Emergent Phenomena
in Cochlear
Mechanics
Christopher A. Shera
Eaton-Peabody Laboratory of Auditory
Physiology
Harvard Medical School
What is the Biophysical Origin of the Cochlear
Amplifier? Or active hair-bundle motility?
Is it somatic
electromotility?
(Hudspeth 1997)
“The rapid conformational change associated with channels closing
together tightens tip links and moves the hair bundle by several
nanometers. It has been suggested that this mechanism, if timed
appropriately to different stimulus frequencies for each hair cell, could
amplify the vibration of the cochlea’s basilar membrane (a process termed
the ‘cochlear amplifier’).
If
If so,
so, the
the TRPA1
TRPA1 protein
protein could
could be
be at
at once
once
the hair-cell transduction channel, the gating spring, and the cochlear
amplifier.”
amplifier.”
The Debate is Misleadingly Framed
The cochlear amplifier is not
EITHER somatic motility OR hair-bundle motility.
The cochlear amplifier is not BOTH.
The cochlear amplifier is NEITHER.
Insights from Cochlear Modeling
Inverse method (e.g., Zweig, de
Boer)
Determines functional properties of the
organ of Corti from measurements of BM
motion
The Impedance of the Organ of Corti
ZBM(x,f )=
Psv - Psv
VBM
= ZPassive + ZActive
Psv
Pst
Cochlear cross section at
location x
What are the relative
contributions of the passive and
active components?
VBM
BM-Admittance Frequency Responses
Passive
Active
Total
(passive
component
component
& active)
The Impedance of the Organ of Corti
ZBM(x,f )= ZPassive + ZActive
Cochlear cross section at
location x
Effects of Fluid Coupling Between the Oscillators
The Impedance of the Organ of Corti
ZBM(x,f )= ZPassive + ZActive
Cochlear cross section at
location x
Effects of Scalae Height (Nature of Fluid Coupling
“The rapid conformational change asssociated with channels closing
together tightens tip links and moves the hair bundle by several
nanometers. It has been suggested that this mechanism, if timed
appropriately to different stimulus frequencies for each hair cell, could
amplify the vibration of the cochlea’s basilar membrane (a process termed
the ‘cochlear amplifier’).
If so, the TRPA1 protein could be at once
the hair-cell transduction channel, the gating spring, and the cochlear
amplifier.”
a^force-producing element of
Principle of Emergence
In a structured system, new properties emerge at higher
levels of integration which could not have been predicted
from a knowledge of the lower-level components.
Ernst Mayr
Spontaneous Otoacoustic Emissions
(SOAEs)
(Allen et al. 1995)
Gold’s (1948) Local-Oscillator Model
“…if the feedback ever exceeded the losses, then a
resonant element [in the organ of Corti] would
become self-oscillatory, and oscillations would build
up [to] a level where linearity was not preserved.”
“In spite of [the] self-regulating mechanism we might
expect that occasional disturbances would bring an
element into the region of self-oscillation, when it is
normally so close to this condition. If this occurred,
then we should hear a clear note which would persist
until the adjusting mechanism has regained control, or
until the nervous sensitivity has decreased
sufficiently.”
Spontaneous Hair-Bundle Oscillations
(Martin et al. 2001, 2003)
Models for Hair-Bundle Oscillators
Oscillation/SOAE frequencies are
determined by cellular properties
such as
• Hair-bundle stiffness and
geometry
• Gating compliance
• Adaptation and/or
transduction kinetics
• Ca2+ equilibration kinetics
(Hudspeth 1997)
SOAEs Used to Argue Against Somatic
Motility as the “Active Process” in
Mammalian Hearing
• The motor element of the cochlear
amplifier is the source of SOAEs
• Unprovoked mechanical oscillations of the
motor element underlie the production of
• SOAEs
Although hair bundles can oscillate
spontaneously, no spontaneous OHC
contractions have ever been observed
The hair bundle is both the source of SOAEs
and the motor element of the cochlear
amplifier
Gold’s Local-Oscillator
Model Gets the Chain of
Causality Exactly Backwards
The ear does not produce SOAEs because
hair cells oscillate spontaneously.
Rather, hair cells oscillate spontaneously (in
vivo) because the ear produces SOAEs.
Kemp’s (1979) Global Standing-Wave
Model
SOAEs are continuously self-evoking stimulusfrequency otoacoustic emissions (SFOAEs)
• initiated either by sounds from the
environment or by physiological noise
Spacetime Diagram Illustrating SFOAE
Generation
Interference Patterns in Ear-Canal Pressure
Spacetime
SpacetimeDiagram
DiagramIllustrating
IllustratingStanding
SFOAE
Generation
Waves
Effective Reflection Coefficients
For ingoing-waves at
stapes:
For outgoing-waves at stapes:
Human SFOAE Amplitude and Phase
Spontaneous Otoacoustic Emissions
(Allen et al. 1995)
Human SFOAE Amplitude and Phase
Quantifying the Model Predictions
9 ears in 9 subjects
(Data from Shera & Guinan
2003 and Dreisbach et al.
Human SOAE Spacings
556 SOAE
pairs 73 ears
47 subjects
(Data from Talmadge et al.
1993 and Burns et al. 1992)
Variability of SOAE Spacings
Summary of Results
The global standing-wave model correctly predicts:
• Multiple SOAEs with a characteristic minimum frequency spacing
• The mean value of this spacing
• Its standard deviation
• Its power-law dependence on frequency
• The magnitude, sign, and frequency dependence of SOAE
frequency shifts induced by modulations in middle-ear stiffness
Predictions arise naturally in the standing-wave framework
but require ad-hoc adjustment of local-oscillator models.
Local-Oscillator vs Global Standing-Wave
SOAEs
Local-Oscillator
Global Standing-Wave
Autonomous oscillators are cells or
subcellular structures
Autonomous oscillator is the cochlea
as a whole
Macromechanical structures and
processes play no fundamental role:
They simply provide a conduit for
energy to escape from the cochlea
Macromechanical structures and
processes determine SOAE
characteristics (e.g., SOAEs
would not occur if Rstapes=0)
SOAE frequencies are set by local
properties of hair cells (e.g., hairbundle geometry, transduction
kinetics, etc)
SOAE frequencies are set by global
properties (e.g., round-trip travelingwave phase shifts, middle-ear
impedance, etc)
The Cochlea is Acting as a Biological
Laser
Implications for the Cellular
Basis of the Cochlear Amplifier
Hudspeth and colleagues have repeatedly invoked Gold’s local-oscillator
model to argue that OHC somatic motility is unlikely to constitute the
“active process” in mammalian hearing (e.g., Martin & Hudspeth 1999,
2001; Martin et al. 2001, 2003; Duke 2002; Jülicher et al 2003).
• Based on the apparent absence of spontaneous OHC contractions
But Hudspeth’s argument that
“unprovoked mechanical oscillations of some constituent of the inner
ear must underlie the production of spontaneous otoacoustic
emissions”
is based
on a logical
fallacy.
The Principle of Emergence
In a structured system, new properties emerge at higher
levels of integration which could not have been predicted
from a knowledge of the lower-level components.
Ernst Mayr
The local-oscillator model gets the causality exactly
backwards…
SOAEs arise through the collective action of the entire cochlea.
Spontaneous emission of sound from the ear does not require
the autonomous mechanical oscillation of its cellular
constituents.
Characteristics of Emergent Phenomena
Emergence occurs when a relatively small number of copies
of relatively simple components are coupled together in
relatively simple ways.
The whole is more than the sum of its parts.
Since the interactions are usually nonlinear, the collective behavior
cannot be obtained by summing the behaviors of the isolated parts.
The whole obeys different laws than the parts.
Its behavior can be described by “macrolaws” without recourse to
the detailed microlaws that govern the behavior of the components.
The parts acquire new properties by virtue of their
embedding in the whole.
Context and coupling are crucial.
The OHC Membrane Time-Constant
Problem
Conjecture: The problem is artificial
because the solution is “emergent.”
When embedded in situ, OHCs have
an effective response bandwidth much
greater than they do in isolation.
Basic idea proposed long ago by
modelers (e.g., Mountain & Hubbard
1994); for latest experimental
evidence, see Scherer & Gummer,
2004.
The Crucial Role of Mathematical
Modeling in the Study of Hearing