February 8, 2005 :

1. February 8, 2005 : • Homework • Read Ch. 4, 5; Appendix • Biophysics Review • Cell Types; Mechanical Testing • Percolation • Kinetics

2. Prokaryotes • Most have elevated osmotic pressure, I.e a few tens of atmospheres. • Challenger Deep sea dropped to 10,896 m in last 8 million years (Deepest place in ocean) • Deficient in CaCO3 at that depth • Foraminifera (shelled protists) quickly evolved soft, non-calcareous shells • Likely are highly pressurized.

3. Biomembrane as an isotropic material Bilayer compression resistance, KA = 4 g g= 0.04 J/M2 (g = surface tension)

4. Homogeneous lipid sheet: Biomembrane Stretching membrane thins it exposing hydrophobic core to Water. Rupture occurs at 2-10% area expansion, so say lysis tension ~ 0.016 J/M2. For a 1 mm cell : P= 64,000J/M3 ~ 0.6 atm. at rupture. • 10 atm = 106 J/m3

5. Life @ 1,200 atmoshperes • How thick does the membrane need to be? • How thick does the wall need to be? • Compressibility properties:

6. Cell Walls for strength How thick does wall need to be to withstand normal pressures inside a bacterium, I.e. 30-60 atm. ? Lets say lysis occurs when wall tension exceeds 5% of KA. We can approximate KA by KVd, and for isotropic wall material, Kv ~ E, so, assume a material E= 3 x 109 J/m3 tfailure= 0.05 KA= RP/2=0.05 E d So to not fail, d> RP/E So for R = 0.5 mM, P= 10 atm,

7. Thick wall sphere

8. Thick walled sphere • Equilibrium • Pressure inside • Average stress in wall • Pressure from outside • Pressurized both sides

9. Alternate method (not too thick wall)

10. Laplace Law for Cylinder under pressure • Homework: • Find wall stress for cylinder. • Calculate stress for a foraminefora not • Assuming a thin wall.

11. Compression of a network • A cartesian lattice of fibers (a) subject to compressive strain (b). The boundary conditions are that the angles between the segments arising from each junction are fixed at 90 and the deformation consists in movement of the junctions toward each other along the three orthogonal axes of the lattice, with no shear deformation. The junctions, however, are allowed to rotate as • compression progresses. This is equivalent to the boundary conditions in Feynman et al.36 in which fiber ends are fixed but direction changes under compression.

13. Power from electrochemical gradients (I.e batteries) Distributed Model Driving Force determined by Nernst

14. Electrical Model of Cell Membrane Molecular model Ca Wave in Oocyte

15. Mechanotransduction What opens channels?

16. Types of mechanical analysis • Kinematics - just the connections • Statics- forces without motion • Dynamics- forces with motion • Rigid versus deformable body • FBDs FELFBL FBR FER

17. Loading Types • Tension- compression • Shear • Reaction • Traction • Friction • Bending • Uniaxial/bi-axial

18. Cytomechanical forces: • Gravitational: • Muscle contraction: • Contact: • Buoyant: • Hydraulic: (Static or dynamic) • Pneumatic

19. Cell Deformation and Stiffness • Most cells are constantly deformed in vivo by both internal and external forces. • Experimental deformations can be done by poking, squishing, osmotic swelling, electrical/magnetic fields, drugs, etc. • Cells have both area and shear stiffness, mostly due to the cytoskeleton, although lipids contribute some.

20. Material Parameters • Moduli: Young’s, area, shear, bending (flexural) • Stiff versus compliant • Strength versus weakness • Brittle versus ductile • Incompressible/Compressible • Failure • Ultimate tensile strength • Hardness: Moh’s scale

22. Steel Wood Bone Stress s Cells Comparative Mechanical Properties Steel Wood Bone Cells Strain e Cellular ‘pre-stress’

24. Elasticity • “ut tensio sic vis” • Young’s Modulus: Stress over strain • Shear Modulus: Related to Poisson • Comparative Strains • Comparative Stiffnesses

25. Poisson’s Effect Incompressible Means no volume change swelling

26. Elastic Behaviours Unixaxial stress Pressure n < 1 n< 0 E = s/e KA = P/DA/A 1 2

27. Applying forces (testing types)

28. Testing methods Q: What are the relative resolutions?

29. AFM Q? Why doesn’t the AFM needle poke right through?

30. Micropipet methods

31. Magnetic tweezers Wang et al, Science

32. Shear and compression

33. Example: Blood flow forces

34. Optical Tweezers • High resolution • Refractivity of bead • Trapping in the beam • Limited force

35. Optical Tweezer

38. Swelling RBCs • Necturus erythrocytes loaded with fluo-4 (10 µM) and exposed to UV light emitted from a mercury vapor bulb and filtered through a FITC cube (400x). (A) Cells display little fluorescence under isosmotic conditions (n=6). (B) Addition of A23187 (0.5 µM) to the extracellular medium increased fluorescence under isosmotic conditions (n=6). (C) Exposure to a hypotonic (0.5x) Ringer solution increased fluorescence compared to basal conditions (n=6). (D) A low Ca2+ hypotonic Ringer solution (5 mM EGTA) did not display the level of fluorescence normally observed following hypotonic swelling (n=6). • Light et al.

39. Stimulation Protocols

40. Bone Loading Waveforms

41. Sickle Cell: A gel problem • Single point defect causes Hbs- a polymerizing tendency in deoxygenated state • The stiff and deformed cells damage vessels • Main approaches: • 1. Controlling kinetics of polymerization • 2. Regulating stiffness (rheology) of sickle cells.

44. Thermal shape variations Stiff Flexible

45. (a)-(c) Serial images of a 23 mm long relatively stiff fiber. (b) and (c) are, respectively, 21.9 and 41.4 seconds after (a). There is little visible bending (see also Figure 2(a)), consistent with a long persistence length, lp . 12.0 mm. (d)-(f) Serial images of a 20 mm long ¯flexible fiber. (e) and (f) are, respectively, 51.8 and 60.8 seconds after (d). There is marked bending and a short persistence length, lp.0.28 mm (see also Figure 2(b)). The fibers undergo diffusional motion and hence are not adhering to a glass surface, rather are free in solution, a necessary condition for using statistical mechanics to obtain persistence lengths. The width of each frame is 25 mm.

46. Statistics of fluctuations in 1 dimension

47. Statistical Mechanics

48. Dilute Semi-concentrated Concentrated Floppy Chains Rods Isotropic Nematic

49. Harmonic motion (undamped) Gel motion follows simple rules Model will predict dynamic and Static equilibrium. Natural Frequency

50. Damped Spring