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 Nucleus

Microtubules (MT) are like freeways and actin filaments are like local surface streets. Dynein Kinesin Vesicle Mitochondria Nucleus +

Filaments Actin filament 10 nm diameter 2.77 nm rise 26 subunits/74 nm repeat Microtubule  25 nm diameter  13 protofilaments + end- end + 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.movVirusMov.mov

KinesinMyosin-VDynein Head (ATPase) c 6 2 Head (ATPase) Lever (?) Stalk PiPi PiPi KAPP KHC KLC KR2 KR3 Cargo Ca 2+ MR2 MR1 Cargo KR1 Dynactin binding 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) ATP ADP+Pi Microtubule Stalk Stem

Dynein Can Shift Gears Roop Mallik 1, Brian Carter 1, Stephanie Lax 2, Stephen King 2, Steven Gross 1 1 UC Irvine 2 Univ. of Missouri-Kansas City Dynein c 6 2 Head (ATPase) Lever (?) Stalk Dynactin binding

Microtubule Plastic bead (450 nm) Optical trap FTFT FMFM Dynein head Burgess et al, Nature 2003 Dynein Bead displacement proportional to backward force …. Calibrate and measure !!! The basic experiment

Typical trace of motion Optical trap stiffness = spring constant = k = 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 load 8nm 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 FTFT FMFM 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 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 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) # ATP bound 1234 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) ATP ADP+Pi MT Stalk stem

Monte Carlo Simulation 1. Bind (or unbind) ATP: Probability for n → n ± 1, P bind (site i) = k i on [ATP] Δt k 2-4 on = k 2-4 on (F=0)exp{Fa/kT} 2.Hydrolyze ATP at site 1: P hydrolyze = p o exp{-αFd/kT} Δt where p o → p o /100 if n = 1 3. Reverse hydrolysis: P reverse = p r exp{(1- α )Fd/kT)} or take a step 4. 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. Load Open 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 Nucleus

Intracellular Traffic © Scientific American  How is intracellular transport regulated?

Motors Walk Along Filaments

Motor proteins Myosin Kinesin

+ + Dynein Kinesin Vesicle Mitochondria 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 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.

Position along microtubule (nm) Time (sec) Step size as function of load High load 8nm 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]

Load step Large

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) ATP ADP+Pi MT Stalk

Monte Carlo Simulation Low ATPHigh 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 Theory Experiment (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