Team:Technion HS Israel/Modelling
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Modelling
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i. AHL self-degradation.
o Law: Mass action
o Explanation: Each molecule of AHL has a certain probability to degrade, hence the corresponding change rate in the amount of the AHL is proportional to the amount of AHL in all the cells. The coefficient is noted by C2 for cell internal AHL and C2' for cell external AHL.
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Results:
ii. Diffusion of AHL
o Law: Simple passive diffusion
o Explanation: Will be explained in the processes section.
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Results:
Change in external AHL concentration:
Change in total amount inside of AHL inside all the cells:
iii. AHL degradation by AiiA
o Law: Michaelis Menten
o Explanation: AiiA is an enzyme, and simple Mass Action doesn't work well for enzymatic reactions. The reason for it is the fact that the enzyme and the substrate form a complex, which is then converted to a product and the original enzyme. Therefore, two mass actions are required to describe this process, but under quasi-steady-state assumption we can derive a single equation, which is the Michaelis Menten law. It has two parameters, the maximal reaction rate and the turnover number.
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Results:
iv. Pairing of AHL and LuxR into AHL-LuxR complex
o Law: Mass action
o Explanation: The chance of a molecule of AHL to meet a molecule of LuxR is proportional to both the concentration of AHL and LuxR (the more AHL you have, the higher the chance for reaction between AHL and LuxR). We get that the reaction rate is proportional to the product of the concentrations of AHL and LuxR.
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Results:
v. Disassociation of the AHL-LuxR complex to its components
o Law: Mass action
o Explanation: Each AHL-LuxR complex has a certain probability to disassociate, hence the corresponding change rate in the amount of the AHL is proportional to the amount of AHL-LuxR. The coefficient is denoted by C4.
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Results:
vi. Pairing of 2 AHL-LuxR complexes into the dimer (AHL-LuxR)2
o Law: Mass action
o Explanation: The chance of a molecule of AHL-LuxR complex to meet another one is proportional, again, to the product of their concentrations, (which this time are equal and we get [AHL-LuxR]^2).
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Results:
vii. Disassociation of (AHL-LuxR)2 to its components
o Law: Mass action
o Explanation: Each (AHL-LuxR)2 dimer has a certain probability to disassociate, hence the corresponding change rate in the amount of the AHL is proportional to the total amount of AHL-LuxR in the cells. The coefficient is denoted by C6.
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Results:
viii. (AHL-LuxR)2 binds to the pLuxR promoter
o Law: Mass action
o Explanation: The activation rate is proportional to the product of the concentrations of the dimer and the number of plasmid plasmids with pLuxR promoters. It will be explained later in the processes section.
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Results:
ix. (AHL-LuxR)2 unbinds from the pLuxR promoter
o Law: Mass action
o Explanation: Each activated promoter has a certain probability to deactivate and to release its (AHL-LuxR)2, and therefore the rate of this process is proportional to the number of activated promoters. It will be explained later in the processes section.
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Results:
x. Transcription of RNATRLV by pLuxR promoter without the complex
o Law: Mass action
o Explanation: Each inactivated promoter transcripts mRNA in a certain rate. This rate is called leakiness. We multiply it by the number of inactivated LuxR promoters to get the total rate. It will be explained further in the processes section.
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Results:
xi. Transcription of RNATRLV by pLuxR promoter with the complex
o Law: Mass action
o Explanation: Each activated promoter transcripts mRNA in a certain rate. We multiply it by the number of activated LuxR promoters to get the total rate. It will be explained further in the processes section.
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Results:
xii. Translation of TRLV from RNATRLV
o Law: Mass action
o Explanation: mRNA of TetR translates to the protein TetR in a certain rate. We multiply it by the concentration of RNA to get the total rate. It will be explained further in the processes section.
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Results:
xiii. TRLV self-degradation
o Law: Mass action
o Explanation: Each molecule of TRLV has a certain probability to degrade, hence the corresponding change rate in the amount of the TRLV is proportional to the amount of TRLV all the cells.
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Results:
xiv. TRLV binds to the pTetR repressor
o Law: Mass action
o Explanation: The activation rate is proportional to the product of the concentrations of the dimer and the number of plasmid plasmids with pTetR promoters. It will be explained later in the processes section.
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Results:
xv. TRLV unbinds from the pLuxR repressor
o Law: Mass action
o Explanation: Each activated promoter has a certain probability to deactivate and to release its TRLV, and therefore the rate of this process is proportional to the number of activated promoters. It will be explained later in the processes section.
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Results:
xvi. Transcription of RNAccdB by ptetR promoter without the TRLV
o Law: Mass action
o Explanation: For each inactivated repressor there is transcription to mRNA in a certain rate. We multiply it by the number of inactivated ptetR promoters to get the total rate. It will be explained further in the processes section.
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Results:
xvii. Transcription of RNAccdB by ptetR promoter with the TRLV
o Law: Mass action
o Explanation: For each activated repressor there is still transcription to mRNA in a certain rate. We multiply it by the number of activated ptetR promoters to get the total rate. It will be explained further in the processes section.
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Results:
xviii. Translation of ccdB from RNAccdB
o Law: Mass action
o Explanation: mRNA of ccdb translates to the protein ccdb in a certain rate. We multiply it by the concentration of RNA to get the total rate. It will be explained further in the processes section.
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Results:
xix. ccdB self-degradation
o Law: Mass action
o Explanation: Each molecule of ccdB has a certain probability to degrade, hence the corresponding change rate in the amount of the ccdB is proportional to the amount of ccdB all the cells.
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Results:
xx. producing of the desired protein x by the pCONST promoter
o Law: Mass Action
o Explanation: Each plasmid with our circuit produces the desired enzyme, X, in a certain amount.
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Results:
xxi. producing of LuxR by the pCONST promoter
o Law: Mass Action
o Explanation: Each plasmid with our circuit produces LuxR in a certain amount.
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Results:
xxii. producing of AiiA by the pCONST promoter
o Law: Mass Action
o Explanation: Each plasmid with our circuit produces AiiA in a certain amount.
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Results:
xxiii. plasmid loss
o We model the effect of plasmid loss on the system. It affects the equations by having both bacteria with plasmids (N+) and without plasmid (N-).
o Further explanation is here.
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Results:
