Transport in cells Intracellular transport

• introduction: transport in cells, molecular players etc. • cooperation of motors, forces good and bad • transport regulation, traffic issues, …

Stefan Klumpp image source: wikipedia Smith, Gross, Enquist, PNAS 98: 3466 (2001) Transport physics on different length scales

macroscopic microscopic intracellular

objects: cm – m objects: µm – mm objects: nm – µm transport over. m – km transport over: mm – cm transport over µm-cm

inertia friction, viscosity fluctuations, turbulent flow Stokes flow Brownian motion

image source: wikipedia Transport physics on different length scales

diffusion vs. directed transport

x ≈ Dt x ≈ vt

typical values in cells: v ~ 1 µm/s D ~ 1 µm2/s (for , less for larger cargoes, more for small molecules)

over 10 µm: diffusion takes 100 s, directed transport 10 s Transport in cells

filaments

nucleus ,

image source: wikipedia Cytoskeletal motors

• fuel: ATP

• forces: few pN • speeds: ~µm/s

• motor moves in defined direction [Vale & Milligan 2000]

– + on microtubules – - - + – V + – myosin VI - on actin

[J. Beeg] Transport by motor teams

• Transport along filaments of the well characterized at single-molecule level (forces, speeds, chemomechanical coupling)

• In cells, large cargoes often transported by several motors

• Bidirectional transport: different types of [Ashkin et al. Nature (1990)] motors

[Hendricks et al. Curr. Biol. (2010)] Transport by motor teams

• Transport along filaments of the cytoskeleton well characterized at single-molecule level (forces, speeds, chemomechanical coupling)

• In cells, large cargoes often transported by several motors

• Bidirectional transport: different types of [Ashkin et al. Nature (1990)] motors

→ how are the motors coordinated ? (tug-of-war vs. “coordination complex”) ?

Tug-of-war model

N plus motors N minus motors + – n bound n bound + -

- +

• stochastic binding/unbinding of motors → force-dependent rates

• deterministic movement of cargo → velocity from force balance

tug-of-war: force btw. the two motor species

Müller, Klumpp, Lipowsky, PNAS 105, 4609 (2008) Tug-of-war model

• stochastic binding/unbinding of motors d P(n+, n− ) = −(ε+ (n+, n− )+ε− (n+, n− ))P(n+, n− ) dt

+ π + (n+ −1, n− )P(n+ −1, n− )+ π − (n+, n− −1)P(n+, n− −1) • deterministic movement of cargo tug-of-war: force btw. the two motor species → force-dependent rates → force balance (both motor types move with same velocity) Müller, Klumpp, Lipowsky, PNAS 105, 4609 (2008)

Two force scales force-dependence of velocity and unbinding rate

" F % F/Fd v(F) = v0 $1− ' ε(F) = ε0e # Fs &

stall force Fs detachment force Fd unbinding in tug-of-war: ε+ (n+, n− ) ~ exp[~ Fs / Fd+n+ ]

→ key parameter: Fs/Fd strong motors (high F /F ): weak motors (low Fs/Fd): s d • little movement • switching between fast plus and fast minus movement • typically n-=n+ • typically only plus or minus motors

bound (n-=0 or n+=0)

Müller, Klumpp, Lipowsky, PNAS 105, 4609 (2008), Biophys. J. 98, 2610 (2010)

Tug-of-war instability

Why not only blockade? slight predominance of plus motors → minus motors experience larger force than plus motors, are more likely to unbind

remaining minus motors experience even larger force Cascade of unbinding until only

plus motors left

motors must be strong enough to pull other motors off : Fs>Fd Experimental evidence for a tug-of-war

in Dictyostelium cells: elongates during slow phase Soppina et al., PNAS (2009)

but also: some observations point to additional biochem. regulation e.g. lipid droplets likely to continue moving in same direction after forced unbinding (Leidel et al., Biophys J 2012)

[Derr et al. Science (2012)] Strain forces between motors of one team? motor stepping is stochastic → distances between motors fluctuate → stretching elastic elements of the motors negative effect of forces between motors ? new experimental systems: synthetic motor complexes • defined number, type and geom. arrangement • defined coupling

[Rogers et al. PCCP (2009), Derr et al. Science (2012)]

Rogers ... Diehl, PCCP 2009 Strain forces between motors of one team? explicit theoretical description of stepping: different interference effects with different motor types kinesins – enhanced unbinding myosins – reduced velocity Berger et al. Phys Rev Lett (2012), Molec Bioeng (2013)

in agreement with experiments Rogers et al. PCCP (2009), Lu et al. J Biol Chem (2012)

Rogers ... Diehl, PCCP 2009 Traffic control in the cell - without signs and traffic lights (?) coordination without a coordinator random bidirectional transport effective diffusion (but more rapid, D~v Δx) circumvent obstacles

can be biased or steered (modification of microtubules, MAPs)

Verhey & Hammond, Nature Rev Mol Cell Biol 10, 765 (2009)

self-organized traffic limited control: • localized loading of motors/ activation • plus steering by filament modification big question: logistics how many motors needed? recycling of motors? motors needed for recycling? Traffic systems dense traffic: >10 years of theory (traffic jams, formation of lanes etc.) systematic experiments recent [Leduc et al PNAS 109:6100 (2012)]

main difference: unbinding + diffusion Synthetic transport systems

detection/diagnostics with small concentrations

typically inverted geometry van den Heuvel & Dekker Science 317, 333 (2007) by geometrically or chemically defined ‘roads’

Fischer et al. Nat Nanotech 4, 162 (2009) Summary

• Traffic in cells, based on molecular motors moving along cytoskeletal filament • bidirectional motion: coordination by mechanics (and biochem signaling?)

• traffic issues: jamming etc • self-organized traffic, minimal external control

Thanks to Melanie Müller, Yan Chai, Reinhard Lipowsky, Florian Berger, Corina Keller