Modeling protein motors

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Modeling protein motors
Jianhua Xing University of California, Berkeley
F1Fo ATPase
Bacterial flagellar motor
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Question 1 What are appropriate theoretical
and simulation frameworks?
A theoretical model should be

• Simple
• Not over-simplified
• Useful

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• Atomic level simulations
• Provide atomic details
• Limited by system size and simulation length
• Require detailed structures

Kinetic models
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I. General discussion
1. Molecular motors use chemical energy to
perform mechanical work
Occupied
Potential
Empty

Occupied state
Empty state
x
Chemical transitions switch the system from one
potential curve to another, and result in
mechanical motion
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A generic molecular motor
Free energy
Angular position q
Keller, Bustamante (2000), Biophys. J., 78
541-556
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II. The Bacteria Flagellar motor
1. Summary of experimental studies
H. Bergs website
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a). Structure of bacterial flagellar motor
Vibrio alginolyticus
D. Thomas, N. Francis, and D. Derosier,
unpublished
EM image
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The fuels trans-membrane ion motive force
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b) Mechano-chemical studies

• The flagellar motor can
• Generate torque 2700 4000 pN.nm
• Rotate as fast as 1700 Hz
• (1 Hz 1 cycle/second)

Under viscous load
Under rotating electric field
Fung, Berg (1995), Nature, 375 809-812 Ryu,
Berry, Berg (2000), Nature, 403444-447 Chen,
Berg (2000), Biophys. J. 78 1036-1041 Gabel,
Berg (2003), PNAS, 1008748-8751 Sowa et al.
(2005), Nature, 437 916-919
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c) The Puzzle
Linear decrease
Torque Constant
Speed ? pmf
Fung, Berg (1995), Nature, 375 809-812 Ryu,
Berry, Berg (2000), Nature, 403444-447 Chen,
Berg (2000), Biophys. J. 78 1036-1041 Gabel,
Berg (2003), PNAS, 1008748-8751
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2. Our model
a) We proposed the working mechanism based on
available information
Xing, Bai, Berry , Oster (2005), submitted
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b) We identified key ingredients from
experiments
The power stroke is driven by a conformational
transformation in the stator that is triggered by
the protons hopping onto and off the stator
Elastic coupling
Tight coupling
The rotation of the motor is observed through a
soft elastic linkage between the motor and the
viscous load
The ion channel through the stator is gated by
the motion of the rotor
Xing, Bai, Berry , Oster (2005), submitted
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c) Mathematical modeling
Brownian Torque
Motor Torque
Markovian chemical transitions
Viscous Torque
Load Torque

Langevin
Fokker-Planck
Potential based kinetic model
Wang, Peskin, Elston (2003), J. Theor. Biol.
221491-511
Xing, Wang, Oster (2005), Biophys. J. 891551-1563
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d) Our model can fit the data well
Xing, Bai, Berry, Oster (2005), submitted
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3. Physical explanation of the torque-speed
relation
a) Plateau time scale separation soft
linkage
Spring constant
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Crossover between the two time scales
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Elastic linkage allows multiple time-scales
Conservative load
Viscous load with spring
Viscous load with rigid linkage
Xing, Bai, Berry, Oster (2005), submitted
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b) Sharp transition positive feedback
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c) Prediction
more stators ? more power
High speed region Destructive interference
Xing, Bai, Berry, Oster (2005), submitted
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more stators ? more steps depends on relative
phases between stators
Free energy
Angular position q
2 stators
1 stator
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d) The same physics explains other puzzles
Yasuda et al. (1998), Cell (93) 1117-1124
Mycoplasma causes diseases like pneumonia. Its
sliding rate depends on temperature linearly.
Miyata, Ryu, Berg (2002), J. Bacter., 1827-1131
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4. Summary of flagellar motor

• The observed flagellar motor dynamics
  is due to
• Internal conformational change
• Soft elastic linkage between motor and load
• Tight coupling
• Localized chemical transitions

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Mathematical modeling
Question 2 How to construct a mesoscopic model?
Fit data and suggest experiments
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III. ATP synthesis with the F1Fo ATPase
1. the F1Fo ATPase
THE F1Fo ATPase
THE F1 PART
Fo model F1 model
Xing, et al. (2004), Biophys. J. 87 2148-2163
Xing, Liao, Oster (2005), PNAS, in press
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2. The F1 part
Various experimental studies serve as the model
basis
Crystal structures
Single molecule measurements
Biochemistry measurements
Mutation studies
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Constructing the potentials qualitative thinking
Berzborn, Schlittler (2002), FEBS Lett. 26828,
1-8 Ma, et al. (2002), Structure 10, 921-931
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Constructing the potentials qualitative thinking
open
open
close
Rotation without synthesis
Correct sequence
Free energy G
ADPPi
ATP
ADP
Empty
200
300
0
100
Rotation angle degree
Xing, Liao, Oster (2005), PNAS, in press
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Right timing/tight coupling is ensured by
specific b/g b/e interactions
Xing, Liao, Oster (2005), PNAS, in press
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Reveal dynamic features without any calculation!
Free energy G
Xing, Liao, Oster (2005), PNAS, in press
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The model can fit steady state ATP synthesis data
The model reveals multiple reaction pathways
Tomashek, JJ et al. (2004), J. Biol. Chem. 279
4465-4470 Xing, Liao, Oster (2005), PNAS, in press
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3. Summary of the model on ATP synthesis

• Our model
• integrates a large body of experimental
  observations
• proposes a set of free energy potentials,
  which contains
• almost all dynamic information
• makes many experimentally testable predictions

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IV. SUMMARY
Theoretical/Computational/Systems biology
require intimate collaboration between
experimentalists theoretician

• I have used molecular motor studies to show
  that theoretical
• modeling can
• Integrate and transform information
• Bridge structural and dynamical studies
• Predict dynamical behaviors
• Suggest new experiments

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V. ACKNOWLEDGMENT

• George Oster
• Jung-Chi Liao
• Oleg Igoshin
• Andrew Spakowitz
• Oleksii Sliusarenko
• Jing Chen
• Joshua Adelman
• Hongyun Wang (UC Santa Cruz)
• Sean Sun (JHU)

• Richard Berry (Oxford)
• Fan Bai (Oxford)
• Peter Dimroth (ETH, Switzerland)
• Christoph v. Balmoos (ETH, Switzerland)

Financial support NIH
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The End
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