Team:KULeuven/Modeling

Modeling Overview

1. Description of the whole system

To make predictions for are plasmid transformed E.coli, a structured segregated model is designed in Simbiology. A graphical representation of the model was build in the block diagram editor . Afterwards reaction equations and parameters were added. We designed one model for the whole system and 3 models for 3 subsystems. The 3 subsystems are antifreeze, freeze and cell death. For more information about these 3 subsystems, we refer to the extended project description and the 3 modelling pages: freeze, antifreeze and cell death.

2. Full Model

There are in total 5 different kinetic equations we used in the model Transcription equation For most promoters, hill kinetics is used, it is a way of quantitatively describing cooperative binding processes, it was developed for hemoglobin in 1913. A Hill coefficient (n) is a measure for the cooperativity. Translation equation RNA degradation Protein degration Assimiliation

3. Simulation tests

In the table below the parameters for our full model are displayed. However it was hard to find accurate parameters, because databases for kinetic parameters are limiting.

The parameters used in this model are:

Parameter	Description	Value	Reference
	Active LacI concentration (LacI which is not inactivated by IPTG)	NA	Notation convention
	IPTG concentration	NA	Notation convention
	Inactived LacI concentration	NA	Notation convention
	Total LacI concentration	TBD	Steady state for equation
	T7 RNA polymerase (emitter, T7') concentration	NA	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
	GFP concentration	NA	molecules per cell	Notation convention
	mRNA associated with GFP concentration	NA	molecules per cell	Notation convention
	RFP concentration	NA	molecules per cell	Notation convention
	mRNA associated with RFP concentration	NA	molecules per cell	Notation convention
	Maximal production rate of pVeg promoter (constitutive)	0.02	molecules.s-1 or pops	Estimated, see the justification
	Maximal production rate of pLac promoter	0.02	molecules.s-1 or pops	Estimated, see the justification
	Maximal production rate of pT7 promoter	0.02	molecules.s-1 or pops	Estimated, see the justification
	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	10	molecules per cell	We used the classic assumption 1nM=1 molecule per cell and [1]
	Translation rate of proteins	0.9	s-1	Estimated, see the justification
	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)
	Degradation rate of GFP	10-4	s-1	BioNumbers
	Degradation rate of RFP	10-4	s-1	Estimated equal to GFP degradation rate
	Delay due to T7 RNA polymerase production and maturation	300	s	[2]
	Delay due to GFP production and maturation	360	s	BioNumbers
	Delay due to RFP production and maturation	360	s	Estimated equal to GFP delay (similar molecules)
	Delay due to mRNA production	30	s	BioNumbers with an approximation: all our contructs are around 1-2kb