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Complex networks are found throughout
biology
Can we define the basic building
blocks of networks?
Generalize the notion of MOTIFS, widely used in sequence
analysis, to the level of networks.
Sequence motif: a sequence that appears much more frequently
than in randomized sequences.
‘Network motif’: a pattern that appear much more frequently
than in randomized networks.
Database of direct transcription interactions in
E. coli
Transcription factors
X
Directed graph
Y
Z
X
Y
operons
Z
424 nodes, 519 interactions
Based on selected data from RegulonDB + 100 interactions from literature search
Shen-Orr 2002, Thieffry Collado-Vides 1998
Algorithm that finds n-node network motifs
Find all n-node circuits in real graph
N
Examples of 3-node circuits
X
X
Y
X
Y
Z
U
Y
Z
X
Z
T
Y
Z
M
W
And in a set of randomized graphs with the same distribution
of incoming and outgoing arrows.
Assign P-value probability of occurring more at random than
in the real graph
Randomization: Newman, 2000, Sneppen& Malsov 2002
The thirteen 3-node connected subgraphs
Two types of feed-forward loops are significant
X
Y
Z
Coherent
X
Y
Z
Incoherent
Dynamics of the feed-forward loop system
X(t) = time varying input
dY / dt = F(X) – a Y
dZ / dt = F(X) F(Y) – b Z
F
Threshold
Mangan, PNAS, JMB, 2003
The feed-forward loop is a filter for
transient signals allowing fast shutdown
Mangan, PNAS, JMB, 2003
GFP Reporter plasmid system for promoter activity
Lutz, Bujard 1997
Kalir, Leibler, Surette, Alon, Science 2001
Construct strains, each reporting for a different promoter
Plasmid with promoter for gene X
controlling a reporter
Gene X intact on chromosome
High throughput cloning:
Promoter PCR, restriction, ligation, preps all in 96well format.
Construct strains, each reporting for a different promoter
Grow strains under same conditions and
measure reporter fluorescence or luminescence
Each well reports
for a different
promoter
Commercial fluorimeter/luminometer
shakes, temperature control, imjectors.
Measure at the same time cell optical density.
Activity of 96 promoters across 20 h growth in 20 conditions
6
10
6
10
5
10
4
10
GFP/OD
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5
10
7 min resolution
4
10
0
100
minimal + aa
200
300
LB
400
500
minimal - aa
600
700
arabinose 0.5mM
GFP repeat 2
Day-day reproducibility of better than 10%
*2
*1.1
*0.9
10%
*0.5
2-fold
GFP repeat 1
Maximal response to a pulse of X is filtered by FFL
Input pulse to X of duration T
Response
T
X
Z
X
Y
Z
Pulse duration T
Simulation
Sign-sensitive filtering by arabinose feed-forward loop
Max
response
crp
lacZ
crp
araC
araB
cAMP Pulse duration [min]
Experiments: Mangan, Zaslaver, Alon, JMB (2003).
Feedforward loop is a sign-sensitive filter
Vs.
=lacZYA
=araBAD
OFF pulse
Mangan Zaslaver, Alon JMB 2003
Shen-Orr, Milo, Mangan, Alon Nature genetics 2002
The single-input module can generate a temporal
program of gene expression
Flagella operons are activated in temporal order
Kalir, Leibler, Surette, Alon Science 2001
Laub, McAdams, Shapiro Science 2000
Temporal order matches position of proteins
along the flagella motor
Temporal order in Arginine biosynthesis system
with minutes between genes
Turn ON (arg removed)
Turn OFF (arg added)
Time [min]
Time
Zaslaver, Surette, Alon,
Nature Genetics 2004
Temporal order matches enzyme position in the pathway
Turn ON (arg removed)
Turn OFF (arg added)
Glutamate
N-Ac-Glutamate
N-Ac-glutamyl-p
N-Ac-glutamyl-SA
N-Ac-Ornithine
Citrulline
Time [min]
Arginine
Time
Klipp, Heinrich
199 4-node directed connected subgraphs
4-node motifs in E. coli network: overlapping regulation
X
X
Y
Z
W
Overlapping regulation
Y
Z1
Z2
Generalization of
Feedforward loop
to two controlled genes
Hengge-Aronis
Mapping Logic gates using GFP
reporter arrays (LacZ)
IPTG
cAMP
AND
GATE?
LacZ
Setty, Mayo, Surette, Alon, PNAS 2003
Can we draw complex networks in an understandable way?
E. coli and yeast transcriptional networks show the same motifs
X
Y
Z
X
Feed-forward loop: coli 40, yeast 74,
over 10 STDs from random networks!
Same two types out of eight,
coherent and incoherent FFL
X
Y
The same 4-node motifs
Y
Also SIMS and DORs
Z
W
Z1
Z2
The same network motifs characterize transcriptional
regulation in a eukaryote and a prokaryote
Milo et al 2002, Lee at al 2002
Developmental transcription network made of
feed-forward loops: B. subtilis sporulation
X1
Y1
AND
AND
Z1
X2
Y2
AND
Z2
AND
Z3
R. Losick et al. , PLOS 2004
Feed-forward loops drive temporal pattern
of pulses of expression
X1
Z
Y1
Z1
1
Z3
Z2
0.8
0.6
AND
0.4
AND
Z1
0.2
X2
0
Y2
AND
Z2
AND
Z3
0
1
2
3
4
5
6
7
8
9
time
10
Food webs represent predatory
interactions between species
Skipwith pond (25 nodes), primarily invertebrates
Little Rock Lake (92 nodes), pelagic and benthic species
Bridge Brook Lake (25 nodes), pelagic lake species
Chesapeake Bay (31 nodes), emphasizing larger fishes
Ythan Estuary (78 nodes) birds, fishes, invertebrates
Coachella Valley (29 nodes), diverse desert taxa
St. Martin Island (42 nodes), lizards
Source: Williams & Martinez, 2000
Foodwebs have
“consensus motifs”
• Consensus motifs –
different from
transcription networks
• Feedforward is not motif
- omnivores are underrepresented
Links between WWW Pages – a
completely different set of motifs is found
• WebPages are nodes and
Links are directed edges
• 3 node results
Full reverse engineering of electronic
circuit from transistor to module level
Each node represents a transistor
Each node represents a transistor motif:
Logic gate
Each node represents a gate motif:
D-flipflop
Each node represents a gate-flipflop motif:
counter
Itzkovitz 2004
Map of synaptic connections between C. elegans neurons
White, Brenner, 1986
Feedforward loops in C. elegans avoidance reflex circuit
Nose touch
Noxious chemicals, nose touch
FLP
ASH
Sensory neurons
AVD
Interneurons
AVA
Backward movement
Thomas & Lockery 1999
Networks can be grouped to super-families
based on the significance profile
Normalized
Z-score
Milo et al Science 2004
Summary –network motifs
Network motifs, significant patterns
in networks
Three motifs in transcription networks
and their functions
High-accuracy promoter activity measurements
from living cells
Milo Science 2002, Shen-Orr Nat. Gen. 2002, Itzkovitz PRE 2003,
algorithms at www.weizmann.ac.il/mcb/UriAlon
Acknowledgments
Weizmann Institute, Israel
Alex Sigal
Naama Geva
Galit Lahav
Nitzan Rosenfeld
Shiraz Kalir
Ron Milo
Adi Natan
Shmoolik Mangam
Shalev Itzkovitz
Nadav Kashtan
M. Elowitz, Caltech
S. Leibler, Rockefeller
M.G. Surette, Calgary
H. Margalit, Jerusalem
Alon Zaslaver
Erez Dekel
Avi Mayo
Yaki Setty
Negative feedback loop with one
transcription arm and one protein
arm is a common network motif
across organisms
Bacteria
Yeast
Fruit-Flies
x
sH
Ime1
smo
y
dnaK
dnaJ
Ime2
Ptc
HIF
p53
iNOS
Mdm2
Mammals
HSF1
hsp70
hsp90
NFkB
IkB
Negative feedback in engineering
uses fast control on slow devices.
Power
supply
Heater
Temperature
slow
Thermostat
fast
Engineers tune the feedback parameters to obtain rapid
and stable temperature control
Negative Feedback can show over-damping, damped
or un-damped oscillations, depending on parameters
Negative Feedback can show over-damping, damped
or un-damped oscillations, depending on parameters
Engineers usually prefer damped oscillationsfast response, not too much overshoot
Negative Feedback can show over-damping, damped
or un-damped oscillations, depending on parameters
Engineers usually try to avoid parameters that give Undamped oscillations
real-time proteomics in single
living cells for p53-mdm2 dynamics
0.2Kb
0.7Kb
1.2Kb
pMT-I
p53
CFP
3.5Kb
15Kb
pMdm2
Mdm2
Hygro
0.7Kb
YFP
Neo
P53-CFP
Mdm2-YFP
p53-CFP and Mdm2-YFP fusion protein allow imaging of p53 and
MDM2 protein in living cells
G. Lahav
Undamped p53 pulses in individual cells
following DNA damage
‘Digital behavior’ in the p53mdm2 feedback loop
Number of cells with multiple pulses increases
with damage, but not the size/shape of pulse.
Analog design
Digital design
Dynamics of the p53-mdm2
loop in single living cells,
and the design principles of
biological feedback
Galit Lahav
Uri Alon
Weizmann Institute
Israel
overview
• Introduction- negative feedback
loop motif
• System for real time proteomics
of p53-mdm2 in living human cells
• Dynamics of p53-mdm2 at the
single cell level
• Design principles of biological
feedback
Negative feedback loop with one
transcription arm and one protein
arm is a common network motif
across organisms
Bacteria
Yeast
Fruit-Flies
x
sH
Ime1
smo
y
dnaK
dnaJ
Ime2
Ptc
HIF
p53
iNOS
Mdm2
Mammals
HSF1
hsp70
hsp90
NFkB
IkB
Negative feedback in engineering
uses fast control on slow devices.
Power
supply
Heater
Temperature
slow
Thermostat
fast
Engineers tune the feedback parameters to obtain rapid
and stable temperature control
Negative Feedback can show over-damping, damped
or un-damped oscillations, depending on parameters
Negative Feedback can show over-damping, damped
or un-damped oscillations, depending on parameters
Engineers usually prefer damped oscillationsfast response, not too much overshoot
Negative Feedback can show over-damping, damped
or un-damped oscillations, depending on parameters
Engineers usually try to avoid parameters that give Undamped oscillations
What about biological feedback control?
P53-CFP
Mdm2-YFP
Kohn, Mol Biol Cell, 1999
Our model system- perhaps the best studied example
in mammals, p53-mdm2 negative feedback loop
The p53 Network
MDM2
p53
One cell death =
Protection of the
whole organism
Cell cycle arrest
G1/S
G2/M
Is the damage
repairable?
no
Apoptosis
yes
DNA repair
Damped oscillations in p53-mdm2 and
NFkB-IkB negative feedback loops
western
p53-mdm2
Hrs after g 0 1 2
3 4
5
6
7 8
p53
western
MDM2
6
5
4
3
2
1
0
p53
0
Lev Bar-Or et al, PNAS, 2000
1
2
3
mdm2
4
5
6
Tim e (hours after g irradiation)
Damped oscillations
NFkB-IkB
Electro Mobility
Gel-Shift Assay
Hoffman et al, Science, 2002
Measurements on populations!
7
8
System for real-time proteomics in single
living cells for p53-mdm2 kinetics.
0.2Kb
0.7Kb
1.2Kb
pMT-I
p53
CFP
3.5Kb
15Kb
pMdm2
Mdm2
Hygro
0.7Kb
YFP
Neo
P53-CFP
Mdm2-YFP
p53-CFP and Mdm2-YFP fusion protein allow imaging of p53 and
MDM2 protein in living cells
p53-CFP shows damped oscillations in
western following DNA damage
similar to endogenous p53.
Hours after g:
0
½
1
2
3
4
5
6
7
8
9
p53-CFP
p53
100
90
80
70
60
50
p53
40
30
20
p53-CFP
10
0
0
2
4
6
8
10
Mcf7 p53+/+
Mdm2-YFP kinetics are
similar to endogenous Mdm2.
Hours after g Irradiation
0
½
1 2 3 4
5
6
7
8
9
Mdm2-YFP
Mdm2
120
100
80
Mdm2-YFP
60
40
Mdm2
20
0
0
2
4
6
8
10
Mcf7 p53+/+ Mdm2 +/+
Mdm2-YFP appears to undergo the same decrease
as endogenous mdm2 at early times
p53-CFP and Mdm2-YFP expression after DNA
damage in living human cells.
p53 pulses in the nucleus
Mdm2 pulses follow p53 pulses in the nucleus
Different behavior of individual cells
following DNA damage
Different behavior of individual cells
following DNA damage
Different behavior of individual cells
following DNA damage
Different behavior of individual cells
following DNA damage
Different behavior of individual cells
following DNA damage
Two groups of behavior: one peak
and two peaks, with small variations
inside each group
Ymax2
Ymax1
Peak Width=350±60min (SD)
1st Peak Width=360±50min (SD)
2nd Peak Width=340±40min (SD)
Ymax2/Ymax1=1.1±0.2 (SD)
T(Ymax2)-T(Ymax1)=370±50min (SD)
Average of single cell data is similar to
Western: damped oscillations are an
artifact of mixing two behavior classes
The irradiation level determines
the distribution of cells
undergoing 0,1 or 2 oscillations
100
% of cells
80
60
40
2.5Gy
20
0
0
1
Numbers of pulses
2+
The irradiation level determines
the distribution of cells
undergoing 0,1 or 2 oscillations
100
% of cells
80
10Gy
60
40
2.5Gy
20
0
0
1
Numbers of pulses
2+
The irradiation level determines
the distribution of cells
undergoing 0,1 or 2 oscillations
100
% of cells
80
10Gy
60
40
2.5Gy
20
0
0.3Gy
0
1
Numbers of pulses
2+
The irradiation level determines
the distribution of cells
undergoing 0,1 or 2 oscillations
100
% of cells
80
10Gy
60
40
2.5Gy5Gy
20
0
0.3Gy
0
1
Numbers of pulses
2+
0Gy
Mean pulse widths do not depend on DNA
damage level
First pulse width
0.3Gy 2.5Gy 5Gy
10Gy
Second pulse width
2.5Gy 5Gy
10Gy
Mean pulse height does not depend on DNA
damage level
First pulse height Second pulse height
0.3Gy 2.5Gy
5Gy
10Gy
2.5Gy 5Gy
10Gy
‘Digital behavior’ in the p53mdm2 feedback loop
Number of cells with multiple pulses, not the
size/shape of the pulse, increases with damage.
Analog design
Digital design
dxt 
    S  S 0   xt   α1  y t   xt   β x
dt
dx * t 
   S  S 0   xt   α2  y t   x * t 
dt
dy0 t 
y t 
 0
 y  β y    x * t 
dt
dy t 
y t 
 0
 y  α y  y t 
dt
dS t 
2
  s  D  D0   as  y t   S t 
dt
Show limit cycle figure
Individual cells show large amplitude variation
But peak timing is more precise
What's next?
• What is the mechanism for the ‘digital behavior’
in the p53-Mdm2 loop?
• Could different numbers of pulses convey
different 'meanings' to the cell in terms of
expression of downstream genes?
• What about other negative feedback loops…
do they also display ‘digital behavior’?
The goal: dynamic proteomics in
individual living human cells
• Protein concentration and location at high
temporal-resolution and accuracy
• In individual living human cells
• For most of the expressed proteins
Annotated library of cells each of which
Expressed a chromosomally YFP-tagged protein
+automated microscopy and image-analysis
Exon tagging a gene with a fluorescent protein
SA
DNA
RNA
YFP
SD
puro
intron3
intron1
exon1
SA
SD
exon1
exon2
SA
SD
exon2
intron2
exon3
transcription
SA
SD
YFP
puro
exon4
SA
SD
exon3
splicing
mRNA
Protein
exon1 exon2
YFP
exon3
exon4
translation
N
YFP
C
Tagged protein identified using RACE
A
Exon n
YFP
Exon n+1
AAAAAAAAAA
Added seq
472
YFP
Exon n+1
AAAAAAAAAA Added seq
546
B
clone
4c18
4d8
RACE stage
1
1
2
1d13
2
1
2
1d22
1 2
1e18
1
2
C
Clone 1e18
YFP
Ribosomal protein L5
Clone 1e18
1f21
1 2
A wide variety of localization patterns
Dynamic proteomics in individual cells
0 min
10 min
20 min
30 min
Summary
• Network motifs and their biological
function
• Digital pulses of p53
• Dynamic proteomics in individual living
cells
Acknowledgments
Weizmann Institute, Israel
Galit Lahav
Alex Sigal
Naama Geva
Lior Ben-Arzi
Nitzan Rosenfeld
Shiraz Kalir
Inbal Alaluf
Ron Milo
Adi Natan
Shmoolik Mangam
Shalev Itzkovitz
Nadav Kashtan
Ido Zelman
Alon Zaslaver
Shai Shen-Orr
Erez Dekel
Avi Mayo
Yaki Setty
Zvi Kam
Benjamin Geiger
Moshe Oren
Varda Rotter
Stan Leibler, Rockefeller -coli
Mike Surette, Calgary -coli
Arnold Levine, IAS Princeton –p53
Michael Elowitz, Caltech –p53
The heat-shock single-input-module
s32
1
k1
1
dnaKJ
2
k2
2
groEL
3
k3
3
htpG
n
kn
n
d
lon
SINGLE INPUT MODULE NETWORK MOTIF
Heat shock promoters are activated
after ethanol step, and then adapt
4% ethanol
Added at t=0,
Natan et al 2004
Heat shock promoters are turned ON
together and OFF in a temporal
order
Natan et al 2004
Heat-shock promoters are turned
OFF in temporal order
Normalized Promoter Activity
groEL
ftsJ
0.5
htpG
0.4
hslUV
htpX
0.3
Lon
0.2
clpB
clpP
0.1
dnaK
54
60
66
72
78
84
90
96
0
Time from ethanol shock [minutes]
Temporal turn-off order
~3 minutes difference
Natan et al 2004
Turn-off order matches severity of repair
Same principle found in SOS DNA repair [Ronen, Shraiman, Alon PNAS 2002]