Model for comS diffusion system

Summary

Design

Model

LacI

We use 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 - comS

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 - comK

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 comS as the signaling molecule going through the nanotubes.

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