Team:NYMU-Taipei/Modeling/Ethanol

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Revision as of 14:16, 27 October 2013

National Yang Ming University

1 Ethanol model
2 parameters:

Ethanol model

Background:

TrxC promoter is an oxyR-activated promoter. Behind trxC promoter are several terminals to inhibit T7 polymerase-producing gene from being opened easily ; namely, it will not open until the concentration of oxyR is high enough, which means the bees are facing disastrous infection. Once oxyR concentration overcomes the threshold and conquers the terminal obstacles, T7 polymerase is produced and will bind to T7 promoter, which is a specific promoter binding only to T7 polymerase. Behind the T7promoter are enzyme PDC and ADH-producing genes, which will convert pyruvate to ethanol, and thus kill spores of Nosema Ceranae.

Pathway of ethanol:

PDC= pyruvate decarboxylase; ADH= Acetaldehyde

Aims

To simulate how many terminal do we need as a threshold to have the T7 polymerase-producing gene open at a proper 　　time.
To simulate the threshold concentration of oxyR to conquer the terminal.
To determine the time of opening to see if the circuit could open in time (useful).

As for how we measure promoter strengths, we choose PoPS, which is the rate of RNA polymerase binding to the DNA and trigger the transcription of the certain gene.

It is assumed that the dose of pyruvate is sufficient in bees’ body through enough proliferation/copy number of Beecoli; the possibility of RNApolymerase skipping terminators is assumed to be proportional to time span; equilibrium between pyruvate and acetaldehyde is dominantly rightward, while equilibrium between acetaldehyde and ethanol is bidirectional; concentration of ethanol will not easily decrease and will sustain for a period of time.

Equation1:

\frac{d[mRNAT7]}{dt}=\frac{ [ROSoxyR]^{nROSoxyR} }{ KdROSoxyR^{nROSoxyR}+[ROSoxyR]^{nROSoxyR} }\times{PoPStrxC}\times\frac{N}{V}\times{a}+\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAPDC]

KdROSoxyR = dissociation constant of ROSoxyR
n ROSoxyR = Hill coefficient of ROSoxyR
PoPStrxC = promoter strength of trxC
KdT7 = dissociation constant of T7
NT7 = Hill coefficient of T7
PoPST7 = promoter strength of T7 promoter
KdegmRNA = degrading constant of sensor promoter mRNA
N = number of plasmid in a single cell
V = volume of a cell

Equation2:

\frac{d[protein of T7 polymerase ]}{dt}=RBS\times{PoPStrxC}\times\frac{N}{V}\times{a}\times{\frac{ [ROSoxyR]^{n1} }{ [Kd]^{n1}+[ROSoxyR]^{n1} }}}+PoPST7\times{T7 effect}\times\frac{N}{V}-{KdegT7}\times{T7}

PoPStrxC = promotor strength of trxC promoter
PoPST7 = promoter strength of T7 promoter
RBS = binding site strength
kdegT7 = degrading constant of T7 polymerase
a = posibility of conquering the threshold concentration
n1 = Hill coefficient of ROSoxyR (complex of ROS+oxyR)
N = number of plasmid in a single cell
V = volume of a cell

The aim of the equation is to know the threshold concentration of oxyR to conquer the terminal and when T7 polymerase can reach the required concentration to activate T7 promoter.

Equation3:

\frac{d[mRNAPDC]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAPDC]

KdT7 = dissociation constant of T7
NT7 = Hill coefficient of T7
PoPST7 = promoter strength of T7 promoter
KdegmRNA = degrading constant of sensor promoter mRNA
N = number of plasmid in a single cell
V = volume of a cell

The aim of the equation is to know mRNA of enzyme PDC production rate and when it can reach the level to translate enough PDC.

Equation4:

\frac{d[PDC]}{dt}=RBS\times{PoPST7effect}\times\frac{N}{V}-{kdegPDC}\times[PDC}]

RBS = binding site strength
PoPST7 = promoter strength of T7 promoter
N = number of plasmid in a single cell
V = volume of a cell
KdegPDC = degrading constant of PDC (pyruvate decarboxylase)

The aim of the equation is to know PDC production rate and when it can reach the concentration of ethanol pathway equilibrium.

Equation5:

\frac{d[mRNAADH]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAADH]

KdT7 = dissociation constant of T7
NT7 = Hill coefficient of T7
PoPST7 = promoter strength of T7 promoter
KdegmRNA = degrading constant of sensor promoter mRNA
N = number of plasmid in a single cell
V = volume of a cell

Equation6:

\frac{d[ADH]}{dt}=RBS\times{PoPST7effect}\times\frac{N}{V}-{KdegADH}\times[ADH]}

RBS = binding site strength
PoPST7 = promoter strength of T7 promoter
N = number of plasmid in a single cell
V = volume of a cell
KdegADH = degrading constant of ADH (Acetaldehyde)

The aim of the equation is to know ADH production rate and when it can reach the concentration of ethanol pathway equilibrium.

Equation7:

\frac{d[ethanol]}{dt}=Kpyruvateacetaldehyde\times{Kacetaldehydeethanol}\times\frac{[PDC]^{nPDC} }{ KdPDC^{nPDC}+[PDC]^{nPDC}}\times\frac{[ADH]^{nADH} }{ KdADH^{nADH}+[ADH]^{nADH}}-Km\times\frac{[ADH]^{nADH}}{ KdADH^{nADH}+[ADH]^{nADH}}\times[ethonal]

Kpyruvateacetaldehyde = pyruvate→acetaldehyde reaction rate constant
Kacetaldehydeethanol = acetaldehyde→ethanol reaction rate constant
Km = ethanol→acetaldehyde reaction rate constant
KdADH = dissociation constant of ADH

The aim of the equation is to know ethanol production rate and when it can reach the concentration to kill the spores of Nosema Ceranae.

The code of ethanol production:

parameters:

Model	Parameter	Description	Value	Unit	Reference
Ethanol	pyruvate	Initial concentration of pyruvate in MG1655	1.18 x 2	g/L	Expression of pyruvate carboxylase enhances succinate production in Escherichia coli without affecting glucose uptake
	nPDC	Hill coefficient of PDC	2.1	-	Purification, characterization and cDNA sequencing of pyruvate decarboxylase Zygosaccharomyces biporus
	nADH	Hill coefficient of ADH	at high pH values, 30◦C, n=1; at low temperature, n=3	-	Evidence for co-operativity in coenzyme binding to tetrameric Sulfolobus solfataricus alcohol dehydrogenase and its structural basis: ﬂuorescence, kinetic and structural studies of the wild-type enzyme and non-co-operative N249Y mutant

Retrieved from "http://2013.igem.org/Team:NYMU-Taipei/Modeling/Ethanol"

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 ===Equation2:===
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 '''The aim of the equation is to know the threshold concentration of oxyR to conquer the terminal and when T7 polymerase can reach the required concentration to activate T7 promoter.'''
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 ===Equation3:===
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 '''The aim of the equation is to know mRNA of enzyme PDC production rate and when it can reach the level to translate enough PDC.'''
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 ===Equation4:===
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 '''The aim of the equation is to know PDC production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
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 ===Equation5:===
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 ===Equation6:===
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 '''The aim of the equation is to know ADH production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
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 ===Equation7:===
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 '''The aim of the equation is to know ethanol production rate and when it can reach the concentration to kill the spores of Nosema Ceranae.'''
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