Difference between revisions of "Team:ETH Zurich/Switch Module"
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1) \quad & k_{mRNAint} \cdot P_{hyb}^{ON} \\ | 1) \quad & k_{mRNAint} \cdot P_{hyb}^{ON} \\ | ||
2) \quad & k_{Bxb1} \cdot mRNA_{int} \\ | 2) \quad & k_{Bxb1} \cdot mRNA_{int} \\ | ||
| − | 3) \quad & k_{DBxb1} \cdot Bxb1 \cdot (Bxb1-1) | + | 3) \quad & k_{DBxb1} \cdot Bxb1 \cdot (Bxb1-1) \\ |
& k_{-DBxb1} \cdot DBxb1\\ | & k_{-DBxb1} \cdot DBxb1\\ | ||
4) \quad & 2 \cdot k_{attBP} \cdot S_0 \cdot DBxb1 \\ | 4) \quad & 2 \cdot k_{attBP} \cdot S_0 \cdot DBxb1 \\ | ||
| Line 246: | Line 246: | ||
<div> | <div> | ||
<h2>RESULTS</h2> | <h2>RESULTS</h2> | ||
| + | <h3>INTEGRASE STOCHASTIC MODEL</h3> | ||
| + | <p>Based on the known mechanics of integrases we developed a novel stochastic model for integrases capturing the mechanics of the switching process. Figure 5 shows an example simulation of the switching process. We planned to use the stochastic model for estimating the parameters of the model using the <a href="https://2016.igem.org/Team:ETH_Zurich/Parameters">INSIGHT</a> tool. Unfortunately the flow cytometry data of the recombinase couldn't be collected in time for performing the estimation before the wiki freeze.</p> | ||
| + | |||
| + | <div class="image_box full_size"> | ||
| + | <a href="https://2016.igem.org/File:T--ETH_Zurich--switch_comparison.png"> | ||
| + | <img src="https://static.igem.org/mediawiki/2016/4/43/T--ETH_Zurich--switch_comparison.png"> | ||
| + | </a> | ||
| + | <p><b>Figure 3:</b> Stochastic simulation of the switch. The plots show the evolution of the four possible states of a slipping cassette. In this case 1000 trajectories (colored) were simulated. The mean behavior of the population is shown in black.</p> | ||
| + | </div> | ||
<h3>DESIGN IMPROVEMENTS</h3> | <h3>DESIGN IMPROVEMENTS</h3> | ||
| Line 256: | Line 265: | ||
<img src="https://static.igem.org/mediawiki/2016/4/43/T--ETH_Zurich--switch_comparison.png"> | <img src="https://static.igem.org/mediawiki/2016/4/43/T--ETH_Zurich--switch_comparison.png"> | ||
</a> | </a> | ||
| − | <p><b>Figure | + | <p><b>Figure 4:</b> Comparison of the behavior of two designs of the switch in leakiness and activation conditions. The new design is clearly more suitable for our system.</p> |
</div> | </div> | ||
| − | <p>Figure | + | <p>Figure 4 shows the differences in the qualitative bahavior. The plots qualitatively describe the percentage of flipped cassettes over 6 hours. The simulation proves that the new design is slighlty more sensible to leakiness (0.2% over 6 hours) but takes the percentage of switched cassettes from 80% to 100%. Since 20% is an important difference in the signal, we discarded the initial design and implemented the new one.</p> |
<h3 id="tuning">TUNING FOR THE TARGET EXPOSURE TIME</h3> | <h3 id="tuning">TUNING FOR THE TARGET EXPOSURE TIME</h3> | ||
| Line 270: | Line 279: | ||
<img src="https://static.igem.org/mediawiki/2016/5/5c/T--ETH_Zurich--sensitivity_activation.png"> | <img src="https://static.igem.org/mediawiki/2016/5/5c/T--ETH_Zurich--sensitivity_activation.png"> | ||
</a> | </a> | ||
| − | <p><b>Figure | + | <p><b>Figure 5:</b> Sensitivity of the promoter switching towards the main parameters. The integrase RBS strength (k_Bxb1) and the strength of the integrase degradation tag (d_Bxb1, d_DBxb1) are biologically tunable parameters and have significant influence on the response of the switch to activation.</p> |
</div> | </div> | ||
| Line 277: | Line 286: | ||
<img src="https://static.igem.org/mediawiki/2016/8/80/T--ETH_Zurich--sensitivity_leakiness.png"> | <img src="https://static.igem.org/mediawiki/2016/8/80/T--ETH_Zurich--sensitivity_leakiness.png"> | ||
</a> | </a> | ||
| − | <p><b>Figure | + | <p><b>Figure 6:</b> Sensitivity of the promoter switching towards the main parameters in leakiness conditions. The integrase RBS strength (k_Bxb1) and the strength of the integrase degradation tag (d_Bxb1, d_DBxb1) are biologically tunable parameters and have significant influence on the response of the switch to leakiness.</p> |
</div> | </div> | ||
| − | <p>Figure | + | <p>Figure 5 and 6 shows which parameters have the greatest influence on the final state of the system in response to both activation of the AND gate and leakiness. We decide to tune the integrase RBS strength (k_Bxb1) and the strength of the integrase degradation tag (d_Bxb1, d_DBxb1), since they are sensitive and biologically tunable.</p> |
<h4>REQUIREMENTS</h4> | <h4>REQUIREMENTS</h4> | ||
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</li> | </li> | ||
<li> | <li> | ||
| − | <p><i>When the AND gate activates in presence of the inflammation and candidate markers, the system must switch to the on state within 8 hours. A system in the on state has > | + | <p><i>When the AND gate activates in presence of the inflammation and candidate markers, the system must switch to the on state within 8 hours. A system in the on state has >80% of flipped reporters promoters on average.</i></p> |
<p>The intensity and placement of inflamations in the gut vary a lot between different patients and types of IBDs. Based on the available informations seems to be a reasonable average of the total exposure time<sup> <a href="#cit2" class="cit">2</a>, <a href="#cit3" class="cit">3</a></sup>.</p> | <p>The intensity and placement of inflamations in the gut vary a lot between different patients and types of IBDs. Based on the available informations seems to be a reasonable average of the total exposure time<sup> <a href="#cit2" class="cit">2</a>, <a href="#cit3" class="cit">3</a></sup>.</p> | ||
</li> | </li> | ||
| Line 299: | Line 308: | ||
</ol> | </ol> | ||
| − | <h4> | + | <h4>RESULTING SPECIFICATIONS</h4> |
<p>We assume that our sensor is only slightly leaky (1%) and that Bxb1 degrades at the same rate in monomer and dimerized form. We identify constraints on the ratio $r=\frac{k_{Bxb1}}{d_{Bxb1}}$ between RBS strenght and degradation rate respecting the first two requirements as follows:</p> | <p>We assume that our sensor is only slightly leaky (1%) and that Bxb1 degrades at the same rate in monomer and dimerized form. We identify constraints on the ratio $r=\frac{k_{Bxb1}}{d_{Bxb1}}$ between RBS strenght and degradation rate respecting the first two requirements as follows:</p> | ||
<ol> | <ol> | ||
| Line 305: | Line 314: | ||
<li>We simulate the system for 4 days, the system is affected by leakiness and is exposed to strong inflammation (the sensor promoter is completely on) for 8 hours. The second requirement is satisfied for $r \leq 1.4$.</li> | <li>We simulate the system for 4 days, the system is affected by leakiness and is exposed to strong inflammation (the sensor promoter is completely on) for 8 hours. The second requirement is satisfied for $r \leq 1.4$.</li> | ||
</ol> | </ol> | ||
| − | <p>This gives us a linear region | + | <div class="image_box full_size"> |
| + | <a href="https://2016.igem.org/File:T--ETH_Zurich--switch_tuning.png"> | ||
| + | <img src="https://static.igem.org/mediawiki/2016/0/0a/T--ETH_Zurich--switch_tuning.png"> | ||
| + | </a> | ||
| + | <p><b>Figure 7:</b> <b>Left:</b> Functional regions of the parameter space satisfying the first two requirements. <b>Right:</b> The intersection of the two regions defines a range of parameter ratios that allows the switch to function as required.</p> | ||
| + | </div> | ||
| + | <p>Figure 7 shows the contrains and the final feasible region. This gives us a linear region that defines the feasible ratios $r$ for our switch.</p> | ||
<p>Assuming that after exposure the integrase mRNA concentration reaches steady state quickly we can express the steady state of Bxb1 as:</p> | <p>Assuming that after exposure the integrase mRNA concentration reaches steady state quickly we can express the steady state of Bxb1 as:</p> | ||
<p>\begin{align*} | <p>\begin{align*} | ||
| − | [Bxb1]_{SS} = \frac{k_{Bxb1}\cdot mRNA_{int}}{d_{Bxb1}}\cdot\left(1-e^{-d_{Bxb1}\cdot t}\right) | + | [Bxb1]_{SS} = \frac{k_{Bxb1}\cdot [mRNA_{int}]}{d_{Bxb1}}\cdot\left(1-e^{-d_{Bxb1}\cdot t}\right) |
\end{align*}</p> | \end{align*}</p> | ||
| − | <p>The equation above is the analytical solution of the ODEs for simple production-degradation systems and tells us that the degradation rate is the only factor determining how quickly steady state is reached. Since at higher concentrations of Bxb1 we have | + | <p>The equation above is the analytical solution of the ODEs for simple production-degradation systems and tells us that the degradation rate is the only factor determining how quickly steady state is reached. Since at higher concentrations of Bxb1 we have faster flipping, we can satisfy the third requirement by maximizing the degradation rate.</p> |
| − | |||
<p>Given the above results, we informed the experimentalists that an optimal system should have maximal degradation rate under the constraint that: | <p>Given the above results, we informed the experimentalists that an optimal system should have maximal degradation rate under the constraint that: | ||
\begin{align*} | \begin{align*} | ||
Revision as of 20:52, 19 October 2016
SWITCH MODULE
OVERVIEW
Figure 1: The memory element of our circuit: the switch module.
The switch is the memory element of our circuit. We designed and tested different variants, all of them are based on editing of the plasmids (integrase-based switches) or of the chromosome (CRISPR-based switches).
In general switches are binary elements. However, in biological systems switching doesn't happen at the same time on different plasmids and in different cells. We exploit this property to obtain quantitative outputs by relating the measured fluorescence to the exposure time/concentration of the sensed molecules.
A key concern during the design of the system was the leakiness of the AND gate in the sensor module. We use the model to tune our switch so that we minimize the risk of false positives and optimize the kinetics for the expected exposure time. Moreover the model allowed us to identify a flaw in the original design of the circuit and validate the improved version.
GOALSGOALS
- Provide a proof that the switch can work as expected.
- Assist the design of the switch.
- Optimize the parameters for the requirements of our application.
- Model the kinetics of the integrase.
MODEL
Figure 2: Integrase switch design, the same design applies to Bxb1, Tp901 and PhiC31. Click to enlarge.
The switch is based on the integrase family of recombinases. On this page we focus on the Bxb1 integrase, but the same model and analysis applies to Tp901 and PhiC31.
From the literature1, the mechanics of the integrase appear to be well known. When the AND gate in the sensor module activates, Bxb1 is expressed and dimerizes. In its dimerized form, Bxb1 can bind to the attB and attR binding sites placed around the Pout promoter. When both sites are occupied, synapsis between the two can happen, enabling flipping.
The flipping process changes the direction of the reporter promoter and transforms the attB and attP sites in attL and attR. At this point the switch is in the ON state, Bxb1 dimers can still bind to the attL and attR sites, but wihtout flipping DNA again.
The following section describes the species and reactions involved.
REACTIONS
\begin{align*} 1) && P_{hyb} & \rightarrow P_{hyb} + mRNA_{int} \\ 2) && mRNA_{int} & \rightarrow mRNA_{int} + Bxb1 \\ 3) && Bxb1 + Bxb1 & \rightleftharpoons DBxb1 \\ 4) && S_0 + DBxb1 & \rightleftharpoons S_1 \\ 5) && S_1 + DBxb1 & \rightleftharpoons S_2 \\ 6) && S_2 & \rightarrow P^{switched} \\ 7) && attLR_0 + DBxb1 & \rightleftharpoons attLR_1 \\ 8) && mRNA_{int} & \rightarrow \\ 9) && Bxb1 & \rightarrow \\ 10) && DBxb1 & \rightarrow \\ \end{align*}SPECIES
| Name | Description |
|---|---|
| $P_{hyb}$ | Active AND gate hybrid promoter |
| $mRNA_{int}$ | mRNA of the integrase |
| $Bxb1$ | Integrase protein |
| $DBxb1$ | Dimerized form of the integrase protein |
| $S_{0}$ | Plasmid with free attB and attP sites. |
| $S_{1}$ | Plasmid with DBxb1 bound to the attB or attP site. |
| $S_{2}$ | Plasmid with DBxb1 bound to both the attB and attP sites. |
| $P_{switched}$ | Plasmid with switched reporter promoter. |
| $attLR_0$ | Free attL or attR site of a switched plasmid. |
| $attLR_1$ | attL or attR site of a switched plasmid with DBxb1 bound. Can be expressed as $attLR_1=2\cdot P_{switched}-attLR_0$. |
STOCHASTIC REACTION RATES:
\begin{align*} 1) \quad & k_{mRNAint} \cdot P_{hyb}^{ON} \\ 2) \quad & k_{Bxb1} \cdot mRNA_{int} \\ 3) \quad & k_{DBxb1} \cdot Bxb1 \cdot (Bxb1-1) \\ & k_{-DBxb1} \cdot DBxb1\\ 4) \quad & 2 \cdot k_{attBP} \cdot S_0 \cdot DBxb1 \\ & k_{-attBP} \cdot S_1 \\ 5) \quad & k_{attBP} \cdot S_1 \cdot DBxb1 \\ & 2 \cdot k_{-attBP} \cdot S_2 \\ 6) \quad & k_{flip} \cdot S_2 \\ 7) \quad & k_{attLR} \cdot attLR_0 \cdot DBxb1 \\ & k_{-attLR} \cdot attLR_1 \\ 8) \quad & d_{mRNAint} \cdot mRNA_{int} \\ 9) \quad & d_{Bxb1} \cdot Bxb1 \\ 10) \quad & d_{DBxb1} \cdot DBxb1 \\ \end{align*}
PARAMETERS
| Name | Description |
|---|---|
| $P_{hyb}^{ON}$ | Fraction of the maximal activity of the hybrid AND gate promoter. This value is computed by the sensor module. |
| $k_{mRNAint}$ | Integrase mRNA transcription rate. |
| $k_{Bxb1}$ | Bxb1 translation rate. |
| $k_{DBxb1}$ | Bxb1 dimerization rate. |
| $k_{-DBxb1}$ | DBxb1 dissociation rate. |
| $k_{attBP}$ | Binding rate of DBxb1 to an attB or attP site. |
| $k_{-attBP}$ | Dissociation rate of DBxb1 from an attB or attP site. |
| $k_{attLR}$ | Binding rate of DBxb1 to an attL or attR site. |
| $k_{-attLR}$ | Dissociation rate of DBxb1 from an attL or attR site. |
| $k_{flip}$ | Flipping rate of a plasmid in the $S_2$ state. |
RESULTS
INTEGRASE STOCHASTIC MODEL
Based on the known mechanics of integrases we developed a novel stochastic model for integrases capturing the mechanics of the switching process. Figure 5 shows an example simulation of the switching process. We planned to use the stochastic model for estimating the parameters of the model using the INSIGHT tool. Unfortunately the flow cytometry data of the recombinase couldn't be collected in time for performing the estimation before the wiki freeze.
Figure 3: Stochastic simulation of the switch. The plots show the evolution of the four possible states of a slipping cassette. In this case 1000 trajectories (colored) were simulated. The mean behavior of the population is shown in black.
DESIGN IMPROVEMENTS
We used the model to suggest important changes to the initial design of the system. In the initial version of the system, the integrase gene was placed inside the flipping cassette. This choice was taken with the intention to reduce the effect of the leakiness: on the plasmids where the cassette with the gene is flipped, the integrase protein is not expressed anymore. We expected cells where leakiness causes partial switching to express less integrase and thus reduce further switching.
However, simulations of the system showed that this approach indeed reduces switching under leakiness conditions, but it also makes more difficult to reach complete switching when the AND gate is fully active. We proposed a different design in which the integrase gene and the flipping cassette are placed on different plasmids and compares its behavior with the initial design.
Figure 4: Comparison of the behavior of two designs of the switch in leakiness and activation conditions. The new design is clearly more suitable for our system.
Figure 4 shows the differences in the qualitative bahavior. The plots qualitatively describe the percentage of flipped cassettes over 6 hours. The simulation proves that the new design is slighlty more sensible to leakiness (0.2% over 6 hours) but takes the percentage of switched cassettes from 80% to 100%. Since 20% is an important difference in the signal, we discarded the initial design and implemented the new one.
TUNING FOR THE TARGET EXPOSURE TIME
In the context of IBD investigation, we have specific requirements for our system. Informally, the aim is to minimize the chance of false positives due to leakiness and to optimize the switching time for the expected exposure time.
In order to determine which parameters of the system can be tuned for our purpose, we perform a sensitivity analysis of the percentage of switched reporter promoters towards the main parameters. This allows us to indentify the parameters that have the greatest influence on the final state of the system.
Figure 5: Sensitivity of the promoter switching towards the main parameters. The integrase RBS strength (k_Bxb1) and the strength of the integrase degradation tag (d_Bxb1, d_DBxb1) are biologically tunable parameters and have significant influence on the response of the switch to activation.
Figure 6: Sensitivity of the promoter switching towards the main parameters in leakiness conditions. The integrase RBS strength (k_Bxb1) and the strength of the integrase degradation tag (d_Bxb1, d_DBxb1) are biologically tunable parameters and have significant influence on the response of the switch to leakiness.
Figure 5 and 6 shows which parameters have the greatest influence on the final state of the system in response to both activation of the AND gate and leakiness. We decide to tune the integrase RBS strength (k_Bxb1) and the strength of the integrase degradation tag (d_Bxb1, d_DBxb1), since they are sensitive and biologically tunable.
REQUIREMENTS
An interesting feature of our switch is the fact that it's based on multiple plasmid copies, and can thus contain quantitative information.
-
When the inflammation and cadidate marker are not present, the switch must be off for at least 4 days. A system in the off state is defined to have <20% of flipped reporter promoters on average.
This is necessary to minimize the effect of leakiness from the AND gate. 4 days have been fixed basing on the available estimates of stool transit times in the human body 2.
-
When the AND gate activates in presence of the inflammation and candidate markers, the system must switch to the on state within 8 hours. A system in the on state has >80% of flipped reporters promoters on average.
The intensity and placement of inflamations in the gut vary a lot between different patients and types of IBDs. Based on the available informations seems to be a reasonable average of the total exposure time 2, 3.
-
The response of the system must be as quick as possible.
It looks like in some cases there are many, short inflamated regions 3. A quick response is desirable for detecting them.
RESULTING SPECIFICATIONS
We assume that our sensor is only slightly leaky (1%) and that Bxb1 degrades at the same rate in monomer and dimerized form. We identify constraints on the ratio $r=\frac{k_{Bxb1}}{d_{Bxb1}}$ between RBS strenght and degradation rate respecting the first two requirements as follows:
- We simulate the system for 4 days without applying any signal, only leakiness causes switching. The first requirement is satisfied for $r \geq 0.08$.
- We simulate the system for 4 days, the system is affected by leakiness and is exposed to strong inflammation (the sensor promoter is completely on) for 8 hours. The second requirement is satisfied for $r \leq 1.4$.
Figure 7: Left: Functional regions of the parameter space satisfying the first two requirements. Right: The intersection of the two regions defines a range of parameter ratios that allows the switch to function as required.
Figure 7 shows the contrains and the final feasible region. This gives us a linear region that defines the feasible ratios $r$ for our switch.
Assuming that after exposure the integrase mRNA concentration reaches steady state quickly we can express the steady state of Bxb1 as:
\begin{align*} [Bxb1]_{SS} = \frac{k_{Bxb1}\cdot [mRNA_{int}]}{d_{Bxb1}}\cdot\left(1-e^{-d_{Bxb1}\cdot t}\right) \end{align*}
The equation above is the analytical solution of the ODEs for simple production-degradation systems and tells us that the degradation rate is the only factor determining how quickly steady state is reached. Since at higher concentrations of Bxb1 we have faster flipping, we can satisfy the third requirement by maximizing the degradation rate.
Given the above results, we informed the experimentalists that an optimal system should have maximal degradation rate under the constraint that: \begin{align*} 0.08 \leq \frac{k_{Bxb1}}{d_{Bxb1}} \leq 1.4 \end{align*} Moreover we suggested to choose, between the different AND gate designs, the one with the higher fold-change activation. Given the shape of the feasibel parameter space this property is preferable over absolute activation.
REFERENCES
- [1] Singh, Shweta, Pallavi Ghosh, and Graham F. Hatfull. "Attachment site selection and identity in Bxb1 serine integrase-mediated site-specific recombination." PLoS Genet 9.5 (2013): e1003490.
- [2] Friend, David R. "New oral delivery systems for treatment of inflammatory bowel disease." Advanced drug delivery reviews 57.2 (2005): 247-265.
- [3] Rutgeerts, Paul, Gaston Vantrappen, and Karel Geboes. "Endoscopy in inflammatory bowel disease." Scandinavian Journal of Gastroenterology 24.sup170 (1989): 12-15.
Thanks to the sponsors that supported our project:
