1. Protein adhesion, friction, unfolding, compaction
D. Horinek, A. Alexander-Katz, A. Serr,
Roland Netz, TU München
spider-silk peptide adhesion and friction at surfaces
hydrophobic versus hydrophilic adhesion
(all-atomistic MD simulations)
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)

2. 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.

3. consider proteins
as materials

4. Orb weaving spiders produce various silks
Thomas Scheibel
TUM Biochemistry
Orb weaving spiders produce various silks
Major ampullate
silk (dragline)
Flagelliform silk
(capture spiral)

5. Thomas Scheibel
TUM Biochemistry
Andreas Bausch
TUM Biophysics

6. Structural building blocks of spider silk
ductile / amorphous
crystalline
unknown function
Thomas Scheibel
TUM Biochemistry
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

7. Single-molecule protein-diamond-interaction
Thorsten Hugel
TUM Medical Engineering
diamond-surface
(Garrido/Walter/Stutzmann)
H-terminated diamond
OH-terminated diamond
AFM-tip with one spider-silk molecule
NH2
NH2
NH2
NH2
NH2
PEG
PEG
spider silk (Scheibel)
C16: MASMTGGQQMGRGSM(GSSAAAAAAAASGPGGYGPENQGPSGPGGYGPGGP)16

8. AFM results, hydrophobic surface (Hugel, TUM)
plateau-length-distrib.
plateau-force-distrib.
average 58 pN
strong adsorption, yet small friction

9. Vertical pulling at constant speed, low friction
Vertical pulling at constant speed, high friction R F FT
if applied tangential force FT smaller
than rate-dependent frictional resistance,
polymer sticks;
--> angle self-adjusts
Serr, Netz, EPL 73, 292 (2006) FN 

10. 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

11. Simulations of AFM Desorption of Spider Silk from Surfacesb
AFM tip
pulled group
solid
peptid is pulled from
surface via a moving spring
attached to the terminal group
high mobility on surface!

12. Single-molecule-friction on Hydrophobic Diamond
from lateral diffusion of adsorbed peptides
friction coefficient per length
≈ 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.
hydrophobic binding is self-lubricating

13. Desorption Forces from MD at various pulling rates
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)

14. energy decomposition - hydrophobic attraction
forget simple-minded theories concentrating on one aspect !!
first 3 contributions nearly compensate
spontaneous desorption
vertical pull
U is a result of partial compensation of large individual energies

15. 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 !!

16. spider silk friction for lateral pulling Andreas Serr
Hydrophobic diamond
pulling rate 8 m/s

17. Spider silk friction
Hydrophilic diamond (50% OH)
pulling rate 1 m/s

18. 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)
o.k. agreement with exp. data
simulation 0.1m/s -> 5pN
simulation 0.1m/s -> 200pN
experimental friction forces:
peptide glides on vacuum: „hydrophobic binding is self-lubricating“

19. - 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!

20. hydrophobic / philic homopeptides Salt EffectsN
hydrophobic / philic homopeptides
Salt Effects
Hugel lab
Specific Ion Adsorption at Hydrophobic Solid Surfaces
D. Horinek / RRN, PRL 99, (2007)

21. 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!

22. 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

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

24. since the endothelial layer is thin, it ruptures easily !
action
since the endothelial layer is thin, it ruptures easily !
the von-Willebrand-factor (vWF) helps fixing capillaries

25. von-Willebrand Faktor
vWf unfolds in shear
Blood
von-Willebrand Faktor
(fibers !!!)
Docking
Fusion
Transport
von-Willebrand Faktor (globular !!!)
Vesicels (packaged proteins)
Intracellular

27. bleeding of small vessels with shear rates > 1000 s-1
von-Willebrand desease
caused by unspecific deficiency of vW-factor
bleeding of small vessels
with shear rates > 1000 s-1

29. monomer
(2500 aminoacids)
dimer
multimer (a few hundred units)
the vWf is the largest watersoluble protein in the body --- why ???

30. Large globular structure
von-Willebrand factor (vWf)
Lines 120 nm apart
Large globular structure
~ 25x6.5 nm
Rod + central nodule
~ nm
Fowler et al
vWf bietet Bindungsstellen für Kollagen und Blutplättchen,
Kollagen schaut aus kaputten Blutgefäßen heraus!

31. 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!

32. Flow-chamber Chip - Wixforth&Schneider, Augsburg
Surface Acoustic Wave
(Nanopump)
Hydrophobic Surface
High Frequency Input
(Source of SAW)
V = 8µl
LiNbO3
(Piezoelectric)
200µm
1mm
40mm
Hydrophilic Channel

33. Real-time movie of stretched vWf above critical shear rate

34. unfolding occurs
also in bulk
(without collagen
substrate)
Schneider/Wixforth
(Augsburg)
relaxation into globular state
once shear is turned off

35. Quantitative experimental measurements
linear vWf extension
vWf adhesion efficiency
on collagen substrate
vWf unfolds abruptly at shear rates of about s-1
(close to shear rates in capillaries)
adsorption on collagen starts at about the same shear rate!
Seek deeper understanding through theoretic modeling !

36. 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

37. Hydrodynamics at low Reynolds numbers
Stationary Navier-Stokes equation
one obtains the creeping flow equation.
If the Reynolds number ,
human
bacterium sinking cylinder
H2O:  = Pa s;
 = 1000 kg/m3
v = 1 m/s
l = 1 m
Re = 106
v ~ 10-7 m/s
l = 1 
 Re = 10-7
v = 10-5 m/s
 Re = 10-5

38. flow-field due to point-force at origin:
(Oseen-Tensor)
flow-field due to point-force at origin:

for many particles the superposition principle is valid:
invert to get forces for prescribed
solvent velocity distribution !!
Next: add thermal noise

39. Hydrodynamic Brownian simulation techniques
Velocity of
i-th particle:
deterministic force
Mobility matrix:
self mobility:
hydrodyn. interact.
Random force
equivalent to Smoluchowski equation for particle distribut. W(rj,t) :
with solution:

40. attractive Lennard-Jones potential between all monomers
simple model for protein coil-globule transition
Alfredo Alexander-Katz, RRN


attractive Lennard-Jones potential between all monomers

41. globule in shear flow, =2.5, =1.2
Alfredo Alexander-Katz, RRN

42. unfolding dynamics shear-induced unfolding Rg2  ~ *
time (a. u.)
shear-induced
unfolding
unfolding becomes abrupt for
strongly folded proteins
(in agreement with experiments)

43. out (outside viscosity) in
protrusion-instability mechanism is fundamentally
different from classical droplet instability (Taylor 1934)
out (outside viscosity)
in
- 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

44. minimal model for shear-induced globule unfolding:
“force balance on protrusions”
cohesive force on protrusion
(sharp interface, diffuse interface)
from equipartition theorem lf=kBT
--> „typical“ protrusion length
--> typical cohesive force on protrusion fcoh
relative velocity
sphere/solvent
# monomers
friction coefficient
of one monomer
shear-force on protrusion
-free draining (with slip)
-hydrodynamic case (no slip)

45. critical protrusion length fcoh = fshear
free draining
hydrodynamic

46. enormously large monomer size !!! instability at small
L: protein contour length
a: protein monomer radius
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, =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 
instability at small
length scales !!
A. Alexander-Katz, RRN: PRL (2006), PNAS (2007) ……..

47. 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-

48. 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!
EJ Ralston/VN Schumaker 1974 / 1979
circular episome
1338 DNA
Sedimentation rate
linear episome 1338 DNA
at low concentrations
Rotor speed

49. 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

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

51. short chains, small fields:
hydrodynamic collapse of sedimenting polymers
radius
sedimentation
force v
hydrodynamic drag -> internal recirculation with velocity
-> recirculation time scale
compare with coil relaxation time
„scrambled/collapsed coil“ for R>flow or Ga/kBT >N-1-

52. Long chains, large driving fields: tadpole structure
(recirculation too weak to pull tail in …..)
sedimentation force
sedim. rate
head velocity vh ≈ Nh2/3
tail velocity vt ≈ ln(Nt)
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!)

53. realistic theory needs to incorporate hydrodynamic interactions
hydrodynamic simulation using Zimm‘s preaveraging approximation
tadpoles obtained
with ring-polymers
only in full
hydrodynamic
simulation !
full hydrodynamic
simulation
realistic theory needs to incorporate hydrodynamic interactions
and entanglement effects (essential for compaction) !

54. protein adhesion / dynamics
interfacial water structure
non-equilibrium
effects
hydrodynamic effects
conformational fluctuations