intracellular cargo transport: molecular motors playing tug-of-war

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

Outline

1) Intracellular cargo transport & molecular motors

3) Why such weird motion?

2) Motors playing tug-of-wara) fair playb) unfair

1) Intracellular cargo transport& molecular motors

Cell = chemical micro-factory

Alberts et al., Essential cell biology (1998)

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

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)

Bidirectional motion in vivo

Transport of endsosomes in fungus Ustilago maydisGero 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]

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

Why?

• Why bidirectional motion? → later

• 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• Tug-of-war model:

- model for single motor- mechanical interaction

or tug-of-war?

v

π ε

• Velocity v• Binding rate π• Unbinding rate ε

Theoretician‘s view of a motor

• Motor characterized byv(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)

• 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

2) Molecular motorsplaying

tug-of-war

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

• Master equation• Observation time sec - min → stationary state• Analysis: numerical calculations, simulations,

analytical approximations

Tug-of-war model

Types of motion

Motors block each other → no motion

Minus motors win → motion to minus

end

Plus motors win → motion to plus end

Types of motion

Stochastic motion → what are the probabilities?

Plus motion

Slow motion

Minus motion

Symmetric: Plus and minus motors only differ in forward directionE.g. in vitro antiparallel microtubules

2a) Tug-of-war: fair play

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

Weak motors• highest probability for same number of bound motors

(0,0)

• blockade!

'Strong' motors: switching between fastplus / minus motion

'Weak' motors:little motion

motor number

trajectory [μm]

time [s]

(−)

(+)

(0)

motor number

probability

(0)

Motility states

trajectory [μm]

time [s]

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

Strong motors• Unbinding cascade → only one team remains bound

(0,0)

• Unbinding cascade

'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)

(+)

(0) (−+)(−0+)

Motility states

trajectory [μm]

time [s]

trajectory [μm]

time [s]

4 plus and 4 minus motors

zz

deso

rptio

n co

nsta

nt K

=ε0/π

0

stall force Fs / detachment force Fd

ungebunden

(0)

(−+)

(−0+)trajectory [μm]

trajectory [μm]

trajectory [μm]

Weak motors‘Weak' motors:stall force Fs < detachment force Fd

→ motors don’t feel each other→ analytical solution

deso

rptio

n co

nsta

nt K

=ε0/π

0

(0)

(−+)


→ slow motion (0)

(−0+)

Strong motors

Unbindingcascade

→ fast bidirectional motion (−+)

deso

rptio

n co

nsta

nt K

=ε0/π

0

(0)

(−+)


(−0+)

‘Strong' motors:stall force Fs > detachment force Fd

Strong motors• Unbinding cascade → 1D random walk → exact solution

(0,0)

• Unbinding cascade

Strong motorsde

sorp

tion

cons

tant

K=ε

0/π0

(0)

(−+)


(−0+)

‘Strong' motors:stall force Fs > detachment force Fd

Intermediate casede

sorp

tion

cons

tant

K=ε

0/π0

(0)

(−+)


(−0+)

Intermediate case:stall force Fs ~ detachment force Fd

Mean field approximationde

sorp

tion

cons

tant

K=ε

0/π0

(0)

(−+)


(−0+)

deso

rptio

n co

nsta

nt K

=ε0/π

0


Stationary solution ↔ fixed pointsTransitions between motility

states ↔ bifurcations

saddle-nodebifurcation transcritical

bifurcation

2D nonlinear dynamical system for <n+>, <n–>

Sharp maxima approximation• Probability concentrated around maxima

→ dynamics only on maxima and nearest neighbours

(0,0)

Sharp maxima approximationde

sorp

tion

cons

tant

K=ε

0/π0

(0)

(−+)


(−0+)

deso

rptio

n co

nsta

nt K

=ε0/π

0

(−0+)

(−+)

(0)


Tug-of-war animation

C:\Dokumente und Einstellungen\Melanie\Eigene Dateien\MPIKG\Movies\TugOfWarApplication\TugOfWar.jar

4 plus and 4 minus motors

• Change of motor parameters ↔ cellular regulation

zz

deso

rptio

n co

nsta

nt K

=ε0/π

0

(0)


ungebunden

Kin1cDyn cDynKin2 Kin3

Kin5

• Sensitivity → efficient regulation of cago motion

Biological parameterrange

(−0+)

(−+)

Asymmetric: e.g. dynein and kinesin→ Motility states: all combinations of (+), (-), (0)

2b) Tug-of-war: unfair play

Asymmetric tug-of-war→ 7 motility states (+), (–), (0), (–+), (0+), (–0), (–0+)

→ net motion possible

Comparison to experiment

• Slow motion (blockade)

Experiment:Fast motion in each direction

• Why people didn’t believe in a tug-of-war before:

• Slow motion (blockade)Unbinding cascade

→ fast motion

Comparison to experiment• Why people didn’t believe in a tug-of-war before:


• Stronger motors determine direction

Stronger = higher stall forceExperiment: stall forces do not determine direction




→ 'Stronger' can mean- generate larger force- bind stronger to filament- resist pulling force better

→ direction not only determined by (stall) forces


Run times and lengths• Experimental characterization → run times and lengths

distance [μm]

time [s]

runlength

run time

• determine net direction, velocity, diffusivity

• target of cellular regulation



• Impairing one direction enhances the other

→ impairing one direction can have various effects

plus minuscellular regulation ↓ ─dynein mutations ↓ ↓kinesin mutation ↓ ↑


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



• Impairing one direction enhances the other

Impairing one direction(regulation / mutation)can have various effectson the other direction


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

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

3) Why

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 ?

SummaryBidirectional 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

Thank you

Yan Chai

Stefan Klumpp

Janina BeegChristian

KornSteffen

Liepelt

Thank youfor your attention!

Reinhard Lipowsky