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Lecture: Modeling intracellular cargo transport by several molecular motors

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The complex internal structure of cells depends to a large extend on active transport by molecular motors. These molecular motors are 'nano-trucks' that transport various cargoes, like vesicles, organelles or mRNA, along cytoskeletal filaments, the 'roads'.

Many cargoes are transported by small teams of about 1-10 motors. Some cargoes make use of just one team of motors of the same kind, while other cargoes are propelled by two different motor teams. These teams might move into opposite directions on the same filament, or move on different types of filaments.

In this talk, we will describe systematic stochastic models for cargo transport by one or two small teams of molecular motors. These models are based on single motor properties as determined in single molecule experiments, and can be used to explain and predict various properties of the movements of cargoes inside of cells. By providing a direct connection between the behavior of single motors and†intracellular transport, the models lead to an improved understanding of this transport†and†its biological functions.

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Lecture: Modeling intracellular cargo transport by several molecular motors

  1. 1. Modeling intracellular cargo transport by several molecular motors Melanie J.I. Mueller School ‘Modelling Complex Biological Systems‘, Évry 2010 May 7 Harvard University Physics Department Max Planck Institute for Colloids and Interfaces
  2. 2. Max Planck Institute of Colloids and Interfaces, Potsdam Palace of Sanssouci, ‘le Versailles prussien’
  3. 3. Outline • Tasks of intracellular transport • Why motors work in teams, and • How to model transport by motor teams • Molecular motors are cool nanomachines
  4. 4. Imagine… …billions of tiny machines inside your body… …a thousands of the thickness of human hair… …designed for a variety of functions… …science fiction? Selvin, The Scientist Cover 2005
  5. 5. Motors - biological nanomachines Mitochondria:
  6. 6. Motors - biological nanomachines Linear motors: move stuff inside cell Kinosita lab Rotary motors: ATP synthase makes ATP = cellular energy Schmidt lab • here: 50 r.p.m. • can do 8000 r.p.m 2μm
  7. 7. Linear motors in muscles muscle Fibre bundle fibre fibril sarcomere
  8. 8. Myosin motors Myosin head Actin filament Energy supply Linear motors in muscles
  9. 9. muscle Fibre bundle fibre fibril sacromere Linear motors in muscles contraction animation
  10. 10. Linear motors in cells • Cell = chemical microfactory Albertset al., Essential Cell Biology
  11. 11. Molecular motors = cellular nano-trucks: • walk rather than drive - 'Roads': cytoskeletal filaments - 'Fuel': ATP - Cargos: vesicles, organelles … animation Vale lab Travis, Science 1993
  12. 12. How good are motors? • velocity = 800 nm/sec 8nm • Are motors fast? • 1 step = 1 m instead of 8nm → 100m/sec = 360km/h → racing car speed → 100 steps/sec !! Vale lab
  13. 13. Outline • Tasks of intracellular transport • Why motors work in teams, and • How to model transport by motor teams • Molecular motors are cool nanomachines
  14. 14. African clawed frog (Xenopus laevis) • only frog with clawed toes • size ~ 1cm • African frog… until late 1950s • widely used in research
  15. 15. • Pigment cells contain melanosomes (vesicles filled with black pigment) Nascimento et al (2003) African clawed frog (Xenopus laevis) • can adapt skin colour to background • Melanie: from latin/greek: dark
  16. 16. How to change colour Aggregation movie: Pedley lab (2002) Dispersion movie (16min): Borisy lab (1998) Nascimento et al (2003) Dispersion(MSH, caffeine) Aggregation (melatonin, adrenalin)
  17. 17. How to change colour Molceular motors transport melanosomes along microtubules Rogers, UCSF Melano- some Aggregation movie: Pedley lab (2002)
  18. 18. Scales of melanosome transport Molceular motors transport melanosomes along microtubules • Cell radius ~ 20 μm Melano- some • Melanosome size ~ 0.5 μm → time to diffuse 20 μm ~ 30 hours • Melanosome velocity v ~ 1 μm/s → time to travel 20 μm ~ 20 s (Similarly: other vesicles, organelles, proteins, mRNAs...)
  19. 19. Linear molecular motors • Molecular motors = nanotrucks Travis, Science 261:1112 (1993)www.herculesvanlines.com (2008) www.inetnebr.com/stuart/ja (2008) • Motor size: ~ 100 nm → nanoscale → Stochastic (Brownian) motion → Unbinding from filament ('fly') after ~ 1 μm • Motor velocity: ~μm/s Melano- some
  20. 20. Scales of motor transport Kinesin motor : Melanosome transport: - Velocity v ~ 1 μm/s - Cell diameter ~ 15-50 μm - Unbinds from microtubule after 'run length' ~ 1 μm - Velocity v ~ 1 μm/s
  21. 21. Motors work in teams • In vivo: 1-10 motors transport a single cargo Ashkin et al. (1990) 100nm
  22. 22. Outline • Tasks of intracellular transport • Why motors work in teams, and • How to model transport by motor teams • Molecular motors are cool nanomachines
  23. 23. Outline • Why motors work in teams, and • How to model transport by motor teams One team Two teams Three teams
  24. 24. A team of motors • Cargo transported by N motors • Model: 1) Model for a single motor 2) put motors together
  25. 25. Modeling molecular motors • Good model depends on scale ~ 1 -100 nm: - protein structure - stepping mechanism Hancock lab Mandelkow lab ~100 nm – many μm: motion along filament ~ many μm – mm: interplay directed and diffusive motion Lipowsky et al. 2001
  26. 26. v π ε • bind to filament with rate π • walk along filament with velocity v • unbind from filament with rate ε • Melanophore transport: Lengths: many μm → protein stucture irrelevant (≤100nm) Times: many sec → step details irrelevant (≤0.01s) → motor unbinding relevant • Motor can Melano- some Modeling melanosome transport
  27. 27. One team of motors • N=3 motors transport a cargo Klumpp et al. 2006 • Stochastic binding and unbinding of motors: • Rate for unbinding of one motor = ε if 1 motor bound • Rate for binding of one motor = (N-n) π if n motors bound • Velocity: independent of n if 2 motors bound if n motors bound = 2 ε = n ε Master equation for binding and unbinding
  28. 28. • Distance covered until cargo unbinds?  xb ¼ v N ² µ ¼ ² ¶N ¡  Mean run length [μm] Motor number N • Run length distribution: One team of motors N=1 → 1 μm N=2 → 4 μm N=3 → 14 μm N=4 → 65 μm N=10→>1 m ... Klumpp et al. 2006 • Mean run length: Ã xb  NX i  R¡ zi e¡ zi  xb
  29. 29. One team of motors • Experiments? Need: - cargo with several motors → latex bead in kinesin solution - racetrack
  30. 30. The racetrack 1) Gliding assay: 3) Fix micotubules 5μm Böhm et al. 2005 2) Apply flow: Direction of flow
  31. 31. One team of motors
  32. 32. One team of motors • Velocity is independent of kinesin concentration
  33. 33. One team of motors • Put latex bead in kinesin solution • Problem 1: How many kinesins on the bead? How many can reach the microtubule? → Average number ~ kinesin concentration • Problem 2: Number different for each bead → average with Poisson distribution
  34. 34. One team of motors • Run length distributions for 9 different kinesin concentrations • 2 fit parameters: binding rate π, concentration constant c0 → allows to convert kinesin concentration to motor number
  35. 35. Melanosome transport • Run length with 4 motors: 65 μm Melano- some • Cell radius ~ 20 μm
  36. 36. Frictional forces → Friction force in cytoplasm ~ 1-10 pN • Melanosome size: 0.5 μm • Cytoplasm is very crowded → friction force Ffriction = γv • γ depends on cargo size r large size r → large friction γ Goodsell, Our molecular nature Melano- some
  37. 37. v π ε • Under load F: force-dependent parameters v(F)F π(F) ε(F) Motion against force • Velocity v • Binding rate π • Unbinding rate ε • Motor characterized by parameters • Experimentally: optical trap Visscher et al., Nature 400: 184 (1999)
  38. 38. • Velocity Motion against force Stall force Load F [pN] Carter et al. 2005 Velocity [nm/s] Melanosome friction force Velocity [μm/s] Load F [pN] Stall force FS
  39. 39. • Binding rate independent of force • Unbinding rate increases exponentially with force (Kramers, Bell) Schnitzer et al. 2000 ~ 1/unbinding rate Load F [pN] Force scale: detachment force. Kinesin ~ 3pN Motion against force Load F [pN] Unbinding rate [1/s] ~ exp[F/Fd]
  40. 40. • Motors in a team share the force: F → F / (number of bound motors) Motion against force
  41. 41. Force-velocity relation: Forced unbinding • Motors share force: F → F/n Teams have larger forces with larger velocities Average number of bound motors: Motion against force Melanosome friction force
  42. 42. Motion against force Velocity depends on the number of bound motors → stochastic switching between velocity values → velocity distributions have several maxima Levi et al. 2006
  43. 43. Outline • Why motors work in teams, and • How to model transport by motor teams One team Two teams Three teams
  44. 44. One team is not enough • unidirectional cytoskeleton + + + + ++ + _ • Motors are 'one-way' machines: kinesin → plus end dynein → minus end
  45. 45. One team is not enough Steinberg lab time [s] trajectory [μm] Aggregation Dispersion + + + + ++ + _
  46. 46. Ashkin et al., Nature 348: 346 (1990) 0.1 μm • Two teams of 1-10 motors One team is not enough • How does it work? Why no blockade? trajectory [μm] time [s] ~ 2 μm/s as for one species alone
  47. 47. Coordination • Hypothetical coordination complex Coordination complex • mechanical interaction or tug-of-war?
  48. 48. Coordination • Hypothetical coordination complex Coordination complex • mechanical interaction • Tug-of-war model: - model for single motor - mechanical interaction or tug-of-war? Tug-of-war (tir à la corde)
  49. 49. One team of motors
  50. 50. Two teams of motors 2 motors against 3 motors:
  51. 51. Two teams of motors • Opposing motors act as load, motors share force • Independent motors with single motor rates v(F)F π(F) ε(F) • Newton's 3rd law → n+ F+ = n–F– • Plus and minus motors move at same velocity: → v+(F+) = v-(F-)
  52. 52. → random walk, Master equation Two teams of motors
  53. 53. Types of motion Minus motion Slow motion Plus motion • Stochastic motion → probabilities • depend on motor properties
  54. 54. • Instructive: symmetric case: Plus and minus motors only differ in forward direction Motility states • E.g. in vitro antiparallel microtubules
  55. 55. '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) (+) Motility states trajectory [μm] time [s] trajectory [μm] time [s]
  56. 56. Motor tug-of-war Blockade, slow
  57. 57. Motor tug-of-war Blockade, slow fast Unbinding cascade → no blockade, fast motion
  58. 58. Motor tug-of-war • Unbinding cascade → only one team remains bound• Unbinding cascade • Bidirectional motion with stochastic switching
  59. 59. Tug-of-war simulation
  60. 60. ‘Nice’ motor properties • Fast bidirectional motion requires unbinding cascade • Motors must pull opposing motors off the filament: stall force Fs > detachment force Fd Fs ≈ 6 pN Fd ≈ 3 pN kinesin-1: • Motors must drop off the filament unbinding rate ε0 ~ binding rate π0 ε0 ≈ 1/s π0 ≈ 5/s
  61. 61. zz plus, minus plus, minus, pause pause 4 plus and 4 minus motors desorptionconstantK=ε0/π0 stall force Fs / detachment force Fd unbound
  62. 62. zz 4 plus and 4 minus motors • Change of motor parameters ↔ cellular regulation desorptionconstantK=ε0/π0 stall force Fs / detachment force Fd unbound Kin1cDyn cDyn Kin2Kin3 Kin5 • Sensitivity → efficient regulation of cargo motion Biological parameter range plus, minus plus, minus, pause pause
  63. 63. Asymmetric tug-of-war In vivo: dynein and kinesin → net motion possible +−
  64. 64. Asymmetric tug-of-war → 7 motility states (+), (–), (0), (–+), (0+), (–0), (–0+)
  65. 65. Comparison to experiment • Motors with large stall force Steinberg lab time [s] distance [μm] Experimental trajectory time [s] distance [μm] Simulation trajectory: → looks very much alike → good comparison: data with statistics
  66. 66. 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 (UCI): - 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 %
  67. 67. 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 • What we learn: - no coordination complex necessary - different cell states (embryonic phases): net transport direction regulated by changes in run times - mutation in minus motors affects minus AND plus motion
  68. 68. 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 ?
  69. 69. Outline • Why motors work in teams, and • How to model transport by motor teams One team Two teams Three teams
  70. 70. Cellular road network microtubule filaments = highways nuclei Wittmann lab actin filaments = side roads
  71. 71. Cellular road network microtubule filaments = highways nuclei Wittmann lab actin filaments = side roads Ross et al 2008 for long-range traffic of kinesin and dynein for short-range traffic of myosin V and VI
  72. 72. Melanosomes have three ‘legs‘ • Melanosomes are transported by kinesin dynein myosin kinesindynein myosin along microtubules along actin
  73. 73. Melanosome transport Rogers et al 1998 10μm aggregated melanosomes disrupt microtubules 1 hour later dispersed melanosomes disrupt actin 1 hour later → transport on actin keeps melanosomes dispersed
  74. 74. Myosin as a tether • Myosin can also diffuse passively on microtubules [Ali et al 2008] • Myosin walks actively on actin • Myosin acts as tether → enhances cargo processivity • Model: moving kinesin, diffusing myosin. Can fit data. • Prediction: Run length increases exponentially with number of myosins kinesin myosin
  75. 75. Motors work in teams Why teams? Why not work with one strong motor per direction? • Robustness: one motor may fail • Easy regulation • large run lengths • large forces • bidirectional motion
  76. 76. Molecular motors work in teams to accomplish intracellular transport: Summary • Stochastic models can help to understand transport by teams of molecular motors Molecular motors are cool nanomachines • 1 team: increased range, force, velocity • 3 teams: switch highways ↔ side roads • 2 teams: bidirectional, easy to regulate
  77. 77. Thank you Yan Chai Stefan Klumpp Janina BeegChristian Korn Steffen Liepelt Thank you for your attention! Reinhard Lipowsky

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