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Simulating A Gene Regulatory Network (GRN)
A Delay Flip-Flop Implementation
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Simulation
Why do we simulate ?
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Simulation Cost effective Fast Proven method
An “analytic” model is appropriate when mathematics can be used to find the exact (deterministic) or probable (stochastic) values of the measures of performance.
We cannot test
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Hill Equation
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Hill Equation
ndegradatio
R from inhibition
tion transcripmax.
][][
1
1.
][mX
KRdt
mXdmXn
R
Q R
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Hill Equation
ndegradatio
R from inhibition
leakagetion transcripmax.
][][
1
1.1.
][mX
KR
aadt
mXdmXn
R
Q R
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Hill Equation
ndegradatio
R2 from inhibition
2
R1 from inhibition
1
leakagetion transcripmax.
][]2[
1
1.
]1[1
1.1.
][21
mX
KR
KR
aadt
mXdmXn
R
n
R
Q RR
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Hill Equation
ndegradatio
A from activationR from inhibition
leakagetion transcripmax.
][][
1
][
.][
1
1.1.
][mX
KA
KA
KR
aadt
mXdmXn
A
n
An
R
Q A
A
R
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Michaelis-Menten
http://en.wikipedia.org/wiki/Enzyme_kinetics
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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BioD
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BioD
][]4[
1
][4
4
1 mCIcr
KGaldt
mCIcrdmCIcrn
Gal
Gal
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BioD
][][
1
][
.][
1
1.
][1
][mCI
KOmpR
KOmpR
KOmpRP
KCIIdt
mCIdmCIn
OmpR
n
OmpR
n
OmpRP
n
CII
ompf
OmpR
OmpR
OmpRPCII
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BioD
OmpR
OmpR
OmpRPCI n
OmpR
n
OmpR
n
OmpRP
n
CI
ompf
KOmpR
KOmpR
KOmpRP
KCIdt
mCIId
][1
][
.][
1
1.
][1
][
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BioD
][][
1
][ 2 mCII
KCIdt
mCIIdmCIIn
CI
CI
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BioD
][][
3 mOmpRdt
mOmpRdmOmpR
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BioD
]4[][
1
][
.][
1
1.
][1
]4[4 mGal
KOmpR
KOmpR
KOmpRP
KCIdt
mGaldmGaln
OmpR
n
OmpR
n
OmpRP
n
CI
ompf
OmpR
OmpR
OmpRPCI
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BioD
OmpR
OmpR
OmpRPCI n
OmpR
n
OmpR
n
OmpRP
n
CI
ompf
KOmpR
KOmpR
KOmpRP
KCIdt
mTetRd
][1
][
.][
1
1.
][1
][
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BioD
][][
1
][ 6 mTetR
KLacIdt
mTetRdmTetRn
LacI
LacI
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BioD
OmpR
OmpR
OmpRPCII n
OmpR
n
OmpR
n
OmpRP
n
CII
ompf
KOmpR
KOmpR
KOmpRP
KCIIdt
mLacId
][1
][
.][
1
1.
][1
][
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BioD
][][
1
][ 7 mLacI
KTetRdt
mLacIdmLacIn
TetR
TetR
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BioD
].[].[][
CIImCIIdt
CIIdCIICII
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BioD
].[].[][
CImCIdt
CIdCICI
31
].[].[]].[12[
.][
12
CImCIK
mCIcrtaR
dt
CIdCICI
taRCI
BioD
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Law of Mass Action
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].[].[]].[12[
.][
12
CImCIK
mCIcrtaR
dt
CIdCICI
taRCI
BioD
34
BioD
].[].[][
OmpRmOmpRdt
OmpRdOmpROmpR
35
BioD
][
]).[1.(].[
][
OmpRk
OmpRLVOmpRPV
dt
OmpRd
phos
phosdePhos
36
BioD
].[].[][
]).[1.(][OmpRPOmpRPV
OmpRk
OmpRLV
dt
OmpRPdOmpRPdePhos
phos
phos
37
BioD
]4.[]4.[]4[
44 GalmGaldt
GaldGalGal
38
BioD
].[].[][
TetRmTetRdt
TetRdTetRTetR
39
BioD
].[].[][
LacImLacIdt
LacIdLacILacI
40
Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Outline Simulation Hill Equation Michaelis-Menten BioD Results
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Results
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BioD
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Results
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Results
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Results
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Results
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Results
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BioD
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Results
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Results
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Results
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Results
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Questions…
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