Lecture: Modeling intracellular cargo transport by several molecular motors

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