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Robustness in protein circuits:
adaptation in bacterial chemotaxis
Information in Biology 2008
Oren Shoval
1
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
2
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
3
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:
Elowitz et al., Science, 2002
– External noise of
surrounding temperature
– Internal noise of body
weight, size, food intake
4
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 ()
SY , 
% change output Y
% change parameter
• Robustness means zero sensitivity
• For example, dependence of body
temperature on body weight:
SY , 
Robust
% changeTbody
% changeWeightbody
0
Savageau, Nature, 1971
5
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
6
Chemotaxis: Bacteria can “swim” towards an
attractant and away from a repellent
Repellant
(poison)
Attractant
(food)
7
Swimming is done by a spiraling motor (flagella)
• Flagella can rotate in two directions:
Clock wise
(advancing ~sec)
Counter clock wise
(tumble ~0.1sec)
• Speed of about 50m/sec. Is this fast?
Organism
Kilometers per hour
Body lengths per second
Cheetah
111
25
Human - Michael Johnson
37.5
5.4
Bacteria
0.00018
25
8
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
• Positive
Gradient
Lower
tumbling
rate
Continue
in correct
direction
• Biased random walk
Berg, Nature, 1972
9
Automated analysis of the bacteria trails
enables extracting the chemotaxis parameters
Parameters:
• Mean free path
• Tumbling rate
Berg, Nature, 1972
10
Tumbling rate shows exact adaptation to
nutrient level
addition of nutrient
Steady state
tumbling rate
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
Addition of attractant
reduces tumbling
immediately
Adaptation
11
Adaptation increases the dynamic range of
sensors
• Adaptation keeps sensor sensitive to changes
regardless of average stimulus
System unable to
sense changes
Stimulus
level
Possible stimulus range
System dynamic range
• Bacteria without adaptation show <1% chemotaxis
ability
12
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
13
Motor control by a two component system:
receptor and regulator
Receptor without an attractant
Receptor
Sensor
activity
level
Activate Y by adding a P
more
tumbling
P
Y-P binds to motor
Y
Y
Increase rate of tumbling
Shorter runs
Motor
Removal of P at
constant rate
14
An attractant inhibits the receptor, thus
reducing motor activity
Sugar
Adding attractant
Less receptor activity
Receptor
Sensor
activity
level
P
Less Y-P is created
Y
Less
tumbling
Y
Reduced tumbling
Motor
Longer runs
Removal of P at
constant rate
Fast process (miliseconds)
15
Again:
Less sugar
Shorter runs
More sugar
Longer runs
Sugar
Receptor
Sensor
activity
level
P
Y
Receptor
Sensor
activity
level
more
tumbling
Y
P
Y
Y
Motor
Removal of P at
constant rate
Less
tumbling
Motor
Removal of P at
constant rate
16
Adaptation is achieved by reactivating the
receptor
• Adding M (Methylation)
overcomes deactivation
due to sugar
• R add M, B removes M
M
Reactivation (R)
Sensor
activity
level
M
Deactivation (B)
Negative
feedback
Slow process (minutes)
17
The adaptation cycle:
Steady
State
Tumbling
Tumbling
increases
Slow (minutes)
Receptor
reactivation
(methylation)
Sugar
addition
Fast (miliseconds)
Tumbling
decreases
(running)
Receptor
activity
decreases
18
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
19
Is adaptation accuracy sensitive or robust to
internal protein levels?
• Example: If the level of protein R (reactivation)
changes by 20%, will we still have adaptation?
Two mechanisms for adaptation
20
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
CheR
Barkai, Nature, 1997
21
Let’s have fun with some equations
• The attractant governs the
active vs. inactive ratio:
Xm
  ( sugar)
*
Xm
• Methylation rate:
CheR
d ( X m  X m* )
 R  BX m*
dt
• At steady state:
X m* 
R
B
Adaptation is robust!
22
Experiments can measure the sensitivity of
chemotaxis parameters to internal protein level
• Alon experimentally varied the level of proteins that make up
chemotaxis
• Three parameters were extracted for each mutant:
Adaptation time
Steady state
tumbling
Adaptation
precision
Alon et al., Nature, 1999
23
Experiments have proven that adaptation precision
is robust to variations in protein levels
x3 receptors
x50 CheR
x0.5 CheY
x12 CheB
x0 CheZ
x0 CheZ
•Adaptation is precise in all cases
•Steady state tumbling rate and adaptation time change
Alon et al., Nature, 1999
24
Perfect adaptation is important, so the network
is designed to keep it robust
• Partial adaptation leads to <1% of wildtype 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)
However,
nonessential
features are
sensitive to
protein levels
25
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
26
Robust adaptation in chemotaxis is an
example of integral feedback control
r
b
A
Error
x  r bA b A r   by
b

Yi et al., PNAS, 2001
27
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
28
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