Module 2: Robustness in Biochemical Signaling Networks

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Module 2 Robustness in Biochemical Signaling
Networks
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Bacterial Chemotaxis
The chemosensory pathway in bacterial chemotaxis
and propulsion system it regulates have provided
an ideal system for probing the physical
principles governing complex cellular signaling
and response.

• Hydrogen atom of biochemical signal
  transduction networks
• Paradigm for two-component receptor-regulated
  phosphorylation pathways
• Accessible for study by structural, biochemical
  and genetic approaches

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Chemotaxis in E. coli
(Courtesy of Howard Berg group)

• Dimensions
• Body size 1 µm in length
• 0.4 µm in radius
• Flagellum 10 µm long

Physical constants Cell speed 20-30
µm/sec Mean run time 1 sec Mean tumble time
0.1 sec
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E. coli in Motion
From Berg Brown, Nature (1972).
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Signal Transduction and Behavioral Response
Stimulus
Signal Transduction Pathway
CheY-P
Motor Response
Flagellar Bundling
Motion
(Courtesy of Howard Berg lab).
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Flagellar motor
Flagellum
Basal part of flagellar motor
C-ring
Number of FliM subunits 34
From Thomas et al. PNAS (1999).
From Cluzel et al. Science (2000).
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Response to Step Stimulus
From Sourjik et al., PNAS (2002).
From Block et al., Cell (1982).
Fast response
Slow adaptation
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Excitation and Adaptation
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Precision of Adaptation
Squares Unstimulated cells Circles Cells
stimulated at t0
(Each point represents data from 10s motion of
100-400 cells.)
Precision of adaptation steady state tumbling
frequency of unstimulated cells / steady state
tumbling frequency of stimulated cells
From Alon et al. Nature (1999).
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Robustness of Perfect Adaptation
Precision of adaptation robust to 50-fold change
in CheR expression while Adaptation time
and steady state tumbling frequency vary
significantly.
Robustness of perfect adaptation
From Alon et al. Nature (1999).
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Detailed model of the E. coli chemotaxis network
Ligand binding (fast) Phosphorylation
(fast) Methylation (slow)
From Alon et al. Nature (1999).
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Ligand Binding

• E receptor complex
• a ligand (eg., aspartate)
• Rapid equilibrium
• Rates1
• E KD 1.71x10-6 M-1
• E KD 12x10-6 M-1

1 Morton-Firth et al., J. Mol. Biol. (1999)
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Receptor Activation
En methylated receptor complex activation
probability, P1(n) Ena ligand-bound receptor
complex activation probability, P2(n) En
active form of En Ena active form of
Ena Table 1 Activation Probabilities
n P1(n) P2(n)
0 0.02 0.00291
1 0.125 0.02
2 0.5 0.125
3 0.875 0.5
4 0.997 0.98
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Methylation
(1) (2)

• R CheR
• En(a) En, Ena
• En()(a) En, En, Ena, Ena
• Rate constants
• k1f 5x106 M-1sec-1
• k1r 1 sec-1
• k2f 0.819 sec-1

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Demethylation
(1) (2)
Bp CheB-P En(a) En, Ena Rate
constants k1f 1x106 M-1sec-1 k1r 1.25
sec-1 k2f 0.15484 sec-1
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Autophosphorylation
E En, Ena Rate constant kf 15.5 sec-1
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CheY Reactions
Y CheY Yp CheY-P Rate constants k1f
1.24x10-3 sec-1 k1r 4.5x10-2 sec-1 k2f
14.15 sec-1
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CheY Phosphotransfer
Rate constants k1f 5x106 M-1sec-1 k2f 20
sec-1 k2r 5x106 M-1sec-1 k3f 7.5 sec-1 k3r
5x106 M-1sec-1
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CheB Reactions
B CheB Bp CheB-P Rate constant kf 0.35
sec-1
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CheB Phosphotransfer
Rate constants k1f 5x106 M-1sec-1 k2f 16
sec-1 k2r 5x106 M-1sec-1 k3f 16 sec-1 k3r
5x106 M-1sec-1
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Robustness of Receptor Activity to Network
Parameters
B-L model simplified model based on
two-state model of chemoreceptors
no phosphorylation (!) precision of
adaptation defined in terms of receptor
activity
Robustness of perfect adaptation to variations in
kinetic rate constants not so for adaptation
time.
From Barkai et al. Nature (1997).
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Next time

• What are the essential features of the BL model
  allowing robustness of perfect adaption to
  network parameters (rate constants, total protein
  concentrations)?
• What are the expected variations in these
  parameters in a population of (clonally
  identical) cells?
• What is integral feedback control and where does
  it come from?