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
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