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Intracellular cargo transport: Molecular motors playing tug-of-war

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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.

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Intracellular cargo transport: Molecular motors playing tug-of-war

  1. 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. 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. 3. 1) Intracellular cargo transport & molecular motors
  4. 4. Cell = chemical micro-factory Alberts et al., Essential cell biology (1998)
  5. 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. 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. 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. 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. 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. 10. Coordination • Hypothetical coordination complex Coordination complex • mechanical interaction • Tug-of-war model: - model for single motor - mechanical interaction or tug-of-war?
  11. 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. 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. 13. 2) Molecular motors playing tug-of-war
  14. 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. 15. • Master equation • Observation time sec - min → stationary state • Analysis: numerical calculations, simulations, analytical approximations Tug-of-war model
  16. 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. 17. Types of motion Stochastic motion → what are the probabilities? Plus motion Slow motion Minus motion
  18. 18. Symmetric: Plus and minus motors only differ in forward direction E.g. in vitro antiparallel microtubules 2a) Tug-of-war: fair play
  19. 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. 20. Weak motors • highest probability for same number of bound motors (0,0) • blockade!
  21. 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. 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. 23. Strong motors • Unbinding cascade → only one team remains bound (0,0) • Unbinding cascade
  24. 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. 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. 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. 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. 28. Strong motors • Unbinding cascade → 1D random walk → exact solution (0,0) • Unbinding cascade
  29. 29. Strong motors desorptionconstantK=ε0/π0 (0) (−+) stall force Fs / detachment force Fd (−0+) ‘Strong' motors: stall force Fs > detachment force Fd
  30. 30. Intermediate case desorptionconstantK=ε0/π0 (0) (−+) stall force Fs / detachment force Fd (−0+) Intermediate case: stall force Fs ~ detachment force Fd
  31. 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. 32. Sharp maxima approximation • Probability concentrated around maxima → dynamics only on maxima and nearest neighbours (0,0)
  33. 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. 34. Tug-of-war animation
  35. 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. 36. Asymmetric: e.g. dynein and kinesin → Motility states: all combinations of (+), (-), (0) 2b) Tug-of-war: unfair play
  37. 37. Asymmetric tug-of-war → 7 motility states (+), (–), (0), (–+), (0+), (–0), (–0+) → net motion possible
  38. 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. 39. • Slow motion (blockade) Unbinding cascade → fast motion Comparison to experiment • Why people didn’t believe in a tug-of-war before:
  40. 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. 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. 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. 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. 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. 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. 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. 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. 48. 3) Why
  49. 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. 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. 51. Thank you Yan Chai Stefan Klumpp Janina BeegChristian Korn Steffen Liepelt Thank you for your attention! Reinhard Lipowsky

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