Modeling Dynein: The Gear-Shifting
Motor
step
Manoranjan Singh, Roop Mallik, Steve Gross,
and Clare Yu
University of California, Irvine
A Cell Is Like a City
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Workers
Power Plant
Roads
Trucks
Factories
Library
Recycling center
Police
Post office
Communications
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Proteins
Mitochondria
Actin fibers, microtubules
Kinesin, dynein, myosin
Ribosomes
Genome
Lysosome
Chaperones
Golgi apparatus
Signaling networks
Intracellular Traffic
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Nucleus
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© Scientific American
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Nucleus
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Kinesin
Dynein
Mitochondria
Vesicle
Microtubules (MT)
are like freeways
and actin filaments
are like local
surface streets.
Filaments
Actin filament
• 10 nm diameter
• 2.77 nm rise
• 26 subunits/74 nm repeat
- end
+ end
+ end
Microtubule
 25 nm diameter
 13 protofilaments
- end
Motors Walk Along Filaments
Yildiz et al.
Science 2003.
Motor
proteins
move cargo
along
filaments
Molecular Biology of the Cell, 3rd Ed, 1994
Biochemistry, 4ht Ed, 1995
Herpes Virus Transport in
Neurons Along Microtubules
• Virus Movie: VirusMov.mov
Kinesin
Myosin-V
Dynein
Cargo
Cargo
KLC
Pi
KR1
Dynactin
binding
KR2
MR2
Ca2+
Pi
Head
(ATPase)
Stalk
1 c
3
6
4 5
2
KAPP
KR3
MR1
Lever (?)
KHC
Head (ATPase)
MT binding
The anatomy of a dynein molecule
Microtubule
Stalk
4
5
3
6
2
7
ATP
1
ADP+Pi
N.Hirokawa, Science, 279, 519 (1998)
Figure edited to show stalk
Stem
Burgess et. al.
Nature 421, 715 (2003)
Dynein Can Shift Gears
Dynein
Dynactin
binding
Roop Mallik1, Brian Carter1,
Stephanie Lax2, Stephen
King2, Steven Gross1
Head
1UC Irvine
(ATPase)
2Univ. of Missouri-Kansas City
2 1
3
Stalk
c
6
4 5
Lever (?)
The basic experiment
Optical
trap
Plastic bead
(450 nm)
Burgess et al,
Nature 2003
FT
FM
Dynein
Load  FTrap   kx
Bead displacement proportional to backward force
…. Calibrate and measure !!!
Typical trace of motion
F = - kx
Optical trap stiffness = spring constant = k = 0.011 pN/nm
Mallik et al., Nature 427, 649 (2004).
Dynein can change the size of
its steps as it walks along
microtubules depending on
• Load
• ATP Concentration
• Possible step sizes ≈ 8, 16, 24, 32 nm
• High load → small steps
• Low load → large steps
Step Size as a Function of Load at High [ATP]
High load
8nm steps
Intermediate load
15 nm steps
Low load
~25 nm steps
Very Low ATP, No Load
Position vs. time
Step Size Distribution
Mostly 24, 32 nm steps
Optical
trap
Stalling Force
bead
FT
FM
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Motor attached to bead
Motor walks along microtubules
Dynein
Laser tweezers pull on bead
As bead moves a distance x from center of
trap, it feels a spring force = F = -kx
• If force = stalling force, motor cannot pull
bead.
Stalling force strongly
dependent on available ATP
Linear force-ATP curve
Histogram of stall
forces, 1 mM ATP
Goal of Theoretical Modeling
To reproduce dependence of step size,
stalling force and velocity on [ATP] and
load F
• Traditional approach :
Coupled differential
eqns.
• Alternative approach:
Monte Carlo Simulations
(Advantage: easy to deal
with complicated
nonlinear dependencies)
MT
Stalk
4
5
3
6
2
7
ATP
1
ADP+Pi
stem
Desired Features of ATP
Binding
MT
Stalk
• ATP can bind to (or unbind from) sites 1-4
• Step size decreases as number of bound sites
increases
# ATP
1
2
3
4
bound
Step
32
24
16
8
size
nm
nm
nm
nm
5
6
7
4
ATP
3
2
1
ADP+Pi
stem
• Binding probability increases with [ATP]
• Problem: High [ATP], no load → small step size (nonsense)
• Solution: Different ATP binding affinities on different sites
1
3
kon
 kon
 kon4  kon2
• Dictates sequential binding: site #1, then #3, then #4, then #2
• Binding probability on sites 2-4 increases with load F (need
fuel to haul cargo)
ATP Hydrolysis needed
for step to occur
MT
Stalk
5
6
7
4
ATP
• Sites 1 and 3 hydrolyze ATP, but energy for step
probably comes from hydrolysis at site 1
• Problem: Why is there a mixture of 24 and 32 nm
steps at low [ATP] and no load?
• Answer: Probability to hydrolyze ATP at site 1
increases if ATP bound to other sites, esp. site 3
• Question: What produces stalling?
• Answer: Probability to hydrolyze ATP decreases
with load (Harder to walk with load)
• Reverse hydrolysis can occur (ADP + Pi → ATP)
(reversal rate increases with load)
3
2
1
ADP+Pi
stem
Monte Carlo Simulation
n = number of sites bound = {0, 1, 2, 3, 4}
d = step size = (5 – n) · 8 nm (conjecture)
1. Bind (or unbind) ATP: Probability for n → n ± 1,
Pbind(site i) = kion [ATP] Δt
k2-4on= k2-4on(F=0)exp{Fa/kT}
2. Hydrolyze ATP at site 1:
Phydrolyze = po exp{-αFd/kT} Δt
where po → po/100 if n = 1
3. Reverse hydrolysis: Preverse = pr exp{(1- α )Fd/kT)}
or take a step
4. Repeat
Theoretical Position vs. Time
high [ATP]
low [ATP]
Step Size Distribution with No Load
Compare Theory and
Experiment (low [ATP])
Monte Carlo results
At various [ATP]
Simulation Results of Step Size
• Step size decreases as load increases
• Agrees with experiment
Low [ATP] = 100 μM
High [ATP] = 1 mM
Theoretical
Predictions
Velocity vs. [ATP]
concentration at
various loads
Velocity vs. Load
at various [ATP]
concentrations
Conclusions about Dynein
• Dynein can change step size depending
on load and [ATP]
• Monte Carlo simulations in good
agreement with experiment
• No load: sites # 1 and # 3 bind ATP →
large step size ~ 32 and 24 nm
• Large load, 4 sites bind ATP → small step
size ~ 8 nm
Collaborators
Dmitri Petrov, Steve Gross, Clare Yu, Manoranjan Singh
(missing: Roop Mallik)
THE END
Kinesin: Comparison of Monte
Carlo and Experiment
Velocity vs. [ATP]
Velocity vs. Load
Open symbols: Experiment (Vissher et al., 1999); closed symbols: Monte Carlo;
solid line: Michaelis-Menten formula
Modeling Dynein: The Gear-Shifting
Motor
+
Nucleus
+
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Manoranjan Singh, Roop Mallik, Steve Gross,
and Clare Yu
University of California, Irvine
Intracellular Traffic
 How is intracellular
transport regulated?
© Scientific American
Motors Walk Along Filaments
Motor proteins
Myosin
Kinesin
Highway System of a Cell
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Nucleus
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Kinesin
Mitochondria
Dynein
Vesicle
MT
ATP Fuels the Motor
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Stalk
4
5
3
6
2
7 1
ATP = Adenosine Triphosphate
ATP ADP+Pi
ATP has 3 phosphate ions
Hydrolysis: 1 phosphate ions breaks off
Stem
ADP = Adenosine Diphosphate has 2 phosphate
ions
• Energy is released
ATP → ADP + Pi
Laser Tweezers
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Focused laser beam
Electric field E most intense at focal point
E induces a dipole moment p in particle
U=-p·E
U minimized at focal point
Particle trapped at focal point
Particle moving away from focal point feels
spring force: F = -kx = load
Microtubules (MT)
are like freeways and
actin filaments are
like local surface
streets.
How does the cell regulate
the transport of vesicles?
Position along microtubule (nm)
Step size as function of load
High load
8nm steps
Intermediate load
15 nm steps
Low load
~25 nm steps
(High [ATP])
Time (sec)
Stepsize changes as a function of load
Intermediate load
~ 0.4 to 0.8 pN
15 nm steps
Low load
< 0.4 pN
~25 nm steps
(High [ATP])
Motion at very low ATP
No load
Video tracking
Step Size Distribution at No Load
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40% 24 nm steps
40% 32 nm steps
~19% 16 nm steps
~1% 8 nm steps (?)
• Low [ATP]
 Mixture of steps at no load
 Mean step-size is load-dependent
Large
Load
step
Small
step
Large
Load
step
Small
step
Model for implementation of a gear
Desired Features
MT
4
• ATP can bind to sites 1-4
5
3
Stalk
6
• Step size decreases as number of bound sites
2
7 1
increases
• Binding probability increases with [ATP]
ADP+Pi
ATP
• Different ATP binding affinities on different sites
dictates sequential binding (1, 3, 4, 2)
• Binding probability on sites 2-4 increases with load
F (need fuel to haul cargo)
• ATP can unbind
• Hydrolysis needed for step to occur
• Sites 1 and 3 hydrolyze ATP, but energy for step
probably comes from hydrolysis at site 1
• Probability to hydrolyze ATP at site 1 increases if
ATP bound to other sites, esp. site 3
• Probability to hydrolyze ATP decreases with load
(Harder to walk with load)
• Reverse hydrolysis can occur (ADP + Pi → ATP)
Monte Carlo Simulation
• Low ATP
• High ATP
Theoretical Position vs. Time
high [ATP]
low [ATP]
Step Size Distribution
Low ATP
High ATP
Step Size Distribution
Low ATP
High ATP
Step Size Distribution with No Load
• Theory
Experiment (low [ATP])
Step Size Distribution with No Load:
Compare Theory and Experiment
Step Size Distribution with No Load
Compare Theory and
Experiment (low [ATP])
Monte Carlo results
At various [ATP]
Step Size Distribution with No Load
• Theory vs. Experiment
• Low [ATP]
• Monte Carlo Results
• Varying [ATP]
Simulation Results of Step Size
• Step size decreases as load increases
• Agrees with experiment
Low [ATP] = 100 μM
High [ATP] = 1 mM
Predicted Velocity vs. Load