Uri Alon’s lab 10/02

Network of transcriptional interactions in E. coli

Thieffry, Collado-Vides, 1998Shen-Orr, Alon, Nature Genetics 2002

(Rosenfeld,Elowitz,Alon, JMB 323:785 2002)

The assumptions

• X is always expressed

• X requires Sx to be active X*

• Y requires Sy to be active Y*

• Functional FFL - a change in Sx causes a change in Y sufficient to cause a change in Z

Mangan et. al, PNAS (2003)

Logical gate

• AND gate– f(X*,Kxz) * f(Y*,Kyz)

• where X and Y are either activators or repressors

• OR gate– Sum of X and Y regulation functions taking

competitive binding into account – question – why not allow for competitive binding in

AND gate

Steady state :Coherent Type 1 – AND gate

X

Y

Z

Sx

Sy

Sx Sy Change in Z

0 0 0

0 1 0

1 0 0

1 1 1

Z production requires

Sx AND Sy

Steady state :Coherent Type 2 – AND gate

X

Y

Z

Sx

Sy

Sx Sy Change in Z

0 0 0

0 1 1

1 0 0

1 1 0

Z production requires

Not Sx AND Sy

Steady state :Coherent Type 3 – AND gate

X

Y

Z

Sx

Sy

Sx Sy Change in Z

0 0 1

0 1 1

1 0 0

1 1 0

Z production requires

(Not Sx +Sy) OR

(Not Sx + Not Sy)in other words

Not SxSy does notmatter becauseY is not expressed

Steady state :Coherent Type 4 – AND gate

X

Y

Z

Sx

Sy

Sx Sy Change in Z

0 0 0

0 1 0

1 0 1

1 1 1

Z production requires

Sx

Sy does notmatter becauseY is repressed

Steady state: Summary of coherent AND gate FFL

• Type 1 Sx AND Sy• Type 2 Not Sx AND Sy• Type 3 Not Sx• Type 4 Sx

• Type 1 & 2 appear abundantly in coli and yeast unlike type 3 & 4

Steady state: Quick Summary of incoherent AND gate FFL

• Type 1 Sx AND Not Sy• Type 2 Not Sx AND Not Sy• Type 3 0• Type 4 0

• Again, only 1 & 2 use both Sx and Sy and in yeast they are the only ones to appear abundantly (in coli incoherent FFL are rare)

Kinetics: Coherent FFL are sign sensitive delay elements

Sign sensitive – Get response (i.e. delay) in one direction (i.e. on to off) but not in the other (off to on)

X

Y

Z

Sx

Sy

Sign sensitivity direction depends on Z’s steady state activation functions – when Sx is required for activation delay is in on step and when NOT Sx delay is in off step

FFL function – a filter

• Persistence detector• A sign-sensitive delay• Database -> Motifs -> Theory -> Experiments

Threshold for Y being active

Mangan et. al, PNAS (2003)

Maximal response to a pulse is filtered by FFL

Simulation

X

ZX

Y

Z

Input pulse to X of duration T T

Response

Pulse duration T

Glucose pulse experiment shows filtering by arabinose FFL

Max response

crp

lacZ

crp

araC

araB

Pulse duration [min]Mangan, et. al. JMB (2003).

Delay per cascade step ~ one cell cycle

Kinetics: Incoherent FFL can generate pulses controlled by Sy

X

Y

Z

Sx

Sy

X

Y

Sx

Sy

Z

Kinetics: Incoherent FFL can accelerate response

X

Y

Sx

Sy

Z

make promoter stronger X

Y

Z

Sx

Sy

OR gates – generally reversed

X

Y

Z

Sx

Sy

comparing networks of different sizes for similarity in local structure

Different Subgraphs

Normalized significance

Uri Alon’s lab 10/02