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Team:Paris Bettencourt/Modeling/T7 diffusion
From 2011.igem.org
Model for T7 RNA polymerase diffusion
Abstract
Design
The T7 diffusion design is our first original construct. In this design, the T7 RNA polymerase acts both as the signal transmited and as the amplifier (auto-amplification). T7 RNA polymerase is produced in the emitter cell, then diffuses through the nanotubes and arrives in the receiver cell. In this cell, the T7 RNA polymerase activates on a pT7 promoter. Behind this promoter, we put a gene coding for the same T7 RNA polymerase (amplifier) and for GFP (reporter).
This construction was put in two different settings. One is what we just described, where the emitting gene network is in one cell and the receiving gene network is in another. In the other construction, everything is in one cell. We use the second construct as a control to really see the impact of the cell-to-cell communication on the behaviour of the cells.
We ran our models for those two configurations. We used a steady flow of signaling molecules in the receiver cell for the "one emitting cell - one receiving cell" construction. You can find our justifications about this assumption here.
Model
LacI
We use the ''LacI'' as a repressor for the emitter gene construct. LacI repression can be cancelled by ''IPTG''. This way we can induce production of RFP and ''T7''' by puttig ''IPTG'' on the cells.
Inactivated LacI can not repress the pLAC promoter anymore. Note that we consider that the reaction between IPTG and LacI fires without any delay. This assumption is justified by the fact that this reaction is much faster than any other in our gene network.
Emitter gene construct - T7'
The emitter gene construct is modeled by the following equations:
The reporter for the emitter gene construct (RFP) is modeled by the following equations:
Receiver and amplification gene construct - T7''
The receiver and amplification gene construct is modeled by the following equations:
The reporter for the receiver and amplification gene construct (GFP) is modeled by the following equations:
Parameters
This design relies on the T7 RNA polymerase (which is noted T7) both as the signaling molecule going through the nanotubes and as the auto-amplification system when it acts on the pT7 promoter. In our equations however, we chose to distinguish these functions.
- T7' represents the signaling T7 RNA polymerase
- T7'' represents is the auto-amplifying molecule
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The parameters used in this model are:
| Parameter | Description | Value | Unit | Reference |
|---|---|---|---|---|
 |
Active LacI concentration (LacI which is not inactivated by IPTG) | NA | molecules per cell |
Notation convention |
 |
IPTG concentration | NA | molecules per cell |
Notation convention |
 |
Inactived LacI concentration | NA | molecules per cell |
Notation convention |
 |
Total LacI concentration | TBD | molecules per cell |
Steady state for equation |
 |
T7 RNA polymerase (emitter, T7') concentration | NA | molecules per cell |
Notation convention |
 |
mRNA associated with T7' concentration | NA | molecules per cell |
Notation convention |
 |
T7 RNA polymerase (auto-amplification, T7'') concentration | NA | molecules per cell |
Notation convention |
 |
mRNA associated with T7'' concentration | NA | molecules per cell |
Notation convention |
 |
Maximal production rate of pVeg promoter (constitutive) | ??? | molecules.s-1 or pops |
Estimated |
 |
Maximal production rate of pLac promoter | 0.02 | molecules.s-1 or pops |
Estimated |
 |
Maximal production rate of pT7 promoter | 0.02 | molecules.s-1 or pops |
Estimated |
 |
Dissociation constant for IPTG to LacI | 1200 | molecules per cell |
Aberdeen 2009 wiki |
 |
Dissociation constant for LacI to LacO (pLac) | 700 | molecules per cell |
Aberdeen 2009 wiki |
 |
Dissociation constant for T7 RNA polymerase to pT7 | 3 | molecules per cell |
Estimated ADD EXPLANATION |
 |
Translation rate of proteins | 1 | s-1 | Estimated ADD EXPLANATION |
 |
Dilution rate in exponential phase | 2.88x10-4 | s-1 | Calculated with a 40 min generation time. See explanation |
 |
Degradation rate of mRNA | 2.88x10-3 | s-1 | Uri Alon (To Be Confirmed) |
 |
Delay due tT7 RNA polymerase production and maturation | 300 | s | http://mol-biol4masters.masters.grkraj.org/html/Prokaryotic_DNA_Replication13-T7_Phage_DNA_Replication.htm |
 |
Delay due to mRNA production | 30 | s | http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=104902&ver=5&hlid=58815 2kb/(50b/s) --> approximation: all our contructs are around 2kb |
Results & discussions
We launched this simulation in matlab and obtained the following results:
Matlab simulation for the T7 polymerase construct (all in one cell)
The behaviour of the cell is as expected. The IPTG input triggers the mRNA T7' production, which then is translated in T7'. This T7' polymerase activates the mRNA T7'' production. Finally, this last mRNA is translated into T7''.
This is exactly the results we wanted. The T7 RNA polymerase acts both as a transmission molecule and an amplifier. Once the pT7 is activated it auto-amplifies itself and gives us a clear result.
The IPTG imput is here theoritical. We can not in an experiment remove the IPTG from the medium. However, this input signal is an excellent way to understand the way the system behaves. After IPTG disappears, we can see the levels of mRNA T7' and T7' decreasing as expected since they are regulated by pHyperSpank. On the other hand, mRNA T7'' and T7'' regulated by pT7 are not affected.
Limits
The most obvious limit is that we supposed the pT7 promoter to be not leaky at all, since it needs very little T7 RNA polymerase to be activated. If the leak is too important in pratice the model and the design might need some adjustments.
Most parameters are well defined, but promoter strengths tend to be quite difficult to find or to evaluate. In this model, changing moderately these strengths does not impact much on the overall behaviour of the system. It could be troubling however in our experiments with two cells if very few T7 RNA polymerase pass through the nanotubes.
