Polymer and Protein Dynamics at Membranes Far from Equilibrium

1. polymers/proteins at membranes far from equilibrium C. Sendner, X. Schlagberger, A. Alexander-Katz, Y.-W. Kim, TUM Sedimenting rods (birefringence) Driven polymers at surfaces (glycocalix deformation under shear) Globules in shear flow (unfolding of proteins in blood flow) Pumping with stiff polymers

2. Hydrodynamics Elasticity Thermal Fluctuations

3. Anomalous Electric Birefringence of Charged Polymers Xaver Schlagberger i light bead i Polymers anisotropic refractive index n  birefringence E

4. Konski , Zimm (1950) 0.073 % TMV normal birefr. Tobacco Mosaic Virus charge -1000 e length 300 nm 1.4 % TMV 2.75 % TMV anorm. birefr.

5. Weber 1992 fd virus : charge -500 e length 880 nm normal (parallel) anormal (perpendicular) anomalous behavior for -large polymer conc. -low salt conc. conclusion: Overlapping screening clouds do not contribute to electric polarization??

6. Hydrodynamics at low Reynolds numbers Stationary Navier-Stokes equation , , If the Reynolds number human bacteriumsinking cylinder one obtains the creeping flow equation. H2O:  = 0.001 Pa s;  = 1000 kg/m3 v = 1 m/s l = 1 m v = 10-5 m/s l = 1   Re = 10-5 v ~ 10-7 m/s l = 1   Re = 10-7 Re = 106

7. look at a rod (virus, tubulin, actin, short DNA) force F velocity U= F mobility  (Stokes-flow, neglecting inertia) parallel cylinder moves faster; is there some hydrodynamic orientation effect?

8. Simple Example: elastic rod under uniform force in the presence of hydrodynamic interactions orthotropic bodies (with three perpendicular planes of symmetry) are not oriented by hydrodynamic interactions (Brenner 1964) 2) coupling tensor non-zero if one plane of symmetry is broken force torque transverse (bending) mode longitudinal mode

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

10. straightforward way to satisfy no-slip in multi-particle system solvent-velocity due to other particles velocity of j-th particle solvent-velocity at particle position cohesive/elastic forces in objects automatically lead to solvent flow stagnation Next: add thermal noise

11. Theoretical Framework: Position Langevin Equation Velocity of i-th particle: deterministic force Random force Mobility matrix: self mobility: hydrodyn. interact. equivalent to Smoluchowski equation for particle distribut. W(rj,t) : with solution:

12. hydrodynamic simulation of elastic rod motion camera moves with central monomer lp / L = 100, isotrop. elast. rod

13. equilibration of hydrodynamic and elastic forces direct forces acting on monomers direct force+hydrodynamic force hydrodynamic torque for bent rod leads to perpendicular alignment ! bending force in stationary case cancels other forces

14. Scaling laws (Xaver Schlagberger, RRN)  Hydrodynamic deformation, bending angle  bending torque Tb = l / L g L3 / a l Hydrodynamic torque Th = g L2 / a  Hydrodynamic orientation, angle  thermal noise vs orienting torque kBT = Th low T high T L5 / l) (g / kBT)2 sin L5 / l) (g / kBT)2 Electrostatic polarization orientation, angle  high T sin L3 (g / kBT)2

15. field pulse dynamic behavior: hydrodyn. orientation: r = L-2 polarization orient: r = L-0 hydrodyn. relaxation: r = L3 n overshoot after switching off the field due to bending relaxation W. Oppermann, Makromol. Chem. 189, 2125 (1988) time

16. action Shear-induced denaturation of von-Willebrand factor

17. Blood von-Willebrand Faktor (fibers !!!) Transport Docking Fusion Intracellular Vesicels (packaged proteins) von-Willebrand Faktor (globular !!!) Imune Response (Wound)

19. monomer (2500 aminoacids) dimer multimer (few hundred units) The vWf is the biggest soluble protein in the body - why?

20. vWF-Release at the surface of Endothelial Cells Schneider, LMU Munich 50 m What‘s it‘s purpose and how is it streched ?

21. Oberflächenwelle (Nanopumpe) Hydrophobe Oberfläche IDT‘s mit HF Anschluß (Quelle für OFW) LiNbO3 (Piezoelektrika) Kanal mit Zellen oder Beads 40mm 200µm 1mm micro-flow-chamber Wixforth, Schneider, Augsburg V = 8µl

22. vWF - Globular 25μm 25μm vWF under Shear Flow SAW

23. 2.0 µm 0 12 µm Functionality Test „Super Glue“ for Blood Platelets 50 m

24. unfolding occurs also in bulk (without collagen substrate) relaxation into globular state once shear is turned off

25. transition quite abrupt as a function of shear rate

26. equilibrium coil-to-globule transition Alfredo Alexander-Katz   attractive Lennard-Jones potential

27. in shear, =2.5, =1.2

28. stretching dynamics Rg2  ~ * time (a. u.) stretching response unfolding becomes abrupt for globular proteins (in agreement with experiments)

29. Collapsed polymer under shear flow: unfolding transition induced by single-chain excitations cohesive force on protrusion (sharp interface, diffuse interface) from equipartition theorem lf=kBT --> „typical“ protrusion length relative velocity sphere/solvent # monomers shear-force on protrusion -free draining (with slip) friction coefficient of one monomer -hydrodynamic case (no slip) --> typical cohesive force on protrusion fcoh

30. critical protrusion length fcoh = fshear free draining hydrodynamic Scaling of critical shear rate: =2kBT, N=100, =1000s-1, ----> a = 10nm !!

31. Glycocalix in Cells -Glycocalix stabilizes outer leaflet of cell surface as well as microdomains by side-by-side interactions (electrostatic, hydrogen bonds, van der Waals) - Controlls near surface viscosity (effects diffusion of proteins)

32. grafted polymers in shear flow v

33. Grafted Neutral Polymers under Shear Flow (Kim/Netz) (homogeneous sparse coverage) lateral force at some height generates shear flow; flow profile calculated self-consistently, coupled to polymer deformation. hydrodynamic periodic boundary conditions shear: measure time-dependent response ! persistence length:

34. Measuring the fluid-velocity profile -> stagnation length D decreasing shear velocity increasing stiffness

35. DNA-grafted sphere held in laminar flow by laser trap Gutsche, Kremer (Leipzig) hydrodynamic radius as function of flow velocity -> DNA bends down as flow increases Next: diffusion of particles through layer in shear flows

36. Ciliae produce shear with beating polymers propulsion pumping

37. apply asymmetric torque at the polymer base -> measure net pumping velocity, efficiency, etc.

38. net solvent velocity pumping efficiency = power input 1. condition: threshold force for deformation: 2. Condition: asymmetry ratio forward torque/ backward torque rescaled stiffness Symmetric motion: no net pumping No elasticity: no net pumping (since reciprocal motion…)

39. Pushing grafted DNA around with vertical electric fields Rant, Arinaga, Tornow, Abstreiter for single-stranded (flexible) DNA the field-driven down-motion is faster than up-motion !? ss-DNA different from ds-DNA --> biosensors …

40. for single-stranded (flexible) DNA the field-driven down-motion is faster than up-motion !? ss-DNA different from ds-DNA --> biosensors …

41. hydrodynamic simulations of DNA in electric fields Woon Kim, RRN range of electric field (screening) double-stranded DNA (stiff) up/down motion symmetric single-stranded DNA (flexible) up motion diffusive (slow) down motion driven (fast)

42. driven polymers at solid surfacechristian sendner how to desorb stiff polymers from surfaces? - by driving them laterally ! (E-field or shear) no-slip surface breaks spatial symmetry and exerts hydrodynamic torque on moving polymer Initial angle 130o Initial angle 110o parameters: N = 10, 0 = 5.0E-6, persistence length l/L =100, external field E/kT = ( 100, 0, 0 ) tendency to move away from surface !

43. 1) free-space flow field 2) no-slip wall 3) surface „polarization forces“ 4) symmetry-broken flow-field (Blakes Greens function) 5) Elongated object receives hydrodynamic torque --> hydrodynamic lift

44. angular velocities for angles with x-axis () and z-axis () center of mass velocity Vz perpendicular to the wall Top view • Vz(,=/2) = Vz(,=/2) = 0  Ex side view  Ex distance from the wall: z = 2 force in x-direction: E = 1

45. E /kBT = (100,0,0), z0 = 2a, lp/L=10.000 i) orientation parallel to external force ii) orientation perpendicular to external force 0 = 1.0E-6 2.0E5 MD-steps

46. movie for E/kBT = (1.0, 0.0, -0.025) to obtain average lift force, average over long simulations and push rod down to surface (umbrella sampling)

47. Ez/kT=0.005 0.01 0.025 equilibrium No driving field (entropic rod-wall repulsion) lateral driving field Ex/kT = 1 Probability distribution of polymer in presence of vertical pressure from difference in probability distribution obtain hydrodynamic repulsive potential of mean force……

48. Hydrodynamics Elasticity Thermal Fluctuations