Team:USTC CHINA/Modeling/ReporterSystem
From 2013.igem.org
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<td >k<sub>0</sub></td> | <td >k<sub>0</sub></td> | ||
- | <td >Constant describes the normal expression rate of | + | <td >Constant describes the normal expression rate of SdpC</td> |
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<td >k<sub>1</sub> </td> | <td >k<sub>1</sub> </td> | ||
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- | Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. | + | Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI. |
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Revision as of 21:34, 26 September 2013
Introduction
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time. Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.User-friendly visualizing system
T-vaccine is also a user-friendly product. Our potential users are not medical professionals. They activate T-vaccine by exposing it to water, and the patch gives visualized signal to notify users whether the status of engineered bacteria is all right and when to stick the patch to arms. We achieve this simply with the regulation of promoter 43,which is recognized by sigma factor A. The activity of promoter 43 is maximal during the exponential growth phase. In other word,s we expect engineered bacillus to express blue pigment a few hours before expressing massive antigens and adjuvants. It is the perfect time. When the product being used, user shall stick the Sticker to the skin when the blue pigment displayed.So the system is visualized and user-friendly.Results
①![](https://static.igem.org/mediawiki/2013/thumb/f/fc/Reporter_1.jpg/750px-Reporter_1.jpg)
Improving
In our experiment , we discovered that the promoter P43 is too weak to express amilCP for a blue-color display. So we redesigned the circuits , aiming to find a more feasible plan, and test the part amilCP simultaneously. The new disign contains two circuits:1 Pgrac-amilCP-Terminator
We use the Promoter grac , a promotor with lac promotor ,on the PHT vector to express amilCP, instead of Promoter 43. The Promoter grac is strong enough ,so we can easily see the results theoretically.![](https://static.igem.org/mediawiki/2013/thumb/a/ae/Reporter_2.jpg/750px-Reporter_2.jpg)
2 P43-amilcp-SigB-Terminator
We plan to use a positive feedback to magnify the expressing of amilCP. Because the P43 is a sigma B factor binding promotor, we designed a circuit, that the P43 is fused to the sigma B factor. We hope this could increase the response of P43. Course of time limitation, we haven’t put this design to experiment.Designing of the suicide system
We design a circuit of killing switch based on its endogenous genetic system. In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.![](https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png)
Results
![](https://static.igem.org/mediawiki/2013/thumb/c/c1/Reporter_4.jpg/750px-Reporter_4.jpg)
![](https://static.igem.org/mediawiki/2013/thumb/0/0c/Reporter_5.jpg/750px-Reporter_5.jpg)
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.
The ODE model of singular cells
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:Mark | Meaning |
Imax | Mole number of free SdpI in cytoplasm. |
Im | Mole number of SdpI in the cell membrane. |
Cf | Mole number of free SdpC in cytoplasm. |
Ci | Mole number of SdpC captured by SdpI. |
Rf | Mole number of free SdpR in cytoplasm. |
Ri | Mole number of SdpR captured by SdpI |
![](https://static.igem.org/mediawiki/2013/b/bb/For1.png)
![](https://static.igem.org/mediawiki/2013/a/aa/For2.png)
![](https://static.igem.org/mediawiki/2013/9/9a/For3.png)
![](https://static.igem.org/mediawiki/2013/7/71/For4.png)
![](https://static.igem.org/mediawiki/2013/7/7e/For5.png)
![](https://static.igem.org/mediawiki/2013/7/70/For6.png)
Mark | Meaning |
Imax | The maximal number of SdpI than can be fixed on the cell membrane. |
k0 | Constant describes the normal expression rate of SdpC |
k1 | Constant describes the self-repression effects of SdpC |
k2 | Constant describes the repression of SdpR on the expression of SdpC. |
k3 | Constant describes the rate of SdpI capturing SdpC |
k4 | Constant describes the normal expression rate of SdpR |
k5 | Constant describes the self-repression effects of SdpR |
k6 | Constant describes the rate of SdpI capturing SdpR |
k7 | Constant describes the normal expression rate of SdpI |
k8 | Constant describes the self-repression effects of SdpI |
k9 | Constant describes the repression of SdpR on the expression of SdpI |
k10 | Constant describes the rate of SdpI binding to the cell membrane |
Discussions on the constants
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k0 by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system. Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:- k0>>k4≈k7: k0,k4 and k7 represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;
- k2>>k9: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;
- k10>>k3,k6:it is hard to predict the value of k3 and k8, yet we suppose both of them is much smaller than k10 because SdpI is a kind of membrane protein inherently, and rarely exists as free protein
- The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally
Stimulation and discussion
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers. When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:k0 | k1 | k2 | k3 | k4 | k5 | k6 | k8 | k8 | k9 | k10 | Imax | Cf0 | Rf0 | If0 | Im0 | Ci0 | Ri0 |
50 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 20 | 500 | 5 | 5 | 1 | 5 | 3 | 2 |
![](https://static.igem.org/mediawiki/2013/2/26/Suicide1.png)
![](https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png)
k0 | k1 | k2 | k3 | k4 | k5 | k6 | k8 | k8 | k9 | k10 | Imax | Cf0 | Rf0 | If0 | Im0 | Ci0 | Ri0 |
100 | 5 | 5 | 5 | 5 | 5 | 5 | 20 | 5 | 5 | 20 | 500 | 5 | 5 | 1 | 5 | 3 | 2 |
![](https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png)
k0 | k1 | k2 | k3 | k4 | k5 | k6 | k8 | k8 | k9 | k10 | Imax | Cf0 | Rf0 | If0 | Im0 | Ci0 | Ri0 |
100 | 5 | 5 | 5 | 5 | 5 | 5 | 20 | 5 | 5 | 20 | 500 | 5 | 5 | 1 | 5 | 3 | 2 |
![](https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png)
k0 | k1 | k2 | k3 | k4 | k5 | k6 | k8 | k8 | k9 | k10 | Imax | Cf0 | Rf0 | If0 | Im0 | Ci0 | Ri0 |
400 | 5 | 5 | 5 | 5 | 5 | 5 | 20 | 5 | 5 | 20 | 500 | 5 | 5 | 1 | 5 | 3 | 2 |
![](https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png)
![](https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png)
k0 | k1 | k2 | k3 | k4 | k5 | k6 | k8 | k8 | k9 | k10 | Imax | Cf0 | Rf0 | If0 | Im0 | Ci0 | Ri0 |
0 | 5 | 5 | 5 | 5 | 5 | 5 | 30 | 5 | 5 | 20 | 500 | 8 | 5 | 1 | 5 | 3 | 2 |
![](https://static.igem.org/mediawiki/2013/1/19/Suicide7.png)
k0 | k1 | k2 | k3 | k4 | k5 | k6 | k8 | k8 | k9 | k10 | Imax | Cf0 | Rf0 | If0 | Im0 | Ci0 | Ri0 |
0 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 20 | 500 | 8 | 5 | 1 | 5 | 3 | 2 |
![](https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png)
![](https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png)
- The character of free SdpC is most affected by k0, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;
- The influence of the value of Imax and k2 is much limited;
- The amount of free SdpI is always near zero;
- SdpC will not increase limitlessly however we transform parameters;
- To ensure the success of suicide, it is required k0>>k4>>k7; The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.
Discussion on colonies
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules. As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.References
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008
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