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Network MotifsSimple Building Blocks of Complex Networks
Moritz Bitterling
Universität Freiburg
13.12.2016
outline
introduction
genetics
motifs
introduction
introductionmotivationmethods
genetics
motifs
introduction motivation
fraction of transcription network of E. coli
1 / 33
introduction motivation
fraction of transcription network of E. coli
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1 / 33
introduction motivation
fraction of transcription network of E. coli
1 / 33
introduction motivation
transcription network - autoregulation
2 / 33
introduction motivation
transcription network - outstanding nodes
3 / 33
introduction motivation
transcription network - loops
4 / 33
introduction motivation
Is there a statistically significant aggregationof local patterns or ”motifs” in the network?
Compare to a randomized network→ YES!
Which are the motifs that evolution prefers?
What are their functions in the network?
5 / 33
introduction methods
fraction of transcription network of E. coli
6 / 33
introduction methods
random network
7 / 33
introduction methods
histogram of E.coli transcription network
0 5 10 15 20 25 30 35
0.5
1
5
10
50
100
neighbours per node
nodes
Randomization: Choose two random edges, swap target nodes→ the histogram is preserved
8 / 33
genetics
introduction
geneticstranscriptiontranslationdynamics
motifs
genetics transcription
gene expression - transcription
9 / 33
genetics transcription
gene expression - transcription
geneDNA
transcription start site reading direction
9 / 33
genetics transcription
gene expression - transcription
geneDNA
transcription start site reading direction
messenger RNA
RNA polymerase
- RNAp transcribes DNA to mRNA
9 / 33
genetics transcription
gene expression - transcription
gene
transcription start site reading direction
DNA
messenger RNA
RNA polymeraseactivator/repressor
promoter region
- RNAp transcribes DNA to mRNA- Activator/repressor interacts with transcription start site→ Enhances/inhibits attachment of RNAp
9 / 33
genetics translation
gene expression - translation of mRNA to protein
en.wikipedia.org/wiki/Translation (biology)
10 / 33
genetics translation
regulation of gene expression
DNA RNA A protein Atranscription translation
11 / 33
genetics translation
regulation of gene expression
DNA RNA A protein Atranscription translation
11 / 33
genetics translation
regulation of gene expression
DNA RNA A protein Atranscription translation
DNA RNA B protein B
activator
11 / 33
genetics translation
regulation of gene expression
DNA RNA A protein Atranscription translation
DNA RNA B protein B
activator
DNA RNA C protein C
repressor
11 / 33
genetics translation
regulation of gene expression
DNA RNA A protein Atranscription translation
DNA RNA B protein B
activator
DNA RNA C protein C
repressor
DNA
DNA
nodes: genesedge: transcription
factorRNA A protein A
transcription translation
activator
11 / 33
genetics dynamics
dynamics of simple gene regulation
Transcription factor X regulates expression of protein Y: X → YSimple assumptions:- If X is in active form X∗, Y is produced at a constant rate β- Degradation rate of Y is α
⇒ dYdt = β −αY
Stable state: dYdt!= 0 ⇒ Yst =
βα
12 / 33
genetics dynamics
dynamics of simple gene regulation
Transcription factor X regulates expression of protein Y: X → YSimple assumptions:- If X is in active form X∗, Y is produced at a constant rate β- Degradation rate of Y is α
⇒ dYdt = β −αY
Stable state: dYdt!= 0 ⇒ Yst =
βα
12 / 33
genetics dynamics
dynamics of simple gene regulation
Transcription factor X regulates expression of protein Y: X → YSimple assumptions:- If X is in active form X∗, Y is produced at a constant rate β- Degradation rate of Y is α
⇒ dYdt = β −αY
Stable state: dYdt!= 0 ⇒ Yst =
βα
12 / 33
genetics dynamics
dynamics of simple gene regulationdYdt = β −αY
Yst =βα
0
Yst
time t / a.u.
level
of
Y
Y = Yst (1-ⅇ-t α)
X*
active
Y = Yst ⅇ-t α
X inactive
12 / 33
genetics dynamics
Hill-function
More realistic model: Rate of production of Y is a function of X∗
f[X∗] has three parameters → each edge carries three numbers- K : Level of X∗ to significantly activate expression- β : Maximal expression level- n: Cooperativity: Number of molecules needed for activation
Rate of production of Y: f [X ∗] = β X ∗n
Kn +X ∗n
13 / 33
genetics dynamics
Hill-function
More realistic model: Rate of production of Y is a function of X∗
f[X∗] has three parameters → each edge carries three numbers- K : Level of X∗ to significantly activate expression- β : Maximal expression level- n: Cooperativity: Number of molecules needed for activation
Rate of production of Y: f [X ∗] = β X ∗n
Kn +X ∗n
13 / 33
genetics dynamics
Hill-function
0 K 2 K 3 K
0
β/2
β
activator concentration X *
rate
of
pro
duct
ion
of
Y:
f[X
*]
n = 1
n = 2
n = 3
n = 4
n → ∞
f [X ∗] = β X ∗n
Kn +X ∗n
14 / 33
genetics dynamics
Hill-function
Parameters can be tuned during evolution:K : Mutations of binding site in the promoter areaβ : Mutations in the RNAp binding site
Rate of production of Y: f [X ∗] = β X ∗n
Kn +X ∗n
15 / 33
motifs
introduction
genetics
motifsautoregulationfeed forward loopsingle-input moduledense overlapping regulonoccurrence of motifs in various networks
motifs autoregulation
autoregulationProbability of a self-edge in random network with N nodes:
pself =1N
Probability of k self-edges in a random network with N nodes and E edges:
P(k) =(
Ek
)·pkself · (1−pself)E−k
The expectation value for the number of self-edges is
< Nself >= E ·pself =EN
For the E.coli network this yields EN =519424 = 1.2 self-edges
The real network has 40 self-edges → high statistical significance16 / 33
motifs autoregulation
negative autoregulation
X 0.0 0.5 1.0 1.5 2.00.0
0.2
0.4
0.6
0.8
1.0
repressor concentration X / K
rate
of
pro
duct
ion
of
X/β
- System with simple regulation: Yst = βα→ unstable, many factors influence β and α- System with negative autoregulation: Yst ≈ K→ stable, K is specified by strength of chemical bonds⇒ Noise suppression
17 / 33
motifs autoregulation
negative autoregulation
X
- High production rate β can cause strong initial rise- High autorepression leads to saturation at stable level K⇒ response acceleration
18 / 33
motifs autoregulation
positive autoregulation
X
⇒ higher response time⇒ noise amplifyingWhy is noise good for a cell?→ diversity
19 / 33
motifs feed forward loop
feed forward loops
20 / 33
motifs feed forward loop
coherent type 1 feed forward loop
AND connection for Z→ only respond to persistent stimulation, elevator door effectOR connection for Z→ no delay after stimulation, but delay after stimulation stops
21 / 33
motifs feed forward loop
incoherent type 1 feed forward loop
- Response acceleration- Pulse generator
22 / 33
motifs single-input module
single-input module
→ timed expression of different genes
23 / 33
motifs dense overlapping regulon
dense overlapping regulon
- Not yet very well understood- Detailed information about connection strength is needed
24 / 33
motifs occurrence of motifs in various networks
motifs in the transcription network of E. coli
X
Y
Z
X Y
Z Wfeed-forward loop bi-fan
Nreal = 40 Nrand = 7±3 Nreal = 203 Nrand = 47±12
25 / 33
motifs occurrence of motifs in various networks
motifs in the neural network of C. elegans
X
Y
Z
X Y
Z Wfeed-forward loop bi-fan
X
Y Z
Wbi-parallel
Nreal = 125Nrand = 90±10
Nreal = 127Nrand = 55±13
Nreal = 227Nrand = 35±10
26 / 33
motifs occurrence of motifs in various networks
motifs in the food web of little rock
X
Y
Zthree chain
X
Y Z
Wbi-parallel
Nreal = 3219 Nrand = 3120±50 Nreal = 7295 Nrand = 2220±210
27 / 33
motifs occurrence of motifs in various networks
motifs in the world wide web
X
Y
Z
X
Y Zfeedback with two
mutual dyadsfully connected triad
X
Y Zuplinked mutual dyad
Nreal = 110000Nrand = 2000±100
Nreal = 6800000Nrand = 50000±400
Nreal = 1200000Nrand = 10000±200
28 / 33
motifs occurrence of motifs in various networks
motifs developmental networks
X
Y Z
X
Y Z
29 / 33
motifs occurrence of motifs in various networks
a careful look at the statistical methods
What has been done?
- Real network randomization−→ random network- Posing of null hypothesis:
“The occurrence of motifs is the same in both networks“- The null hypothesis is rejected by a statistical test
→ Conclusion:Evolution prefers motifs that are overrepresented and disfavours others
30 / 33
motifs occurrence of motifs in various networks
a careful look at the statistical methods
- Create a random toy model- Probability of connection between two nodes
reduces with distance
- Test model against random network with same # of nodes and edges- There is a significant occurrence of motifs in the toy model!→ It is clearly not evolution which prefers those motifs
→ Spatial clustering can create motifs
31 / 33
motifs occurrence of motifs in various networks
a careful look at the statistical methods
- Create a random toy model- Probability of connection between two nodes
reduces with distance
- Test model against random network with same # of nodes and edges- There is a significant occurrence of motifs in the toy model!→ It is clearly not evolution which prefers those motifs
→ Spatial clustering can create motifs
31 / 33
motifs occurrence of motifs in various networks
a careful look at the statistical methods
- Create a random toy model- Probability of connection between two nodes
reduces with distance
- Test model against random network with same # of nodes and edges- There is a significant occurrence of motifs in the toy model!→ It is clearly not evolution which prefers those motifs
→ Spatial clustering can create motifs
31 / 33
references
references
• Alon, U. Network motifs: theory and experimental approaches.Nature Rev. Genet. 8, 450-461 (2007).
• Shen-Orr, S. S., Milo, R., Mangan, S. & Alon, U. Network motifs inthe transcriptional regulation network of Escherichia coli.Nature Genet. 31, 64–68 (2002).
• Milo, R. et al. Network motifs: simple building blocks of complexnetworks. Science 298, 824–827 (2002).
• Alon, U. Introduction to Systems Biology: Design Principles OfBiological Circuits (CRC, Boca Raton, 2007).
• Artzy-Randrup, Y. et al. Comment on “Network Motifs: SimpleBuilding Blocks of Complex Networks” and “Superfamilies of Evolvedand Designed Networks”. Science 305, 1107 (2004).
32 / 33
résumé
résumé
- We can identify repeated small patterns in real networks
- Comparison to randomized networks shows a significant accumulation ofmotifs in real networks
- We have to be careful which random network to use as null hypothesis
- We can describe the behaviour of the isolated motif
33 / 33
introductionmotivationmethods
geneticstranscriptiontranslationdynamics
motifsautoregulationfeed forward loopsingle-input moduledense overlapping regulonoccurrence of motifs in various networks