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Nonlinear amplification by active sensory hair bundles [Elektronische Ressource] / von Kai Dierkes

139 pages
Nonlinear ampli cationby active sensory hair bundlesDissertationzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)vorgelegtder Fakultat Mathematik undNaturwissenschaftender Technischen Universitat DresdenvonKai Dierkesgeboren am 21.2.1977 in EssenEingereicht am 10. Juni 2010Eingereicht am 10. Juni 2010Verteidigt am 12. August 20101. Gutachter: Prof. Dr. Frank Julic her2.hter: Prof. Dr. Alexander NeimanAbstractThe human sense of hearing is characterized by its exquisite sensitivity, sharp fre-quency selectivity, and wide dynamic range. These features depend on an activeprocess that in the inner ear boosts vibrations evoked by auditory stimuli. Sponta-neous otoacoustic emissions constitute a demonstrative manifestation of this phys-iologically vulnerable mechanism. In the cochlea, sensory hair bundles transducesound-induced vibrations into neural signals. Hair bundles can power mechanicalmovements of their tip, oscillate spontaneously, and operate as tuned nonlinear am-pli ers of weak periodic stimuli. Active hair-bundle motility constitutes a promisingcandidate with respect to the biophysical implementation of the active process un-derlying human hearing.The responsiveness of isolated hair bundles, however, is seriously hampered byintrinsic uctuations. In this thesis, we present theoretical and experimental resultsconcerning the noise-imposed limitations of nonlinear ampli cation by active sensoryhair bundles.
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Nonlinear ampli cation
by active sensory hair bundles
Dissertation
zur Erlangung des akademischen Grades
Doctor rerum naturalium
(Dr. rer. nat.)
vorgelegt
der Fakultat Mathematik und
Naturwissenschaften
der Technischen Universitat Dresden
von
Kai Dierkes
geboren am 21.2.1977 in Essen
Eingereicht am 10. Juni 2010Eingereicht am 10. Juni 2010
Verteidigt am 12. August 2010
1. Gutachter: Prof. Dr. Frank Julic her
2.hter: Prof. Dr. Alexander NeimanAbstract
The human sense of hearing is characterized by its exquisite sensitivity, sharp fre-
quency selectivity, and wide dynamic range. These features depend on an active
process that in the inner ear boosts vibrations evoked by auditory stimuli. Sponta-
neous otoacoustic emissions constitute a demonstrative manifestation of this phys-
iologically vulnerable mechanism. In the cochlea, sensory hair bundles transduce
sound-induced vibrations into neural signals. Hair bundles can power mechanical
movements of their tip, oscillate spontaneously, and operate as tuned nonlinear am-
pli ers of weak periodic stimuli. Active hair-bundle motility constitutes a promising
candidate with respect to the biophysical implementation of the active process un-
derlying human hearing.
The responsiveness of isolated hair bundles, however, is seriously hampered by
intrinsic uctuations. In this thesis, we present theoretical and experimental results
concerning the noise-imposed limitations of nonlinear ampli cation by active sensory
hair bundles. We analyze the e ect of noise within the framework of a stochastic
description of hair-bundle dynamics and relate our ndings to generic aspects of the
stochastic dynamics of oscillatory systems.
Hair bundles in vivo are often elastically coupled by overlying gelatinous mem-
branes. In addition to theoretical results concerning the dynamics of elastically
coupled hair bundles, we report on an experimental study. We have interfaced dy-
namic force clamp performed on a hair bundle from the sacculus of the bullfrog with
real-time stochastic simulations of hair-bundle dynamics. By means of this setup,
we could couple a hair bundle to two virtual neighbors, called cyber clones. Our
theoretical and experimental work shows that elastic coupling leads to an e ective
noise reduction. Coupled hair bundles exhibit an increased coherence of sponta-
neous oscillations and an enhanced ampli cation gain. We therefore argue that
elastic coupling by overlying membranes constitutes a morphological specialization
for reducing the detrimental e ect of intrinsic uctuations.Acknowledgments
Above all, I would like to thank Dr. Benjamin Lindner for the patient and intense
supervision of my research. I greatly appreciate all the time and e ort that he spent
in helping me with my project.
Furthermore, I would like to thank Prof. Dr. Frank Julic her for giving me the
opportunity to join his group at the MPIPKS and for guiding my work during the
last years.
Some of the results presented in this thesis were obtained in close collaboration
with our colleagues at the Institut Curie in Paris. I would like to thank Dr. Pascal
Martin for many stimulating discussions and for giving me the opportunity to spend
several weeks of my PhD in his laboratory. A special thanks also goes to Jeremie
Barral for spending numerous hours with me at the microscope and in front of the
computer in order to perform the experiments discussed in chapter 5.
During my research, I have greatly pro ted from discussions with Johannes Baum-
gart, Dr. Nils Becker, Diana Clau nitzer, Christian Gnodtke, and Dr. Dhaibhid
O’Maoileidigh. I thank them for their interest and enthusiasm.
Also, I would like to thank Dr. Thomas Bittig, Florian Fruth, and Dr. Abigail
Klopper for proofreading and commenting on this manuscript.
Many more people in Dresden and Berlin had their share in making these last
years what they have been, scienti cally as well as non-scienti cally. Not to run the
risk of presenting an incomplete list: Thanks to all of you!
Last but not least, I would like to thank my parents and my sister for their loving
support throughout all these past years.Contents
1 Introduction 1
1.1 Hearing in vertebrates . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 From resonance theory to the cochlear ampli er . . . . . . . . . . . . 5
1.3 Ampli cation by critical oscillators . . . . . . . . . . . . . . . . . . . 13
1.4 Active hair-bundle motility . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.1 Hair-bundle morphology . . . . . . . . . . . . . . . . . . . . . 16
1.4.2 Ha oscillations in the sacculus of the bullfrog . . . . . 18
1.4.3 Physical description of hair-bundle dynamics . . . . . . . . . . 21
1.4.4 Coupling of hair bundles in vivo . . . . . . . . . . . . . . . . . 31
1.5 Coupled oscillators and synchronization . . . . . . . . . . . . . . . . . 32
1.6 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Noise-imposed limits of hair-bundle performance 35
2.1 Quality of spontaneous oscillations . . . . . . . . . . . . . . . . . . . 35
2.2 Ampli cation gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 Local exponents of nonlinear compression . . . . . . . . . . . . . . . . 45
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3 Limit-cycle dynamics in the presence of uctuations 49
3.1 Dynamics close to a Hopf bifurcation . . . . . . . . . . . . . . . . . . 49
3.2 Phase di usion and partial entrainment . . . . . . . . . . . . . . . . . 52
3.3 Amplitude growth vs. phase locking . . . . . . . . . . . . . . . . . . . 58
3.4 Local exponents of nonlinear compression . . . . . . . . . . . . . . . . 61
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4 Theory of coupled hair bundles 67
4.1 Physical description of coupled hair bundles . . . . . . . . . . . . . . 67
4.2 Spontaneous noisy oscillations and synchronization . . . . . . . . . . 71
4.3 Nonlinear ampli cation . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Transient responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Heterogeneities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.6 A mean- eld argument . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Contents
5 The hair bundle and its cyber clones - A hybrid experiment 91
5.1 Dynamic force clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2 Cyber clones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Synchronization and increased phase coherence . . . . . . . . . . . . . 97
5.4 Enhancement of mechanical ampli cation . . . . . . . . . . . . . . . . 99
5.5 E ects of gentamicin . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.6 Parameter mismatches . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6 Conclusions and outlook 107
A Discretization of cyber-clone dynamics 113
Bibliography 116Chapter 1
Introduction
Hearing has an impact on a multitude of human activities. Auditory cues, such as
the sounding of a cyclist’s bell, help us to generate an internal representation of the
surrounding environment. In order for another individual’s utterances to be intelli-
gible as speech, our ear must be capable of resolving their frequency content, as well
as their dynamic and temporal structure. The intellectual and emotional pleasures
induced by a piece of music are likewise dependent on our ability to appropriately
analyze auditory stimuli.
The human ear performs the task of hearing with remarkable acuity. With audi-
tory frequencies stretching over a range from about 20 Hz up to 20 kHz, an untrained
individual can readily discern two tones that di er in frequency by less than 0.5%.
As for temporal resolution, humans can detect gaps on the order of only a few
milliseconds separating two pure tones. At the same time, the ear operates over a
vast dynamic range, covering about six orders of magnitude in sound pressure level
(SPL). Being able to perceive the faintest sounds, such as the rustling of leaves in
a tree at about 0 dB SPL, the human ear also copes with the roaring of a starting
airplane’s engine at about 120 dB SPL.
The last century has seen remarkable progress with regard to our understanding
of the biophysical principles underlying hearing. Some fundamental issues, however,
are left unresolved and continue to challenge researchers from various elds.
Within the inner ear, the transduction of sound-induced mechanical vibrations
into neural signals is achieved by cells which are equipped with a specialized sen-
sory organelle, the so-called hair bundle. The hair bundle is a tuft of interlinked
stereocilia emanating from the hair cell’s apical surface. Hair bundles constitute
active elements, possessing the ability to oscillate spontaneously and to operate as
nonlinear ampli ers of appropriate mechanical stimuli. Active hair-bundle motility
has been proposed as a key element in understanding the origin of the inner ear’s
exquisite sensitivity, broad dynamic range and acute frequency resolution.
In this thesis, we present both theoretical and experimental results regarding the
dynamics and signal detection properties of single and coupled hair bundles. In
particular, we analyze the e ects of intrinsic uctuations on hair-bundle operation2 1.1. Hearing in vertebrates
and show that elastically coupled hair bundles are expected to outperform isolated
ones due to a noise-reduction e ect. We relate our ndings to results dealing with
generic aspects concerning the dynamics of noisy oscillators.
1.1 Hearing in vertebrates
In the inner ear of vertebrates, several sensory organs are dedicated to the trans-
duction of mechanical stimuli into neural signals. In mammals, the utricle and
sacculus are sensors of linear accelerations of the head. Together with the semicir-
cular canals, which are detectors of rotational head movements, they constitute the
vestibular system. The auditory system in mammals comprises a single inner ear
organ, the cochlea. In all the other vertebrate classes, structurally similar inner ear
organs have evolved for the detection of sound and head accelerations [68, 105, 88].
In humans, the pinna performs the function of a hearing horn (see g. 1.1A).
Incoming sound stimuli are funneled toward the tympanic membrane via the external
auditory meatus . The outer ear constitutes a complex resonant cavity with a sound
pressure gain of about 20dB at 2.5 kHz, measured at the ear drum [146].
The air- lled middle ear transmits vibrations of the tympanic membrane to the
uid- lled cochlea via three miniscule bones, the so-called ossicles. More speci cally,
the chain of ossicles comprises the malleus, the incus, and the stapes. The latter
is embedded into the oval window, a membranous opening in the cochlea’s boney
wall. In order to minimize the re ection of acoustic energy at the interface between
the low-impedance tympanic membrane and the high-impedance oval window, the
middle-ear has evolved to perform an e ective impedance matching [125].
The cochlea is a coiled cavity in the temporal bone, forming part of the inner ear.
It is divided longitudinally, i.e. from base to apex, into three scalae (see g. 1.1B and
g. 1.2A). The perilymph- lled scalae tympani and vestibuli are joined at the apical
end of the cochlea by an opening known as the helicotrema. The scala media is lled
with endolymph. It is separated from the scala vestibuli by Reissner’s membrane
and from the scala tympani by the basilar membrane, the latter being an elastic
membrane with a length of about 35mm in humans [164]. The oval window opens
onto the scala vestibuli. A movement of the stapes displaces cochlear uids towards
a second membranous window, the round window opening onto the scala tympani
(see g. 1.2B).
Oscillatory movements of the stapes induce pressure gradients across the three
scalae, causing a wave-like displacement of the basilar membrane to travel from
base to apex [170, 138]. After a gradual build up, the traveling waves’ amplitude
peaks at a location determined by its frequency, and rapidly decays thereafter. The
cochlea therefore exhibits a tonotopic organization. For each location on the basilar
membrane there is a characteristic frequency which elicits a maximal response. This
characteristic frequency gradually varies along the cochlea, with high frequencies
close to the base and low frequencies close to the apex [57].

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