Transcription Network: Basic Concepts

2IF35 Formal Modelling in Cell Biology

Technische Universiteit Eindhoven

November 18, 2009

Introduction

2IF35 (2009) Alon Chapter 2 2 / 17

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

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

Transcription Networks

2IF35 (2009) Alon Chapter 2 4 / 17

E. coli transcription network

2IF35 (2009) Alon Chapter 2 5 / 17

elements of transcription networks

2IF35 (2009) Alon Chapter 2 6 / 17

gene transcription regulation (base case)

2IF35 (2009) Alon Chapter 2 7 / 17

gene transcription regulation (base case)

2IF35 (2009) Alon Chapter 2 7 / 17

activated gene transcription regulation

2IF35 (2009) Alon Chapter 2 8 / 17

activated gene transcription regulation

2IF35 (2009) Alon Chapter 2 8 / 17

activated gene transcription regulation

2IF35 (2009) Alon Chapter 2 8 / 17

activated gene transcription regulation

2IF35 (2009) Alon Chapter 2 8 / 17

activated gene transcription regulation

2IF35 (2009) Alon Chapter 2 8 / 17

repressed gene transcription regulation

2IF35 (2009) Alon Chapter 2 9 / 17

repressed gene transcription regulation

2IF35 (2009) Alon Chapter 2 9 / 17

repressed gene transcription regulation

2IF35 (2009) Alon Chapter 2 9 / 17

repressed gene transcription regulation

2IF35 (2009) Alon Chapter 2 9 / 17

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

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

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

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

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

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

multiple input

X AND Y

f (X ∗,Y ∗) = β · θ(X ∗ > KX ) · θ(Y ∗ > KY )

2IF35 (2009) Alon Chapter 2 14 / 17

multiple input

X OR Y

f (X ∗,Y ∗) = β ·max{ θ(X ∗ > KX ), θ(Y ∗ > KY ) }

2IF35 (2009) Alon Chapter 2 14 / 17

multiple input

other f (X ∗,Y ∗)

2IF35 (2009) Alon Chapter 2 14 / 17

activated gene transcription regulation

“gene X activates gene Y ”

2IF35 (2009) Alon Chapter 2 15 / 17

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

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