Energetics

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Lecture 11

• Energetics Kinetics of cellular rxns
• Regional stiffness motion
• AFM Yeast Myocytes
• Mechano-electrical coupling
• Electro-mechanical coupling
• Homework

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Free energy landscapes

• Large activation barrier is reduced by the
  interaction ( with a small cost of deforming E).
  The barrier is reduced.

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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.

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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

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1/v
1/S
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• 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

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Koster, DA et al. Nature , 2004
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TOP1B removing supercoils
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Model of TOP1B
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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?

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Regional Elasticity

• Motion of beads inside cells measured by mean
  squared displacement.
• Material stiffness, E, and Poissons ratio
  determines overall stiffness of object, the
  surface stiffness. From Hertzian model of
  continuum mechanics.

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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
  . klever lt kcell
• If klever gt kcell then no motion fidelity
  because cell needs to overcome cantilever
  stiffness before it moves.
• If klever lt kcell then OK

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Measuring spring constant with AFM
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• Deflection image of trapped yeast
• Bud scar shown

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• Height map
• Deflection Map
• Force map

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• Mica is infinitely stiff recantilever, so slope
  is 1.
• F klever d
• To account for drift,
• F klever (d-d0)
• Neglect tip surface adhesion.

Deflection
Sample Height
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• 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

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Do cells emit sound?

• Myocytes beat in culture
• Insect muscles
• eg., in vivo muscle, hair cells, flagella all
  oscillate, _at_ fs 1 to 300 Hz Ca waves.
• Single myofibrils
• Coupled molecular motors theoretically up to 10
  KHz.

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yeast deflection mode images Pelling, AE, et
al. Science, 3051147, 2004
Color represents deflection
Dried cells
Live cells trapped in filter
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Resonance of AFM
Lngmuir 194539, 2003
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Source of sound

• wn2 Y (Resonance)
• Arrhenius plot
• Similar to activation energies for molecular
  motors, dynein, myosin, kinesin.
• Yeast has these

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What is the origin of the sound?

• Motion
• Active metabolic process Azide stops ATP
  production by mitochondria. Does not D Y, nor
  morphology.
• Mechanical resonance/ Brownian

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Speeds

• Speed 3 nm X 1 kHz 3 mm/sec
• myosin 0.2 to 8 mm/sec
• MT proteins 0.02 to 7 mm/sec
• Other cell activities have 10X these speeds

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and forces

• Force 3 nm X 0.06 N/m 0.2 nN
• When AFM force , no D in amplitude until F gt 10
  nN
• 10 nN too big for a single protein
• Must be many proteins coordinated

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Origin of Sonocytology

• Cooperativity is common, eg., muscle, hair cells,
  flagella all oscillate, but _at_ lower fs 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?

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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
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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..

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

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C. Elegans mechanotransductionGoodman, 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

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EC mechanoregulation
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• Hundreds of molecular motors
• Homologous proteins
• Gene Knockouts have shown many other functions
  for motor proteins

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Homework

• What is the average

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Comparative motors
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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 2p/3) equivalent to free energy from ATP
  hydrolysis
• Can see rotation by attaching an actin filament

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Rotary Cellular Motors

• The rotary mechanism of ATP synthase , Stock D,
  Gibbons C, Arechaga I, Leslie AGW, Walker
  JECURRENT OPINION IN STRUCTURAL BIOLOGY ,10 (6)
  672-679 DEC 2000
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• 2. ATP synthase - A marvellous rotary engine of
  the cell, Yoshida M, Muneyuki E, Hisabori
  TNATURE REVIEWS MOLECULAR CELL BIOLOGY 2 (9)
  669-677 SEP 2001
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• 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
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• 4. Constructing nanomechanical devices powered by
  biomolecular motors.C. Montemagno, G Bachand,
  Nanotechnology 10 225-2312, 1999.

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• When Lgtgt x, the chain has many bends and is
  always crumpled in solution the FJC model
  applies, with each link approximated as 2 x, and
  perfectly flexible joints.
• To count all possible curved states in a
  smooth-bending rod in solution- its a WLC-
  supercoiling is possible.