Transcript Roland Netz
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 Zur Anzeige w ird der QuickTime™ Dekompressor „YUV420 codec“ Zur Anzeige wbenötigt. ird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. 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 Zur Anzeige w ird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. 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 Zur Anzeige w ird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. • pulling rate 8 m/s Spider silk friction • Hydrophilic diamond (50% OH) Zur Anzeige w ird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. • 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 Zur Anzeige w ird der QuickTime™ Dekompressor „Cinepak“ benötigt. 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) 8r 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 6R 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 Zur Anzeige w ird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. 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 R1a11 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) Zur Anzeige w ird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. 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 /kB 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