Team:USTC CHINA/Modeling/ReporterSystem

From 2013.igem.org

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<h1>The ODE model of singular cells</h1>
<h1>The ODE model of singular cells</h1>
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 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.</br></br>
+
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:</br></br>
 +
<table border="1">
 +
  <tr>
 +
    <td >Name</td>
 +
    <td >Meaning</td>
 +
  </tr>
 +
  <tr>
 +
    <td >I<sub>max</sub> </td>
 +
    <td >The maximal number    of SdpI than can be fixed on the cell membrane.</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k0</td>
 +
    <td >Constant    describes the normal expression rate of SdpI</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>10</sub> </td>
 +
    <td >Constant    describes the self-repression effects of SdpI</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>2</sub> </td>
 +
    <td >Constant    describes the repression of SdpR on the expression of SdpC.</a></td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>4</sub> </td>
 +
    <td >Constant    describes the rate of SdpI capturing SdpC</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>4</sub> </td>
 +
    <td >Constant describes the normal expression rate of SdpR</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>5</sub> </td>
 +
    <td >Constant    describes the self-repression effects of SdpR</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>6</sub> </td>
 +
    <td >Constant describes    the rate of SdpI capturing SdpR</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>7</sub> </td>
 +
    <td >Constant describes the normal expression rate of SdpI</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>8</sub> </td>
 +
    <td >Constant describes    the self-repression effects of SdpI</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>9</sub> </td>
 +
    <td >Constant describes the repression of SdpR on the expression of SdpI</td>
 +
  </tr>
 +
  <tr>
 +
    <td >k<sub>10</sub> </td>
 +
    <td >Constant describes    the rate of SdpI binding to the cell membrane</td>
 +
  </tr>
 +
</table>
 +
 

Revision as of 16:51, 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



B.subtilis Plasmid PHT43+p43+amilCP
Colony PCR 14 single clones

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.

pgrac-amilCP overlap PCR(Right Three) PSBC3(Left Four )

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.

We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device. We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.

Results


Colony PCR E.coli PHT43 + Promotor grac + SdpABC

PHT43 + Promotor SdpRI + SdpABC Enzyme digestion


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:

Name Meaning
Imax The maximal number of SdpI than can be fixed on the cell membrane.
k0 Constant describes the normal expression rate of SdpI
k10 Constant describes the self-repression effects of SdpI
k2 Constant describes the repression of SdpR on the expression of SdpC.
k4 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

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