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+ | <!-- Content --> | ||
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+ | <!-- Head End --> | ||
+ | <!-- Content Begin --> | ||
+ | <img id="TopPicture" width="800" src="https://static.igem.org/mediawiki/2017/7/78/T--Munich--FrontPagePictures_Software.svg"> | ||
+ | <table width="960" border=0 cellspacing=0 cellpadding=10> | ||
+ | <tr> | ||
+ | <td width=160></td> | ||
+ | <td width=160></td> | ||
+ | <td width=160></td> | ||
+ | <td width=160></td> | ||
+ | <td width=160></td> | ||
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+ | <tr><td colspan=6 align=left valign=center> | ||
+ | <font size=7 color=#51a7f9><b style="color: #51a7f9">Modelling</b></font> | ||
+ | </td> | ||
+ | </tr> | ||
+ | <tr class="lastRow"> | ||
+ | <td colspan = 6 align="left"> | ||
+ | <p class="introduction"> | ||
+ | Modelling in Biosciences is a powerful tool that allows one to get a deeper understanding | ||
+ | of one's system. We mainly used Modelling to help with the design of our device. | ||
+ | By this, we could avoid spending time on dead-end-designs that otherwise might have | ||
+ | cost us a significant amount of time. Rather simple models can already give | ||
+ | fair amount of information about one's system. That is why we decided at an early stage to incorporate | ||
+ | Modelling in our device design. | ||
+ | </p> | ||
+ | </td> | ||
+ | </tr> | ||
+ | |||
+ | |||
+ | <tr class="lastRow"><td colspan=6 align=left valign=center> | ||
+ | <h2>Detection Limit</h2> | ||
+ | <p> | ||
+ | One major concern when dealing with the problem of diagnostics on patients is obtaining the sample with which | ||
+ | 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. First approximations from | ||
+ | different papers already showed that virological samples show concentrations no higher than low pM and can even go as low | ||
+ | as fM. Thus, we characterised the theoretical detection limit of the Cas13a RNAse activity. In order to do this, we first | ||
+ | fitted parameters using experimental data to the model shown below and used these in target RNA concentration dependent | ||
+ | simulations. The results are shown in Figure 1. It shows that the detection limit in the time range of an hour is | ||
+ | approximately one- to two-digit nM region. 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. Instead, we had to explore amplification methods we could | ||
+ | perform upstream in the detection process. | ||
+ | <br> | ||
+ | As a side note, the detection limit could most probably have been pushed a bit to lower concentrations by using higher | ||
+ | concentrations in Cas13a and crRNA, but by doing this production cost per paperstrip would have increased a lot. Also, | ||
+ | it is known from literature that Cas proteins at high concentrations show activity independent of their activation mechanism | ||
+ | which is why the concentration of Cas13a in the detection system could not be increased by higher orders of magnitude. | ||
+ | </p> | ||
<p> | <p> | ||
− | + | <img width=800 align=center valign=center src="https://static.igem.org/mediawiki/2017/c/c5/T--Munich--ModellingPagePicture_Theoretical_Detection_Limit.png" alt="Theoretical Detection Limit"> | |
</p> | </p> | ||
+ | |||
+ | |||
<p> | <p> | ||
− | + | <i>Figure 1: Theoretical Detection Limit determined for the Cas13a system using 20 nM concentrations of Cas13a and crRNA. </i> | |
</p> | </p> | ||
− | </ | + | </td> |
− | < | + | <tr class="lastRow"><td colspan=6 align=left valign=center> |
− | < | + | <h2>Lysis on Chip</h2> |
+ | <p> | ||
+ | We modelled the lysis process on chip to get an idea of how long lysis would need to take place | ||
+ | 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 | ||
+ | protocols which use a 10 minute lysis step at 95 °C for thermolysis. Thus, we considered a half-time of Bacteria | ||
+ | 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-time using Arrhenius equation. | ||
+ | </p> | ||
+ | <p> | ||
+ | Equations 1+2 | ||
+ | </p> | ||
+ | <p> | ||
+ | where R is the gas constant and k describe the rate constant at Temperature T_1 and Temperature T_2. The Arrhenius | ||
+ | energy E_A was fitted to a barrier that follows the common rule of thumb that lysis should increase twice in | ||
+ | efficiency every temperature increase of 10 °C. The model for lysis is shown below: | ||
+ | </p> | ||
+ | <p> | ||
+ | <img width=800 align=center valign=center src="https://static.igem.org/mediawiki/2017/f/f1/T--Munich--ModellingPagePicture_Lysis_Temperature.png" alt="Lysis_Temperature"> | ||
+ | </p> | ||
<p> | <p> | ||
− | + | <i> Effect of lysis temperature on the lysis efficiency of bacterial cells | |
− | + | and Determination of the released concentration of target RNA from lysis assuming a ratio of 30 | |
− | + | RNA molecules per cell. </i> | |
</p> | </p> | ||
+ | <p> | ||
+ | The full model can then be described by the coupled ordinary differential equations:<br> | ||
+ | Equations 3+4 | ||
+ | </p> | ||
+ | <p> | ||
+ | The full model at 95 °C looks as follows: | ||
+ | </p> | ||
+ | </td> | ||
− | |||
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− | < | + | </tr> |
− | < | + | |
+ | |||
+ | <tr class="lastRow"><td colspan=6 align=left valign=center> | ||
+ | <h2>Signal Amplification</h2> | ||
+ | <p> | ||
+ | For the simulation of an amplification system, we circuit amplifying an RNA system. Therefore, | ||
+ | we couple a Reverse Trancription to an isothermal PCR-like amplification called Recombinase Polymerase Amplification (RPA) | ||
+ | and do In-Vitro Transcription from the build template. A scheme for the model is shown in Figure 2. | ||
+ | For simplicity, we made assumptions to this model:<br> | ||
+ | First, the RPA reaction is thought to be in the linear region, independent of Primer concentration since we | ||
+ | work in an environment of very high primer and dNTP concentrations (up to 1000 nM) and only want to reach RNA concentration within the | ||
+ | range of the detection limit of our Cas13a protein, which is in the nM region. Therefore, since we are amplifying the RNA by | ||
+ | Transcription from the cDNA, this assumption is reasonable. The same argument goes for the In-Vitro Transcription; since we | ||
+ | are in an environment of excessive rNTP concentrations, thus first order approximation is valid. <br> | ||
+ | Rate constants were approximated by experiments or taken from literature. The only rate constant that was not available was | ||
+ | the rate of Reverse Transcription. We, thus, took producer's information about commercial RT kits and estimated from these very | ||
+ | conservatively (two orders of magnitude less in reaction speed) to not be biased in the simulation by overfitting parameters. <br> | ||
+ | The rate constants are the following: | ||
+ | COUNT ALL 4 RATE CONSTANTS | ||
+ | </p> | ||
+ | |||
<p> | <p> | ||
− | + | <img width=600 align=center valign=center src="https://static.igem.org/mediawiki/2017/d/dc/T--Munich--ModellingPagePicture_RT-RPA-TX_scheme.svg" alt="RT-RPA-TX_scheme"> | |
</p> | </p> | ||
− | < | + | |
− | < | + | <p> |
− | < | + | <i>Figure 2: Scheme for the RT-RPA-Tx Amplification system </i> |
− | < | + | </p> |
− | < | + | |
− | </ | + | <p> |
+ | <img width=800 align=center valign=center src="https://static.igem.org/mediawiki/2017/8/8c/T--Munich--ModellingPagePicture_RT-RPA-TX.png" alt="RT-RPA-TX"> | ||
+ | </p> | ||
+ | <p> | ||
+ | <i>Figure 3: Target RNA concentration dependent on initial concentrations to determine the cycle time in RT-RPA-Tx needed for reaching | ||
+ | the Cas13a detection limit of 10 nM (red line). </i> | ||
+ | </p> | ||
+ | <p> | ||
+ | The overall dynamics of the RT-RPA-Tx system are shown below for several starting concentrations of RNA. | ||
+ | </p> | ||
+ | </td> | ||
+ | |||
+ | <tr class="lastRow"><td colspan=6 align=left valign=center> | ||
+ | <h2>Theoretical Detection Limit using the Amplification Circuit and Cas13a Detection</h2> | ||
+ | <p> | ||
+ | Since the reasoning behind using an amplification method was to bring down the detection limit, a new theoretical | ||
+ | detection limit of the device may be determined combining model of lysis and isothermal amplification. For this, | ||
+ | a reasonable cycle time for point-of-care application of one hour was chosen. | ||
+ | </p> | ||
+ | <p> | ||
+ | <img width=800 align=center valign=center src="https://static.igem.org/mediawiki/2017/1/13/T--Munich--ModellingPagePicture_Cycle_Times.png" alt="RT-RPA-TX"> | ||
+ | </p> | ||
+ | <p> | ||
+ | <i>Determining Cycle times to reach 10 nM Detection Limit using Amplification Circuit. Red dashed line marks the end of the thermolysis</i> | ||
+ | </p> | ||
+ | |||
+ | <p> | ||
+ | When comparing this to cycle times needed for reaching the detection limit at 65 °C, one sees that lysis temperatures is not very important | ||
+ | to the amplification and only results in a slight shift to longer time scales. This is reasonable, since RPA, and PCR in general, | ||
+ | are enormously sensitive methods, and thus only need few templates to show a signal. Also, when comparing the concentrations | ||
+ | in the temperature screen above, one can observe that the concentrations of RNA within the sample only change insignificantly, all showing concentrations that range | ||
+ | within three-digit attomolar region or higher. | ||
+ | </p> | ||
+ | </td> | ||
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Revision as of 14:11, 28 October 2017