Post on 11-Jan-2017
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
Max Planck Institute of Colloids and Interfaces,
Potsdam
Palace of Sanssouci,‘le Versailles prussien’
Outline
• Tasks of intracellular transport
• Why motors work in teams, and• How to model transport by motor teams
• Molecular motors are cool nanomachines
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
Motors - biological nanomachines
Mitochondria:
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
Linear motors in muscles
muscle
Fibre bundlefibre
fibril
sarcomere
Myosin motorsMyosin head
Actin filament
Energy supply
Linear motors in muscles
muscle
Fibre bundlefibre
fibril
sacromere
Linear motors in muscles
contraction animation
Linear motors in cells • Cell = chemical microfactory
Albertset al., Essential Cell Biology
Molecular motors
= cellular nano-trucks:
• walk rather than drive
- 'Roads': cytoskeletal filaments - 'Fuel': ATP - Cargos: vesicles, organelles …
animation
Vale lab
Travis, Science 1993
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
Outline
• Tasks of intracellular transport
• Why motors work in teams, and• How to model transport by motor teams
• Molecular motors are cool nanomachines
African clawed frog (Xenopus laevis)
• only frog with clawed toes
• size ~ 1cm
• African frog… until late 1950s
• widely used in research
• 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
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)
How to change colour
Molceular motors transport melanosomes along microtubules
Rogers, UCSF
Melano-some
Aggregation movie: Pedley lab (2002)
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...)
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
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
Motors work in teams
• In vivo: 1-10 motors transport a single cargo
Ashkin et al. (1990)
100nm
Outline
• Tasks of intracellular transport
• Why motors work in teams, and• How to model transport by motor teams
• Molecular motors are cool nanomachines
Outline
• Why motors work in teams, and• How to model transport by motor teams
One team Two teams Three teams
A team of motors
• Cargo transported by N motors
• Model: 1) Model for a single motor
2) put motors together
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
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
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
• 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
One team of motors• Experiments? Need:
- cargo with several motors → latex bead in kinesin solution
- racetrack
The racetrack1) Gliding assay:
3) Fix micotubules
5μmBöhm et al. 2005
2) Apply flow:
Direction of flow
One team of motors
One team of motors• Velocity is independent of kinesin concentration
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
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
Melanosome transport
• Run length with 4 motors: 65 μm
Melano-some
• Cell radius ~ 20 μm
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
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)
• 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
• 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]
• Motors in a team share the force:
F → F / (number of bound motors)
Motion against force
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
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
Outline
• Why motors work in teams, and• How to model transport by motor teams
One team Two teams Three teams
One team is not enough
• unidirectional cytoskeleton
+
+ +
+ + +
+ _
• Motors are 'one-way' machines:kinesin → plus enddynein → minus end
One team is not enough
Steinberg labtime [s]
trajectory [μm]
Aggregation
Dispersion
+
+ +
+ + +
+ _
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
Coordination
• Hypothetical coordination complex
Coordination complex
• mechanical interaction
or tug-of-war?
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)
One team of motors
Two teams of motors2 motors against 3 motors:
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-)
→ random walk, Master equation
Two teams of motors
Types of motion
Minus motion
Slow motion
Plus motion• Stochastic motion → probabilities• depend on motor properties
• Instructive: symmetric case:Plus and minus motors only differ in forward direction
Motility states
• E.g. in vitro antiparallel microtubules
'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]
Motor tug-of-war
Blockade, slow
Motor tug-of-war
Blockade, slow fast
Unbinding cascade → no blockade, fast motion
Motor tug-of-war• Unbinding cascade → only one team remains bound• Unbinding cascade
• Bidirectional motion with stochastic switching
Tug-of-war simulation
‘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
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
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
Asymmetric tug-of-war
In vivo: dynein and kinesin→ net motion possible
+−
Asymmetric tug-of-war→ 7 motility states (+), (–), (0), (–+), (0+), (–0), (–0+)
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
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 %
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
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 ?
Outline
• Why motors work in teams, and• How to model transport by motor teams
One team Two teams Three teams
Cellular road network
microtubule filaments= highways
nucleiWittmann lab
actin filaments= side roads
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
Melanosomes have three ‘legs‘ • Melanosomes are transported by
kinesin
dynein
myosin
kinesindynein
myosin
along microtubules
along actin
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
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
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
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
Thank you
Yan Chai
Stefan Klumpp
Janina BeegChristian
KornSteffen
Liepelt
Thank youfor your attention!
Reinhard Lipowsky