Download Biological networks and network motifs

Network Motifs: simple Building Blocks of
Complex Networks
R. Milo et. al. Science 298, 824 (2002)
Y. Lahini
The cell and the environment
•
•
•
Cells need to react to their environment
Reaction is by synthesizing task-specific proteins, on demand.
The solution – regulated transcription network
•
E. Coli – 1000 protein types at any given moment >4000 genes (or possible
protein types) – need regulatory mechanism to select the active set
We are interested in the design principles of this network
•
Proteins are encoded by DNA
Protein
translation
RNA
transcription
DNA
DNA – the instruction manual, 4-letter
chemical alphabet – A,G,T,C
Gene Regulation
• Proteins are encoded by the DNA of the organism.
• Proteins regulate expression of other proteins by interacting
with the DNA
protein
Transcription factor
external signal
DNA
promoter region
ACCGTTGCAT
Coding region
Two types of Transcription Factors: 1.Activators
X
No transcription
X binding site
X
Y
gene Y
Y
Sub-second
Y
Sx
X
X*
Y
Y
Seconds
X*
INCREASED TRANSCRIPTION
Hours
Bound activator
Separation of time scales: TF activation level is in steady state
Two types of Transcription Factors: Repressors
X
Y
Y
Unbound repressor
Y
Y
X
Bound repressor
Sx
X
X*
No transcription
X*
Bound repressor
Y
Equations of gene regulation
 
• If X* regulates Y, the net production rate of gene Y is dY  f X *  Y
dt
• α- Dilution/degradation rate
f ( X * )   ( X *  K )
f ( X * )   ( X *  K )

/2
0
•
•
•
X*
Y promoter activity
Y promoter activity
X* Y

/2
0
0
0.5
1
1.5
Activator concentration X*/K
2
Y
0
1.5
1
0.5
Repressor concentration X*/K
K – activation coefficient [concentration]; related to the affinity
β – maximal expression level
Step approximation – gene is on (rate β) or off (rate 0) with threshold K
2
The gene regulatory network of E. coli
• Nodes are proteins (or the genes that encode them)
• Edges = regulatory relation between two proteins
X
Y
Analyzing networks
• The idea- patterns that occur in the real network much more then in
a randomized network, must have functional significance.
• The randomized networks share the same number of edges and
number of nodes, but edges are assigned at random
The known E. Coli transcription network
A random graph based on the same node statistics
3-node network motif – the feedforward loop
Nreal=40
Nrand=7±3
The feedforward loop : a sign sensitive filter
The feedforward loop is a filter for transient signals while allowing fast shutdown
Mangan, Alon, PNAS, JMB, 2003
The Feedforward loop : a sign sensitive filter
Vs.
=lacZYA
=araBAD
OFF pulse
Mangan, Alon, PNAS, JMB, 2003
Single Input Module
kk 3
3
kk 22
kk 11
Z1Z1
Z2Z2
Z3Z3
Temporal and expression level program generator
• The temporal order is encoded in a hierarchy of thresholds
• Expression levels hierarchy is encoded in hierarchy of promoter activities
Single Input Module motif is responsible for exact
timing in the flagella assembly
Single Input Module motif is responsible for exact
timing in the flagella assembly
Kalir et. al., science,2001
The gene regulatory network of E. coli
Single input modules
• Shallow network, few long cascades.
• Modular
Shen-Orr et. al. Nature Genetics 2002
Feed-forward loops
Evolution of transcription networks
• In 1 day, 1010 copies of e-coli, 1010 replication of DNA.
• Mutation rate is 10-9
– 10 mutations per letter in the population per day
• Even single DNA base change in the promoter can change the
activation/repression rate
• Edges can be lost or gained (i.e. selected) easily.
Links between WebPages – a completely
different set of motifs is found
•
•
WebPages are nodes and Links are directed edges
3 node results:
Structure of a nematode neuronal circuitry
Head Sensory
Ring Motor
[White, Brenner 1986; Durbin, Thesis, 1987]
Ventral Cord
Motor
Neurons and transcription
share similar motifs
C. elegans
Summary
• The production of proteins in cells is regulated using a complex
regulation network
• Network motifs: simple building blocks of complex networks
• An algorithm to identify network motifs
• Example: the transcription network of E. coli.
• The feed forward loop as a sign sensitive filter
• The single input module: exact temporal ordering of protein
expression
Thanks
Equations of gene regulation
•
•
If X* regulates Y, the net production rate of gene Y is dY  f X *   Y
dt
α- Dilution/degradation rate
f (X ) 
*
•
•
•
•
 X *n
K n  X *n
  ( X *  K )
f (X *) 

1
 
*
X
K
n
  ( X *  K )
K – activation coefficient [concentration]; related to the affinity
Β – maximal expression level
n – the Hill parameter (steepness of the response, usually 1-4)
Step approximation – gene is on (rate β) or off (rate 0) with threshold K
Actors’ web
Mathematicians &
Computer Scientists
Sexual contacts: M. E. J. Newman, The structure and function of complex networks, SIAM Review 45, 167-256 (2003).
High school dating: Data drawn from Peter S. Bearman, James Moody, and Katherine Stovel visualized by Mark Newman
Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.
Metabolic networks
KEGG database: http://www.genome.ad.jp/kegg/kegg2.html
Transcription regulatory networks
Bacterium: E. coli
Single-celled eukaryote:
S. cerevisiae
C. elegans neuronal
net
Dense Overlapping Regulons (DOR)
X1
X2
X3
…
Xn
Bi-fan
Z1
Z2
Z3
…
Zm
Nreal = 203
Nrand = 47±12
Z Score = 13
Array of gates for hard-wired decision making
Buchler, Gerland, Hwa, PNAS 2003
Setty, Mayo, Surette, Alon, PNAS 2003