Tympanal travelling waves in migratory locusts
1 School of Biological Sciences, University of Bristol, Woodland Road,
Bristol, BS8 1UG, UK
2 Volkswagen-Foundation-research group, Institute of Zoology, University of
Cologne, Weyertal, 119 50923, Cologne, Germany
* Author for correspondence (e-mail: james.windmill{at}bristol.ac.uk)
Accepted 5 October 2004
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Summary |
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Key words: bioacoustics, frequency detection, hearing, travelling wave, tympanum, locust.
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Introduction |
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The ears of locusts and grasshoppers (Orthoptera: acrididae) have been
known and studied for quite some time
(Schwabe, 1906;
Autrum, 1941
;
Gray, 1960
;
Michelsen, 1971
) and their
structure and function are among the better known in insects. The main
anatomical components of locust ears are an external tympanal membrane (TM)
and a mechanosensory organ - Müller's organ - that contains four clusters
of multicellular mechanoreceptive units: the scolopidia
(Gray, 1960
). It was also
established, using electrophysiological techniques, that the ears of locusts
could perform some form of frequency discrimination
(Horridge, 1960
). Further
investigations testing the presence of a `place principle' in invertebrates
then showed that discrete groups of mechanosensory cells from Müller's
organ convey different frequency information and attach at different locations
to the TM (Michelsen, 1968
,
1971
;
Miller, 1977
;
Römer, 1976
). The
logical, but difficult, step forward required establishing a direct relation
between the vibrational patterns of the TM and the attachment loci of the
mechanosensory cells. This task was first undertaken by Michelsen
(1971
), using laser holography
as a technique and membrane-drum resonance theory as a conceptual background.
Data were mostly gathered in isolated ear preparations yielding amplitude and
phase information on membrane deflections that coincided with theoretical
deflection modes of a circular isotropic drum. Thus, a correspondence was
established between the frequency response of the four types of
mechanoreceptors, the resonant frequencies of Müller's organ and the
mechanical response of the TM. The evidence pointed then to a process in which
the locust TM undergoes different resonant modes at different frequencies. The
locations of maximal membrane displacements - the antinodes - were seen to
vary as a function of the frequency driving the mechanical system, and
correspond to the attachment points of mechanoreceptor clusters. This was the
place principle applied to the locust ear.
Despite the careful considerations given at the time, the evidence may not
have been conclusive. Numerous valid cautionary statements were expressed in
the original work (Michelsen,
1971) and merit mention here. First and foremost was the
acknowledgement that the TM was assumed to behave as an ideal circular
membrane. It was then plainly recognised that "it is obvious that the
entire tympanum is very far from being homogeneous and that the thin part of
the membrane [...] is not circular"
(Michelsen, 1971
,
p. 80). Although good agreement
was obtained between the numerical values of the predicted resonance
frequencies and those measured by laser holography and a capacitance
electrode, resonance frequencies were observed to vary by 10-15%, depending on
the desiccation level of the isolated preparation. The data also provided
evidence that there is much uncertainty in the actual position of the nodes
and anti-nodes on the TM. It was repeatedly observed that: "the most
surprising deviation from theory is that the spatial position of the centre of
vibration is not constant"
(Michelsen, 1971
,
p. 80). The extent of, and
possible reasons for, discrepancy - and agreement - between Michelsen's
results and those of the present study will be more thoroughly presented in
the discussion.
Here, the vibration characteristics of the locust's tympanal system are
examined using intact, live animals, and with noninvasive methods. The sound
levels used to drive the tympanal system are of mild intensities, i.e. 60 dB
SPL (Sound Pressure Level, 0 db relative to 20 µPa) or about 12-18 dB above
neural thresholds, and are most unlikely to elicit non-linearities associated
with high-intensity stimuli. The remote sensing method used for vibration
measurement is microscanning laser Doppler vibrometry, a method allowing the
coherent and load-free measurement of the vibration velocities of the entire
surface area of the locust's TM, over a broad range of driving frequencies
(1-30 kHz) and small amplitudes (down to 10 pm)
(Robert and Lewin, 1998). This
study measures in spatio-temporal detail the vibrational deflections of the
locust's TM. Travelling waves are identified and their propagation paths are
described in three-dimensions for different stimulus frequencies. The temporal
and spatial characteristics of the waves are compared and discussed in
relation to previous works, including those on mammalian auditory systems.
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Materials and methods |
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Mechanical and acoustic measurements
Tympanal vibrations were examined in response to acoustic stimulation with
wideband (chirp) signals of frequency range 1-30 kHz. The vibrations were
analysed by simultaneous recording of the vibration velocity, U, of the
TM, and the SPL adjacent to the tympanum. U was measured using a
microscanning laser Doppler vibrometer (Polytec PSV-300-F; Waldbronn, Germany)
with an OFV-056 scanning head fitted with a close-up attachment. This allowed
the laser spot (5 µm diameter) to be positioned with an accuracy of
1 µm. Measurements across the entire TM could be taken without
readjusting the position of any component in the experiment. The laser spot
position was monitored via a live video feed to the vibrometer's
controlling computer. The surface area of the TM could thus be scanned with
high spatial accuracy, each scanning lattice comprising hundreds of
measurements points (Fig. 2C).
The laser vibrometer thus allowed accurate measurement of the topography of
tympanal motion in the amplitude, time and frequency domains, in a
contact-free way and without requiring the use of a reflective medium.
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The acoustic signals were generated by the PSV 300 internal data acquisition board (National Instruments PCI-4451; Austin, TX, USA), amplified (Sony Amplifier Model TAFE570; Tokyo, Japan) and passed to a loudspeaker (ESS AMT-1; ESS Laboratory Inc., Sacramento, CA, USA) positioned 300 mm from the animal. Thus, for the relevant frequency range (3-30 kHz), the animal was in the far-field of the sound source. SPL was measured using a 1/8 inch (3.2 mm) precision pressure microphone (Bruel & Kjaer, 4138; Nærum, Denmark) and preamplifier (Bruel & Kjaer, 2633). The microphone has a linear response in the measured frequency range. The microphone's sensitivity was calibrated using a Bruel & Kjaer sound level calibrator (4231, calibration at 1 kHz, 94 dB SPL). The microphone was positioned 10 mm from the tympanum, with its diaphragm parallel to the sound direction, thus maximizing the response. A calibrated stimulus sound level, at the tympanum, of 20 mPa (60 dB SPL) was used throughout these experiments. Computer correction of the stimulus acoustic signals ensured that their amplitude was kept to a constant level (60 dB SPL) across the complete range of frequencies (1-30 kHz). The incident sound spectrum, as measured by the reference microphone, was measured in signal voltage and inverted with respect to amplitude. The resulting voltage-frequency function was fed back to the waveform generator to create another, corrected spectrum to flatten the frequency composition of the stimulus at the position of the reference microphone (Fig. 3A).
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Evaluation of data
The analysis of the membrane velocity, U, and SPL was carried out by
the vibrometer's control PC. The signals were simultaneously sampled at 102.4
kHz. Sets of 25 data windows of 80 ms duration were acquired and averaged for
each point across the TM. Using an FFT (Fast Fourier Transform) with a
rectangular window, a frequency spectrum was produced for each signal with a
resolution of 12.5 Hz. The laser and microphone signals were then used to
calculate different quantities, such as gain and phase responses. By combining
the results from all the points scanned across the TM, oscillation profiles
and animations of tympanal deflections were generated for specific
frequencies. In this work we calculated the transfer function
(H1) of the membrane velocity U (ms-1)
to reference sound level SPL (Pa), to produce the amplitude gain and the phase
response of the system at different frequencies. Therefore,
![]() | (1) |
where, Gab(f) is the cross-spectrum of the
velocity signal and reference signal, and Gaa(f)
is the auto-spectrum of the reference signal. The magnitude-squared coherence
(C) between the vibrometer and microphone signals were also computed
for each data point to assess data quality for the entire data set, given by
![]() | (2) |
where, Gba(f) is the cross-spectrum of the reference signal and velocity signal, and Gbb(f) is the auto-spectrum of the velocity signal.
Data were considered of sufficient quality when coherence exceeded 85%. Typical coherence maps are shown in Fig. 2D, illustrating high data reliability over the entire extent of the tympanal surface area.
Characterisation of travelling waves - the criteria
Characterisation of travelling waves was carried out as part of the
analysis of the tympanum's vibrations. Unlike standing waves, such as the
vibrations of a violin string, travelling waves do not remain constant in
position but move with time, so that the vibrations vary with both distance,
x, and time, t. In the cochlea, this wave propagation
induces characteristic mechanical signatures into the mechanics of the basilar
membrane that are used here as operational criteria to characterize the
travelling waves in the locust ear. The three main response characteristics of
the basilar membrane introduced by the travelling wave are as follows
(von Békésy,
1960; Robles and Ruggero,
2001
).
Travelling waves can be both identified and characterized if the phase
responses at closely spaced locations are compared
(Robles and Ruggero, 2001).
The wavelength and velocity of the travelling wave is then calculated
according to the following equations
(Robles and Ruggero, 2001
):
![]() | (3) |
![]() | (4) |
![]() | (5) |
where f is wave frequency, is phase
difference between the two locations,
t is the travel time,
x is the distance travelled, Vwave is wave
velocity and Lwave is wavelength.
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Results |
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TM vibrations: LDV scans
The TM of the locust S. gregaria is completely accessible to
non-contact mechanical measurements by laser Doppler vibrometry. Hundreds of
measurement points were selected and repeatedly measured during controlled
acoustic stimulation (Fig. 2C).
The quality of each measurement point was evaluated by estimating the
magnitude-squared coherence (Equation 2; see Materials and methods) for
different frequency bands (Fig.
2D). Each single measurement point provides coherent (thus
reliable) amplitude and phase data on the mechanical response of the membrane
at that point. The mechanical response of the attachment point of the PV to
the TM (blue dot in Fig. 2B) was measured in response to broadband (1-30 kHz) iso-intensity stimulation and
evaluated as an amplitude frequency spectrum
(Fig. 3B). The amplitude
response, displayed as the response gain (Equation 1), shows a steady increase
across the frequency range. For higher frequencies, in the range from 10 to 30
kHz, the amplitude frequency spectrum indicates larger response fluctuations
in the mechanical response, an effect most probably related to some variation
in local diffractive acoustics around the locust's body
(Miller, 1977).
The entire TM of S. gregaria was scanned to determine its response
at a variety of frequencies. In Fig.
4, examples of scans of the entire membrane are presented. To ease
orientation, a video capture of the tympanum
(Fig. 4A, left panel) and of
the associated topographically calibrated scan data
(Fig. 4A, right panel) are
shown. The response gain of the membrane was evaluated for four different
frequencies, and shown for each frequency, at four different phase angles,
90° apart, in the cycle of that frequency. The scans reveal that, at each
of the different frequencies, travelling waves are generated on the TM. For
each frequency the tympanal deflections do not stay in position, but travel
across the tympanum from posterior to anterior (from left to right in
Fig. 4B), starting at the edge
of the thin membrane. At 3.3 kHz the wave travels across the thin membrane,
moving towards a focus point located at the folded body (see Movie 1 in
supplementary material). At 6.1 kHz the wave propagates across the thin
membrane along the same line as at 3.3 kHz, but dissipates (ends) at the
locations of the elevated process and styliform body. At 12.21 kHz and 22.76
kHz the wave takes a semi-concentric shape at the location of its initiation,
on the thin membrane. As the wave travels across the tympanum
(Fig. 4B, see 22.76 kHz, phase
angles 90°, 180°, 270°, and see Movie 2 in supplementary material)
the advancing wave front converges towards a single point, creating a focal
point of vibration. This location corresponds to the point of attachment of
the PV to the TM. The focusing of the travelling waves to different attachment
sites of the mechanoreceptors at different frequencies corresponds to those of
previous mechanical and physiological studies
(Michelsen, 1971;
Jacobs et al., 1999
).
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Interestingly, the propagation of the travelling wave does not depend on the angle of incidence of sound impinging on the TM. Irrespective of the angle of stimulation (i.e. the relative angle between loudspeaker and tympanum), the waves always propagated in one direction (from the thin membrane to the thick membrane), converging on identified mechanoreceptive attachment sites (data not shown).
The characterisation of travelling waves
The mechanical deflection shapes observed on the locust TM present the
three key characteristics of cochlear travelling waves.
Criterion 1: the phase response across the locust's TM shows an increasing phase lag as a function of stimulus frequency (Fig. 5). This phase lag is substantial, exceeding the phase lag expected for the velocity response of a simple resonator (maximum of -90° at frequencies above resonance). Lag increases as a function of frequency; at higher frequencies, such as 30 kHz, the phase lag reaches nearly 900° (2.5 cycles).
|
Criterion 2: the magnitudes of TM displacement show an asymmetric envelope around the point of the maximal deflection. This point is also the location where the wave is seen to compress, before dying off. Wave asymmetry was evaluated as the response gain (U/SPL) along a transect line across the membrane (Fig. 6A) for five different frequencies (Fig. 6B-F). The envelope of the wave in motion across the tympanum becomes apparent when the response is displayed for every 10° of phase. As expected, the envelope of the travelling wave varies with the driving frequency. At 3.3 kHz (Fig. 6B) the wave is asymmetrical about a point 1.2 to 1.4 mmalong the transect. This location coincides with the insertion point (the elevated process) of low frequency mechanoreceptors. At 6.05 kHz (Fig. 6C), the wave is asymmetrical about a point 0.8 to 1.0 mm along the transect. Maximal deflection does not directly correspond to mechanoreceptor location, which, in this case, is not completely aligned with the chosen transect. At 12.1 kHz (Fig. 6D), the wave is sharply asymmetrical about a point 0.9-1.0 mm along the transect. The location of maximal amplitude corresponds to the insertion point of the PV to the TM. Direct comparison with the deflection envelope at lower frequencies (eg. Fig. 6B,C) shows that higher frequencies do not elicit motion past 1.1-1.2 mm along the transect. Notably, past the point of maximal deflection (0.9-1.0 mm along the transect, Fig. 6D) the slope of the envelope is very steep, resulting in little motion of the thick part of the membrane, the part to which low frequency receptors attach. The energy of the wave is thus maximally focussed, in a frequency specific manner, to the relevant mechanoreceptors. At both 22.6 kHz (Fig. 6E) and 26 kHz (Fig. 6F) the wave is sharply asymmetrical 1.0 mmalong the transect. For both frequencies, the location of maximal deflection corresponds with the position of high frequency mechanoreceptors. Notably, these high frequency travelling waves have shorter wavelength and thus undergo several cycles along the span of the membrane they propagate across. Again, nearly all of the membrane motion elicited by the wave is focussed at the 1 mm location, with very little motion of the thick membrane (past 1.1 mm along the transect). Thus, the energy of the travelling wave is compressed into the maximal displacement at the PV, and efficiently dissipated there, resulting in no further propagation of the high frequency wave to other mechanosensory connection sites (thick membrane).
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Criterion 3: Travelling waves result from the mechanical properties of the wave propagating substrate (mass, stiffness, damping). In that sense they are not related to the physiological mechanisms linked to the process of mechanoreception and transduction. In locusts, scanning measurements indicate that the pattern of the travelling waves in dead animals (Fig. 7) is not distinguishable from that of live specimens (Fig. 4B). This is true for both lower frequencies (6.1 kHz; Fig. 7) and higher frequencies (16.24 kHz; Fig. 7).
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The travelling wave's length and propagation velocity
The wavelengths and wave velocities for the locust's TM were calculated
using Equations 3, 4 and 5. Wavelengths and wave velocities are reported in
Fig. 8, along with results for
cochlear sites in several mammalian species. In the locust, for example, it
was found that for 60 dB SPL stimulus at 12.21 kHz, the phase shift calculated
over a transect length of 1.1 mm amounts to 1.33 periods. This results in an
average wavelength of 0.82 mm (S.D.=±5
x10-5, N=10) and an average wave velocity of 9.99
ms-1 (S.D.=±1.11, N=10). Wave
velocity in the locust is somewhat higher at lower (<10 kHz) than at higher
frequencies (up to 30 kHz). In effect, wave velocity ranges from 9.6 to 15.9
ms-1, values that are in the same order of magnitude as those of
mammalian species (Fig. 8). In
the locust's low frequency range, length of the travelling wave is relatively
long, displaying a top value around 5 mm, exceeding all those reported for
mammalian species (Fig. 8). At
higher frequencies, wavelengths in the order of 1 mm were measured, a length
similar to that of mammals for that frequency range.
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Travelling waves in Locusta migratoria
Tympanal vibrations were also investigated in L. migratoria using
the same experimental procedure as for S. gregaria. In L.
migratoria, a flap of cuticle partly obscures the anterior aspect of the
TM. This flap was not removed to respect the protocol of intact, non-invasive
measurements. The deflection shapes from the TMs of both locust species
display the propagation of a travelling wave
(Fig. 9). For L.
migratoria, the 3.4 kHz wave travels across the thin membrane, as seen
for S. gregaria, before disappearing out of view behind the cuticle
flap. It is presumed that the wave progresses to the area of the folded body,
the site of low frequency reception. At 6.1 kHz, the wave crosses the thin
membrane in a way identical to that described before
(Fig. 4) and can be seen
dissipating at the location of the elevated process and styliform body
(Fig. 9). At 12.6 kHz and 22.64
kHz the wave appears semi-concentric again, and as with S. gregaria,
converging as it propagates towards the PV. In this case, the average
wavelength and wave velocity at a frequency of 22.64 kHz were found to be 0.67
mm (S.D.=±1.4 x10-4,
N=5), and 15.15 ms-1
(S.D.=±3.19, N=5), respectively. The
values are similar to those found in S. gregaria.
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Discussion |
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The findings of the present study concur with those of the 1971 study on
several aspects of tympanal mechanics, but not, crucially, on the mechanical
basis of frequency discrimination in the locust. Our observations on tympanal
structures corroborate point 1 listed above. The distribution of maximal
tympanal deflections across different areas of TM is also observed, and
generally is in accord with point 2 above. Addressing point 3, our study fails
to confirm Michelsen's report of the presence of nodal lines (figs 13-15 in
Michelsen, 1971) in the
mechanical deflections of the TM. Importantly, the presence of nodal lines is
characteristic to standing waves and constituted the basis for identifying
modes of deflection using drum theory. These modes were then used to attribute
phase relationships to distinct tympanal areas and compare them with data
gathered with a capacitance electrode. Frequency-specific locations of large
deflection were then described, and said to coincide with tympanal locations.
Incidentally, Michelsen also observed that the location of maximal deflection
(the centre of vibration) on the thin membrane moved across the drum surface
area (Michelsen, 1971
, p. 80). In the logic of drum
theory, the centre of vibration ought not to wander. This observation seems to
coincide with the phenomenology of the travelling wave reported here.
Supporting the general message of point 4, the present study shows that
different tympanal areas undergo different vibrational regimes, but through a
mechanical process that is not related to drum resonance.
Several issues related to methodology may explain the similarities and the
discrepancies between the results of Michelsen's study and the present one. In
the 1971 study, the locust's auditory mechanics was investigated using two
different measurement techniques; laser holography and a capacitance
electrode. Fundamentally, the complete characterisation of the mechanical
response of a vibrating object requires characterisation of three basic
variables: the location of vibration, its amplitude, and its time course. It
was plainly recognised then that each technique has its pros and cons: laser
holography provided information on two variables, the static topography of
membrane deflections and their relative amplitudes. Crucially, laser
holography did not provide phase information
(Michelsen, 1971, p. 70). The capacitance electrode
method, in turn, provided some topographical information and quite accurate
time domain information, but yielded unreliable amplitude data
(Michelsen, 1971
,
p. 70). These methodological
shortcomings constrained data interpretation, requiring theoretical support to
make sense of the observed mechanical behaviour. Of the two theories available
at the time, the resonance theory and the travelling wave theory, the former
was favoured to provide the background against which to evaluate the data
(Michelsen, 1971
, p. 64). The travelling wave
theory (von Békésy, 1969) was mentioned but not considered as an
alternative explanation.
Tympanal deflections measured by laser holography were interpreted using
the motions theoretically expected from drum resonances. It was assumed that
the TM would behave like a circular homogenous drum, although it was
recognised at the time that the membrane was neither circular nor homogeneous
(Michelsen, 1971,
p. 66). Different modes of drum
resonance with central symmetry were used to explain the observed concentric
rings of amplitude maxima and minima (figs 13-15 in
Michelsen, 1971
). Laser
holography has limited sensitivity, dynamic range and temporal resolution. In
effect, that technique produced static contour images of high amplitude
tympanal deflections. Thus the data did not contain information of membrane
motion over the entire deflection cycle resulting from incident acoustic
energy. What were interpreted as the transitions between antinodes and nodal
lines can now be regarded as the crests of converging travelling waves. As
expected, high frequency (12 kHz and above,
Fig. 6B,C) stimulation
generates several travelling wave peaks across the tympanum, while low
frequencies do not (Fig. 6E,F).
Variation of multiple peaks was observed, although in a static manner, in the
former study (fig. 15 in Michelsen,
1971
).
Another possible source of uncertainty may lie in the intensity of the
acoustic stimuli used. The acoustic stimuli used to drive the tympanal system
were delivered at high sound pressure levels (96-112 dB SPL), a necessity
imposed by the relative insensitivity of the techniques. The use of high SPL
raises the possibility that the tympanal system may have been driven in the
non-linear range of its mechanical response. The system was deemed to obey
Hooke's law over a narrow range of amplitudes (50-100 µm)
(Michelsen, 1971, p. 72), and there is no
indication of Young's modulus in the sub-micrometre range (fig. 7 in
Michelsen, 1971
). This point
may bear some importance since measurements at biologically relevant sound
pressure levels (60 dB SPL) yield membrane motions on different membrane
locations with amplitudes between 1 and 10 nanometres. Motions at this length
scale have also been reported in previous studies on insect hearing organs
(Göpfert and Robert,
2000
). On a linear scale, the observed displacement amplitudes are
smaller by three to four orders of magnitude (60-80 dB), leaving the
possibility open that the modes of tympanal motion differ between moderate (60
dB SPL) and high (104 dB SPL) sound pressure levels.
Two other investigations have described the mechanical vibrations of the
locust tympanum in terms of resonances with different modes
(Stephen and Bennet-Clark,
1982; Breckow and Sippel,
1985
). Although capable of greater sensitivity, the methods used
then, e.g. stroboscopy, still provided a relatively poor sensitivity (1 µm)
(Breckow and Sippel, 1985
). The
acoustic stimulation required for reliable measurements was also at very high
sound pressure levels (100-112 dB SPL). An analysis of the mass and thickness
distribution of the TM was undertaken by Stephen and Bennet-Clark
(1982
), in a study that
established that important mechanical interactions take place between the
tympanal mechanics and Müller's organ. As in other studies, the tympanal
system had to be removed from the animal, and the surrounding cuticle was
sometimes removed to gain access to the tympanum (depending on species). At
this time it was again assumed that the tympanal system would behave linearly
up to such sound pressures, and thus mechanical displacements at mid-range
sound levels (60 dB SPL) were extrapolated. Most recently, Jacobs et al.
(1999
) directly correlated the
soma position, the attachment site of the dendrite and the physiologies of
individual mechanosensory neurons using intracellular recordings and
neuroanatomical evidence from cell-specific neurobiotin staining. Using S.
gregaria, this work established a solid link between neural sensitivity
and mechanoreceptor topography for three distinct groups of cell: cells
attached to the folded body with responses ranging from 400 to 700 Hz and from
1.5 to 2 kHz, cells attached to the PV with responses from 12 to 25 kHz, and a
combination of cells attached to either the elevated process or to the
styliform body with responses from 3 to 4 kHz.
It was pointed out earlier that frequency selectivity in locusts seems to
rely primarily on the mechanical processing of incoming sound waves
(Michelsen, 1971). The present
study finds no evidence of change in the shape and propagation of the
travelling waves in living and post-mortem animals, pointing only to the
sufficiency of the passive mechanical process to generate topographic
separation of sound frequencies (Fig.
7). It would, however, be premature to conclude that frequency
selectivity is solely brought about by passive mechanical processing in the
locust ear. An earlier study has indeed reported the presence of acoustic
distortion products in the locust
(Kössl and Boyan, 1998
),
pointing to the possibility of active auditory mechanics in insects, as shown
for mosquitoes and fruit flies
(Göpfert and Robert, 2001
;
Göpfert and Robert, 2003
).
Further studies are required to investigate low-level non-linear mechanics in
an insect tympanal ear (J.F.C.W. et al., in preparation).
The comparison between the locust tympanal travelling wave and that of
different mammalian species highlights interesting similarities
(Fig. 8). Although the
geometries and length scales of the two types of auditory systems vastly
differ, wave velocities and lengths are similar. For all mammalian species
considered, wave velocity tends to increase with the frequency of acoustic
stimulation. Velocities can vary, possibly linearly, from 1 ms-1
(Chinchilla) to 28 ms-1 (Guinea pig). In humans, for example, wave
velocity increases quite rapidly from 1 to 5 kHz (data from
Serbetcioglu and Parker,
1999). Interestingly, at around 4-5 kHz, wave velocities are very
similar for humans and locusts (Fig.
8). A steep increase in wave velocity implies a broader
topographic spread of sound frequencies along the cochlea, reflecting the
exquisite capacity of frequency discrimination in humans
(Rhode and Recio, 2000
). By
comparison to other species, wave velocity in the locust remains relatively
constant over the frequency range representative of the thin part of the
tympanum (>10 kHz), but displays higher values for lower frequencies (3-4
kHz). This variation arises because the wave's travel time is a ratio between
frequency and phase change (Equation 3). For higher frequencies, as frequency
increases, so does the phase difference, whereas at lower frequencies, the
phase difference is relatively small (Fig.
5). Therefore for the high range of frequencies the travel time is
invariable, but for the low frequency range the travel time changes. In the
locust's case both the higher and lower frequencies are measured over a
constant distance from membrane edge to PV (higher frequencies) or thick
membrane (lower frequencies). Therefore, for higher frequencies the wave's
velocity (Equation 4) remains approximately constant, but for lower
frequencies it varies as a function of frequency. For the Guinea pig, for
instance, phase change appears to be an order of magnitude lower than the
frequency change and the analysis of high frequencies is performed over
several millimetres of basilar membrane, resulting in a relative increase of
wave velocity with frequency. A similar argument can be made for variation in
the length of the travelling wave. In the locust, the wavelength is long at
lower frequencies because it is a ratio between travel distance and phase
change (Equation 5). At lower frequencies, the phase change is small over the
distance considered, thus yielding a long wavelength. For higher frequencies,
the phase change increases while the distance of travel remains constant.
Thus, the wavelength decreases, producing the wave compression effect seen in
Fig. 6.
While the locust's TM shows some functional similarity to the basilar
membrane of the mammalian cochlea, it clearly differs in many respects. The
main functional difference is the way that the locust membrane compresses a
large range of frequencies into a short spatial dimension. On the basilar
membrane, a continuous gradient of stiffness contributes to the arising of
travelling waves, spreading the amplitude maxima along its length and thus
spreading the different frequency components along a series of distinct
topographical locations. For the locust, a more abrupt change in stiffness can
be expected that presumably contributes to generating possibly only two types
of travelling waves. Such dichotomy is reflected at another level of analysis,
that of the locust's sensory ecology. The locust's auditory world seems to be
split in two major categorical units comprising low and high frequency sounds.
As in field crickets (Wyttenbach et al.,
1996), the frequency parameter space in locusts seems to be
divided in two logical categories, that of intra-specific communication and
that of predator detection (Robert,
1989
).
The locust's solution to the problem of mechanical and neural frequency analysis, as revealed by the present study, seems economical and elegant. A single morphological structure - the tympanal membrane - carries out both the functions of sound reception and frequency discrimination; converting acoustic energy into mechanical energy, and channelling the energy of specific frequencies to distinct neuron attachment locations.
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Acknowledgments |
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Footnotes |
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![]() |
References |
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![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Autrum, H. (1941) Ueber Gehörund
Erschütterungssinn bei Locustiden. Z. Vergl.
Physiol. 28,580
-637. Breckow, J. and Sippel, M. (1985). Mechanics of
the transduction of sound in the tympanal organ of adults and larvae of
locusts. J. Comp. Physiol. A
157,619
-629. Cooper, N. P. and Rhode, W. S. (1992). Basilar
membrane mechanics in the hook region of cat and guinea-pig cochleae: sharp
tuning and nonlinearity in the absence of baseline position shifts.
Hear. Res. 63,163
-190. Cooper, N. P. and Rhode, W. S. (1996). Fast
travelling waves, slow travelling waves and their interactions in experimental
studies of apical cochlear mechanics. Auditory
Neurosci. 2,289
-299. Göpfert, M. C. and Robert, D. (2000).
Nanometre-range acoustic sensitivity in male and female mosquitoes.
Proc. R. Soc. Lond. B. Biol. Sci.
267,453
-457. Göpfert, M. C. and Robert, D. (2001).
Active auditory mechanics in mosquitoes. Proc. R. Soc. Lond. B.
Biol. Sci. 268,333
-339. Göpfert, M. C. and Robert, D. (2003).
Motion generation by Drosophila mechanosensory neurons.
Proc. Natl. Acad. Sci. USA
100,5514
-5519. Gray, E. G. (1960). The fine structure of the
insect ear. Philos. Trans. R. Soc. Lond. B. Biol. Sci.
243, 75-94. Horridge, G. A. (1960). Pitch discrimination in
Orthoptera (Insecta) demonstrated by responses of central auditory neurones.
Nature 185,623
-624. Jacobs, K., Otte, B. and Lakes-Harlan, R.
(1999). Tympanal receptor cells of Schistocerca
gregaria: Correlation of soma positions and dendrite attachment sites,
central projections and physiologies. J. Exp. Zool. A
283,270
-285. Kohllöffel, L. U. E. (1972). A study of
basilar membrane vibrations. II. The vibratory amplitude and phase pattern
along the basilar membrane (postmortem). Acoustica
27, 66-81. Kössl, M. and Boyan, G. S. (1998).
Acoustic distortion products from the ear of a grasshopper. J.
Acoust. Soc. Am. 104,326
-335. Michelsen, A. (1968). Frequency discrimination
in the locust ear by means of four groups of receptor cells.
Nature 220,585
-586. Michelsen, A. (1971). The physiology of the
locust ear. I. Frequency sensitivity of single cells in the isolated ear, II.
Frequency discrimination based upon resonances in the tympanum, and III.
Acoustical properties of the intact ear. Z. Vergl.
Physiologie 71,49
-128. Miller, L. A. (1977). Directional hearing in
locust Schistocerca gregaria Forskal (Acrididae, Orthoptera).
J. Comp. Physiol. 119,85
-98. Narayan, S. S. and Ruggero, M. A. (2000).
Basilar-membrane mechanics at the hook region of the chinchilla cochlea. In
Recent Developments in Auditory Mechanics (ed. H.
Wada, T. Koike, T. Takasaka, K. Ikeda and K. Ohyama), pp.95
-101. Singapore: World Scientific. Nobili, R., Mammano, F. and Ashmore, J. (1998).
How well do we understand the cochlea? Trends
Neurosci. 21,159
-167. Olson, E. S. (1999). Direct measurement of
intra-cochlear pressure waves. Nature
402,526
-529. Olson, E. S. and Mountain, D. C. (1991). In
vivo measurement of basilar-membrane stiffness. J. Acoust.
Soc. Am. 89,1262
-1275. Ren, T. (2002). Longitudinal pattern of basilar
membrane vibration in the sensitive cochlea. Proc. Natl. Acad. Sci.
USA 99,17101
-17106. Rhode, W. S. (1971). Observations of the
vibration of the basilar membrane in squirrel monkeys using the Mössbauer
technique. J. Acoust. Soc. Am.
49,1218
-1231. Rhode, W. S. and Recio, A. (2000). Study of
mechanical motions in the basal region of the chinchilla cochlea.
J. Acoust. Soc. Am. 107,3317
-3332. Robert, D. (1989). The auditory behavior of
flying locusts. J. Exp. Biol.
147,279
-301. Robert, D. and Lewin, A. (1998). Microscanning
laser vibrometry applied to the biomechanical study of small auditory systems.
Proc. Int. Soc. Opt. Eng.
3411,564
-571. Robles, L. and Ruggero, M. A. (2001). Mechanics
of the mammalian cochlea. Physiol. Rev.
81,1305
-1352. Römer, H. (1976). Processing of
information by tympanal receptors of Locusta migratoria (Acrididae,
Orthoptera). J. Comp. Physiol.
109,101
-122. Russell, I. J. and Nilsen, K. E. (1997). The
location of the cochlear amplifier: Spatial representation of a single tone on
the guinea pig basilar membrane. Proc. Natl. Acad. Sci.
USA 94,2660
-2664. Schwabe, J. (1906). Beiträge zur
Morphologie und Histologie der tympanalen Sinnesapparate der Orthopteren.
Zoologica 20,1
-154. Serbetcioglu, M. B. and Parker, D. J. (1999).
Measures of cochlear travelling wave delay in humans: I. comparison of three
techniques in subjects with normal hearing. Acta
Otolaryngol 119,537
-543. Stephen, R. O. and Bennet-Clark, C. (1982). The
anatomical and mechanical basis of stimulation and frequency analysis in the
locust ear. J. Exp. Biol.
99,279
-314. von Békésy, G. (1960).
Experiments in Hearing. New York:
McGraw-Hill. Wyttenbach R. A., May, M. L. and Hoy, R. R.
(1996). Categorical perception of sound frequency by crickets.
Science 273,1542
-1544.