robustness in protein circuits: adaptation in bacterial chemotaxis 1 information in biology 2008...
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Robustness in protein circuits:adaptation in bacterial chemotaxis
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Information in Biology 2008Oren Shoval
Outline
• Noise is a part of life
• Overview of bacterial chemotaxis
• Internal mechanism of chemotaxis control
• The robust model of perfect adaptation
• Perfect adaptation and control theory
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Outline
• Noise is a part of life
• Overview of bacterial chemotaxis
• Internal mechanism of chemotaxis control
• The robust model of perfect adaptation
• Perfect adaptation and control theory
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Many biological processes are robust to external and internal fluctuations
• Internal protein levels vary significantly between genetically identical cells
• Humans keep body temperature at 36.7° despite:
– External noise of surrounding temperature
– Internal noise of body weight, size, food intake
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Elowitz et al., Science, 2002
Sensitivity to noise is a measure of biological system performance
• Sensitivity is the change in system output (Y) due to changes in the internal parameter ()
• Robustness means zero sensitivity
• For example, dependence of body temperature on body weight:
Savageau, Nature, 1971
parameterchange
YoutputchangeSY %
%,
5
0%
%,
body
bodyY Weightchange
TchangeS
Robust
Outline
• Noise is a part of life
• Overview of bacterial chemotaxis
• Internal mechanism of chemotaxis control
• The robust model of perfect adaptation
• Perfect adaptation and control theory
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Chemotaxis: Bacteria can “swim” towards an attractant and away from a repellent
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Repellant(poison)
Attractant(food)
Swimming is done by a spiraling motor (flagella)
• Flagella can rotate in two directions:
• Speed of about 50m/sec. Is this fast?
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Clock wise(advancing ~sec)
Counter clock wise (tumble ~0.1sec)
Organism Kilometers per hour Body lengths per second
Cheetah 111 25
Human - Michael Johnson 37.5 5.4
Bacteria 0.00018 25
Bacteria find their way up a nutrient gradient by changing the tumbling rate
• Bacteria are too small to measure gradient
• Gradient found by temporal change during running
• PositiveGradient
• Biased random walk
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Berg, Nature, 1972
Lower tumbling rate
Continue in correct direction
Automated analysis of the bacteria trails enables extracting the chemotaxis parameters
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Berg, Nature, 1972
Parameters:• Mean free path• Tumbling rate
Tumbling rate shows exact adaptation to nutrient level
addition of nutrient
bacteria stop tumbling
Adaptation: slowly return to a steady state tumbling
• Adaptation is commonly found in sensory systems
• Adaptation is the focus of Barkai’s paper
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Addition of attractant reduces tumbling immediately
Adaptation
Steady state tumbling rate
Adaptation increases the dynamic range of sensors
• Adaptation keeps sensor sensitive to changes regardless of average stimulus
• Bacteria without adaptation show <1% chemotaxis ability
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Possible stimulus range
System dynamic range
Stimulus level
System unable to sense changes
Outline
• Noise is a part of life
• Overview of bacterial chemotaxis
• Internal mechanism of chemotaxis control
• The robust model of perfect adaptation
• Perfect adaptation and control theory
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Motor control by a two component system: receptor and regulator
Receptor without an attractant
Activate Y by adding a P
Y-P binds to motor
Increase rate of tumbling
Shorter runs
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Y YP
Removal of P at constant rate
Motor
more tumbling
ReceptorSensor activity level
An attractant inhibits the receptor, thus reducing motor activity
Adding attractant
Less receptor activity
Less Y-P is created
Reduced tumbling
Longer runs
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Y YP
Removal of P at constant rate
Motor
Lesstumbling
Receptor
Sugar
Sensor activity level
Fast process (miliseconds)
Again:
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Y Y
P
Removal of P at constant rate
Motor
Lesstumbling
Receptor
Sugar
Sensor activity level
Y Y
P
Removal of P at constant rate
Motor
more tumbling
ReceptorSensor activity level
Less sugar Shorter runs More sugar Longer runs
Adaptation is achieved by reactivating the receptor
• Adding M (Methylation) overcomes deactivation due to sugar
• R add M, B removes M
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Sensor activity level
Reactivation (R)
M
Negative feedback
Deactivation (B)
M
Slow process (minutes)
The adaptation cycle:
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Fast (miliseconds)
Slow (minutes)
Outline
• Noise is a part of life
• Overview of bacterial chemotaxis
• Internal mechanism of chemotaxis control
• The robust model of perfect adaptation
• Perfect adaptation and control theory
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Is adaptation accuracy sensitive or robust to internal protein levels?
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• Example: If the level of protein R (reactivation) changes by 20%, will we still have adaptation?
Two mechanisms for adaptation
Barkai proposed a robust model of adaptation that depends on two assumptions
1. Methylation (R) works at maximum rate (saturation)
2. Demethylation (B) occurs only on activated receptors
Barkai, Nature, 199721
CheR
Let’s have fun with some equations
• The attractant governs the active vs. inactive ratio:
• Methylation rate:
• At steady state:
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)(*
sugarX
X
m
m
** )(
mmm BXR
dt
XXd
B
RXm *
CheR
Adaptation is robust!
Experiments can measure the sensitivity of chemotaxis parameters to internal protein level
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• Alon experimentally varied the level of proteins that make up chemotaxis
• Three parameters were extracted for each mutant:
Adaptation time
Adaptation precision
Steady state tumbling
Alon et al., Nature, 1999
Experiments have proven that adaptation precision is robust to variations in protein levels
Alon et al., Nature, 199924
x3 receptors
x0.5 CheY
x0 CheZx0 CheZ
x12 CheB
•Adaptation is precise in all cases•Steady state tumbling rate and adaptation time change
x50 CheR
Perfect adaptation is important, so the network is designed to keep it robust
• Partial adaptation leads to <1% of wild-type chemotaxis ability
• Changing the tumbling frequency and adaptation time does not affect chemotaxis ability
• Exact adaptation is displayed in taxis of many other bacterial species (B. subtillis, R. sphaeroides)
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However, nonessential features are sensitive to
protein levels
Outline
• Noise is a part of life
• Overview of bacterial chemotaxis
• Internal mechanism of chemotaxis control
• The robust model of perfect adaptation
• Perfect adaptation and control theory
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Robust adaptation in chemotaxis is an example of integral feedback control
bybrAbbArx
Error
A
br
Yi et al., PNAS, 200127
Summary
• Biochemical networks need to cope with noise
• Chemotaxis is the ability of bacteria to swim towards an attractant
• Chemotaxis adaptation is robust to internal protein levels
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