1. Lecture 11 Energetics & Kinetics of cellular rxns Regional stiffness & motion –AFM : Yeast; Myocytes Mechano-electrical coupling –Electro-mechanical coupling Homework

2. Free energy landscapes Large activation barrier is reduced by the interaction ( with a small cost of deforming E). The barrier is reduced.

3. Mechanical model of enzyme E has a binding site with a shape, charge distribution, hydrophobicity, and H-binding sites, ~matching those on the substrate. To match perfectly, S (and possibly E) must deform. One bond (spring) may stretch close to breaking point. Bond can be broken by thermal energy, stabilizing the P, that no longer fits in the enzyme.

4. Getting rate eqns from rxn scheme: 1. Each node leads to a diffEq for #molecules in the corresponding state 2. Find all arrows impinging on a node. The time derivative of the # in this state is positive for each arrow pointing toward the node, and negative for each pointing away

6. 1/v 1/[S]

7. Promoters have different abilities to uncoil Twisting DNA torsional buckling instability Unwinding and causes local denaturation Many motors are needed: RNA plymerase, DNA polymerase: 100 nucleotides/sec. Forces (pN) can stop transcription

8. Koster, DA et al. Nature :, 2004

9. TOP1B removing supercoils

10. Model of TOP1B

11. Elasticity of cells Nano versus macro elasticity Behaviour relative to kT: Stretch a rubber band and a string of paper clips. Significant for The nanometer-scale monomers of a macromolecule, but not for a string of paper clips. The retracting force exerted by a stretched rubber band is entropic. It increases disorder. Do most polymers have persistence lengths longer than their total (contour) length?

12. Regional Elasticity Motion of beads inside cells measured by mean squared displacement. Material stiffness, E, and Poisson’s ratio determines overall stiffness of object, the surface stiffness. From Hertzian model of continuum mechanics.

13. nanoscale mapping of cells Regional (topographic) distribution of stiffness. AFM Cantilever must be more (or at least as) compliant than the cell, I.e. impedance matching. k lever < k cell If k lever > k cell then no motion fidelity because cell needs to overcome cantilever stiffness before it moves. If k lever < k cell then OK

14. Measuring spring constant with AFM

15. Deflection image of trapped yeast Bud scar shown

16. Height map Deflection Map Force map

17. Mica is infinitely stiff re:cantilever, so slope is 1. F= k lever d To account for drift, F*= k lever (d-d 0 ) Neglect tip surface adhesion. Sample Height Deflection

18. Cantilever k = 0.05 +- 0.01 nN/m Yeast C.B. k = 0.06 nN/m Mammalian C.B. k = 0.002 nN/m Yeast have thick cell wall, chitin Cantilever & C.W. are 2 springs in series Noise (rms) of combination is 0.06 nm Resonance of free cantilever is 3.7 KHz Resonance of PZ tube scanner is 4.5 KHz

19. Do cells emit sound? Myocytes beat in culture Insect muscles eg., in vivo muscle, hair cells, flagella all oscillate, @ f’s 1 to 300 Hz; Ca waves. Single myofibrils Coupled molecular motors theoretically up to 10 KHz.

20. yeast deflection mode images: Pelling, AE, et al. Science, 305:1147, 2004 Dried cells Live cells trapped in filter Color represents deflection

22. Resonance of AFM Lngmuir 19:4539, 2003

23. Source of sound  n  ~ Y (Resonance) Arrhenius plot Similar to activation energies for molecular motors, dynein, myosin, kinesin. Yeast has these

24. What is the origin of the sound? Motion : –Active metabolic process : Azide stops ATP production by mitochondria. Does not  Y, nor morphology. –Mechanical resonance/ Brownian

25. Speeds Speed: 3 nm X 1 kHz = 3  m/sec myosin 0.2 to 8  m/sec MT proteins : 0.02 to 7  m/sec Other cell activities have 10X these speeds

26. and forces Force 3 nm X 0.06 N/m = 0.2 nN When AFM force, no  in amplitude until F > 10 nN : 10 nN too big for a single protein Must be many proteins coordinated

27. Origin of Sonocytology Cooperativity is common, eg., muscle, hair cells, flagella all oscillate, but @ lower f’s 1 to 300 Hz; Ca waves. Coupled molecular motors theoretically up to 10 KHz. Non-invasive w/o dyes or quantum dots Communication; pumping? For softer cells, need refined cantilever. Cancer cell sound differential?

32. How does muscle fatigue? Test of a ‘skinned’ muscle fiber from EDL of rat. Can activate by direct stimulation of any step in the cascade. Pederson, TH: Science 305: 1144, 2004

34. Mechano - regulation Growth, proliferation, protein synthesis, gene expression, homeostasis. Transduction process- how? Single cells do not provide enough material. MTC can perturb ~ 30,000 cells and is limited. MTS is more versatile- more cells, longer periods, varied waveforms..

35. Tactile sensation in us: Pacinian corpuscles Gating by mechanical energy What governs the transient behaviour?

36. C. Elegans mechanotransduction: Goodman, MB, Science 306, 427, 2004 Cellular anatomy is entirely described First animal to be genetically coded 12 proteins mediate the response and are coded by mec genes Knocking out MEC 2,4 & 6 abolishes the current Allele of MEC 10 reduces it ( substitutes a glutamate for a glycine). Insert into Xenopus oocytes

37. EC mechanoregulation

42. Hundreds of molecular motors Homologous proteins Gene Knockouts have shown many other functions for motor proteins

43. Homework What is the average

49. Comparative motors

50. ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL< previous next >

51. ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL< previous next >

52. F1 ATPase: A rotary motor Can either make or break ATP, hence is reversible Torque of 40 pN-nM; work in 1/3 rev. is 80 pn-nM (40 * 2  /3) equivalent to free energy from ATP hydrolysis Can see rotation by attaching an actin filament

54. Nature Reviews Molecular Cell Biology 2; 669-677 (2001) ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL < previous next >

55. Rotary Cellular Motors The rotary mechanism of ATP synthase, Stock D, Gibbons C, Arechaga I, Leslie AGW, Walker JE CURRENT OPINION IN STRUCTURAL BIOLOGY,10 (6): 672- 679 DEC 2000 2. ATP synthase - A marvellous rotary engine of the cell, Yoshida M, Muneyuki E, Hisabori T NATURE REVIEWS MOLECULAR CELL BIOLOGY 2 (9): 669-677 SEP 2001 3. The gamma subunit in chloroplast F-1-ATPase can rotate in a unidirectional and counter-clockwise manner Hisabori T, Kondoh A, Yoshida M FEBS LETTERS 463 (1-2): 35-38 DEC 10 1999 4. Constructing nanomechanical devices powered by biomolecular motors.C. Montemagno, G Bachand, Nanotechnology 10: 225-2312, 1999.

58. When L>>  the chain has many bends and is always crumpled in solution – the FJC model applies, with each link approximated as 2  and perfectly flexible joints. To count all possible curved states in a smooth-bending rod in solution- it’s a WLC- supercoiling is possible.