Intracellular transport is based on molecular motors that pull cargos along cytoskeletal filaments. Kinesin and dynein motors walk along microtubule filaments, while myosin motors move along actin filaments. One motor species walks actively only into one direction along the filament, e.g. kinesin-1 moves to the microtubule plus-end, whereas cytoplasmic dynein moves to the microtubule minus-end. However, many cellular cargos are observed to move bidirectionally, involving both plus- and minus-end-directed motors. The presumably simplest mechanism for such bidirectional transport is provided by a tug-of-war between the two motor species. We have studied this mechanism theoretically, using the load-dependent transport properties of individual motors as measured in single-molecule experiments. In contrast to previous expectations, such a tug-of-war is found to be highly cooperative and can lead to fast bidirectional motion with or without pauses, as observed in vivo. Our model reproduces experimental results on bidirectional transport of lipid droplets in Drosophila embryos, which have previously been thought to be incompatible with a tug-of-war scenario. One motor species walks actively only along one type of filament. However, the motor myosin-5, which walks actively along actin filaments, can passively diffuse along microtubules. Cargos that are transported along a microtubule by one kinesin and one myosin motor exhibit interspersed moving and diffusing events and increased processivity. We explain this behavior by a stochastic tug model similar to the tug-of-war model.

1. Intracellular cargo transport:
Molecular motors playing
tug-of-war
Melanie J.I. Müller,
Stefan Klumpp, Reinhard Lipowsky
Department of Theory & Bio-Systems
Max Planck Institute for Colloids and Interfaces

2. Outline
1) Intracellular cargo transport
& molecular motors
3) Why such weird motion?
2) Motors playing tug-of-war
a) fair play
b) unfair

3. 1) Intracellular cargo transport
& molecular motors

4. Cell = chemical micro-factory
Alberts et al., Essential cell biology (1998)

5. Molecular motors
• Molecular motors
= nanotrucks
- Roads: filaments
- Fuel: ATP
- Cargo: vesicles, organelles…
Travis, Science 261:1112 (1993)www.herculesvanlines.com (2008)
www.inetnebr.com/stuart/ja (2008)
• Nanoscale
→ Stochastic (Brownian) motion
→ Unbinding from filament ('fly')
after ~ 1 μm

6. Cytoskeleton
MTOC
+
+ +
+
+
+
+
-
--
-
-
-- -
Alberts et al., Essential cell biology (1998)
• Filaments are one-way streets:
Filaments:
• actin = side roads
• microtubules = highways
= unidirectional
road network
www.bildarchiv-hamburg.de (2008)

7. Bidirectional motion in vivo
Transport of endsosomes in fungus Ustilago maydis
Gero Fink 2006, Steinberg lab, MPI for Terrestrial Microbiology, ~ 2x real time, 60 μm hypha, endosome velocity ~ 2 μm/sec
+
_
Filament direction
time [s]
trajectory [μm]

8. Bidirectional motion
• Bidirectional motion on
unidirectional filaments
→ plus and minus motors
on one cargo
trajectory [μm]
time [s]
Gero Fink, MPI for Terrestristrial Mikcrobiology (2006)
Ashkin et al., Nature 348: 346 (1990)
0.1 μm
• Teams of 1-10 motors

9. Why?
• Why bidirectional motion?
→ later
• How does it work?
Why no blockade?
trajectory [μm]
time [s]
~ 2 μm/s
as for one species alone

10. Coordination
• Hypothetical coordination
complex
Coordination
complex
• mechanical interaction
• Tug-of-war model:
- model for single motor
- mechanical interaction
or tug-of-war?

11. v
π ε
• Velocity v
• Binding rate π
• Unbinding rate ε
Theoretician‘s view of a motor
• Motor characterized by
v(F)F
π(F) ε(F)
• Under load-force F
→ force-dependent parameters
• (F)
• (F)
• (F)
• Scales: many sec, many μm
→ step details irrelevant (0.01 s)
→ protein stucture irrelevant (100 nm)
→ motor unbinding relevant (1 μm)

12. • Velocity decreases with force
Model for a single motor
Velocity [μm/s]
Load F [pN]
Stall
force FS
• Velocity ≈ 0 for high forces → blockade
Load F [pN]
Unbinding rate [1/s]
~ exp[F/Fd]
detachment
force
• Unbinding rate increases
exponentially with force
• Binding rate independent of force
• ‘strong motor’:
stall force Fs > detachment force Fd

13. 2) Molecular motors
playing
tug-of-war

14. Tug-of-war model
v(F)F
π
ε(F)
Single motors with rates from
single molecule experiments
• Opposing motors → load force
• Motors of one team share force
• Forces determined by:
- Balance of motor forces
(+ cargo friction + external force)
- All motors move with one velocity

15. • Master equation
• Observation time sec - min → stationary state
• Analysis: numerical calculations, simulations,
analytical approximations
Tug-of-war model

16. Types of motion
Motors block each other
→ no motion
Minus motors win
→ motion to minus end
Plus motors win
→ motion to plus end

17. Types of motion
Stochastic motion → what are the probabilities?
Plus motion
Slow motion
Minus motion

18. Symmetric: Plus and minus motors only differ in forward direction
E.g. in vitro antiparallel microtubules
2a) Tug-of-war: fair play

19. Weak motors
• Weak motors := exert less force than they can sustain
stall force Fs < detachment force Fd
• Motors don’t feel each other
→ random binding and unbinding
x x

20. Weak motors
• highest probability for same number of bound motors
(0,0)
• blockade!

21. 'Strong' motors:
switching between fast
plus / minus motion
'Weak' motors:
little motion
motor number
trajectory [μm]
time [s]
(−)
(+)
(0)
motor number
probability
(0)
Motility states
trajectory [μm]
time [s]

22. Strong motors
• For motors with larger stall than detachment force
Force on cargo FC
FC/2 FC/3 FC/1 FC/3
Slow motion Fast motion
Unbinding cascade
leads to fast motion

23. Strong motors
• Unbinding cascade → only one team remains bound
(0,0)
• Unbinding cascade

24. 'Strong' motors:
switching between fast
plus / minus motion
Intermediate case:
fast plus and minus
motion with pauses
'Weak' motors:
little motion
motor number
trajectory [μm]
time [s]
(−)
(+)
(0)
(−)
motor numbermotor number
probability
(0)
(+)
(0) (−+)(−0+)
Motility states
trajectory [μm]
time [s]
trajectory [μm]
time [s]

25. 4 plus and 4 minus motors
zz
desorptionconstantK=ε0/π0
stall force Fs / detachment force Fd
ungebunden
(0)
(−+)
(−0+)trajectory [μm]
trajectory [μm]
trajectory [μm]

26. Weak motors
‘Weak' motors:
stall force Fs < detachment force Fd
→ motors don’t feel each other
→ analytical solution
desorptionconstantK=ε0/π0
(0)
(−+)
stall force Fs / detachment force Fd
→ slow motion (0)
(−0+)

27. Strong motors
Unbinding
cascade
→ fast bidirectional motion (−+)
desorptionconstantK=ε0/π0
(0)
(−+)
stall force Fs / detachment force Fd
(−0+)
‘Strong' motors:
stall force Fs > detachment force Fd

28. Strong motors
• Unbinding cascade → 1D random walk → exact solution
(0,0)
• Unbinding cascade

29. Strong motors
desorptionconstantK=ε0/π0
(0)
(−+)
stall force Fs / detachment force Fd
(−0+)
‘Strong' motors:
stall force Fs > detachment force Fd

30. Intermediate case
desorptionconstantK=ε0/π0
(0)
(−+)
stall force Fs / detachment force Fd
(−0+)
Intermediate case:
stall force Fs ~ detachment force Fd

31. Mean field approximation
desorptionconstantK=ε0/π0
(0)
(−+)
stall force Fs / detachment force Fd
(−0+)
desorptionconstantK=ε0/π0
stall force Fs / detachment force Fd
Stationary solution ↔ fixed points
Transitions between motility
states ↔ bifurcations
saddle-
node
bifurcation
transcritical
bifurcation
2D nonlinear dynamical
system for <n+>, <n–>

32. Sharp maxima approximation
• Probability concentrated around maxima
→ dynamics only on maxima and nearest neighbours
(0,0)

33. Sharp maxima approximation
desorptionconstantK=ε0/π0
(0)
(−+)
stall force Fs / detachment force Fd
(−0+)
desorptionconstantK=ε0/π0
(−0+)
(−+)
(0)
stall force Fs / detachment force Fd

34. Tug-of-war animation

35. 4 plus and 4 minus motors
• Change of motor parameters ↔ cellular regulation
zz
desorptionconstantK=ε0/π0
(0)
stall force Fs / detachment force Fd
ungebunden
Kin1cDyn cDyn
Kin2Kin3
Kin5
• Sensitivity → efficient regulation of cago motion
Biological
parameter
range
(−0+)
(−+)

36. Asymmetric: e.g. dynein and kinesin
→ Motility states: all combinations of (+), (-), (0)
2b) Tug-of-war: unfair play

37. Asymmetric tug-of-war
→ 7 motility states (+), (–), (0), (–+), (0+), (–0), (–0+)
→ net motion possible

38. Comparison to experiment
• Slow motion (blockade)
Experiment:
Fast motion in each direction
• Why people didn’t believe in a tug-of-war before:

39. • Slow motion (blockade)
Unbinding cascade
→ fast motion
Comparison to experiment
• Why people didn’t believe in a tug-of-war before:

40. • Slow motion (blockade)
• Stronger motors
determine direction
Stronger = higher stall force
Experiment:
stall forces do not
determine direction
Comparison to experiment
• Why people didn’t believe in a tug-of-war before:

41. • Slow motion (blockade)
• Stronger motors
determine direction
→ 'Stronger' can mean
- generate larger force
- bind stronger to filament
- resist pulling force better
→ direction not only
determined by (stall) forces
Comparison to experiment
• Why people didn’t believe in a tug-of-war before:

42. Run times and lengths
• Experimental characterization → run times and lengths
distance [μm]
time [s]
run
length
run time
• determine net direction, velocity, diffusivity
• target of cellular regulation

43. • Slow motion (blockade)
• Stronger motors
determine direction
• Impairing one direction
enhances the other
→ impairing one direction
can have various effects
plus minus
cellular regulation ↓ ─
dynein mutations ↓ ↓
kinesin mutation ↓ ↑
Comparison to experiment
• Why people didn’t believe in a tug-of-war before:

44. Regulation and mutation
• Dynein mutation = changing dynein properties
• Examples:
- increase dynein's unbinding rate
→ minus runs, plus runs
• Cellular regulation = changing motor properties
• Change one parameter → impair / enhance
• Change several parameters
→ various effects of changing many properties
shorter
longer
longer
shorter
- increase dynein's resistance to force
→ minus runs, plus runs

45. • Slow motion (blockade)
• Stronger motors
determine direction
• Impairing one direction
enhances the other
Impairing one direction
(regulation / mutation)
can have various effects
on the other direction
Comparison to experiment
• Why people didn’t believe in a tug-of-war before:

46. Comparison to experiment
Gero Fink, MPI for Terrestrial Microbiology (2006)
time [s]
distance [μm]
Endosomes in fungal hypha:
time [s]
distance [μm]
Simulation trajectory:
→ looks similar
→ good comparison: data with statistics

47. Comparison to experiment
• Bidirectional transport
of lipid-droplets
in Drosophila embryos
trajectory [nm]
time [s]
Gross et al., J. Cell Biol. 148:945 (2000)quest.nasa.gov/projects/flies/LifeCycle.html
• Data from Gross lab (UC Irvine):
- Statistics on run lengths, velocities, stall forces
- effect of cellular regulation (2 embryonic phases)
- effect of 3 dynein mutations
→ Tug-of-war reproduces experimental data within 10 %
→ no coordination complex necessary

48. 3) Why

49. Why bidirectional motion?
Why instead of ?
• Search for target
• Error correction
• Avoid obstacles
• Cargos without destination
• Easy and fast regulation
• Bidirectional transport of cargo and motors
Why instead of ?

50. Summary
Bidirectional transport
as tug-of-war of molecular motors
• simple model, but
complex and cooperative motility
• fast bidirectional motion ‘despite’ tug-of-war
• complex parameter-dependence
→ efficient regulation of motility
• consistent with in vivo data

51. Thank you
Yan
Chai
Stefan
Klumpp
Janina
BeegChristian
Korn
Steffen
Liepelt
Thank you
for your attention!
Reinhard
Lipowsky