Team:KU Leuven/Project/Glucosemodel/MeS/Modelling

BLABLABLA

The methyl salicylate pathway contains the following reactions:

with:

• PchA = Pyochelin A
• PchB = Pyochelin B
• BSMT1 = Benzoate/Salicylate carboxyl methyltransferase
• SAM = S-adenosyl-L-methionine
• SAH = Salicylate methyl ester

At first, our intention was to model the entire pathway from the implemented DNA sequence to the resulting production rate. This could be very useful in order to have an approximation of the resulting production rate and in order to figure out the rate-limiting step. In order to achieve this we need a mathematical representation of all of our biological processes, the transcription rate, the mRNA degradation rate, the translation rate, the protein degradation rate and the enzyme kinetics.

We created a set of ordinary differential equations (ODEs), which represents every step in our pathway: transcription, translation and the chemical activity of the protein.

mRNA flux:

See the formulary below for further information about the used terminology.

Comments:
The proteins pyochelin A (PchA) and pyochelin B (PchB) are extracted from the pchDCBA operon and are the structural proteins responsible for salicylate biosynthesis. Serion et al. (1995) describe that expression of the pchA gene appears to depend on the transcription and translation of the upstream pchB gene in P. aeruginosa. They also state “Salicylate formation was demonstrated in an Escherichia coli entC mutant lacking isochorismate synthase when this strain expressed both the pchBA genes, but not when it expressed pchB alone”. This is also confirmed by Gaille, Reimman and Haas (2003): “The pchA gene is strictly co-expressed with the upstream pchB gene; without pchB being present in cis no expression of pchA can be observed”. Finally Serion et al. (1995) also report that the pchB stop codon overlaps the presumed pchA start codon.

Therefore we conclude that transcription and translation of pchA and pchB is coupled and decided to use only one gene (pchBAgene), and only one mRNA molecule (mpchbA) for both proteins (PchA and PchB) in our model.

Protein flux:

See the formulary below for further information about the used terminology.

Methyl salicylate synthesis:

See the formulary below for further information about the used terminology.

Comments:

• For our modeling purposes, we take the chorismate concentration as a pool.
• For every reaction we assume Michaelis-Menten kinetics.
• The division by NA. EcoliCellVolume in the numerator is necessary to convert the amount of molecules of our enzyme to a concentration.
• In equations [3.E] and [3.F ] Km3a represents the Km of salicylate while Km3b represents the Km of SAM.

Formulary:

For example for BSMT1:

Name	Units	Description
BSMT1gene	# genes	Copy number (amount) of bsmt1 gene
mBSMT1	# mRNA	Amount of bsmt1 mRNA
BSMT1	# proteins	Amount of BSMT1 substance (protein/molecule)
γmBSMT1		Transcription rate of PchBA gene
αmBSMT1		Degradation rate of PchBA mRNA
βBSMT1		Translation rate of PchA
αBSMT1		Degradation rate of PchA protein
kcat1		Turnover number
NA		Avogadro constant
EcoliCellVolume	Liter	The average volume of one E. coli cell
Km	Molarity	Michaelis-Menten constant

Symbiology Diagram:

We have put this model in SimBiology, provided by MATLAB, resulting in the following diagram:

Of course this model is useless without any good parameters. In this next section you can read about our search for decent parameters and its complications.

Copy number:

The first step in our model is the determination of the number of genes which can be transcribed. In our system we start with 2 genes (pchBA operon and bsmt1). They are not on the same plasmid but both carry a pMB1 origin of replication. This ORI has a copy number of 100 to 300 genes per cell. Therefore we will assume 200 copies of genes per cell.

Transcription:

An extensive literature survey learned that prediction of transcription rate, and its promoter dependence, is very hard and even impossible to do without any good data. The review article by Shiue and Prather (2012) describes this problem the following way: “due to the large sequence space and relative lack of understanding regarding polymerase-promoter interactions, the development of such predictive models remains a daunting task”. Also the recent discussions about stochastic gene expression make it as good as impossible to do quantitative predictions of mRNA production.

In the past, many iGEM teams predicted their transcription rate using a formula introduced by NTU-Singapore in 2008:

We believe that this formula does not represent the transcription rate on a correct way because:

1. The reference that says that the average transcription speed is 70 nt/s does not exist anymore. We tried to search for an average transcription rate ourselves and we can’t seem to find any decent value.
2. In this formula there is no single association with the promoter strength. This is remarkable, because the strength of a promoter is a measure for how many times a transcript is initiated. (Molecular Biology of the Gene, 7th edition). The stronger your promoter, the more transcripts are initiated, the more the gene is transcribed in time and thus the higher transcription rate.
3. The number of nucleotides could indeed have some influence on the rate of transcription. The longer the gene, the bigger the chance that the polymerase does not properly finish the transcript. But in literature we did not find any reference that uses the gene length as one of the important parameters for determining the rate of transcription.

We hope that other iGEM teams in the future will refrain from using this formula, because it is not a realistic representation of the transcription rate.
In our case we decided that we would bypass the mRNA production step because it is responsible for a large part of the uncertainty in our prediction. In order to attain our goal without needing the transcription rates we tried to determine the in vivo mRNA concentrations using qPCR. This means that we will drop formulas [1.A] and [1.B]. If you want to know more on how we tackled the qPCR, please go to our WETLAB part.