-1 -0.5 0 0.5 1 1.5 2 2.5

0

0.5

1

-1 -0.5 0 0.5 1 1.5 2 2.50

0.5

1

-1 -0.5 0 0.5 1 1.5 2 2.50

0.2

0.4

Kyz

Zst

Sx

Y*Y*

Z

Time

Fig 4.11a: Dynamics of the I1-FFL with AND input function following an ON-step of Sx.The step occurs at t=0, and X rapidly transits to its active form X*. As a Result, the repressor protein Y is produced, and represses Z productionwhen it crosses the repression threshold Kyz. In this figure, all production and decay rates are equal to 1.

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Z t

Z /

Zm

F=2

F=5

F=20

Fig 4.11b: Expression dynamics of Z in an incoherent type-1 FFL with repression coefficients F=2,5,20. The repression coefficientis the ratio of the maximal expression without active repressor to the steady-stateexpression with active repressor. Trep is the time when repression begins, and is themoment of maximal Z concentration.

Trep

T1/2

I1-FFL T1/2 (simple reg.)

Figure 4.12a: Response time of the I1-FFL is shorter than simple regulation that reaches same steady-state level. The normalized response time of simple regulation is log(2)~0.7. Simple regulation- dashed lines, I1-FFL- full lines)

I1-FFL

Simple regulation

Z / Zst

o

0.5

1

1.5

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Ratio of unrepressed to repressed expression, F

Response timeαz T1/2 log(2)

Figure 4.12b: Response time of the I1-FFL as a function of the repressioncoefficient F. F is the ratio of unrepressed to repressed Zexpression. Green horizontal line: normalizedresponse time of simple regulation, αz T1/2 =log(2).

Why Some FFL are rarely selected?

E.g. I1 and I4

-1 -0.5 0 0.5 1 1.5 2 2.50

0.5

1

-1 -0.5 0 0.5 1 1.5 2 2.50

0.5

1

-1 -0.5 0 0.5 1 1.5 2 2.50

0.5

1

Sx

Y

Z

Sy present

Sy absent

Fig 4.13: The effect of input signal Sy on the dynamics of the I1-FFL. When Sy is absent, Y is not active as a repressor, and the concentration of protein Z shows an increase to a high unrepressed steady-state (dashed line)

X

Y

Z

AND

Fig 4.14: The incoherent type-1 FFL and type-4 FFL

X

Y

Z

AND

I1-FFL I4-FFL

-1 -0.5 0 0.5 1 1.5 2 2.5

0

0.5

1

-1 -0.5 0 0.5 1 1.5 2 2.50

0.5

1

-1 -0.5 0 0.5 1 1.5 2 2.50

0.2

0.4

Kyz

Fig 4.15: Dynamics of the I4-FFL following a step of Sx. In the presence of Sx,protein X is active and activates Z production but represses production of Y. When Ylevels decay below the activation coefficientKyz, the concentration of Z begins to drop. Production and decay rates are βZ=1, αz= αy=1, F=10. The signal Sy is present throughout.

Time

X Y

Z

X

Y

X’

Y’

X Y

homologous

non-homologous

non-homologous

Z

Z Z’

Fi g 4.16: On the evolution of the FFLs. (a) The V-shaped pattern in which X and Y regulate Z is stronglyselected because it allows regulation based on two inputs. The edge from X to Y (white arrow) must be selected based on the basis of an additional dynamical functions (e.g. sign sensitive delay, acceleration, pulse generation). (b) In many cases homologous genes Z and Z' in different organisms are regulated in a FFL in response to the same stimuli, but the two regulators X and Y in the FFL are not homologous to the regulators X' and Y'. Homology means sufficient similarity in the genes sequence to indicate that The genes have a common ancestor.

)a()b(

Fig 5.1 The single input module (SIM) network motif. Transcription factor X regulatesa group of genes Z1,.. Zn, with no additional transcription factor inputs. X usually regulates it self. An example of a SIM, the argninine biosynthesis pathway(in this system, all regulations are repression).

E1 E2 E3S0 S1 S2 S3

R

Fig 5.2 A single-input module (SIM) regulating a three-step metabolic pathway. The master repressor R represses a group of genes that encode for enzymes, E1,E2 E3 (each on a different operon). These enzymes catalyze the conversion of substrate S0 to S1 to S2 culminating in the product S3. The product S3 binds to R, and increases the probability that R is in its active state R*, in which it binds the promoters to repress the production of enzymes. This closes a negative feedback loop, where high levels of S3 lead to a reduction in its rate of production.

Gene E1

product

Gene E2 Gene E3

Fig 5.3 The SIM can generate temporal programs of expression. As theactivity of X gradually rises, it crosses the different thresholds for each target promoter in a defined order. When X activity declines, it crosses the thresholds inreverse order (last-in-first out or LIFO order).

Source: shen-orr nature genetics 2002

Fig 5.4 Temporal order in arginine biosynthesis system with minutes between genes. Colored bars showexpression from the promoters of the different operons in the system, measured by means of a luminescent

reporter gene. The position of each gene product in the pathways that produce arginine is shown.

Zaslaver et al Nature genetics 2004

Fig 5.5, the 199 4-node directed connected subgraphsFig 5.5, the 199 4-node directed connected subgraphs

Fig 5.6: Simple topological generalizations of the FFL. Each topological generalization corresponds to duplicating one of the nodes of the FFL and all of its edges. (a) The FFL, (b) generalizations based on duplicating one node ( c) multi-node generalizations. Source: Kashtan et al, PRE 2004.

Fig 5.7: The flagella motor of E. coli and its assembly steps

info.bio.cmu.edu/.../ FlagellaMotor.html

www.aip.org/mgr/png/2002/174.htm

Annual Review of Microbiology

X

Y

OR OR OR

Z1 Z2 Zn

K1K2 Kn

K1’ K2’Kn’

Fig 5.8: Schematic plan of the multi-output FFL that regulates the flagella motor genes. Shown are the logic gates at each promoter, and the activation thresholds. X=flhDC, Y=fliA, Z1=fliL, Z2=fliE etc.

Kxy

5.9 :Temporal order in the flagella system of E. coli. Colored bars are the normalized expression of each promoter, where blue is low and red is high expression. Expression was measured by means of green fluorescent reporter gene. The temporal order matches the assembly order of the flagella, in which proteins are added going from the

intra-cellular to the extra-cellular sides. Source: Kalir etal Science 2001

0 1 2 3 4 5 6 7 8 9 100

0.5

1X

0 1 2 3 4 5 6 7 8 9 100

0.5

1Y

0 1 2 3 4 5 6 7 8 9 100

0.5

1

time

Z1

Z2

X

Y

Z1 Z2

K2K1

K1 ’ K2’

K1<K2

K1’>K2’

Fig 5.10: First-in First out order (FIFO) in the multi-Z FFL with OR-logic input functions.The output genes Z1 and Z2 are turned on when X crossesActivation thresholds K1 and K2 (dashed lines). The genesAre turned off when Y decays below activation thresholdsK1’ and K2’. When the order of K1 and K2 is opposite to that of K1’ and K2’,FIFO order is obtained.

K2K1

K1’

K2’

time

Fig 5.11: The 4-node network motifs in sensory transcription networks.

X1

Z1

X

Y

Z1

X2

Z2 Z2

Bifan Two-output

Feed-forward loop

1

2 2

3

1 1

2 2

3 3

11

2 2

3 31

2 2

1 1

2 2

1 1 1

2 2

1

2

Fig 5.12 bifan

Two-output FFL

The main five-node network motifs in the transcription network ofE. coli. The bi-fan generalizes to larger patterns with a row of inputs and a row of outputs.

Fig 5.13 The Dense-overlapping regulons (DOR) network motif, and an examplein the E. coli stress response and stationary phase system.

Source: Shen-Orr, R Milo, S Mangan & U Alon, Nature Genetics, 31:64-68 (2002) .

Fig 5.14 The global structure of part of the E. coli transcription network. Ellipsesrepresent transcription factors that read the signals from the environment. Circles are output genes and operons. Rectangles are DORs. Triangles are outputs of single- or multi-output FFLs. Squares are outputs of SIMs. Blue and red lines correspond to activation and repression interactions.

X

Y

Z

Fig 5.15 Network Motifs in sensory transcription networks

X

Y

Z

Sign-sensitive delayFilters out brief ON (OFF) input pulseswhen the Z-input functionIs AND (OR) logic.

Pulse generationSigns-sensitiveResponse acceleration

NegativeAuto-regulation

PositiveAuto-regulation

CoherentFeed-forward loop

C1- FFL

IncoherentFeed-forward loop

I1-FFL

X

Slows response timePossible bi-stability Chapter 3.5.1

Xspeeds response time,steady-state robust tofluctuations in production

Chapter 3

Chapter 4.5-4.6

Chapter 4.7

Single- Input Module (SIM)

X

Y1 Y2 . . . Yn

Coordinated controlTemporal (LIFO) order of Promoter activity

X

Y

Z2 Zn

Multi-output Feed-forward loop(multi-output FFL)

Acts as FFL for each input(sign-sensitive delay, etc)FIFO temporal order ofpromoter activity

X1 X2 Xn

Y1 Y2 Ym

Dense overlappingRegulons) DOR(

Combinatorial logicbased on multiple inputs,depends onInput-function of each gene

Chapter5.3-4

Chapter5.5

Chapter5.6

BifanX1 X2

Y1 Y2

Fig 5.15 cont: Network Motifs in Sensory transcription networks

Z1

X Y X Y

X Y

Z

X Y

Z

X Y Z

ON ON ON

OFF OFF OFF

Steady-State 1

Steady-State 2

X Y Z

ON OFF OFF

OFF ON ON

Steady-State 1

Steady-State 2

Double-positive feedback loop

Double-negativefeedback loop

Fig 6.1 Positive transcriptional feedback loops with two nodes. The double positiveloop has two activation interactions, and the double negative is made of two repression interactions.An output gene Z is regulated as shown. Each of the feedback loops has two steady states: both X and Y genes ON or OFF in the double-positive loop, and either ON in the double-negative loop.

X Y X Y

Fig 6.2: a) Two-node feedback loops with auto-regulation are a common network motifIn developmental transcription networks. b) The ten distinct types of regulating feedback motifs, each corresponding to a different combination of regulation signs.

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

a(

b(

X Y

Z

X Y

Z

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

Z*

X

Y

time time

memory

6.3 The regulated-feedback network motif in developmental transcription networks. (a) Double positive feedback loop. When Z is activated, X and Y begin to be produced They can remain locked ON even when Z is deactivated (at times after the dashed line). (b) Double negative feedback loop. Here Z acts to switch the steady states. Initially Y is high and represses X. After Z is activated, X is produced and Y is repressed. This state can persist even after Z is deactivated. Thus, in both a and b, the feedback Implements a memory.

a(b(

memory

Z*

X

Y

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

X

Y

Z

Kxy

Kyz

X Y Z

Cell generations

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

0 1 2 3 4 5 6

0

0.5

1

X Y Z

X

Y

Z

Cell generations

Fig 6.4 Transcription cascades can generate delays on the order of thecell-generation time (in the case of stable proteins). Each step in the cascade activatesor represses the next step when it crosses its threshold (dashed lines). Shown are

a cascade of activators and a cascade of repressors.

a( b(

X1

Y1

Z1

AND

AND

X2

Y2

Z2

AND

AND

Z3

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1Z1 Z2

Z3

time

Z

Fig 6.5: The transcription networkguiding development of the B. subtilisspore. Z1, Z2 and Z3 representgroups of tens to hundreds of genes. This network is made of two type-1 incoherent FFLs, that generate pulses of Z1 and Z2, and two type-1 coherent FFLs, one of whichgenerates a delayed step of Z3. Based on R. Losick, PLOS 2004

X-pX v

v

Y-pYv

v

Z-pZ v

v

T*Tv

v

Transcription of genes

Ligand binds receptor

activating the phosphorylation of kinase X

Phosphatase

6.6 Protein kinase cascade: Ligand binds the receptorwhich leads, usually through adaptor proteins , toPhosphorylation of kinase X. Kinase X is activeWhen phosphorylated, X-p. X-p phosphorylates kinase Y.Y-p, in turn, phosphorylates Z. The last kinase, Z-p,Phosphorylates transcription factor T, makingit active, T*. T* enters the nucleus and activates (or represses)transcription of genes. Phoaphatases remove thephosphoryl groups (light arrows).

6.7 Network motifs in signal-transduction networks. The main four-node motifs are the diamond and the bifan.The diamond has four nodes, and three different roles,labeled 1,2 and 3. Each generalization is obtained by duplicating oneof the nodes and all of its edges. These generalizations are all also network motifs in signaltransduction networks.

bifan diamond

1

2 2

3

1

2 2

3

1 1

2 2

3 3

11

2 2

3 3