Team:NYMU-Taipei/Modeling/MainParts

From 2013.igem.org

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\frac{d[mRNACI]}{dt}=\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }×PoPSpLac×N/V-kdegmRNA×[mRNACI]
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\frac{d[mRNACI]}{dt}=\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }\timesPoPSpLac\times\frac{N}{V}-kdegmRNA\times[mRNACI]
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KdLacI = dissociation constant of CI
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nLacI = Hill coefficient of LacI
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PoPSpLac = promoter strength of pLac
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kdegmRNA = degrading constant of sensor promoter mRNA
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N = number of plasmid in a single cell
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V = volume of a cell
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'''The aim of the equation is to knowmRNACI production rate and when it can reach the level to translate the desired concentration.'''
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===Equation2:===
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\frac{d[mRNALacI]}{dt}=\frac{ [ROSoxyR]^{nROSoxyR} }{ KdROSoxyR^{nROSoxyR}+[ROSoxyR]^{nROSoxyR} }\timesPoPStrxC\times\frac{N}{V}-kdegmRNA\times[mRNAlacI]
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KdROSoxyR = dissociation constant ofROSoxyR
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nROSoxyR = Hill coefficient of ROSoxyR
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PoPStrxC = promoter strength of trxC
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kdegmRNA = degrading constant of sensor promoter mRNA
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N = number of plasmid in a single cell
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V = volume of a cell
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'''The aim of the equation is to know how trxC promoter strength (in PoPS) influences the production of lacI.'''
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===Equation3:===
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\frac{d[mRNAoxyR]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA[mRNAoxyR]
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PoPSconstitutive= promoter strength of constitutive promoter (J23102)
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N = number of plasmid in a single cell
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V = volume of a cell
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kdegmRNA = degrading constant of sensor promoter mRNA
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'''The aim of the equation is to know the production rate ofmRNAoxyR, and choose the proper constitutive promoter for boosting OxyR's concentration.'''
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===Equation4:===
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<div lang="latex" class="equation">
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<img src="https://static.igem.org/mediawiki/2013/e/ee/NYMU-Taipei_modmain_Image008.png"></img>
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KdROSoxyR = dissociation constant ofROSoxyR
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nROSoxyR = Hill coefficient of ROSoxyR
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PoPStrxC = promoter strength of trxC
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KdLuxRAHL = dissociation constant ofLuxRAHL
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nLuxRAHL = Hill coefficient of LuxRAHL
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KdcI = dissociation constant ofcI
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ncI = Hill coefficient ofCi
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PoPSLuxcI = promoter strength of LuxcI hybrid promoter
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kdegmRNA = degrading constant of sensor promoter mRNA
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N = number of plasmid in a single cell
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V = volume of a cell
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'''The aim of the equation is to know how trxC promoter strength (in PoPS) influences the production of LuxI.'''
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===Equation5:===
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<div lang="latex" class="equation">
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<img src="https://static.igem.org/mediawiki/2013/f/fd/NYMU-Taipei_modMain_Image009.png"></img>
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</div>
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</html>
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KdROSoxyR = dissociation constant ofROSoxyR
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nROSoxyR = Hill coefficient of ROSoxyR
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PoPStrxC = promoter strength of trxC
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KdLuxRAHL = dissociation constant ofLuxRAHL
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nLuxRAHL = Hill coefficient of LuxRAHL
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KdcI = dissociation constant ofcI
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ncI = Hill coefficient ofCi
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PoPSLuxcI = promoter strength of LuxcI hybrid promoter
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kdegmRNA = degrading constant of sensor promoter mRNA
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N = number of plasmid in a single cell
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V = volume of a cell
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'''The aim of the equation is to know how trxC promoter strength (in PoPS) influences the production of LuxR.'''
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===Equation6:===
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<div lang="latex" class="equation">
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<img src="https://static.igem.org/mediawiki/2013/a/ab/NYMU-Taipei_modMain_Image010.png"></img>
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</div>
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{{:Team:NYMU-Taipei/Footer}}
{{:Team:NYMU-Taipei/Footer}}

Revision as of 20:48, 27 September 2013

National Yang Ming University


Contents

Function of the parts:

  1. circuit regulators:
  • LacIregulatedpromoter(pLac) : when LacI exists, it will bind to LacIregulatedpromoter(pLac) and represses the promoter.
  • pLux/cIhybridpromoter(plux/cI) : when luxR/AHL exists, it will open pLux/cIhybridpromoter(plux/cI), while cI will repress the promoter. What’s more, plux/cI is cI-dominant, which means when cI exists, the hybrid promoter will be repressed whether luxR/AHL exists or not.
  1. Circuit regulation:
  • Circuit condition without Nosema:
NYMU-Taipei Circuit condition wo nosema.jpg

Without NosemaCeranae, the first circuit will not open, and thus, no LacI will be produced. Since there is no LacI binding to pLac, pLac will not be repressed, which means cI will be produced. After that, cIwill bind to pLux/cI-hybridpromoter, leading the third circuit to be off.

  • Circuit condition with Nosema:
NYMU-Taipei Circuit condition w nosema.jpg

When NosemaCeranae infects the bee, bee’s immune system will be activated, leading to the concentration of ROS(reactive oxygen species) to be high. In response, E. Kobee will enhance the production of oxyR, which binds to transcription binding site ahead of trxC (an oxyR-activated promoter; namely, the sensor), leading to the first circuit to be on.

Since the first circuit is on, the downstream LacI gene will be produced and bind to pLac, leading to the second circuit to be off.

After the second circuit is closed, no cI is produced, leading to the third circuit to be on (no repressor at all). And then, killer protein will be produced and kill NosemaCeranae.

  • Positive feedback:
NYMU-Taipei Mod 3.jpg

Besides the LuxI and LuxR(which then form a complex called luxR/AHL) produced by first circuit, the third circuit will also produce luxR/AHL, which acts as a positive feedback and strongly enhances the production of killer protein.

  • CircuitconditionwhenNosema is killed:
NYMU-Taipei Mod 4.jpg

After Nosema is killed, the sensor will be off and no lacI will be produced. Without LacI, the pLac will not be repressed, and the second circuit will be on, leading to the production of cI. After cI binds topLux/cIhybridpromoter, the third circuit to be off.

The overall circuit will switch to the beginning stage when there is no Nosema.

The purpose of this modeling is:

  1. To know how much time it needs from sensing to killing the Nosema after infection
  2. To know whether the pathway is effectiveor not
  3. To know the range of killer protein concentration(from the minimal concentration which Is effective to kill Nosema to the maximal concentration which will not do harm to the bees)

It is assumed that AHL is abundant and thus the formation of AHL2LuxR is determined only by the concentration of LuxR; CI’s mechanism of binding to the promoter is assumed to act as hill effect form; kill protein will sustain a period of time before it is degraded naturally without any other types of degration.

Equation1:

\frac{d[mRNACI]}{dt}=\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }\timesPoPSpLac\times\frac{N}{V}-kdegmRNA\times[mRNACI]

KdLacI = dissociation constant of CI

nLacI = Hill coefficient of LacI

PoPSpLac = promoter strength of pLac

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 knowmRNACI production rate and when it can reach the level to translate the desired concentration.

Equation2:

\frac{d[mRNALacI]}{dt}=\frac{ [ROSoxyR]^{nROSoxyR} }{ KdROSoxyR^{nROSoxyR}+[ROSoxyR]^{nROSoxyR} }\timesPoPStrxC\times\frac{N}{V}-kdegmRNA\times[mRNAlacI]

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPStrxC = promoter strength of trxC

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 how trxC promoter strength (in PoPS) influences the production of lacI.

Equation3:

\frac{d[mRNAoxyR]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA[mRNAoxyR]

PoPSconstitutive= promoter strength of constitutive promoter (J23102)

N = number of plasmid in a single cell

V = volume of a cell

kdegmRNA = degrading constant of sensor promoter mRNA

The aim of the equation is to know the production rate ofmRNAoxyR, and choose the proper constitutive promoter for boosting OxyR's concentration.

Equation4:

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPStrxC = promoter strength of trxC

KdLuxRAHL = dissociation constant ofLuxRAHL

nLuxRAHL = Hill coefficient of LuxRAHL

KdcI = dissociation constant ofcI

ncI = Hill coefficient ofCi

PoPSLuxcI = promoter strength of LuxcI hybrid 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 how trxC promoter strength (in PoPS) influences the production of LuxI.

Equation5:

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPStrxC = promoter strength of trxC

KdLuxRAHL = dissociation constant ofLuxRAHL

nLuxRAHL = Hill coefficient of LuxRAHL

KdcI = dissociation constant ofcI

ncI = Hill coefficient ofCi

PoPSLuxcI = promoter strength of LuxcI hybrid 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 how trxC promoter strength (in PoPS) influences the production of LuxR.

Equation6:


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