Robustness in protein circuits: adaptation in bacterial chemotaxis 1 Information in Biology 2008 Oren Shoval

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






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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






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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






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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


Motor

Lesstumbling

Receptor

Sugar

Sensor activity level

Fast process (miliseconds)

Again:

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Y Y

P


Motor

Lesstumbling

Receptor

Sugar


Y Y

P


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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Reactivation (R)

M

Negative feedback

Deactivation (B)

M

Slow process (minutes)

The adaptation cycle:

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Fast (miliseconds)

Slow (minutes)

Outline






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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:

22

)(*

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






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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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Robustness in protein circuits: adaptation in bacterial chemotaxis 1 Information in Biology 2008 Oren Shoval