Outer Hair Cells as MEMs

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Outer Hair Cells as MEMs
Electromotility
Mechanism based in plasma membrane Requires
turgor pressure (1-2 kPa) Maximal gains of
gt15 nm/mV and gt 50pN/mV. Independent
of calcium and ATP
salicylate
Whole cell voltage clamp/photodiode
Data of Kakehata and Santos-Sacchi, 1996
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Doth the Answer lie in Mechanics ? I never
satisfy myself until I can make a mechanical
model of a thing. If I can make a mechanical
model I can understand it. As long as I cannot
make a mechanical model all the way through I
cannot understand it and that is why I cannot
get the electromagnetic theory. -- Lord
Kelvin, 1884
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Nanoscale Structure of Lateral Wall
Spectrin -- thin elastic filament 40 nm
long Actin -- thick filament, circumferential Pil
lar -- protein of unknown composition 30 nm long
connecting plasma membrane to cytoskeleton
Plasma Membrane
Pillar
Actin
Spectrin
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Dimpled SurfacesNanoscale Membrane Bending
Force balance on pressurized cylinder supported
by circumferential rings (Timoshenko)
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Stretching Elastic Membrane over Pressurized
Structure
Interior of the Hindenburg (or is it the cortical
lattice of the OHC ?)
The Hindenburg
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Biomembranes as Liquid Crystals

• intermediate state of matter
• display orientational but not positional order
• composed of dipoles free to rotate in an applied
  field

• Protein and lipid molecules comprising
  biomembranes possess dipole moments

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Flexoelectricity

• curvature-induced polarization
• primary mode of electromechancial coupling in
  nematic liquid crystals
• distinguished from piezoelectric effec33t in
  solid crystals

f flexoelectric coefficient cl 1/30 nm,
cj 1/4500 nm
As electric field is increased, dipoles rotate to
align with the field increasing the polarization
of the membrane
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The Langevin Function

• specifies fraction of dipoles oriented with the
  applied field
• statistical mechanics
• continuum of states

polarization
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Nano-Electro-Mechanical Flexion Motor
The regular array of pillar structures gives the
membrane the opportunity to be curved at the
nanoscale. The pressurization of the cell from
the inside also predicts the existence of
nanoscale curvature in the membrane.
A voltage-induced nanoscale deformation in each
motile unit sums to a mircoscale cell deformation.
DV
DP
pillar
Spectrin
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Energetics of Nanoscale Bending
Bending Energy
Spectrin Energy
kc bending stiffness cl
longitudinal curvature co spontaneous
curvature
ks spectrin stiffness nsp spectrin
density xo force-free length
Combine by writing the spring length as a
function of curvature where a and b are
constants The energy is redefined in terms of the
equilibrium curvature ce
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Measurement of Bending Stiffness
Rt 10 -50 nm
Tether
f
Vesicle
Axial View
kc 1.2 x 10-19 J
Raphael and Waugh, 1996
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Constitutive Equations of Orientational Motor
Model
Moment Resultant
Electric Displacement
h membrane thickness
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Electromotility Predictions
It is more important to have beauty in ones
equations than to have them fit experiment.
Paul Dirac
DLm -2.07 mm g 0.09 mV-1 V0 - 43 mV
DLV0 - 0.69 mm c2 0.00274
salicylate
Data of Kakehata and Santos-Sacchi, 1996
Nf number of membrane folds
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Significance of Parameters

• DLm -2.07 mm -- corresponds to flexoelectric
  coefficient 10-19 C
• DLV0 - 0.69 mm -- means xo lt a
• -- spectrin extended by membrane arch

• 0.09 mV-1 -- corresponds to Npo number of
  dipoles and dipole moment
• N 6000/mm2 po 125 Debye -- protein
• N 20 x Np po 8 Debye -- lipid

Santos-Sacchi et al. measures of capacitance in
short cells implied there are more voltage
sensors than particles
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Disrupting Spectrin
Accomplished with diamide
-- Cell should elongate
Zhao et al., submitted
-- Stiffness/force generation decreases
experimentally verified by Adachi Iwasa, 1999
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Liquid Crystal Disorder-Order Transitions
Depolarization or increased pressure
Hyperpolarization or low pressure
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Order, Disorder and Information
Sound Input
NeuralOutput
hearing
speaking
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The grand aim of all science is to cover the
greatest number of empirical facts by logical
deduction from the smallest number of hypotheses
or axioms. Albert Einstein
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Model Accomplishments

• Explains experimental measurements on
  electromotility and dependence of capacitance on
  pressure
• Explains diamide reduction in force generation
• Predicts amphipaths should alter electromotility
• Consistent with excess membrane surface area
• Voltage-Dependent Diffusion -gt Orientational
  Order
• Motivates new series of experiments
• May explain more than outer hair cells

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Outer membrane ripples on motile cells
Coincidence or functional roles?
OHC - Dieler et al. 1991
Oscillatoria - Adams et al. 1999
Flexibacter BH3 - Dickson et al. 1980
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Design of Synthetic MEMs
Actin polymerize in equally spaced rings
Lipid bilayer ( prestin)
Control sensitivity range by pressure
difference Control magnitude of response by
surface charge
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Cochlea Engineering
The Holy Grail Regeneration/Replacement of
compromised cells

• The Realistic Goal Prevention of hair cell
  damage/degeneration
• maintenance of cell-cell signalling
  pathways in the cochlea
• targetted delivery of drugs to compromised
  areas of the cochlea (K channels/gap junctions)

Improvement in design of prosthetics --cochlear
implants/directional hearing aids
Liberman, 1997
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Cochlea Engineering The Beginning

• Interactions of liposomes with outer hair cells

Fast pulling
Slow pulling
PC liposomes
PC/PS/PE lipsomes