Background for cell propulsion

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Lecture 10

• Background for cell propulsion
• Fluid dynamics
• Enzyme kinetics
• How do animals swim?
• 1. pushing fluid backward by limb action
• 2. pushing fluid forward by resistance of body.
• I.e fish starting from release will accelerate
  until the backward forward momentum (of the
  fluid) balance. Viscosity is only significant at
  the boundary layer.

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Cell Propulsion

• Small scale phenomenon slow velocities driven by
  surface forces pressure and viscous stress.
  Fluid resistance is significant, and balances
  propulsive force.
• Motion of a body depends on the ratio of viscous
  and inertial effects Reynolds number Small
  for cells, large for almost all animals. Cellular
  world is ruled by friction.

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• Reynolds number quantifies the relative
  magnitudes of frictional and inertial forces

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Cellular Motors

• Molecular motors must move (swim) in fluids,
  where most of the work is dissipated
• What forces must they overcome?
• Where do the motors get their fuel?
• How do they exhaust spent fuel?
• What is the efficiency?

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Creature R
Bacteria 10-4
Spermatozoa 10-2
Flying Insects Birds 104 105
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Oscillatory muscles
Stretch activation
Synchronous
Asynchronous
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Stretch- activated currents
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Sliding filamentds
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Myosin

• 5.3 pN for each myosin molecule
• 100 molecules per filament.
• Each filament has c.s.a. of 1.8 X 10 15 m2 in
  the relaxed muscle.

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Strain in solids and fluids
A
f
d
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Sample fluid properties
When f gt fcrit- inertial forces dominate
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Swimming is it worth it?

• Cilium with velocity, v, length, d, time scale
• Diffusion time scale
• Swimming time, ts should be lt tD

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Viscous flow

• Newtonian fluids are isotropic
• What is a viscous fluid?
• When flt fcrit

Shear
Planar geometry
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• I.e., 1 mm cilium, D 10-5 cm2/sec,
• so vgt 103 mm /sec
• stirring and swimming is not energetically
  favorable for nutrition.

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Comparative motors
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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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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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Elasticity

• 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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• 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.

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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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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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Markov Chains

• A dynamic model describing random movement over
  time of some activity
• Future state can be predicted based on current
  probability and the transition matrix

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Transition Probabilities
Todays Game Outcome
Win Lose
Win 3/4 1/2
Lose 1/4 1/2
Sum 1 1
Need a P for Todays game
Tomorrows Game Outcome
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Grades Transition Matrix
This Semester
Grade Tendencies
To predict future Start with now What are the
grade probabilities for this semester?
Next Semester
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Markov Chain
Intial Probability Set independently
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Computing Markov Chains
A is the transition probability A .75 .5
.25 .5 P is starting Probability P.1
.9 for i 120 P(,i1)AP(,i) end
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