Difference between revisions of "Template:Team:Utrecht/MainBody"

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<div class="page-heading">Modeling and Mathematics</div>
 
<div class="page-heading">Modeling and Mathematics</div>
  
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The first thing we did to get a good overview of the system dynamics was to try and graphically represent the chemical interactions of the OUTCASST system as a small reaction network. From this network, we can already see that, if we disregard production and degradation of the proteins  (so under conditions of conservation of mass) all target chain proteins will be cleaved over time. For the eventual equilibrium outcome, the cleavage rate does not matter. It only matters for the duration of equilibrium onset. So, if the cleavage speed is of no importance for the end-result, does it affect sensitivity in another way?
+
The first step we took to get a good overview of the system dynamics was to try and graphically represent the molecular interactions of the OUTCASST system in a small reaction network.  
 +
From this network we could already point out two characteristics of the OUTCASST system that are most likely to hamper sensitivity. Fortunately, we were able to find possible solutions for those problems through analysis of the network and mathematical modeling.
 +
<br><br>
 +
For an introduction of the OUTCASST network model, check out the video below!
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<br>
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<video onclick="this.paused?this.play():this.pause();" style="margin-top: 10px; width: 100%; cursor: pointer;" poster="https://static.igem.org/mediawiki/2017/d/d1/UU-modelingvideo-poster.png" controls>
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<source src="https://static.igem.org/mediawiki/2017/d/da/UuModelingVidBecauseWeDid.mp4" type='video/mp4'/>
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<p style="font-style:italic;color:red;border-style:solid;border-width:2px;border-color:red">Your browser either does not support HTML5 or cannot handle MediaWiki open video formats. Please consider upgrading your browser, installing the appropriate plugin or switching to a Firefox or Chrome install.</p>
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</video>
  
 
<br><br>
 
<br><br>
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<h2 class="subhead" id="subhead-2">Optimization of the protease cleavage rate</h2>
+
<h2 class="subhead" id="subhead-2">False positive reduction</h2>
−
Since the concentration of substrate will be exceedingly low for our sensor, the number of binding events due to substrate will also be small. It would be ideal if each binding event would lead to cleavage while transient meetings between the two proteins only rarely lead to cleavage. This would reduce the chance of false positive signals. Considering the great binding affinities of both Cas9 and Cpf1 for gRNA complementary DNA, binding events are much longer in duration than transient meetings of the two proteins.  
+
 
 +
<b>Optimization of the protease cleavage rate</b><br>
 +
 
 +
In the case of detecting pathogen DNA, the concentration of DNA or RNA will be exceedingly low and thus the number of interaction events due to substrate binding will also be small. It would be ideal if each substrate binding event would lead to cleavage while transient meetings, in the absence of substrate, between the two chains only rarely lead to cleavage. This would reduce the chance of false positive signals. Considering the great binding affinities of both Cas9 and Cpf1 for gRNA complementary DNA, binding events are much longer in duration than transient meetings of the two proteins.  
 
<br><br>
 
<br><br>
−
In the image to the side, you can see a schematic illustration of the difference in half-life of the complex formed by transient and substrate-mediated interaction.
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<div style="float: left; margin-right: 35px; width: 305px;">
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<br><br>
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<img style="width: 100%;" src="https://static.igem.org/mediawiki/2017/2/21/UU-model-fig1.png">
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In the image, for clarity, we have taken the half-life of transient complex as 5 arbitrary time units and that of the substrate-mediated complex is set to 100.
+
<br>
−
<br><br>
+
<span class="text-figure" style="display: inline-block; line-height: 20px;">
−
In the real system, these values will be much wider apart, but we took these as a clear illustration of the point we wish to make.
+
<b>Figure 1.</b> Fraction of remaining complex for (orange) substrate mediated binding events and (blue) transient binding events.
 +
</span>
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 +
<br>
 +
 +
<img style="width: 100%; margin-top: 40px;" src="https://static.igem.org/mediawiki/2017/7/7f/UU-model-fig2.png">
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<br>
 +
<span class="text-figure" style="display: inline-block; line-height: 20px;">
 +
<b>Figure 2.</b> Probability of cleavage occurring over time for a (orange) fast and (blue) slow cleaver.
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</span>
 +
<br>
 +
<br>
 +
</div>
 +
In the image to the side, you can see a graphical illustration of the difference in half-life of the complex formed by transient and substrate-mediated interaction. For clarity, we have taken the half-life of transient complex as 5 arbitrary time units and that of the substrate-mediated complex is set to 100. In the real system, these values will be much further apart as the duration of DNA binding for catalytically inactive Cas9 and Cpf1 is rather long.
 
<br><br>
 
<br><br>
 
Consider two different versions of our system: one with a fast-cleaving protease and the second with a slow-cleaving protease. In the image to the left, we plotted the probability distribution of cleavage occurring over time for these two versions of our Protease Chain protein. Note that the probability that it will cleave over time will always be 1, the timespan wherein this happens simply differs.  
 
Consider two different versions of our system: one with a fast-cleaving protease and the second with a slow-cleaving protease. In the image to the left, we plotted the probability distribution of cleavage occurring over time for these two versions of our Protease Chain protein. Note that the probability that it will cleave over time will always be 1, the timespan wherein this happens simply differs.  
 +
<br><br>
 
For the mathematicians amongst those who are reading this: These plots are simple lognormal distributions, for the distribution cannot take negative values as it is impossible to cleave before the complex has been formed.
 
For the mathematicians amongst those who are reading this: These plots are simple lognormal distributions, for the distribution cannot take negative values as it is impossible to cleave before the complex has been formed.
 
<br><br>
 
<br><br>
−
We can now see that the probability of cleavage for the slow cleaver is much smaller than that of the fast cleaver in the timespan that the transient complex persists. Of course, the concentration of the substrate-mediated complex decreases over time, so the total cleavage decreases when it cleaves later. To investigate how much the transient and substrate-mediated complex contribute to signal development for both Protease Chain variants, we define:
+
By comparing the two figures, we can now see that the probability of cleavage for the slow cleaver is much smaller than that of the fast cleaver in the timespan that the transient complex persists. Of course, the concentration of the substrate-mediated complex decreases over time, so the total cleavage decreases when it cleaves later. To investigate how much the transient and substrate-mediated complex contribute to signal development for both Protease Chain variants, we define:
 
<br><br>
 
<br><br>
−
<b>FORMULA</b>
+
S'(t) = p_c (t)⋅C(t)⋅(1-∫_0^t p_c  dt)
 
<br><br>
 
<br><br>
−
Wherein S’ is the increase in signal, given by the probability of cleavage (p_c) for the remaining uncleaved complex. The remaining uncleaved complex is given by the remaining complex fraction (C) and how likely it is that it has not already been cleaved (one minus the integral of p_c from 0 until that timepoint).
+
Wherein S’ is the increase in signal, given by the probability of cleavage (pc) for the remaining uncleaved complex. The remaining uncleaved complex is given by the remaining complex fraction (C) and how likely it is that it has not already been cleaved (one minus the integral of pc from 0 until that timepoint).
 
<br><br>
 
<br><br>
−
When we solve this for each Protease Chain version and for both the transient and substrate-mediated complex, we end up with time-plots of the resulting signal contribution of a single binding event over time. In these plots, we can see that, for the slow cleaver, shown in the top image to the left, the resulting substrate-mediated complex signal is about half of that for the fast cleaver, as shown in the lower image. The signal is less strong but, in theory, this is not a problem since the signal can be amplified by the cells.  
+
<div style="float: left; margin-right: 35px; width: 350px;">
 +
<img style="width: 100%;" src="https://static.igem.org/mediawiki/2017/a/a2/UU-model-fig3.png">
 +
<br>
 +
<span class="text-figure" style="display: inline-block; line-height: 20px;">
 +
<b>Figure 3.</b> Signal accumulation of the slow cleaver for (orange) substrate mediated binding events and (blue) transient binding events. Note that the transient binding signal is very small. For clarity, it is displayed in the inset graph.
 +
</span>
 +
 +
<br>
 +
 +
<img style="width: 100%; margin-top: 25px;" src="https://static.igem.org/mediawiki/2017/5/51/UU-model-fig4.png">
 +
<br>
 +
<span class="text-figure" style="display: inline-block; line-height: 20px;">
 +
<b>Figure 4.</b> Signal accumulation of the fast cleaver for (orange) substrate mediated binding events and (blue) transient binding events.
 +
</span>
 +
</div>
 +
When we solve this for each Protease Chain version and for both the transient and substrate-mediated complex, we end up with time-plots of the signal contribution of a single binding event. In these plots, we see that the resulting substrate-mediated complex signal for the slow cleaver (top) is about half as strong as the signal for the fast cleaver (bottom).In theory, this is not a problem since the signal can be amplified by the cells.  
 
<br><br>
 
<br><br>
−
For the fast cleaver, we can see a much bigger issue. The signal contribution of the transient complex, i.e. the false positive, is ten-fold smaller than the signal contribution of the substrate-mediated complex but, considering that transient encounters will be a lot more frequent than substrate-binding events, the false positive signal can be multiplied many times, making it  a lot stronger than the substrate-mediated signal can ever be. This is not the case for the slower cleaver, where the transient complex signal contribution is in the order of 10^-7, and thus falls on the abscissa.
+
For the fast cleaver, we see a much bigger issue. The signal contribution of the transient complex, i.e. the false positive, is only about ten-fold smaller than the signal contribution of the substrate-mediated complex. Considering that transient encounters will be a lot more frequent than substrate-binding events, the false positive signal can be multiplied many times, making it  a lot stronger than the substrate-mediated signal can ever be.  
 +
<br><br>
 +
This is not the case for the slower cleaver, where the transient complex signal contribution is much smaller.
 
<br><br>
 
<br><br>
 
Using the contributions of a single transient binding event and a single substrate-mediated binding event, we can calculate a proxy for precision by dividing the contribution of the true signal (substrate-mediated) by the contribution of the false signal (transient). For the slow rate, the contribution of a single substrate-mediated event is almost 48 000 times that of the transient occurrence. For the fast cleavage rate, this is only 17 times.
 
Using the contributions of a single transient binding event and a single substrate-mediated binding event, we can calculate a proxy for precision by dividing the contribution of the true signal (substrate-mediated) by the contribution of the false signal (transient). For the slow rate, the contribution of a single substrate-mediated event is almost 48 000 times that of the transient occurrence. For the fast cleavage rate, this is only 17 times.
 
<br><br>
 
<br><br>
−
If we assume that the transient interaction occurs 100 times more frequently than the substrate-binding event, ‘true’ signal strength would only be 0.17 times that of the background for the fast cleaver whereas it would still be 480 times stronger than the background for the slow cleaver.
+
If we assume that the transient interaction occurs 100 times more frequently than the substrate-binding event, a modest estimate, ‘true’ signal strength would only be 0.17 times that of the background for the fast cleaver whereas it would still be 480 times stronger than the background for the slow cleaving protease.
 
<br><br>
 
<br><br>
−
In conclusion, for minimization of false positive results, the cleavage rate should result in a cleavage duration that is near the half-life of the uncleaved complex between target-chain, protease-chain and substrate. Increasing the cleavage rate would not contribute to sensitivity and merely decrease precision.
+
In conclusion, a protease with a slower cleavage rate results in a much higher signal-to-noise ratio than a fast cleaving protease results in. Thus, for increased precision and minimization of false positive results, the cleavage rate should be such that it result in a cleavage duration near the half-life of the complex between target-chain, protease-chain and substrate.  
 
<br><br>
 
<br><br>
−
A full work-out of this demonstration in mathematica notebook can be found <a target=_BLANK href="https://drive.google.com/drive/folders/0B_qbow6tESp8b2FNb3pMa1psLTA" class="url_external">here</a>.
+
The affinity of the protease can be altered in two ways. Firstly, the protease binding affinity itself can be tweaked by amino-acid substitution but this requires careful experimentation and has a low chance of success. Much more easily, the cleavage site can be positioned on the linker such that it is partially obstructed or harder to reach by the protease, thereby reducing the effective cleavage rate.
 +
<br><br>
 +
A full work-out of this demonstration in mathematica notebook format can be found <a target=_BLANK href="https://static.igem.org/mediawiki/2017/2/2f/UuModelingProteaseOptimization.txt" class="url_external">here</a>.
  
 
<br><br>
 
<br><br>
−
<h2 class="subhead" id="subhead-3">Optimization of protein production rates</h2>
+
<h2 class="subhead" id="subhead-3">Substrate trapping reduction</h2>
−
&hellip;
+
 
 +
<b>Optimizing DNA affinity of Target Chain and Protease Chain</b><br>
 +
 
 +
Cleavage of the target chain is required for signal output. Unfortunately, the truncated target chain potentially traps the DNA molecule and thereby reduces the concentration of accessible substrate. The trapped state is visualized in the network model (Fig. 5) as the top node.
 +
<br>
 +
<center><img style="margin-top: 25px; width: 350px;" src="https://static.igem.org/mediawiki/2017/thumb/1/17/UU-model-fig5.png/681px-UU-model-fig5.png"></center>
 +
<span class="text-figure">
 +
<b>Figure 5.</b> Snapshot of the OUTCASST network model assuming identical binding affinities for target and protease chain, as indicated by arrow thickness.
 +
</span>
 +
 
 +
<br><br>
 +
From figure 5, we can already see that the likeliness of this trapped state (Fig. 5, state 8) depends on the rates with which the cut complex (Fig. 5, state 6) goes into either of the two subsequent states (Fig. 5, state 7 & 8). In order to optimize the accessibility of substrate, and thereby signal per substrate, we have to ensure that more of the cut complex turns into state 7. From state 7, the DNA-bound protease chain can encounter new transcription-factor containing target chain and further contribute to signal. This could be achieved by increasing the substrate affinity of the protease chain or conversely, lower the substrate affinity of the target chain, as indicated by the difference in arrow thickness in figure 6.
 +
 
 +
<br>
 +
<center><img style="margin-top: 25px; width: 350px;" src="https://static.igem.org/mediawiki/2017/thumb/7/76/UU-model-fig6.png/681px-UU-model-fig6.png"></center>
 +
<span class="text-figure">
 +
<b>Figure 6.</b> Proposed solution to substrate trapping in the target chain. Increased binding affinity of the protease chain towards the DNA substrate would shift the equilibrium between state 7 and 8 towards the desired state 7.
 +
</span>
 +
<br><br>
 +
Substrate affinity is a measure of how strongly the chain will bind the substrate. Ideally, we want the affinity of both to be high because then small amounts of substrate can result in signal producing events. On the other hand, the affinity of the protease chain needs to be higher than that of the target chain as we want the substrate to dissociate from the target chain more, so that there is a higher turnover of target chain.
 +
<br><br>
 +
Fortunately, the two different Cas-like proteins OUTCASST uses as DNA-binding domains already differ in DNA binding affinity; Cas9 binds DNA more strongly than Cpf1. In addition, the used guide RNA can be used to further tune the binding affinities <i class="ref" data-id="1">1</i> <i class="ref" data-id="2">2</i>.
 +
<br><br>
 +
Hence, the proposed optimization could be achieved by using Cpf1 for the target chain and Cas9 for the protease chain. In addition, the affinities also largely depend on the used guide RNA, and choosing appropriate guide RNA can thus be used to modulate this affinity further.
 +
 
 +
<br><br>
 +
 
 +
<b>Optimization of relative protein concentrations</b><br>
 +
 +
This trapping problem could also be tackled by regulating the concentration of target chain that is available. There are two considerations that are important here. First, we want a high amount of target chain to get a high potential for signal. On the other hand, we want a low amount of target chain so there will also be little cleaved target chain to trap the DNA substrate. Thus, there must be an optimum where these two considerations are balanced.
 +
<br><br>
 +
To demonstrate this, we first need to express the behaviour of the system in equations. First off, we assume that the false positive signal has been minimized by optimization of the used protease and thus the mathematical model described here does not contain the false positive signal mechanism.
 +
<br><br>
 +
In this system of ordinary differential equations, the increase or decrease of the state concentrations are given. Here, we consider association and dissociation of complexes and production and decay of the protein chains. The equations below assume a well-mixed system. The flow from state to state can be characterized with the following equations:
 +
<br><br>
 +
 
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2017/b/bc/UuModelingQuationTable.png">
 +
</center>
 +
 
 +
<br><br>
 +
 
 +
There are eight important parameters in these equations. The k1 and k2 rates are the association and dissociation rates between DNA and the target chain. The k3 and k4 are the association and dissociation rates of the protease chain and DNA. k5 gives the effective cleavage rate. pP and pT are the production rates of the protease and target chain and d gives the decay-rate for proteins in general.
 +
<br><br>
 +
The concentration of each state is given by the name of the state in square brackets, such that T stands for target chain, S stands for substrate (DNA), P stands for protease chain, F stands for effector molecule and Tc stands for cleaved target chain. Binding is indicated by ‘:’ between two components.
 +
<br><br>
 +
The first thing we did was to check whether this system of equations behaves the way we expect it to, on short timescales. At first, we were only interested in the system equilibria. At the time-scale of state transitions, protein production and decay per time-unit are negligible and so the values for d, pT and pP were initially set to zero.
 +
<br><br>
 +
Using the association and dissociation constants from Richardson et al. <i class="ref" data-id="3">3</i>, we set the parameters k3 and k4 to 4 * 104 and 5 * 10-5 respectively. Fonfara et al. <i class="ref" data-id="4">4</i> found a range of Cpf1 affinities in the same order of magnitude as Richardson et al. and so we chose to perform several runs with a variety of Cpf1 parameters going from .9 to 1.1 times the rates of Cas9. All runs resulted in similar equilibria where all target chain would be processed and cleaved.
 +
<br><br>
 +
This result is expected from a well-mixed system but, considering the membrane-bound nature of our proteins, the dynamics might not be accurate. Diffusion in the membrane is limited and thus might limit the interactions of the molecules. We made an attempt to illustrate this, too, using a molecular dynamics model but this will be described later on.
 +
<br><br>
 +
We tried to generate bifurcation diagrams for the equilibrium state of our system, using the above set of equations but this was not possible. The numerical bifurcation analysis toolbox we used, a matlab package called <a target=_BLANK href="https://sourceforge.net/projects/matcont/" class="url_external">matcont</a>, would not attain equilibrium convergence. After checking the eigenvectors of the system using <a target=_BLANK href="http://theory.bio.uu.nl/rdb/grind.html" class="url_external">GRIND</a> we determined that the matcont continuation algorithm would indeed not be able to handle this system, as the majority of the system eigenvectors were in the direction of a single variable. To continue, we had to simplify the system of equations.
 +
<br><br>
 +
From these relations, it is already clear that there can only be a stable signal potential, i.e. a stable fraction of the target chains remains uncleaved, when the production of target chain outweighs the decay and cleavage of it, whilst the acquisition of cleaved target chain is balanced by its decay, such that the following conditions apply:
 +
<br><br>
 +
p_T=d ([T]+[T:S]+[T:S:P])+k_5 [T:S:P]
 +
<br><br>
 +
k_5 [T:S:P]=d([T_c]+[T_c:S]+[T_c:S:P])
 +
<br><br>
 +
Which together forms:
 +
<br><br>
 +
p_T=d ([T]+[T:S]+[T:S:P]+[T_c]+[T_c:S]+[T_c:S:P])
 +
<br><br>
 +
However, the concentrations of the intermediary complexes is dependent on the concentration and hence production of protease chain P. We know that, at equilibrium concentrations, the following must hold:
 +
<br><br>
 +
p_P=d([P]+[P:S]+[T:S:P]+[T_c:S:P])
 +
<br><br>
 +
By combining these equations, we can get an expression for T depending on the production, decay and complex concentrations:
 +
<br><br>
 +
[T]=p_T/p_P ([P]+[P:S]+(p_T/p_P -1)([T:S:P]+[T_c:S:P])-([T:S]+[T_c]+[T_c:S])
 +
<br><br>
 +
By assuming that the DNA binding dynamics of the system occur at much faster timescales than protein production and decay, we can assume that the substrate binding of the protease and target chains is at steady state, yielding the following expressions:
 +
<br><br>
 +
[T:S] =  (k_1  [S] [T] + k_4  [T:S:P])/(d + k_2  + k_3  [P])
 +
<br><br>
 +
[T_c:S] =  (k_1  [S] [T_c] + k_4  [T_c:S:P])/(d + k_2  + k_3  [P])
 +
<br><br>
 +
[P:S]=(k_3  [P] [S] + k_2  [T_c:S:P] + k_2  [T:S:P])/(d + k_4  + k_1 ([T] + [Tc]))
 +
<br><br>
 +
We could then substitute these three concentrations for their expressions in the expression of the target chain concentration. Making further quasi steady state assumptions on the formation of the pre-cleavage and post-cleavage complexes reduces the expression by two more dependencies. This was done in mathematica notebook, found <a target=_BLANK href="https://static.igem.org/mediawiki/2017/2/21/UuModelingQSSAWorkouts.txt" class="url_external">here</a>.
 +
<br><br>
 +
[INSERT WILL FOLLOW]
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 +
<br><br>
 +
<h2 class="subhead" id="subhead-4">Effects of diffusion in membrane</h2>
 +
 
 +
<b>Coarse-grained Molecular Modelling for optimization of linker lengths</b><br>
 +
 
 +
Apart from the systems approach to modeling OUTCASST, we sought to investigate the molecular properties of OUTCASST. The idea originated from our concerns about the linkers that connect the transmembrane domains and their respective intra- and extracellular domains. Our hypothesis was that longer linkers facilitate formation of the effective complex between target and protease chain but as discussed above, may also increase false positive rates since the reach of the protease is increased. We thought that there must be an optimum for all linker lengths to maximize the signal-to-noise ratio.
 +
<br><br>
 +
In order to test our hypothesis, we wrote a python script for a 2D coarse-grained Molecular Dynamics simulation of a target and a protease chain in a membrane, illustrating the limitations of diffusion in the membrane. We aimed to test the effect of different linker lengths on the false positive rate on the number of encounters between protease and transcription factor.
 +
<br><br>
 +
Unfortunately, we never we got to test our hypothesis because we had problems to realistically model the linker. In our current approach the linker is represented by a harmonic potential between the membrane domains and the intra- and extracellular domains but we believe that this does not allow for a realistic sampling of conformational space. Ideally, we would want to model the linker in the form of a polymer chain but we never pursued that idea since we put our focus more on a systems approach to OUTCASST.
 +
<br><br>
 +
 
 +
<video onclick="this.paused?this.play():this.pause();" style="width: 100%; cursor: pointer;" controls>
 +
<source src="https://static.igem.org/mediawiki/2017/9/99/UuModelingMDSimulationVid.mp4" type='video/mp4'/>
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<p style="font-style:italic;color:red;border-style:solid;border-width:2px;border-color:red">Your browser either does not support HTML5 or cannot handle MediaWiki open video formats. Please consider upgrading your browser, installing the appropriate plugin or switching to a Firefox or Chrome install.</p>
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</video>
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<br>
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 +
<span class="text-figure">
 +
Video: This short video records a short molecular dynamics simulation run of our python code.
 +
</span>
 +
 
 +
<br><br>
 +
Nevertheless, we showed that our molecular dynamics simulation works conceptually and that the python code could be used as a basis for other teams to theoretically investigate their transmembrane systems. For people who are curious about the inner working of this simulation, have a look in the <a target=_BLANK href="https://static.igem.org/mediawiki/2017/0/06/UuModelingMDSimulationScript.txt" class="url_external">python code</a>. We tried to comment it as clearly as possible. It is also always possible to contact us via email or facebook.
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<br><br>
 +
 
 +
<b>Spatial modelling of protein interactions</b><br>
 +
 
 +
To clarify the importance of membrane diffusion and as a short demonstration, a small cellular automaton model was written in C code, compiled for Ubuntu 16.04. They were made using the <a target=_BLANK href="http://theory.bio.uu.nl/rdb/software.htm" class="url_external">CASH framework</a>. Several editions were generated, each with different production rates for both protein chains. These are provided with a readme file as executable files in a zipped format <a target=_BLANK href="https://static.igem.org/mediawiki/2017/f/f3/UuModelingCAIllustrations.zip" class="url_external">here</a>.
 +
<br><br>
 +
The simulations display two fields. The first in black and white displays DNA objects diffusing in space. The second field in mustard displays the membrane of a cell. On this membrane, blue and red objects spawn that represent target and protease chains respectively. DNA diffuses
 +
four times as fast as the membrane compounds.
 +
<br><br>
 +
When a chain in the membrane field meets a DNA object in a corresponding location in the sample field, they bind. The DNA object is removed and the state of the chain is updated to
 +
a lighter colour to indicate its DNA bound state. DNA release from a chain that had it bound is also possible.
 +
<br><br>
 +
If this chain now encounters a chain of the other colour that is not bound, they can form an effective complex. The effective complex can decay in two ways. It can either fall apart into the two proteins that formed it, or it can result in a release of a protease chain and a cleaved target chain. Either of the release products remains bound to the DNA but not both. In addition, once the cleaved target chain release occurs, a counter is incremented to keep track of how much signal is produced.
 +
<br><br>
 +
In essence, these simulations do not provide much insight that was not already known beforehand but they do make for a nice illustration.
 +
<br><br>
 +
In the zipped folder, you can find five versions. The first number in its name gives the production rate of the protease chain, the second number gives the production rate of the target chain and the third number gives the decay rate of both proteins. All interactions were determined using pseudo-random number generation according to a preset function and prespecified seed.
 +
 
 +
<br><br>
 +
<h2 class="subhead" id="subhead-5">References</h2>
 +
 
 +
<ol class="references">
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<li data-title="Real-time observation of DNA target interrogation and product release by the RNA-guided endonuclease CRISPR Cpf1." data-author="Singh, Mallon, Poddar, Wang, Tipanna, Yang, Bailey and Ha." data-link="http://dx.doi.org/10.1101/205575" /> Singh, Mallon, Poddar, Wang, Tipanna, Yang, Bailey and Ha, 2017: Real-time observation of DNA target interrogation and product release by the RNA-guided endonuclease CRISPR Cpf1. bioRxiv preprint. <a target=_BLANK href="http://dx.doi.org/10.1101/205575" class="url_external"></a>
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<li data-title="Structure and specificity of the RNA-guided endonuclease Cas9 during DNA interrogation, target binding and cleavage." data-author="Josephs, Kocak, Fitzgibbon, McMenemy, Gersbach and Marszalek." data-link="http://dx.doi.org/10.1093/nar/gkv892" /> Josephs, Kocak, Fitzgibbon, McMenemy, Gersbach and Marszalek, 2015: Structure and specificity of the RNA-guided endonuclease Cas9 during DNA interrogation, target binding and cleavage. Nucleic Acids Research, volume 43, number 18, pages 8924-8941. DOI: 10.1093/nar/gkv892. <a target=_BLANK href="http://dx.doi.org/10.1093/nar/gkv892" class="url_external"></a>
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<li data-title="Enhancing homology-directed genome editing by catalytically active and inactive CRISPR-Cas9 using asymmetric donor DNA." data-author="Richardson, C.D., Ray, G.J., DeWitt, M.A., Curie, G.L. & Corn, J.E." data-link="http://dx.doi.org/10.1038/nbt.3481" /> Richardson, C.D., Ray, G.J., DeWitt, M.A., Curie, G.L. & Corn, J.E., 2016: Enhancing homology-directed genome editing by catalytically active and inactive CRISPR-Cas9 using asymmetric donor DNA. Nature Biotechnology, volume 34, number 3. DOI: 10.1038/nbt.3481. <a target=_BLANK href="http://dx.doi.org/10.1038/nbt.3481" class="url_external"></a>
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<li data-title="The CRISPR-associated DNA-cleaving enzyme Cpf1 also processes precursor CRISPR RNA." data-author="Fonfara, I., Richter, H., Bratovič, M., Rhun, A.L. & Charpentier, E." data-link="http://dx.doi.org/10.1038/nature17945" /> Fonfara, I., Richter, H., Bratovič, M., Rhun, A.L. & Charpentier, E., 2016: The CRISPR-associated DNA-cleaving enzyme Cpf1 also processes precursor CRISPR RNA. Nature, volume 532, pages 517-521, doi:10.1038/nature17945. <a target=_BLANK href="http://dx.doi.org/10.1038/nature17945" class="url_external"></a>
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Revision as of 15:09, 1 November 2017

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  • Home
  • Experimental
  • Human practices
  • Team & Sponsors
Cas9 & Cpf1 secretion
and activity
Comparison of endonuclease activity for Cas9 and Cpf1 that has been produced in, and excreted by, HEK293 cells.
MESA two-component system replication
Details on the MESA two-component system, explanation of its relation to our design and the results of its reproduction.
OUTCASST system production
Detailed explanation of the OUTCASST mechanism, experimental progress and technical prospects.
Modeling and
mathematics
Ordinary differential equations, cellular automaton and an object based model for optimal linker-length estimation.
InterLab study participation
Results and details of our measurements for the iGEM 2017 InterLab Study.
Stakeholders & opinions
Interviews and dialogues with stakeholders, potential users, third parties and experts relating to pathogen detection or DNA-based diagnostics.
Risks & safety-issues
Implications and design considerations relating to safety in the usage and implementation of OUTCASST as a diagnostics tool.
Design & integration
OUTCASST toolkit and product design with factors such as bio-safety and user-friendliness taken into account.
Outreach
Videos we made for the dutch public, together with 'de Kennis van Nu'.
Meet our team
About us, our interests and roles in the team and our supervisors.
Sponsors
A listing of our sponsors, how they assisted us and our gratitude for their assistance.
Collaborations
Read about our exchanges with other iGEM teams and government agencies.
Achievements
A short description of all that we have achieved during our participation in the iGEM.
Attributions
A thank-you for everyone that assited us, both in and outside the lab.
Intro
The problem
The system