Protein adhesion, friction, unfolding, compaction
D. 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
Thomas Scheibel
TUM Biochemistry
Orb weaving spiders
produce various silks
Major ampullate
silk (dragline)
Flagelliform silk
(capture spiral)
Thomas Scheibel
TUM Biochemistry
Andreas Bausch
TUM Biophysics
Thomas Scheibel
TUM Biochemistry
Structural building blocks of spider silk
ductile / amorphous
crystalline
unknown function
Single motifs are repeated up to several hundred times in spider silk proteins.
[
]
150
sequence from the two dragline proteins of the garden spider A. diadematus
Universal protein: hydrophobic/hydrophilic, unstructured and  motifs
Single-molecule protein-diamond-interaction
Thorsten Hugel
TUM Medical Engineering
AFM-tip with one spider-silk molecule
NH2
NH2 NH NH NH2
2
2
diamond-surface
(Garrido/Walter/Stutzmann)
H-terminated diamond
PEG
OH-terminated diamond
spider silk (Scheibel)
C16: MASMTGGQQMGRGSM(GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP)16
AFM results, hydrophobic surface (Hugel, TUM)
plateau-length-distrib.
plateau-force-distrib.
average 58 pN
-strong adsorption, yet small friction
Vertical
Vertical pulling
pulling at
at constant
constant speed,
speed, low
highfriction
friction
F
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 FN
R
FT
if applied tangential force FT smaller
than rate-dependent frictional resistance,
polymer sticks;
--> angle self-adjusts
Serr, Netz, EPL 73, 292 (2006)
MD Simulations (Dominik Horinek)
water (SPC)
peptide fragment (Gromos96)
H-terminated diamond
surface (Gromos96)
OH-terminated diamond
For simulations, the spider silk C16 motif is cut in three pieces:
GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP
GSSAAAAAAA fragment 1GPGGYGPENQGPSGPGGYGPGGP
GSSAAAAAAAASGPGGYGPENQGPSG fragment 2 2GP
GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP fragment 3
Alkane SAM
Simulations of AFM Desorption of Spider Silk from Surfaces
a
b
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AFM tip
pulled group
solid
peptid is pulled from
surface via a moving spring
attached to the terminal group
high mobility on surface!
Single-molecule-friction on Hydrophobic Diamond
from lateral diffusion of adsorbed peptides
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 !!!
3 center-of-mass trajectories of
spider silk at different tip elevations.
Too small for the AFM !
hydrophobic binding is self-lubricating
Desorption Forces from MD at various pulling rates
Horinek, RRN, PNAS (2008)
a
Fdes = k (zspring -zAA)
b
10 pulling rate 10 m/s
c
1 pulling rate 1 m/s
d
0.1 pulling rate 0.1 m/s
hydrophobic surface
average plateau force: 54 pN
(experimental: 58 pN with NaCl)
energy decomposition - hydrophobic attraction
forget simple-minded theories concentrating on one aspect !!
spontaneous
desorption
vertical pull
U is a result of partial
compensation of large
individual energies
600
first 3 contributions
nearly compensate
280 K
300 K
320 K
400
200
0
-200
-400
-600
-800
-1000
S-S
S-W W-W
S-D
W-D
U
F
hydrophilic OH-terminated diamond
Pulling rate 0.1 m/s
Large hysteresis !
desorption (at most) doubled on
hydrophilic surface
large friction due to breaking and
reformation of hydrogen bonds !!
spider silk friction for lateral pulling
Andreas Serr
• Hydrophobic diamond
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• pulling rate 8 m/s
Spider silk friction
• Hydrophilic diamond (50% OH)
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• pulling rate 1 m/s
Single-molecule peptide friction
• mobility per monomer
bulk water
(perfect match with exp.)
hydrophobic diam
hydrophilic diam
30-fold friction increase
for hydrophilic surface:
driven diffusion in corrugated
binding potential of 6kBT
(Frenkel-Kontorova-Tomlinson)
experimental friction forces:
o.k. agreement with exp. data
simulation 0.1m/s -> 5pN
simulation 0.1m/s -> 200pN
peptide glides on vacuum: „hydrophobic binding is self-lubricating“
- 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!
hydrophobic / philic homopeptides
Salt Effects
Hugel lab
F
N
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
vWf unfolds in shear
von-Willebrand Faktor
(fibers !!!)
Blood
Transport
Docking
Fusion
von-Willebrand Faktor (globular !!!)
Vesicels (packaged proteins)
Intracellular
von-Willebrand desease
caused by unspecific deficiency of vW-factor
bleeding of small vessels
with shear rates > 1000 s-1
monomer
(2500 aminoacids)
dimer
multimer (a few hundred units)
the vWf is the largest watersoluble protein in the body --- why ???
von-Willebrand
factor (vWf)
Lines 120 nm apart
Large globular structure
~ 25x6.5 nm
Rod + central nodule
~ 30 + 6 nm
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 bewirkt
Entfaltung des Proteins!
R
Hagen-Poiseuille Gesetz für Strömung im Rohr:
Flüssigkeitsstrom geht wie R4
Strömungsgeschwindigkeit ist Null an der Wand
Scherung verformt Proteine und Blutkörperchen
Experimentelle Untersuchung an künstlichen Blutgefäßen!
Flow-chamber Chip - Wixforth&Schneider, Augsburg
Surface Acoustic Wave
(Nanopump)
High Frequency
Input
(Source of SAW)
Hydrophobic Surface
V = 8µl
LiNbO3
(Piezoelectric)
200µm
40mm
1mm
Hydrophilic Channel
Real-time movie of stretched vWf above critical shear rate
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Below Critical Shear c
Above Critical Shear c
unfolding occurs
also in bulk
(without collagen
substrate)
Schneider/Wixforth
(Augsburg)
10 µm
collapsed
10 µm
stretched
10 µm
0 ms
160 ms
320 ms
relaxation into globular state
once shear is turned off
end to end distanceµm]
[
Quantitative experimental measurements
a.
16
linear vWf extension
12
8
shear rate  [s-1]
4
0
vWf adhesion efficiency
on collagen substrate
100
1000
normalizedrate of adhesion
10
10000
1,0
0,8
b.
0,6
0,4
0,2
0,0
10
100
shear rate  [s-1]
1000
10000
Fig. 4
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!
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
Hydrodynamics at low Reynolds numbers
Stationary Navier-Stokes equation
,
If the Reynolds number
,
one obtains the creeping flow equation.
human
H2O:  = 0.001 Pa s;
 = 1000 kg/m3
v = 1 m/s
l =1m
bacterium
Re =
106
v = 10-5 m/s
l =1
 Re = 10-5
sinking cylinder
v ~ 10-7 m/s
l =1
 Re = 10-7
flow-field due to point-force at origin:
u (r)  H  (r) f 

H (r) 


8r
1

 
ˆ
 r rˆ 
(Oseen-Tensor)
for many particles the superposition principle is valid:
u (r)   H (r  ri ) f i



i
invert to get forces for prescribed
solvent velocity distribution !!
Next: add thermal noise
Hydrodynamic Brownian simulation techniques
Velocity of
i-th particle:
Ý
Ý
mrÝ
j (t)ij  ri (t)  ij f j (t)  i (t)
deterministic force
Mobility matrix:
self mobility:
Random force
f j (t)  U(t) /rj (t)  E
ij  Dij / kBT  0  ij  H(ri ,rj )
0  6R
1
hydrodyn. interact.
 i(t) j ( t)  6 ij kBT  (t  t)
equivalent to Smoluchowski equation for particle distribut. W(rj,t) :

W
  W
U / k BT

Dij
 ij f jW
with
solution:
W e


t
rj
i, j ri 

simple model for protein coil-globule transition
Alfredo Alexander-Katz, RRN

attractive Lennard-Jones
potential between all monomers

globule in shear flow, =2.5, =1.2
Alfredo Alexander-Katz, RRN
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unfolding dynamics
 ~ *
Rg2
time (a. u.)
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)
in
out (outside viscosity)
- 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
minimal model for shear-induced globule unfolding:
“force balance on protrusions”
 1
f  
cohesive force on protrusion
(sharp interface, diffuse interface)
from equipartition theorem lf=kBT
--> „typical“ protrusion length
1/ 
 (kB T /)

--> typical cohesive force on protrusion fcoh
relative velocity
sphere/solvent
shear-force on protrusion
-free draining (with slip)
 
# monomers
f shear  ( R)( /a) 
1

-hydrodynamic case (no slip)
f shear   3 R1a11
friction coefficient
of one monomer
critical protrusion length fcoh = fshear
  a 2 / k B T
free draining
hydrodynamic



*
2 /

*
4 /
   
   
a /R
R /a
scaling of critical shear rate (with hydrodynamics) :

*
  L ( /kB T)
1/ 3
4 /
/a
3
L: protein contour length
a: protein monomer radius
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, =1000s-1, ----> a = 10nm !!
now connect to classical hydrodynamic instability theory
(Taylor, Kelvin-Helmholtz)
and assume protrusions are controlled by
surface tension /a2 and 

*
  L ( /kB T) a
1/ 3
4
5
A. Alexander-Katz, RRN: PRL (2006), PNAS (2007) ……..
polymer separation in the ultracentrifuge:
sedimentation anomaly at large driving fields
G: sedimentation force per monomer
N: monomer number
velocity v = GN 
mobility R N
velocity v ≈ G N1-
sedimentation rate S = v/G ≈ N1-
why gel-electrophoresis is used for separating DNA
(and not the ultracentrifuge)
- sedimentation rate of polymers goes down at high rotor speeds
- crossover is polymer-length dependent!
Sedimentation rate
EJ Ralston/VN Schumaker 1974 / 1979
circular episome
1338 DNA
linear episome 1338 DNA
at low concentrations
Rotor speed
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)
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motion
short chains, small fields:
hydrodynamic collapse of sedimenting polymers
radius
sedimentation
force
v
hydrodynamic drag -> internal recirculation with velocity v  GN /R
-> recirculation time scale
 flow  R/v  R2 /GN
compare with coil relaxation time
 R  R 3 /kB T

„scrambled/collapsed coil“ for R>flow or Ga/kBT >N-1-
Long chains, large driving fields: tadpole structure
sedim. rate
(recirculation too weak to pull tail in …..)
head velocity vh ≈ Nh2/3
tail velocity vt ≈ ln(Nt)
sedimentation force
stable stationary state: vh≈vt and thus Nh ≈ (ln N)3/2
(tail stretched by recirculation force, sedimentation reduced w.r.t. coil)
small fields, long chains: weak stretching perturbation analysis
S = v/G ≈ N1- [ 1 - c G2 N2+2
(same scaling as Zimm!)
hydrodynamic simulation using Zimm‘s
preaveraging approximation
full hydrodynamic
simulation
tadpoles obtained
with ring-polymers
only in full
hydrodynamic
simulation !
realistic theory needs to incorporate hydrodynamic interactions
and entanglement effects (essential for compaction) !
protein adhesion / dynamics
interfacial water structure
non-equilibrium
effects
hydrodynamic effects
conformational fluctuations