas13a system alone with the detection limit of the amplified the reaction cascade, we expanded our model, assuming exponential amplification of the target RNA. As the amplification reaction saturates due to a depletion of resources, the amplification stops as soon as the target RNA level reaches an upper limit of 1000 nM <b>(Figure 4)</b>. | |
</p> | </p> | ||
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− | |||
<div class="captionPicture"> | <div class="captionPicture"> | ||
<img width=800 align=center valign=center src="https://static.igem.org/mediawiki/2017/1/16/T--Munich--ModellingPagePicture_scheme2.png" alt="RT-RPA-TX"> | <img width=800 align=center valign=center src="https://static.igem.org/mediawiki/2017/1/16/T--Munich--ModellingPagePicture_scheme2.png" alt="RT-RPA-TX"> | ||
<p> | <p> | ||
− | Figure | + | Figure 4: Schematic representation of the target RNA amplification during the estimation of the detection limit using the reaction cascade. |
</p> | </p> | ||
+ | </div> | ||
+ | <p> | ||
+ | The kinetics for the amplfication cascade coupled to Cas13a based detection are shown in <b>Figure 5</b>. Strikingly, the start of the reaction seems to be determined by the amplificaiton reaciton, while the consecutive phase is limited by the rate of Cas13a mediated cleavage. | ||
+ | As shown in <b>Figure 2</b>, the detection limit of the reaction cascade decreases by approximately three orders of magnitude. These simulations led us to implement our pre-amplification cascade into our CascAID system. | ||
+ | </p> | ||
+ | <div class="captionPicture"> | ||
+ | <img alt="LightbringerReal" src="https://static.igem.org/mediawiki/2017/1/14/T--Munich--ModellingPagePicture_kinetics_Cas13a.png" width="600"> | ||
+ | <p> | ||
+ | Figure 5: Kinetics of the Cas13a systemusing 1 nM Cas13a and 10 nM crRNA at different target concentrations using the reaction cascade. | ||
+ | </p> | ||
+ | </div> | ||
+ | |||
+ | |||
+ | </td> | ||
+ | </tr> | ||
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in order to release enough RNA for downstream amplification. For this, we constructed a very simplistic | in order to release enough RNA for downstream amplification. For this, we constructed a very simplistic | ||
model for bacterial cell lysis. In this, we estimated the rate constants for cell lysis by common colony PCR | model for bacterial cell lysis. In this, we estimated the rate constants for cell lysis by common colony PCR | ||
− | protocols which use a 10 minute lysis step at 95 °C for thermolysis. Thus, we considered a half- | + | protocols which use a 10 minute lysis step at 95 °C for thermolysis. Thus, we considered a half-life of bacteria |
of 2 minutes at 95 °C. This would result in a lysis efficiency of 96.875%. Starting from this estimation, | of 2 minutes at 95 °C. This would result in a lysis efficiency of 96.875%. Starting from this estimation, | ||
− | we considered the rate constant of lysis and thus the half- | + | we considered the rate constant of lysis and thus the half-life using Arrhenius equation as commonly done in the literature: |
</p> | </p> | ||
<p> | <p> | ||
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/b/b0/T--Munich--Model_Equation_1.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/b/b0/T--Munich--Model_Equation_1.png"><span>(7)</span></div> |
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/3/30/T--Munich--Model_Equation_2.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/3/30/T--Munich--Model_Equation_2.png"><span>(8)</span></div> |
</p> | </p> | ||
<p> | <p> | ||
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</p> | </p> | ||
<p> | <p> | ||
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/7/7d/T--Munich--Model_Equation_3.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/7/7d/T--Munich--Model_Equation_3.png"><span>(9)</span></div> |
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/3/35/T--Munich--Model_Equation_4.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/3/35/T--Munich--Model_Equation_4.png"><span>(10)</span></div> |
</p> | </p> | ||
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<p> | <p> | ||
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/8/81/T--Munich--Model_Equation_5.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/8/81/T--Munich--Model_Equation_5.png"><span>(11)</span></div> |
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<p> | <p> | ||
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/6/6d/T--Munich--Model_Equation_6.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/6/6d/T--Munich--Model_Equation_6.png"><span>(12)</span></div> |
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<p> | <p> | ||
Equation 7 + 8 | Equation 7 + 8 | ||
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/b/b7/T--Munich--Model_Equation_7.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/b/b7/T--Munich--Model_Equation_7.png"><span>(13)</span></div> |
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/e/e5/T--Munich--Model_Equation_8.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/e/e5/T--Munich--Model_Equation_8.png"><span>(14)</span></div> |
</p> | </p> | ||
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</p> | </p> | ||
<p> | <p> | ||
− | <div class="equationDiv"><img style="height: 40px;" src="https://static.igem.org/mediawiki/2017/4/4e/T--Munich--Model_Equation_10.png"><span>( | + | <div class="equationDiv"><img style="height: 40px;" src="https://static.igem.org/mediawiki/2017/4/4e/T--Munich--Model_Equation_10.png"><span>(15)</span></div> |
</p> | </p> | ||
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<p> | <p> | ||
− | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/5/5d/T--Munich--Model_Equation_11.png"><span>( | + | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/5/5d/T--Munich--Model_Equation_11.png"><span>(16)</span></div> |
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<li id=“ref_10”>Licciardello, J. J., & Nickerson, J. T. R. (1963). “Some Observations on Bacterial Thermal Death Time Curves.” Applied Microbiology, 11(6), 476–480. | <li id=“ref_10”>Licciardello, J. J., & Nickerson, J. T. R. (1963). “Some Observations on Bacterial Thermal Death Time Curves.” Applied Microbiology, 11(6), 476–480. | ||
<li id=“ref_11”>Deindoerfer, F. H. (1957). “Calculation of Heat Sterilization Times for Fermentation Media.” Applied Microbiology, 5(4), 221–228. | <li id=“ref_11”>Deindoerfer, F. H. (1957). “Calculation of Heat Sterilization Times for Fermentation Media.” Applied Microbiology, 5(4), 221–228. | ||
+ | |||
+ | <li id="ref_12">M. Weitz, K. Jongmin, K. Kapsner, E. Winfree, E. Franco, and F.C. Simmel. | ||
+ | “Diversity in the Dynamical Behaviour of a Compartmentalized Programmable Biochemical Oscillator.” | ||
+ | (2014) <i>Nature Chemistry</i> 6(4): 295–302. | ||
+ | |||
+ | <li id="ref_13">V. Mekler1, L. Minakhin, E. Semenova, K. Kuznedelov and K. Severinov | ||
+ | "Kinetics of the CRISPR-Cas9 effector complex assembly and the role of 3′-terminal segment of guide RNA" | ||
+ | <i>Nucleic Acids Research</i>, Vol. 44(6): 2837–2845 | ||
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Latest revision as of 03:53, 2 November 2017
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