network motifs - simple building blocks of complex...

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

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transcription network - autoregulation

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transcription network - outstanding nodes

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transcription network - loops

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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?

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introduction methods


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random network

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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

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genetics

introduction

geneticstranscriptiontranslationdynamics

motifs

genetics transcription

gene expression - transcription

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geneDNA

transcription start site reading direction

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geneDNA


messenger RNA

RNA polymerase

- RNAp transcribes DNA to mRNA

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gene


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

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genetics translation

gene expression - translation of mRNA to protein

en.wikipedia.org/wiki/Translation (biology)

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regulation of gene expression

DNA RNA A protein Atranscription translation

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DNA RNA B protein B

activator

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DNA RNA B protein B

activator

DNA RNA C protein C

repressor

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DNA RNA B protein B

activator

DNA RNA C protein C

repressor

DNA

DNA

nodes: genesedge: transcription

factorRNA A protein A

transcription translation

activator

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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

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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

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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

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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

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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

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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


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

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negative autoregulation

X

- High production rate β can cause strong initial rise- High autorepression leads to saturation at stable level K⇒ response acceleration

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positive autoregulation

X

⇒ higher response time⇒ noise amplifyingWhy is noise good for a cell?→ diversity

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motifs feed forward loop

feed forward loops

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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

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incoherent type 1 feed forward loop

- Response acceleration- Pulse generator

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motifs single-input module

single-input module

→ timed expression of different genes

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motifs dense overlapping regulon

dense overlapping regulon

- Not yet very well understood- Detailed information about connection strength is needed

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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

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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



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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

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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

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motifs developmental networks

X

Y Z

X

Y Z

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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

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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

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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).

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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

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introductionmotivationmethods

geneticstranscriptiontranslationdynamics

motifsautoregulationfeed forward loopsingle-input moduledense overlapping regulonoccurrence of motifs in various networks

network motifs - simple building blocks of complex...

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