Protein adhesion, friction, unfolding, compactionD. Horinek, A. Alexander-Katz, A. Serr,

Roland Netz, TU München

1) spider-silk peptide adhesion and friction at surfaces hydrophobic versus hydrophilic adhesion

(all-atomistic MD simulations)

2) shear-induced protein unfolding in blood fluctuation-induced hydrodynamic instabilities(hydrodynamic simulations, scaling arguments)

3) anomalous polymer sedimentation- conformational changes at high sedimentation rates

(compaction versus stretching)

Forces at Hydrophobic Interfaces

E. E. Meyer, K. J. Rosenberg, J. Israelachvili PNAS 2006, 103, 15739

Hydrophobic forces act between particles whose surfaces do not posess polar groups, regardless of the exact chemical composition.

Hydrophobic forces give rise to many different phenomena,

Short-ranged versus long-ranged

Theoretically, hydrophobic forces are not uniquely defined.

consider proteins as materials

Orb weaving spiders produce various silks

Major ampullate silk (dragline)

Flagelliform silk

(capture spiral)

Thomas ScheibelTUM Biochemistry

Thomas ScheibelTUM Biochemistry

Andreas BauschTUM Biophysics

sequence from the two dragline proteins of the garden spider A. diadematus

Single motifs are repeated up to several hundred times in spider silk proteins.[ ]

150

Structural building blocks of spider silkductile / amorphouscrystallineunknown function

Thomas ScheibelTUM Biochemistry

Universal protein: hydrophobic/hydrophilic, unstructured and motifs

Single-molecule protein-diamond-interaction

PEG

NH2

spider silk (Scheibel)

AFM-tip with one spider-silk molecule

NH2

NH2NH2

NH2

PEG

diamond-surface(Garrido/Walter/Stutzmann)

H-terminated diamond

OH-terminated diamond

C16: MASMTGGQQMGRGSM(GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP)16

Thorsten HugelTUM Medical Engineering

AFM results, hydrophobic surface (Hugel, TUM)

plateau-length-distrib.

plateau-force-distrib. average 58 pN

-strong adsorption, yet small friction

R

F

FT

if applied tangential force FT smallerthan rate-dependent frictional resistance, polymer sticks; --> angle self-adjustsSerr, Netz, EPL 73, 292 (2006)

FN

Vertical pulling at constant speed, low frictionVertical pulling at constant speed, high friction

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MD Simulations (Dominik Horinek)

For simulations, the spider silk C16 motif is cut in three pieces:

GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP GSSAAAAAAA fragment 1GPGGYGPENQGPSGPGGYGPGGP GSSAAAAAAAASGPGGYGPENQGPSG fragment 2 2GP GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP fragment 3

water (SPC)

peptide fragment (Gromos96)

surface (Gromos96)

H-terminated diamond

OH-terminated diamond

Alkane SAM

Simulations of AFM Desorption of Spider Silk from Surfaces

AFM tip

pulled group

solid

a

b

peptid is pulled fromsurface via a moving springattached to the terminal group

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high mobility on surface!

friction coefficient per length

≈ 0.05 kg/sm

friction force for

100nm peptide at v=1 m/s :

0.05 kg/sm 1 m/s 100nm =

5 fN !!!

Too small for the AFM !3 center-of-mass trajectories of spider silk at different tip elevations.

Single-molecule-friction on Hydrophobic Diamondfrom lateral diffusion of adsorbed peptides

hydrophobic binding is self-lubricating

10

0.1

a

b

c

d

Desorption Forces from MD at various pulling ratesHorinek, RRN, PNAS (2008)

1

Fdes = k (zspring -zAA)

pulling rate 10 m/s

pulling rate 1 m/s

pulling rate 0.1 m/s

hydrophobic surfaceaverage plateau force: 54 pN(experimental: 58 pN with NaCl)

energy decomposition - hydrophobic attraction

vertical pull

U is a result of partial compensation of large individual energies

-1000

-800

-600

-400

-200

0

200

400

600

S-S S-W W-W S-D W-D U F

280 K300 K320 K

first 3 contributions nearly compensate

spontaneous desorption

-200

-100

0

100

200

300

S-S S-W W-W S-D W-D U F

280 K300 K320 K

forget simple-minded theories concentrating on one aspect !!

hydrophilic OH-terminated diamond

desorption (at most) doubled on hydrophilic surface

large friction due to breaking and reformation of hydrogen bonds !!

Pulling rate 0.1 m/sLarge hysteresis !

spider silk friction for lateral pullingAndreas Serr

• Hydrophobic diamond

• pulling rate 8 m/s

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• Hydrophilic diamond (50% OH)

• pulling rate 1 m/s

Spider silk friction

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Single-molecule peptide friction• mobility per monomer

hydrophilic diam

hydrophobic diam

bulk water (perfect match with exp.)

peptide glides on vacuum: „hydrophobic binding is self-lubricating“

30-fold friction increase for hydrophilic surface: driven diffusion in corrugated binding potential of 6kBT (Frenkel-Kontorova-Tomlinson)

simulation 0.1m/s -> 5pN

simulation 0.1m/s -> 200pN

experimental friction forces: o.k. agreement with exp. data

- adhesive proteins bind to BOTH hydrophilic and hydrophobic surfaces strongly (5 kBT per amino acid)

- nano-friction on hydrophobic/philic substrates is very different (effective adhesive properties depend on binding free energy AND surface friction ! gecko, scotch tape)

- in all cases, effective interaction involves direct interactions as well as water-ordering effects!

FN

hydrophobic / philic homopeptides Salt Effects

Hugel lab

Specific Ion Adsorption at Hydrophobic Solid Surfaces D. Horinek / RRN, PRL 99, 226104 (2007)

pressure between 2 hydrophobic surfaces from Poisson-Boltzmann:

screenable contribution to hydrophobic attraction

1 mM salt: weak but long-ranged

100 mM salt: strong but short-ranged

DOES NOT YET EXPLAIN PEPTIDE ION SPECIFICITY!

blood functions:

- oxygene - transport (& Hemoglobin)- nutrient - transport (glucose, amino-acids, fat ....)- waste - transport (CO2l urea, lactatic acid ...)- immuno reactione ( lymphocytes, antibodies ...)- signal - transduction (hormons ...)- regulation of temperature and pH of body- coagulation, vascular repair

capillaries connect arteries and veins they are 5-10 microns thick and are lined by a single-cell-layer: the endothelium

action

since the endothelial layer is thin, it ruptures easily !

the von-Willebrand-factor (vWF) helps fixing capillaries

DockingTransport Fusion

von-Willebrand Faktor (globular !!!)

von-Willebrand Faktor(fibers !!!)Blood

IntracellularVesicels (packaged proteins)

vWf unfolds in shear

von-Willebrand desease caused by unspecific deficiency of vW-factor

bleeding of small vessels with shear rates > 1000 s-1

the vWf is the largest watersoluble protein in the body --- why ???

monomer(2500 aminoacids)

dimer

multimer (a few hundred units)

von-Willebrand factor (vWf)

Large globular structure~ 25x6.5 nm

Rod + central nodule~ 30 + 6 nm

Lines 120 nm apart

Fowler et al

vWf bietet Bindungsstellen für Kollagen und Blutplättchen,Kollagen schaut aus kaputten Blutgefäßen heraus!

Was stimuliert die Entfaltung des vWf ??

Hypothese: Scherfluss in kleinen Blutgefäßen bewirktEntfaltung des Proteins!

Hagen-Poiseuille Gesetz für Strömung im Rohr:Flüssigkeitsstrom geht wie R4

Strömungsgeschwindigkeit ist Null an der WandScherung verformt Proteine und Blutkörperchen

Experimentelle Untersuchung an künstlichen Blutgefäßen!

R

High Frequency Input

(Source of SAW)

Hydrophilic Channel

Hydrophobic Surface

Surface Acoustic Wave(Nanopump)

LiNbO3

(Piezoelectric)

Flow-chamber Chip - Wixforth&Schneider, Augsburg

200µm

1mm

40mm

V = 8µl

Real-time movie of stretched vWf above critical shear rate

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collapsed stretched10 µm

BelowCriticalShearγc AboveCriticalShearγc

10µm

unfolding occursalso in bulk (without collagensubstrate)

Schneider/Wixforth(Augsburg)

0 ms

320 ms160 ms

10 µm

relaxation into globular stateonce shear is turned off

Fig. 410 100 1000 100000,00,20,40,60,81,010 100 1000 100000481216

shearrate γ[s-1]normalized rate ofadhesion

[end to end distance

µ ]mshearrateγ[s-1]

a.

b.

vWf unfolds abruptly at shear rates of about 3000 s-1

(close to shear rates in capillaries) adsorption on collagen starts at about the same shear rate!

Quantitative experimental measurements

linear vWf extension

vWf adhesion efficiency on collagen substrate

Seek deeper understanding through theoretic modeling !

length and time scales (microns and milliseconds) require coarse-grained simulations techniques!

atomistic resolution - detailed force fields - including explicit water

coarse-grained description - few effective interactions - only implicit solvent

human bacterium sinking cylinder

H2O: = 0.001 Pa s; = 1000 kg/m3

v = 1 m/sl = 1 m

Re = 106 v ~ 10-7 m/sl = 1 Re = 10-7

v = 10-5 m/sl = 1 Re = 10-5

Hydrodynamics at low Reynolds numbers

Stationary Navier-Stokes equation

one obtains the creeping flow equation.

If the Reynolds number , ,

€

Hαβ (r) =1

8πηrδαβ +ˆ r α ˆ r β[ ]

(Oseen-Tensor)

flow-field due to point-force at origin:

€

uα(r)=Hαβ (r) f β1

for many particles the superposition principle is valid:

€

uα(r)= Hαβ (r −ri) fiβ

i

∑

invert to get forces for prescribedsolvent velocity distribution !!

Next: add thermal noise

Hydrodynamic Brownian simulation techniques

Random force

€

ξi(t)ξ j( ′ t ) =6t μ ij kBT δ(t− ′ t )

Mobility matrix:

€

t μ ij =Dij /kBT =μ0 δij +

t H (ri,rj)

€

μ0 = 6πRη( )−1

self mobility: hydrodyn. interact.

equivalent to Smoluchowski equation for particle distribut. W(rj,t) :

€

∂W∂t

=∂∂ri

Dij

∂W∂rj

−μij f jW⎡

⎣ ⎢ ⎤

⎦ ⎥ i, j

∑ with solution:

€

W ≅e−U /kBT

€

m r j(t)t μ ij +˙ r i(t) =

t μ ij f j(t)+ξi(t)Velocity of

i-th particle:

deterministic force

€

f j(t) =−∂U(t) /∂rj (t)+E

simple model for protein coil-globule transition

attractive Lennard-Jones potential between all monomers

0000

Alfredo Alexander-Katz, RRN

globule in shear flow, =2.5, γ=1.2 Alfredo Alexander-Katz, RRN

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unfolding dynamics

Rg2

time (a. u.)

γ~ γ*

shear-induced unfolding

unfolding becomes abrupt for strongly folded proteins(in agreement with experiments)

protrusion-instability mechanism is fundamentally different from classical droplet instability (Taylor 1934)

- critical shear rate is temperature dependent - Taylor: stable for in / out > 4 - instability occurs on small length scales - final results depends on lower spatial cutoff

out (outside viscosity)in

minimal model for shear-induced globule unfolding:“force balance on protrusions”

shear-force on protrusion -free draining (with slip)

€

fshear ≈ (γ•

R)(l /a)μ−1

from equipartition theorem lf=kBT--> „typical“ protrusion length

€

l ≈(kBT /Δε)1/α

€

f ≈ Δεl α −1cohesive force on protrusion(1sharp interface, diffuse interface)

--> typical cohesive force on protrusion fcoh

relative velocitysphere/solvent

# monomers

friction coefficient of one monomer

€

fshear ≈ γ•

l 3R−1a−1μ−1-hydrodynamic case (no slip)

critical protrusion length fcoh = fshear

free draining

hydrodynamic

€

γ*τ•

≈ Δε 2 /α a /R

€

γ*τ•

≈ Δε 4 /αR /a

€

τ =a2 /kBTμ

L: protein contour lengtha: protein monomer radius

€

γ*•

≈ L1/ 3(Δε /kBT)4 /α /a3

scaling of critical shear rate (with hydrodynamics) :

to unfold a protein with typical cohesion energy in a capillary vessel one needs huge monomers with a radius of 10 nm, close to vWf

=2kBT, N=100, γ=1000s-1, ----> a = 10nm !!enormously large

monomer size !!!

now connect to classical hydrodynamic instability theory (Taylor, Kelvin-Helmholtz) and assume protrusions are controlled by surface tension /a2 and 1

€

γ*•

≈ L1/ 3(σ /kBT)4 a5

instability at small length scales !!A. Alexander-Katz, RRN: PRL (2006), PNAS (2007) ……..

polymer separation in the ultracentrifuge:sedimentation anomaly at large driving fields

G: sedimentation force per monomerN: monomer number

velocity v = GN

mobility 1R 1N

velocity v ≈ G N1-

sedimentation rate S = v/G ≈ N1-

why gel-electrophoresis is used for separating DNA(and not the ultracentrifuge)

Sed

imen

tatio

n ra

te

Rotor speed

linear episome 1338 DNAat low concentrations

EJ Ralston/VN Schumaker 1974 / 1979

- sedimentation rate of polymers goes down at high rotor speeds- crossover is polymer-length dependent!

circular episome 1338 DNA

theoretical explanation by Zimm (1974):

-free ends of polymer are typically peripheral-receive more drag in sedimenting flow -stretched arch shape is produced-sedimentation coefficient goes down-NULL EFFECT PREDICTED FOR CIRCULAR CHAINS within pre-averaging approximation- story ended in 1979

flow

Crumpling and stretching of sedimenting flexible chain (Schlagberger, Netz, PRL 2007)

motion

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short chains, small fields: hydrodynamic collapse of sedimenting polymers

radius

sedimentationforce

hydrodynamic drag -> internal recirculation with velocity -> recirculation time scale

€

v ≈GN /ηR

€

τ flow ≈ R /v ≈ ηR2 /GN

compare with coil relaxation time „scrambled/collapsed coil“ for τR>τflow or Ga/kBT >N-1-

€

τR ≈ ηR3 /kBT

v

stable stationary state: vh≈vt and thus Nh ≈ (ln N)3/2

(tail stretched by recirculation force, sedimentation reduced w.r.t. coil)

head velocity vh ≈ Nh2/3

tail velocity vt ≈ ln(Nt)

Long chains, large driving fields: tadpole structure(recirculation too weak to pull tail in …..)

sedimentation force

sedi

m.

rate

small fields, long chains: weak stretching perturbation analysis

S = v/G ≈ N1- [ 1 - c G2 N2+2 (same scaling as Zimm!)

tadpoles obtained with ring-polymersonly in full hydrodynamicsimulation !

full hydrodynamicsimulation

realistic theory needs to incorporate hydrodynamic interactions and entanglement effects (essential for compaction) !

hydrodynamic simulation using Zimm‘s preaveraging approximation

interfacial water structure

non-equilibriumeffects hydrodynamic effects

conformational fluctuations

protein adhesion / dynamics