Modeling Dynein: The Gear-Shifting Motor

Manoranjan Singh, Roop Mallik, Steve Gross, and Clare Yu

University of California, Irvine

step

A Cell Is Like a City• Workers• Power Plant• Roads• Trucks• Factories• Library• Recycling center• Police• Post office• Communications

• Proteins• Mitochondria• Actin fibers, microtubules• Kinesin, dynein, myosin• Ribosomes• Genome• Lysosome• Chaperones• Golgi apparatus• Signaling networks

Intracellular Traffic

© Scientific American

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+Nucleus

Microtubules (MT) are like freeways and actin filaments are like local surface streets.

DyneinKinesin

VesicleMitochondria

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++

Nucleus

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Filaments

Actin filament• 10 nm diameter• 2.77 nm rise• 26 subunits/74 nm repeat

Microtubule 25 nm diameter 13 protofilaments

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+ end

- end

Motors Walk Along Filaments

Yildiz et al.

Science 2003.

Biochemistry, 4ht Ed, 1995

Motor proteins move cargo along filaments Molecular Biology of the Cell, 3rd Ed, 1994

Herpes Virus Transport in Neurons Along Microtubules

• Virus Movie: VirusMov.mov

Kinesin Myosin-V Dynein

Head (ATPase)

1

43

5

c

6

2

Head(ATPase)

Lever (?)

StalkPi

Pi

KAPP

KHC

KLC

KR2

KR3

Cargo

Ca2+

MR2

MR1

Cargo

KR1

Dynactinbinding

MT binding

The anatomy of a dynein molecule

N.Hirokawa, Science, 279, 519 (1998)Figure edited to show stalk

Burgess et. al. Nature 421, 715 (2003)

4

1

5 3

2

7

6

ATP ADP+Pi

Microtubule

Stalk

Stem

Dynein Can Shift Gears

Roop Mallik1, Brian Carter1, Stephanie Lax2, Stephen

King2, Steven Gross1

1UC Irvine2Univ. of Missouri-Kansas City

Dynein

1

43

5

c

6

2

Head(ATPase)

Lever (?)

Stalk

Dynactinbinding

Microtubule

Plastic bead(450 nm)

Optical trap

FT

FM

Dynein head

Burgess et al,Nature 2003

Dynein

Bead displacement proportional to backward force…. Calibrate and measure !!!

The basic experiment

Load TrapF kx

Typical trace of motion

Optical trap stiffness = spring constant = k = 0.011 pN/nm

F = - kx

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

High load8nm steps

Intermediate load 15 nm steps

Low load~25 nm steps

Step Size as a Function of Load at High [ATP]

Very Low ATP, No Load

Position vs. time Step Size Distribution

Mostly 24, 32 nm steps

Stalling Force

• Motor attached to bead

• Motor walks along microtubules

• 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.

Microtubule

Optical trap

FT

FM

Dynein

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

4

1

5 3

2

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ATP ADP+Pi

MT

Stalk

• Traditional approach : Coupled differential eqns.

• Alternative approach: Monte Carlo Simulations (Advantage: easy to deal with complicated nonlinear dependencies) stem

Desired Features of ATP Binding

• ATP can bind to (or unbind from) sites 1-4• Step size decreases as number of bound sites

increases

4

1

5 3

27

6

ATP ADP+Pi

MT

Stalk

• Problem: High [ATP], no load → small step size (nonsense)• Solution: Different ATP binding affinities on different sites • 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)

1 3 4 2on on on onk k k k

# ATP bound

1 2 3 4

Step size

32

nm

24

nm

16

nm

8

nm

• Binding probability increases with [ATP]

stem

ATP Hydrolysis needed for step to occur

• 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)

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1

5 3

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ATP ADP+Pi

MT

Stalk

stem

Monte Carlo Simulation

1. Bind (or unbind) ATP: Probability for n → n ± 1, Pbind(site i) = ki

on [ATP] Δt k2-4

on= 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 = 13. Reverse hydrolysis: Preverse = pr exp{(1- α )Fd/kT)}

or take a step4. Repeat

n = number of sites bound = {0, 1, 2, 3, 4}

d = step size = (5 – n) · 8 nm (conjecture)

Theoretical Position vs. Time

high [ATP]

low [ATP]

Step Size Distribution with No Load

Monte Carlo results

At various [ATP]Compare Theory and

Experiment (low [ATP])

High [ATP] = 1 mM Low [ATP] = 100 μM

Simulation Results of Step Size•Step size decreases as load increases

•Agrees with experiment

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. LoadOpen symbols: Experiment (Vissher et al., 1999); closed symbols: Monte Carlo;

solid line: Michaelis-Menten formula

Modeling Dynein: The Gear-Shifting Motor

Manoranjan Singh, Roop Mallik, Steve Gross, and Clare Yu

University of California, Irvine

+

+

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+Nucleus

Intracellular Traffic

© Scientific American

How is intracellular transport regulated?

Motors Walk Along Filaments

Motor proteins

Myosin

Kinesin

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Dynein

Kinesin

Vesicle

Mitochondria

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+Nucleus

Highway System of a Cell

ATP Fuels the Motor

• ATP = Adenosine Triphosphate• ATP has 3 phosphate ions• Hydrolysis: 1 phosphate ions breaks off• ADP = Adenosine Diphosphate has 2 phosphate

ions • Energy is released

ATP → ADP + Pi

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1

5 3

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ATP ADP+Pi

MT

Stalk

Stem

Laser Tweezers

• 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

How does the cell regulate the transport of vesicles?

Microtubules (MT) are like freeways and actin filaments are like local surface streets.

Pos

ition

alo

ng m

icro

tubu

le (

nm)

Time (sec)

Step size as function of load

High load8nm steps

Intermediate load 15 nm steps

Low load~25 nm steps

(High [ATP])

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

• 40% 24 nm steps• 40% 32 nm steps• ~19% 16 nm steps• ~1% 8 nm steps (?)

Mixture of steps at no load

Mean step-size is load-dependent

• Low [ATP]

Lo

ad

step

Small

Large

step

Lo

ad

step

Large

Small

step

Model for implementation of a gear

Desired Features• ATP can bind to sites 1-4• Step size decreases as number of bound sites

increases• Binding probability increases with [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)

4

1

5 3

27

6

ATP ADP+Pi

MT

Stalk

Monte Carlo Simulation

• Low ATP • High ATP

Theoretical Position vs. Time

low [ATP]

high [ATP]

Step Size Distribution

High ATP

Low ATP

Step Size Distribution

Low ATP

High ATP

Step Size Distribution with No Load

• TheoryExperiment (low [ATP])

Step Size Distribution with No Load: Compare Theory and Experiment

Step Size Distribution with No Load

Monte Carlo results

At various [ATP]Compare Theory and

Experiment (low [ATP])

Step Size Distribution with No Load

• Theory vs. Experiment

• Low [ATP]

• Monte Carlo Results

• Varying [ATP]

High [ATP] = 1 mM Low [ATP] = 100 μM

Simulation Results of Step Size•Step size decreases as load increases

•Agrees with experiment

Predicted Velocity vs. Load