Lecture: Modeling intracellular cargo transport by several molecular motors
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Transcript of Lecture: Modeling intracellular cargo transport by several molecular motors
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Modeling intracellular cargo transport by several molecular motors
Melanie J.I. MuellerSchool ‘Modelling Complex Biological Systems‘, Évry 2010 May 7
Harvard University Physics Department
Max Planck Institute for Colloids and Interfaces
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Max Planck Institute of Colloids and Interfaces,
Potsdam
Palace of Sanssouci,‘le Versailles prussien’
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Outline
• Tasks of intracellular transport
• Why motors work in teams, and• How to model transport by motor teams
• Molecular motors are cool nanomachines
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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
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Motors - biological nanomachines
Mitochondria:
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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
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Linear motors in muscles
muscle
Fibre bundlefibre
fibril
sarcomere
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Myosin motorsMyosin head
Actin filament
Energy supply
Linear motors in muscles
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muscle
Fibre bundlefibre
fibril
sacromere
Linear motors in muscles
contraction animation
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Linear motors in cells • Cell = chemical microfactory
Albertset al., Essential Cell Biology
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Molecular motors
= cellular nano-trucks:
• walk rather than drive
- 'Roads': cytoskeletal filaments - 'Fuel': ATP - Cargos: vesicles, organelles …
animation
Vale lab
Travis, Science 1993
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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
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Outline
• Tasks of intracellular transport
• Why motors work in teams, and• How to model transport by motor teams
• Molecular motors are cool nanomachines
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African clawed frog (Xenopus laevis)
• only frog with clawed toes
• size ~ 1cm
• African frog… until late 1950s
• widely used in research
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• Pigment cells containmelanosomes (vesiclesfilled with black pigment)
Nascimento et al (2003)
African clawed frog (Xenopus laevis)• can adapt skin colour to background
• Melanie: from latin/greek: dark
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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)
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How to change colour
Molceular motors transport melanosomes along microtubules
Rogers, UCSF
Melano-some
Aggregation movie: Pedley lab (2002)
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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...)
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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
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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
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Motors work in teams
• In vivo: 1-10 motors transport a single cargo
Ashkin et al. (1990)
100nm
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Outline
• Tasks of intracellular transport
• Why motors work in teams, and• How to model transport by motor teams
• Molecular motors are cool nanomachines
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Outline
• Why motors work in teams, and• How to model transport by motor teams
One team Two teams Three teams
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A team of motors
• Cargo transported by N motors
• Model: 1) Model for a single motor
2) put motors together
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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
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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
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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
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• Distance covered until cargo unbinds?
xb¼vN²
µ¼²¶N ¡
Mean run length [μm]
Motor number N
• Run length distribution:
One team of motors
N=1 → 1 μmN=2 → 4 μm N=3 → 14 μmN=4 → 65 μm N=10→>1 m
...
Klumpp et al. 2006• Mean run length:
à xb
NX
i R ¡ zi e¡ zi xb
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One team of motors• Experiments? Need:
- cargo with several motors → latex bead in kinesin solution
- racetrack
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The racetrack1) Gliding assay:
3) Fix micotubules
5μmBöhm et al. 2005
2) Apply flow:
Direction of flow
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One team of motors
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One team of motors• Velocity is independent of kinesin concentration
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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
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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
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Melanosome transport
• Run length with 4 motors: 65 μm
Melano-some
• Cell radius ~ 20 μm
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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
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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)
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• 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
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• 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]
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• Motors in a team share the force:
F → F / (number of bound motors)
Motion against force
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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
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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
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Outline
• Why motors work in teams, and• How to model transport by motor teams
One team Two teams Three teams
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One team is not enough
• unidirectional cytoskeleton
+
+ +
+ + +
+ _
• Motors are 'one-way' machines:kinesin → plus enddynein → minus end
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One team is not enough
Steinberg labtime [s]
trajectory [μm]
Aggregation
Dispersion
+
+ +
+ + +
+ _
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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/sas for one species alone
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Coordination
• Hypothetical coordination complex
Coordination complex
• mechanical interaction
or tug-of-war?
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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)
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One team of motors
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Two teams of motors2 motors against 3 motors:
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Two teams of motors
• Opposing motors act as load, motors share force
• Independent motorswith 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-)
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→ random walk, Master equation
Two teams of motors
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Types of motion
Minus motion
Slow motion
Plus motion• Stochastic motion → probabilities• depend on motor properties
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• Instructive: symmetric case:Plus and minus motors only differ in forward direction
Motility states
• E.g. in vitro antiparallel microtubules
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'Strong' motors: switching between fastplus / minus motion
Intermediate case:fast plus and minusmotion 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]
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Motor tug-of-war
Blockade, slow
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Motor tug-of-war
Blockade, slow fast
Unbinding cascade → no blockade, fast motion
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Motor tug-of-war• Unbinding cascade → only one team remains bound• Unbinding cascade
• Bidirectional motion with stochastic switching
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Tug-of-war simulation
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‘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 filamentunbinding rate ε0 ~ binding rate π0
ε0 ≈ 1/sπ0 ≈ 5/s
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zz
plus, minus
plus, minus, pause
pause
4 plus and 4 minus motorsde
sorp
tion
cons
tant
K=ε
0/π0
stall force Fs / detachment force Fd
unbound
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zz
4 plus and 4 minus motors
• Change of motor parameters ↔ cellular regulation
deso
rptio
n co
nsta
nt K
=ε0/π
0
stall force Fs / detachment force Fd
unbound
Kin1cDyn cDynKin2 Kin3
Kin5
• Sensitivity → efficient regulation of cargo motion
Biological parameterrange
plus, minus
plus, minus, pause
pause
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Asymmetric tug-of-war
In vivo: dynein and kinesin→ net motion possible
+−
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Asymmetric tug-of-war→ 7 motility states (+), (–), (0), (–+), (0+), (–0), (–0+)
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Comparison to experiment • Motors with large stall force
Steinberg labtime [s]
distance [μm]Experimental trajectory
time [s]
distance [μm]Simulation trajectory:
→ looks very much alike→ good comparison: data with statistics
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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 %
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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
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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 ?
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Outline
• Why motors work in teams, and• How to model transport by motor teams
One team Two teams Three teams
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Cellular road network
microtubule filaments= highways
nucleiWittmann lab
actin filaments= side roads
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Cellular road network
microtubule filaments= highways
nucleiWittmann lab
actin filaments= side roads
Ross et al 2008
for long-range trafficof kinesin and dynein
for short-range trafficof myosin V and VI
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Melanosomes have three ‘legs‘ • Melanosomes are transported by
kinesin
dynein
myosin
kinesindynein
myosin
along microtubules
along actin
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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
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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
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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
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Molecular motors work in teamsto 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
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Thank you
Yan Chai
Stefan Klumpp
Janina BeegChristian
KornSteffen
Liepelt
Thank youfor your attention!
Reinhard Lipowsky