Model for T7 RNA polymerase diffusion

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

The parameters used in this model are:

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