transcription network: basic conceptsevink/education/2if35/pdf/2if35-alon2.pdf · transcription...
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Transcription Network: Basic Concepts
2IF35 Formal Modelling in Cell Biology
Technische Universiteit Eindhoven
November 18, 2009
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Introduction
2IF35 (2009) Alon Chapter 2 2 / 17
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Escherichia coli
4500 genes, 4000000 proteins
transcription 1 min/gene
translation 2 min/protein
104 ribosomes, mRNA lifetime 2–5 min
regulation of protein levels by transcription networks
300 transcription factors to represent environment
inactive/active switching of protein in 1–100 µsec
2IF35 (2009) Alon Chapter 2 3 / 17
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Escherichia coli
4500 genes, 4000000 proteins
transcription 1 min/gene
translation 2 min/protein
104 ribosomes, mRNA lifetime 2–5 min
regulation of protein levels by transcription networks
300 transcription factors to represent environment
inactive/active switching of protein in 1–100 µsec
2IF35 (2009) Alon Chapter 2 3 / 17
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Transcription Networks
2IF35 (2009) Alon Chapter 2 4 / 17
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E. coli transcription network
2IF35 (2009) Alon Chapter 2 5 / 17
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elements of transcription networks
2IF35 (2009) Alon Chapter 2 6 / 17
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gene transcription regulation (base case)
2IF35 (2009) Alon Chapter 2 7 / 17
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gene transcription regulation (base case)
2IF35 (2009) Alon Chapter 2 7 / 17
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activated gene transcription regulation
2IF35 (2009) Alon Chapter 2 8 / 17
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activated gene transcription regulation
2IF35 (2009) Alon Chapter 2 8 / 17
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activated gene transcription regulation
2IF35 (2009) Alon Chapter 2 8 / 17
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activated gene transcription regulation
2IF35 (2009) Alon Chapter 2 8 / 17
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activated gene transcription regulation
2IF35 (2009) Alon Chapter 2 8 / 17
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repressed gene transcription regulation
2IF35 (2009) Alon Chapter 2 9 / 17
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repressed gene transcription regulation
2IF35 (2009) Alon Chapter 2 9 / 17
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repressed gene transcription regulation
2IF35 (2009) Alon Chapter 2 9 / 17
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repressed gene transcription regulation
2IF35 (2009) Alon Chapter 2 9 / 17
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activators and repressors
60% to 80% activators
transcription factors mostly positive or mostly negative
genes can both be activated and repressed
outgoing signs are correlated, incoming signs not
2IF35 (2009) Alon Chapter 2 10 / 17
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Hill input function for activator
rate of Y -production = f (X ∗)
Hill function for activator f (X ∗) =β · (X ∗)n
K n + (X ∗)n
maximal expression level β, activation coefficient K , Hill coefficient n
2IF35 (2009) Alon Chapter 2 11 / 17
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Hill input function for activator
rate of Y -production = f (X ∗)
Hill function for activator f (X ∗) =β · (X ∗)n
K n + (X ∗)n
maximal expression level β, activation coefficient K , Hill coefficient n
2IF35 (2009) Alon Chapter 2 11 / 17
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Hill input function for repressor
rate of Y -production = f (X ∗)
Hill function for repressor f (X ∗) =β · K n
K n + (X ∗)n
2IF35 (2009) Alon Chapter 2 12 / 17
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Hill input function for repressor
rate of Y -production = f (X ∗)
Hill function for repressor f (X ∗) =β · K n
K n + (X ∗)n
2IF35 (2009) Alon Chapter 2 12 / 17
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step functions as input functions
logical approximation
gene OFF : f (X ∗) = 0 vs. gene ON : f (X ∗) = 1
activated transcription f (X ∗) = β · θ(X ∗ > K )
repressed transcription f (X ∗) = β · θ(X ∗ < K )
threshold K , step-function θ: if expr then 1 else 0 end
2IF35 (2009) Alon Chapter 2 13 / 17
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multiple input
X AND Y
f (X ∗,Y ∗) = β · θ(X ∗ > KX ) · θ(Y ∗ > KY )
2IF35 (2009) Alon Chapter 2 14 / 17
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multiple input
X OR Y
f (X ∗,Y ∗) = β ·max{ θ(X ∗ > KX ), θ(Y ∗ > KY ) }
2IF35 (2009) Alon Chapter 2 14 / 17
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multiple input
other f (X ∗,Y ∗)
2IF35 (2009) Alon Chapter 2 14 / 17
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activated gene transcription regulation
“gene X activates gene Y ”
2IF35 (2009) Alon Chapter 2 15 / 17
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dynamics of simple gene regulation
dynamic equationdY
dt= β − αY
in case of activation Y (t) = Yst · ( 1− e−αt )
steady state Yst =βα
response time T 12
=log 2α
2IF35 (2009) Alon Chapter 2 16 / 17
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dynamics of simple gene regulation (cont.)
dynamic equationdY
dt= −αY
on case of decay Y (t) = Yst · e−αt
steady state Yst = 0 response time T 12
=log 2α
2IF35 (2009) Alon Chapter 2 17 / 17