ATP hydrolysis 1
1
1
ATP hydrolysis 2
2
2
The binding zipper 1
3
3
ATP hydrolysis/synthesis is
coupled to a torque
Yasuda, R., et al (1998). Cell 93:1117–1124.
Abrahams, et al (1994). Nature 370:621-628.
Stock, Leslie, & Walker (1999) Science 286:1700.
Wang & Oster (1998). Nature 369:279-282.
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Which step of the hydrolysis cycle
generates the force?
ATP Hydrolysis cycle in solution:
Hydrolysis
ATP ←⎯⎯⎯⎯→ ADP + Pi
ATP Hydrolysis cycle at a catalytic site:
ATP binding
F1 + ATP ←⎯⎯⎯⎯⎯→ F1 ⋅ ATP
Hydrolysis
Product
release
←⎯⎯⎯⎯→ F1 ⋅ ADP ⋅Pi ←⎯⎯⎯
⎯→ F1 + ADP + Pi
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The catalytic sites lie in the seam between the α and β subunits—
mostly in β, but with a critical residue in α
TOP
β
α
SIDE
γ
β
α
The nucleotide is held in the grip
of loops emanating from the βsheet
6
6
A hinge bending motion is associated
with ATP binding
Abrahams, et al (1994). Nature 370:621-628.
Wang & Oster (1998). Nature 369:279-282.
7
The hinge bending motion is capable of
driving the rotation of γ
Wang & Oster (1998). Nature 369:279-282.
8
Binding transition is an efficient force
generator (Binding zipper)
Diffusion to catalytic site
The binding rate
kon[ATP]
measures this step.
Binding Transition (“Zipper”)
Zipping up the hydrogen
bonds generates force.
This process is
independent of [ATP].
ATP binding free energy is utilized gradually to generate
a constant force.
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The power stroke takes place as the P-loop slides
over the nucleotide
Stereo
MD Corrected Interpolation
Sun, Chandler, Dinner, & Oster (2003)
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10
The Binding Zipper principle
Aqueous Solvent
MD Simulation
Eide, Chakraborty,
& Oster (2003)
F
Binding Surface
The best way to extract work from binding is a smooth, solvent ‘lubricated’ sliding with:
Matching surface geometries
Solvent-solvent interaction ≈ solvent-enzyme
…which is how the P-Loop slides over
ATP to generate the power stroke…
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11
ATP binding affinity of a conformation
vs
ATP binding affinity of a catalytic site
Misconception: The ATP binding affinity of βE is too low.
Therefore ATP binding cannot generate a significant force.
•
The affinity of the rest conformation of βE is low.
•
If βE is fixed at its rest conformation, then the affinity of the site is
low.
ATP binding involves conformational changes.
If βE is allowed to bend, then the ATP will proceed from weak
binding to tight binding and drive the bending of β.
•
•
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Hydrolysis releases products so that
the cycle can repeat
Breaking covalent bonds
Binding is weakened and
distributed over ADP and Pi
(∆H ~ 8.5 kBT)
•
•
Hydrolysis breaks the γ covalent bond, distributing the binding over two
products.
Electrostatic repulsion weakens the binding of two products.
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Summary of the binding zipper model
The binding zipper transduces free energy gradually.
In the hydrolysis cycle, ATP binding free energy is utilized efficiently
to generate a constant force.
•
•
•
Bonds form sequentially between ATP and catalytic site.
Conformational change is coupled continuously to binding affinity.
Hydrolysis resets the cycle.
In the synthesis cycle, the force generated in the Fo is used to
decrease gradually the binding affinity of newly formed ATP.
Diffusion to catalytic site
Binding Transition (“Zipper”)
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Elastic Energy is stored in the curvature
of the β-sheet
~ 6 kBT
Free Energy computed from MD &
the interpolated structures
15
15
The β-sheet is the elastic recoil element
Primary
Power
Stroke
Recoil
Stroke
Binding
Zipper
β-sheet
Elastic recoil of
the β-sheet
Primary Power Stroke
Recoil Power Stroke
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The catalytic sites communicate via mechanical stress
to coordinate the hydrolysis cycles
…helps product release from
the next site
Stress is transmitted asymmetrically
through the α-subunits & γ-shaft.
Binding of ATP…
This results in a multisite enhancement of ~ 105 over the unisite rates!
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Ion Driven Motors
Bacterial Flagellar Motor:
Driven by ion-triggered
conformation change
Fo motor of ATP Synthase:
Driven by coulomb attraction and
brownian motion
Flash an electric field to
Flash an electric field to
switch protein conformation
switch Coulomb attraction
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ATP synthase is composed of two reversible motors
Proton Turbine
c9-14 = rotor
γ,ε = shaft
Hydrolysis Motor
α3β3 = hexamer
γ,ε = shaft
a,b,δ = stator
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19
The Na Fo ATPase
+
ROTOR
STATOR
Top
MEMBRANE
Fo
a
c11
b
Side
γ
c11
F1
Ion binding site
α3β3
δ
Rotor
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The Sodium Fo Motor
Na+
Torque generating interface
The flow of ions through the motor generates >
45 pN.nm of torque in the rotor-stator interface
Balmooth, et. al. (2002), J. Biol. Chem, 277, 3504
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The total driving potential for the rotor has 4 components:
Electrostatic + membrane potential + hydration + Steric
Outlet
Arg227
Front
Side
∆V
Steric
Coulomb
Hydration
Membrane
Potential
Xing, Wang, Dimroth & Oster (2004)
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Operating principle of the Fo motor
Binds Na+ from
Loses
Captured
by Na+ to
Pushed outinput
by channelstator charge
exit channel
next site
Occupied site
enters stator
hydration
well
“Pull-push” principle:
With 2 rotor sites inside the stator, both sites
alternately provide torque (high duty ratio).
Including steric potential
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The bacterial flagellar motor
K. Namba
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Torque ~ 2700 - 4000 pN.nm
Rotate ~ 1700 Hz
D. Thomas, N. Francis, and
D. DeRosier, unpublished
25
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Structure of the motor
Torque: ~ 4000 pN.nm; Speed: ~ 1700 Hz
Lloyd et al. (1999) Nature 400:472-475
Blair (2003), FEBS Lett. 545: 86-95
Braun, Blair (2001), Biochemistry 40: 13051-13059
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Properties sufficient to fit the data
The rotation of the motor is observed
through a soft elastic linkage between
the motor and the viscous load.
Motor rotation and ion transport are
tightly coupled: ~ 1 step/ion pair.
The power stroke is driven by a
conformational transition in the stator
that is triggered by the protons
hopping onto and off the stator
charges.
The ion channel through the stator is
gated by the motion of the rotor.
T. Pollard Cell Biology
D. Goodsell
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27
A model illustrating the operating principle
The power stroke is driven by a conformational
transition in the stator that is triggered by the
protons hopping onto and off the MotB charges.
Elastic coupling Tight coupling
The stator
is ‘bistable’
D. Blair
The rotation of the motor is observed
through a soft elastic linkage between
the motor and the viscous load.
Motor rotation and ion
transport are tightly coupled.
The ion channel through the stator is
gated by the motion of the rotor.
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The stator power stroke
Peptidoglycan
Ion triggered
conformational
change in the
stator drives the
power stroke.
Rotor-stator
interaction has
duty ratio ~ 1
Stator
Inner Membrane
Ion flux is tightly
coupled to rotation
Rotor
Rotor-stator interaction is
steric/electrostatic
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Efficiency
Thermodynamic efficiency
A motor working against a conservative force:
Rate of potential energy increase in the external agent
ηTD =
Rate of energy consumption in motor system
External
agent
Motor
system
Visscher, K., et al (1999)
A laser trap has the same effect as a spring on the motor.
f⋅ v
ηTD =
, ƒ = cont.
(− ΔG) ⋅ r
f ⋅L
If tightly coupled ⇒ v = L ⋅ r , ηTD =
(−ΔG)
Step
size
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Stokes efficiency
A motor working against a viscous drag:
Hunt, A., et al (1994)
Yasuda, R., et al (1998)
ζ⋅ v
ηStokes =
(− ΔG) ⋅ r
2
The Stokes efficiency:
If tightly coupled ⇒
ζ ⋅ v ⋅L
v = L ⋅ r , η Stokes =
(−ΔG)
Question: ηStokes ≤ 100%?
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Stokes efficiency vs thermodynamic efficiency
ψB and
ψC: High thermodynamic efficiency
High Stokes efficiency
ψA: High thermodynamic efficiency
Low Stokes efficiency
A special case of ψA:
−ΔG → ∞
⇒
2D
v →
L
⇒
ζ ⋅ v ⋅L
η Stokes =
→0
(−ΔG)
At stall, ηTD = 100%
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What does a high efficiency tell us about
the motor mechanism?
High thermodynamic efficiency
⇒ the motor is tightly coupled near stall.
High Stokes efficiency
⇒ the driving potential has a nearly constant slope.
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