Download - Seminar in Bioinformatics Winter 11/12 An Introduction To System Biology Uri Alon Chapters 3-4
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Seminar in BioinformaticsWinter 11/12
An Introduction To System BiologyUri Alon
Chapters 3-4
Presented by: Nitsan Chrizman
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What's on the menu? Starter
Reminder
Main course Network motifs
AutoregulationThe feed forward loop
Desert Summary
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let's remind ourselves...
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Transcription Process of
creating a complementary RNA copy of a sequence of DNA
The first step leading to gene expression
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Transcription Factor Protein that binds to specific DNA,
thereby controlling the flow of genetic information from DNA to mRNA
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Transcription Factor (Cont.) Environmental signals activate specific
transcription factor proteins
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Transcription Factor (Cont.)
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Transcription Factor - Activators Increases the rate of mRNA
transcription when it binds
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Transcription Factor - Repressors
Decreases the rate of mRNA transcription when it binds
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Transcription Networks Describes the regulatory
transcription interactions in a cell Input: Signals
GENE X
GENE Y
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Transcription Networks (Cont.)
Bacterium E. coli
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Transcription Networks (Cont.)
Signs on the edges: + for activation - for repression
Numbers on the edges: The Input Function
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The Input Function Rate of production of Y = f(X*) Hill Function
Describes many real gene input functions
Activator:
Repressor:
X Y
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The Input Function (Cont.)Logic Input Function
The gene is either OFF: f(X*)=0 ON: f(X*)=β
The threshold is K
For activator:
For repressor:
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The Input Function (Cont.)
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Dynamics And Response Time β - constant rate in which the cell
produces Y
Production balanced by: Degradation (α deg) α= α dil +
α deg
Dilution (α dil )
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Dynamics And Response Time (Cont.)
Concentration change:dY/dt = β – α*Y
Concentration In steady state: Yst = β/ α
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Dynamics And Response Time (Cont.)
The signal stops (β = 0) :
Response Time- reach the halfway between initial and final levels
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Dynamics And Response Time (Cont.)
Unstimulated gene becoming provided with signal:
Response Time-
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AUTOREGULATION: A network motif
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Autoregulation Goals:
Define a way to detect building blocks patterns- network motifs
Examine the simplest network motif – autoregulation
Show that this motif has useful functions
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Detecting Network Motifs Edges easily lost/ added
Compare real networks to randomized networks
Patters that occur more often in real networks = Network motifs
Real networkN=4 E=5
Randomized networkN=4 E=5
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Detecting Network Motifs (Cont.) N nodes
possible pairs of nodes : [N(N-1)]+N = N2
edge position is occupied: p= E/ N2
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Autoregulation Regulation of a gene by its own gene
product How does it look in the graph?
E. coli network: 40 self edges
34 repressors6 activators
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Cont.)) Autoregulation Probability for self edge: P self =
1/N
Expected number of self edges: < N self< rand ~ E*P self ~
E/N
Standard deviation:
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Cont.)) Autoregulation Number of self edges:
Conclusion: Self edges are a network motif
But… why?
Random network
40 E. coli network
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Negative Autoregulation
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Negative Autoregulation- Response time
Reminder: Logic input function:
Steady- state level:
Response time:
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Negative Autoregulation- Response time (Cont.)
response time comparison:Negative autoregulation
Simple regulation
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Negative Autoregulation- Response time (Cont.)
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Negative Autoregulation- Robustness
Production rate (β) fluctuates over time
Steady- state level comparison:Negative autoregulation
Simple regulation
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THE FEED FORWARD LOOP (FFL): A network motif
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Three nodes subgraphs 13 possible three- nodes patterns
Which ones are motifs?
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Cont.)) Three nodes subgraphs Sub graph G with n nodes and g
edges
N2 possibilities to place an edge
Probability of an edge in a given direction between a given pair of nodes : p = E/ N2
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Cont.)) Three nodes subgraphs Mean number of appearances:
Mean connectivity: λ = E / N -< p = λ /N
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Cont.)) Three nodes subgraphs How <NG< scales with the network
size?
Triangle-shaped patterns (3 nodes and 3 edges):
<NFFL< ~ λ3N0 <N3loop< ~ 1/3 λ3N0
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Cont.)) Three nodes subgraphs
3LOOP FFL0 42 E. coli0.6 1.7 Random
net FFL is the only motif of the 13 three- node
patterns
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FFL- Structure E. coli example:
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FFL- Structure (Cont.)
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FFL- Structure (Cont.) Relative abundance of FLL types in
yeast and E. coli:
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FFL- Structure (Cont.) Logic function
AND logic OR logic
X and Y respond to external stimuli
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Coherent Type-1 FFL – AND logic
Sx appear, X rapidly changes to X* X* binds to gene Z, but cannot
activate it X* binds to gene Y, and begins to
transcript it Z begins to be expressed after Ton
time, when Y* crosses the activation threshold Kyz
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Coherent Type-1 FFL – AND logic
Production rate of Y = βy θ(X*<Kxy)
dY/dt = βy θ(X*<Kxy) – αyY
Production rate of Z = βzθ (Y*<Kyz) θ (X*<Kxz)
dZ/dt = βzθ (Y*<Kyz) θ (X*<Kxz) – αzZ
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Coherent Type-1 FFL – AND logic (Cont.)
definition : ON step- Sx moves from absent to
saturated state OFF step- Sx moves from saturated to
absent state
Sy is present continuously
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Coherent Type-1 FFL – AND logic (Cont.)
On step-
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Coherent Type-1 FFL – AND logic (Cont.)
On step- Y*(t) = YST(1-e-αyt)
Y*(TON) = YST(1-e-αyTON) = Kyz
TON = 1/αy log[1/(1-Kyz/Yst)]
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Coherent Type-1 FFL – AND logic (Cont.)
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Coherent Type-1 FFL – AND logic (Cont.)
OFF step- No delay!
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Coherent Type-1 FFL – AND logic (Cont.)
Why might delay be useful? Persistence detector-
Cost of an error is not symmetric
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Coherent Type-1 FFL – AND logic (Cont.)
Arabinose system of E.coli: TON = 20 min
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Coherent Type-1 FFL – OR logic
Delay for OFF Steps of Sx Flagella system of E. coli:
TOFF = 1 hour
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Incoherent Type-1 FFL
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Incoherent Type-1 FFL-Dynamics
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Incoherent Type-1 FFL-Dynamics (Cont.)
Dynamic equation of Z: Y* < Kyz
dZ/dt = βz – αzZ Zm = βz /αz Z(t) = Zm (1-e-αzt )
Y* < Kyz dZ/dt = β’z – αzZ Zst = β’z /αz Z(t) = Zst + (Z(Trep) – Zst) e-α(1-Trep)
Y*(Trep) = YST(1-e-αyTrep) =< Trep = 1/αy ln[1/(1 -Kyz/Yst)]
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Incoherent Type-1 FFL- Cont.))Dynamics
Repression factor (F)= βZ/β’Z
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Incoherent Type-1 FFL-Response time
Z1/2 = Zst/2 = Zm(1-e-αz t ) T1/2=1/αz log[2F/(2F-1)], (F=Zm/Zst)
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Incoherent Type-1 FFL- Cont.)) Response time
Zst<<Zm=< F << 1 =< T1/2 0
When Zst = Zm =< F = 1
=< T1/2 = log(2)/α
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Incoherent Type-1 FFL- Cont.)) Response time
OFF step: no acceleration or delay
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Incoherent Type-1 FFL- Example (Galactose)
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Other FFL types Why Are Some FFL Types Rare?
I4-FFLFeasible patternSy does not affect the steady-state
level of Z No answer for OR logic
Sx
Y*
Z
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Evolution of FFLs Simple V-shaped structure Function of the third edge
Common form- homologous FFL Not homologous regulators FFL rediscovered by evolution
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Summary 3 kinds of motifes:
Autoregulation
Coherent type-1 Feed-Forward Loop
Inoherent type-1 Feed-Forward Loop
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Questions?