simulating a gene regulatory network (grn)
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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
aadtmXd
mXn
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
aadtmXd
mXn
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
aadtmXd
mXn
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
OmpRn
OmpRP
n
CII
ompf
OmpR
OmpR
OmpRPCII
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BioD
OmpR
OmpR
OmpRPCI n
OmpR
n
OmpRn
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 mOmpR
dtmOmpRd
mOmpR
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BioD
]4[][1
][
.][1
1.][1
]4[4 mGal
KOmpR
KOmpR
KOmpRP
KCIdt
mGaldmGaln
OmpR
n
OmpRn
OmpRP
n
CI
ompf
OmpR
OmpR
OmpRPCI
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BioD
OmpR
OmpR
OmpRPCI n
OmpR
n
OmpRn
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
OmpRn
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
].[].[][ CIImCIIdtCIId
CIICII
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BioD
].[].[][ CImCIdtCId
CICI
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].[].[]].[12[.][
12
CImCIKmCIcrtaR
dtCId
CICItaR
CI
BioD
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Law of Mass Action
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].[].[]].[12[.][
12
CImCIKmCIcrtaR
dtCId
CICItaR
CI
BioD
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BioD
].[].[][ OmpRmOmpRdtOmpRd
OmpROmpR
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BioD
][]).[1.(
].[][OmpRkOmpRLV
OmpRPVdtOmpRd
phos
phosdePhos
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BioD
].[].[][
]).[1.(][ OmpRPOmpRPVOmpRkOmpRLV
dtOmpRPd
OmpRPdePhosphos
phos
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BioD
]4.[]4.[]4[44 GalmGal
dtGald
GalGal
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BioD
].[].[][ TetRmTetRdtTetRd
TetRTetR
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BioD
].[].[][ LacImLacIdtLacId
LacILacI
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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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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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