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DC injection alters spontaneous otoacoustic emission frequency in the frog
Heanng Elsevier
199
Research, 41 (1989) 199-204
HEARES
01258
DC injection
alters spontaneous
otoacoustic
emission frequency
in the frog
H.P. Wit, P. van Dijk and J.M. Segenhout Institute of Audiology, (Received
Universiv
Hospital,
17 February
Groningen, The Neiherlands
1989; accepted
23 May 1989)
A permanent wire electrode was implanted in the inner ear of the green frog (Ram esculenta). Through this electrode direct current was delivered to the inner ear fluid of the frog, during recording of a spontaneous otoacoustic emission (SOAE). Both SOAE frequency and amplitude turned out to depend on DC level and polarity. Possible explanations for the observed phenomena are given, based on a dissipative limit-cycle oscillator model for SOAE generation, and the assumption that SOAE frequency depends on hair cell ion channel inductance. Otoacoustic
emission;
Hair cell: Frog;
Limit-cycle
oscillator;
Direct
Introduction Spontaneous otoacoustic emissions (SOAEs) most problably have their source(s) inside the inner ear. Results of experiments in which an SOAE is suppressed by a strong externally supplied tone are direct support for this statement (Kemp, 1979; Wilson, 1980; Wit et al., 1981; Sloth and Zwicker, 1983; Ziss and Glattke, 1988). Tuning curves obtained in these experiments show that the generator of the otoacoustic emission is at a location where incoming sound turns out to be sharply bandpass filtered. Theoretically the suppression results are satisfactory described by a model in which a self-sustained oscillator is coupled to a one-dimensional cochlear model (Tubis et al., 1989). Further support for an inner ear origin of SOAEs is given by the recording of an electrical correlate of an SOAE from the inner ear fluids of the frog (Wit et al., 1989). That SOAEs are indeed generated by self-sustained oscillators can be derived from measured sound pressure distributions (Bialek and Wit, 1984;
H.P. Wit, Institute of Audiology, University Hospital, 30.001, 9700 RB Groningen, The Netherlands. 0378-5955/89/$03.50
Postbox
0 1989 Elsevier Science Publishers
B.V.
current
Van Dijk and Wit, 1987): a filtered emission signal shows the behaviour of a process that tends to stay away from zero amplitude. (If the emission signal were filtered noise, the sound pressure distribution would have a maximum at zero amplitude, instead of the observed minimum.) Furthermore entrainment (Long et al., 1988) or phase-lock (Bialek and Wit, 1984; Wit 1986; Van Dijk and Wit, 1988) of SOAEs by an externally supplied tone are wellknown properties of self-sustained oscillators. So, experimental results indicate that SOAEs are generated by self-sustained oscillators inside the inner ear. Good candidates for these oscillators are the sensory cells, especially since it has been shown that haircells can have a motor function. (Brownell et al, 1985; Zenner, 1986; Ashmore, 1987). This motor function is thought to play a role in the feedback loop that sharpens frequency selectivity of the inner ear. (For a recent review see: Dallos, 1988) If positive feedback becomes too large the system starts to oscillate and this may produce SOAEs (Gold, 1948). In the mammalian organ of Corti outer haircells have the properties to fullfil a motorfunction task, and in models in which positive feedback is incorporated this motor function drives inner hair cells (Zwicker, 1979; Neely, 1988). Inner haircells
are supposed to be involved in forward transduction only. In this respect the discovery of SOAEs from frog ears (Palmer and Wilson, 1981) may be of importance. Frogs have rather primitive hearing organs with only type II haircells, that have the characteristics of mammalian outer haircells (Lewis et al., 1985). SOAEs from frogs have properties similar to those of human SOAEs; the only observed difference is a smaller frequency stability (broader spectral peaks) for frog SOAEs (Van Dijk and Wit, 1987). Some years ago it was discovered by W~tehead et al. (1986) that body temperature has a strong influence on SOAE frequency in frogs. And recently we discovered that also DC injection into the inner ear of the frog has a strong influence on SOAE frequency. These findings have consequences for models of the inner ear transduction process in which positive feedback is incorporated. In this paper we give results for DC injection in the green frog (Rana esculentu) and try: to give an explanation for these results based on known properties of frog haircells. Mater&
Direct current was supplied to the inner ear fluids through the implanted electrode and a skin needle electrode. Current was delivered by a battery powered home built constant current source and measured with a moving coil meter integrated in the instrument. SOAEs were recorded on videotape after pulse code modulation for different current values (both positive and negative; current was said to be positive if the inner ear electrode was positive with respect to the skin electrode). SOAE signals were monitored during recording and analyzed off-line with a PAR/U~gon type 4512 real-time FFT spectrum analyzer. Results The results presented in this paper are part of the results of an investigation of the properties of t
I
I
I
I
-
-----k-
and Methods
Experiments were performed in 4 green frogs (Rana esculenta). Under anaesthesia with MS 222 a small hole was pierced in the upper part of the skull, about halfway between the tympanic membrane and the skull midline. A 0.3 mm diameter platinum wire with teflon coating (removed at the tip) was fixed into this hole with dental cement. The electrode tip contacted the outside of the membraneous inner ear encapsulation; close to the utricle. After this preparation the frog had an antenna-like electrode protruding from the skin over a few m&meters length. With such a permanent electrode the frog lived among other frogs in a terrarium and could be used for several experiments. During an experiment the frog was again lightly anaesthetized with MS 222. SOARS were measured with a sensitive condenser microphone (Wit et al., 1981), acoustically coupled to the tympanic membrane with 1 cm of PVC tubing. Measurements were performed inside a soundproof box.
I
B __(
-20
L I
0.6
I
I
0.8 frequency
-
I
40
I
1.0
1 1.2
( kHz )
Fig. 1. Frequency spectra of a spontaneous otoacoustic emission from a frog for different values of injected direct cuTrent (expressed in PA, current is positive if the inner ear electrode is positive with respect to the skin reference electrode).
201
--L--
-80
-40
direct Fig. 2. Frequency function of direct
80
cu;rent (:A)
of spontaneous otoacoustic emission as a current through the inner ear. Results are given for 4 frogs.
the electrical correlate of spontaneous otoacoustic emissions in frogs (Wit et al, 1989). All frogs in which an electrode was implanted had one relatively strong SOAE with a frequency between 1.0 and 1.2 kHz. Fig. 1 shows for one frog that DC alters both amplitude and frequency of this SOAE. For sufficiently strong positive current the emission could even be made to disappear. As far as this could be judged from the FFT analyzer display, SOAE frequency and amplitude followed a current change instantaneously. Fig. 2 gives SOAE frequency for different current values for all 4 frogs. The average slope of the curves in this figure is approximately 2 HZ/PA. Discussion Positive current through the inner ear of the frog causes a decrease of SOAE amplitude (fig. 1). The same effect can be observed when body temperature of the frog is lowered (Van Dijk and Wit, 1987). In terms of a Van der Pol-oscillator model for SOAE generation this means that the positive feedback force decreases and/or that the damping force and the negative feedback force increase (see Appendix). The best explanation for the observed amplitude decrease is a reduction of the positive feedback force. The power supplied to the oscillator by the feedback force may even become too small to compensate for the losses in the resistive
elements of the oscillator, which results in complete extinction of the oscillation. (This situation occurs if the feedback force parameter becomes smaller than the damping constant; see Appendix). How positive current or temperature decrease can reduce the positive feedback force remains obscure until more is known about the actual feedback mechanism. Also not known yet are the elements that determine frequency of a frog SOAE. In a mechanical model these elements would be mass and stiffness. It is unlikely that current or temperature will influence mass. So the observed frequency changes through DC injection (fig. 2) or change of body temperature (Van Dijk and Wit, 1987) have to be explained by a stiffness change. This stiffness change has to be large, and it is not known whether there are inner ear structures that exhibit the necessary large stiffness change. Very speculative is the thought that tectorial structures might change their stiffness, as has been observed for gels if temperature or ion concentration is changed (Tanaka, 1981). In a mechano-electrical model for SOAE generation (Weiss, 1982) the frequency determining elements could also be in the electrical domain. (The model cannot be purely electrical; it has to have a mechanical part, because SOAEs are mechanical oscillations). Support for such a type of model comes from the observation in the frog of an electrical counterpart of SOAEs (Wit et al., 1989). Electrical resonances can be evoked in haircells of the amphibian papilla of the frog (Pitchford and Ashmore, 1987). If haircells are the generators of SOAEs (for which no direct proof has been given yet), then recently constructed models for electrical tuning of haircells (Crawford and Fettiplace, 1981; Ashmore and Attwell, 1985; Lewis and Hudspeth, 1989) are of help to explain changes of frog SOAE frequency. In these models tuning frequency for a hair cell is determined by cell membrane capacity and ion channel inductance. The inductive behaviour of an ion channel is caused by the fact that ion current through the channel is time delayed with respect to a voltage change across the channel. Hair cell resonances can be reproduced by a model that incorporates two active conductances: a voltage activated Ca2+ conductance and a Ca2+
activated K’ conductance (Lewis and Hudspeth, 1989). The SOAE frequency change introduced by current injection into the inner ear, as we observe it (fig. 2), may be caused by a change of the properties of these actived conductances. In current-clamped haircells from the amphibian papilla of the bullfrog Roberts et al. (1986) found that the resonant frequencies of the cells increased monotonically with the amplitude of the depolarizing pulse. The only parameter that could explain these results to some extend was the time constant for the onset of potassium current after a voltage step. So it might be that current injection into the inner ear of the frog changes in some way the time constants of ionic channels, which in turn would lead to a change in resonance frequency. If SOAEs are produced by hair cells this would then also lead to a change of SOAE frequency. In a model for electrical tuning in hair-cells Ashmore and Attwell (1985) show that a voltage gated current alone cannot account for the high Q values of the resonance behaviour of the cells, but that a calcium gated current could account for the observed sharp tuning. In this model different resonance frequencies for cells at different locations in the inner ear sensory epithelium can best be explained by a different number of calcium pumps in the cell membrane, leading to a different pump rate for different cells. For individual cells. with a fixed number of calcium pumps, pump rate will change if parameters that determine pump rate are changed. For a higher resonance frequency a higher pump rate is needed. Ion pumps are medium- to large sized membrane spanning proteins. They may be considered as channels that go through a cycle of conformational transitions, during which an ion is taken up from one side, is temporary trapped inside the protein, and is released to the other side. The calcium pump is such a type of pump, driven by ATP-ase (Haynes and Maudveno, 1987). The pump rate of ATP-driven ion pumps depends on temperature and membrane voltage (Lauger, 1987). So if direct current injection into the inner ear of the frog would change hair cell membrane voltage, a mechanism to explain change of ion channel time constant (leading to an inductance change) has been found. The temperature dependence of Ca transport in
human red cells was studied by Lee and Shin (1969) and by Schatzmann and Vincenzi (1969). From the numbers given by the authors an activation energy of approximately 20 kcal/mole for active calcium transport by CaZ’ activated ATPase in human red cells can be derived (Sehatzmann, 1975). For an Arrhenius temperature dependence of pump rate this number yields a 12% increase of pump rate per Kelvin (of centigrade). In the model by Ashmore and Attwell (1985) hair cell resonance frequency is proportional to the square root of Ca pump rate. So a 6% increase of resonance frequency per degree would be predicted. It is interesting to note that temperature effects of this magnitude have been reported for the frequency of voltage ringing in hair cells isolated from the chick cochlea (Fuchs et al.. 1988). A 6% increase per degree corresponds well with the highest value found for the temperature dependence of frog SOAEs: 50 Hz/centigrade at 7 kHz (Whitehead et al., 1986; Van Dijk and Wit, 1987). Direct current injection and temperature both influence SOAE amplitude as well as SOAE frequency. With current injection an amplitude decrease is accompanied by a frequency increase (Figs. 1 and 2). Lowering of body temperature, however, causes a frequency decrease, together with an amplitude decrease (Van Dijk and Wit, 1987). This means that the mechanism that controls SOAE frequency is different from the mechanism that controls its amplitude. Acknowledgements
We thank Ms. Willy Kanis for typing the manuscript. This study was supported by the Heinsius Houbolt Fund and the Netherlands Organization for the Advancement of Research (NWO). Appendix
Consider a mechanical system of mass m on a spring with stiffness K. The differential equation for the displacement x(t) of the mass is: mX+
[y+X(X)]i+KX=o
(1)
203
yi is the damping force and A( force (Bialek and Wit, 1984). For h(x)=
-_,+X,x’
the system tion:
and
is a feedback
Xi>y
is a Van der Pol oscillator
with equa-
To this oscillator energy is supplied for small values of x, while power is dissipated for large x. The result is a limit-cycle oscillation. In order to calculate the amplitude of this oscillator, we start from the mathematical form of the differential equation for a Van der Pol oscillator:
i’+a(z2-
+ cd;z= 0
l)i
with amplitude a = 2 (Hanggi 1982). Substitution of
d
z=x
(4) and
Riseborough,
x2
&-u
A, -Y
Ly=-
m
2,L
w”
m
in eq. (4) gives eq. (3) after some calculation. So, the (physical) Van der Pol oscillator has an amplitude
A=2
A, -
J x
Y
2
References Ashmore, J.F. (1987) A fast motile response in guinea-pig outer hair cells: the cellular basis of the cochlear amplifier. J. Physiol. 388, 323-347. Ashmore, J.F. and Attwell, D. (1985) Models for electrical tuning in hair cells. Proc. R. Sot. Lond. B 226, 325-344. Bialek, W.S. and Wit, H.P. (1984) Quantum limits to oscillator stability: theory and experiments on acoustic emissions from the human ear. Phys. Lett. 104A, 173-178.
Brownell, W.E., Bader, CR., Bertrand, D. and De Ribaupierre, Y. (1985) Evoked mechanical responses of isolated cochlear outer hair cells, Science 227, 194-196. Crawford, A.C. and Fettiplace, R. (1981) An electrical tuning mechanism in turtle hair cells. J. Physiol. 312, 377-412. Dallos, P. (1988) Cochlear neurobiology: some key experiments and concepts of the past two decades. In: G.M. Edelman, W.E. Gall and W.M. Cowan (Eds.) Auditory function; neurobiological Bases of Hearing. John Wiley, New York, pp. 153-188. Fuchs, P.A., Nagai, T. and Evans, M.G. (1988) Electrical tuning in hair cells isolated from the chick cochlea. J. Neurosci. 8, 2460-2467. Gold, T. (1948) Hearing II. The physical basis of the action of the cochlea. Proc. R. Sot. B. 135, 492-498. Hanggi, P. and Riseborough, P. (1983) Dynamics of nonlinear dissipative oscillators. Am. J. Phys. 51, 347-352. Haynes, D.H. and Maudveno, A. (1987) Computer modeling of Ca*+ pump function of Ca2+-Mg*+ ATPase of sarcoplasmic reticulum. Physiol. Rev. 67, 244281. Kemp, D.T. (1979) Evidence of mechanical nonlinearity and frequency selective wave amplification in the cochlea.Arch. Otorhinolaryngol. 224, 37-45. Lauger, P. (1987) Dynamics of ion transport systems in membranes. Physiol. Rev. 67, 1296-1331. Lee, K.S. and Shin, B.C. (1969) Studies on the active transport of calcium in human red cells. J. Gen. Physiol. 54, 713-728. Lewis, R.S. and Hudspeth, A.J. (1989) The ionic basis for electrical resonance in a vertebrate hair cell. II. A model for electrical resonance and frequency tuning. J. Neurosci. (in prep.). Lewis, E.R., Leverenz, E.L. and Bialek. W.S. (1985) The vertebrate Inner Ear, CRC, Boca Raton, Florida. Long, G.R., Tubis T., Jones, K.L. and Sivaramakrishnan, S. (1988) Modification of the external-tone synchronization and statistical properties of spontaneous otoacoustic emissions by aspirin consumption. In: H. Duifhuis. J.W. Horst, and H.P. Wit (Eds.) Basic Issues in Hearing, Academic Press, London, pp. 93-100. Neely, S.T. (1989) A model for bidirectional transduction in outer hair cells. In: D.T. Kemp and J.P. Wilson (Eds.) Cochlear Mechanisms: Structure, Function and Models, Plenum, New York, (in press). Palmer, A.R. and Wilson, J.P. (1981) Spontaneous and evoked acoustic emissions in the frog Ram esculenfa. J. Physiol. 324, 66P. Pitchford, S. and Ashmore J.F. (1987) An electrical resonance in hair cells of the amphibian papilla of the frog Rona temporaria. Hear. Res. 27, 75-83.. Roberts, W.M., Robles, L. and Hudspeth, A.J. (1986) Correlation between the kinetic properties of ionic channels and the frequency of membrane-potential resonance in hair cells of the bull frog. In: B.C.J. Moore and R.D. Patterson (Eds.) Auditory Frequency Selectivity, Plenum. London, pp. 89-95. Schatzmann, H.J. (1975) Active calcium transport and Ca*+activated ATP ase in human red cells. Curr. Topics Memb. Trans. 6, 1266168.
204
Schatzmann, H.J. and Vincenzi, F.F. (1969) Calcium movements across the membrane of human red cells. J. Physiol. 201, 369-395. ScNoth, E. and Zwicker, E. (1983) Mechanical and acoustical influences on spontaneous oto-acoustic emissions. Hear. Res. 11, 285-293. Tanaka, T. (1981) Gels. Sci. Am. 244, 110-123. Tubis, A., Long, G.R., Sivaramakrishnan, S. and Jones, K.L. (1989) Tracking and interpretive models of the active-nonlinear cochlear response during reversible changes induced by aspirin consumption. In: D.T. Kemp and J.P. Wilson (Eds.) Cochlear Mechanisms: Structure, Function and Models, Plenum, New York (in press). Van Dijk, P. and Wit, H.P. (1987) Temperature dependence of frog spontaneous otoacoustic emissions. J. Acoust. Sot. Am. 82, 2147-2150. Van Dijk, P. and Wit, H.P. (1988) Phase-lock of spontaneous oto-acoustic emissions to a cubic difference tone. In: H. Duifhuis, J.W. Horst and H.P. Wit @Is.). Basic Issues in Hearing, Academic Press, London, pp. 101-105. Weiss, T.F. (1982) Bidirectional transduction in vertebrate hair cells: A mechanism for coupling mechanical and electrical processes. Hear. Res. 7, 353-360. Whitehead, M.L., Wilson, J.P. and Baker, R.J. (1986) The effects of temperature on otoacoustic emission tuning prop-
erties.In: B.C.J. Moore and R.D. Patterson (Eds.), Auditory Frequency Selectivity, Plenum. London, pp. 39 - 46. Wilson, J.P. (1980) Evidence for a cochlear origin for acoustic re-emissions, threshold fine-structure and tonal tinnitus. Hear. Res. 2, 233-252. Wit, H.P. (1986) Statistical properties of a strong spontaneous otoacoustic emission. In: J.B. Allen, J.L. Hall, A.E. Hubbard, S.T. Neely and A. Tubis, (Eds.). Peripheral Auditory Mechanisms, Springer, Berlin, pp. 211-228. Wit, H.P., Langevoort, J.C. and Ritsma, R.J. (1981) Frequency spectra of cochlear acoustic emissions (‘Kemp-echoes’). J. Acoust. Sot. Am. 70, 437-445. Wit, H.P., Van Dijk, P. and Segenhout, J.M. (1989) An electrical correlate of spontaneous otoacoustic emissions in a frog; a preliminary report. In: D.T. Kemp and J.P. Wilson (Eds.) CochIear Mechanisms: Structure. Function and Models, Plenum, New York (in press). Zenner, H.P. (1986) Motile responses in outer haircells. Hear. Res. 22, 83-90. Ziss. C.A. and Glattke, T.J. (1988) Reliability of spontaneous otoacoustic emission suppression tuning curve measures. J. Sp. Hear. Res. 31, 616-619. Zwicker, E. (1979) A model describing nonlinearities in hearing by active processes with saturation at 40 dB. Biol. Cybernet. 35, 243-250.
199
Research, 41 (1989) 199-204
HEARES
01258
DC injection
alters spontaneous
otoacoustic
emission frequency
in the frog
H.P. Wit, P. van Dijk and J.M. Segenhout Institute of Audiology, (Received
Universiv
Hospital,
17 February
Groningen, The Neiherlands
1989; accepted
23 May 1989)
A permanent wire electrode was implanted in the inner ear of the green frog (Ram esculenta). Through this electrode direct current was delivered to the inner ear fluid of the frog, during recording of a spontaneous otoacoustic emission (SOAE). Both SOAE frequency and amplitude turned out to depend on DC level and polarity. Possible explanations for the observed phenomena are given, based on a dissipative limit-cycle oscillator model for SOAE generation, and the assumption that SOAE frequency depends on hair cell ion channel inductance. Otoacoustic
emission;
Hair cell: Frog;
Limit-cycle
oscillator;
Direct
Introduction Spontaneous otoacoustic emissions (SOAEs) most problably have their source(s) inside the inner ear. Results of experiments in which an SOAE is suppressed by a strong externally supplied tone are direct support for this statement (Kemp, 1979; Wilson, 1980; Wit et al., 1981; Sloth and Zwicker, 1983; Ziss and Glattke, 1988). Tuning curves obtained in these experiments show that the generator of the otoacoustic emission is at a location where incoming sound turns out to be sharply bandpass filtered. Theoretically the suppression results are satisfactory described by a model in which a self-sustained oscillator is coupled to a one-dimensional cochlear model (Tubis et al., 1989). Further support for an inner ear origin of SOAEs is given by the recording of an electrical correlate of an SOAE from the inner ear fluids of the frog (Wit et al., 1989). That SOAEs are indeed generated by self-sustained oscillators can be derived from measured sound pressure distributions (Bialek and Wit, 1984;
H.P. Wit, Institute of Audiology, University Hospital, 30.001, 9700 RB Groningen, The Netherlands. 0378-5955/89/$03.50
Postbox
0 1989 Elsevier Science Publishers
B.V.
current
Van Dijk and Wit, 1987): a filtered emission signal shows the behaviour of a process that tends to stay away from zero amplitude. (If the emission signal were filtered noise, the sound pressure distribution would have a maximum at zero amplitude, instead of the observed minimum.) Furthermore entrainment (Long et al., 1988) or phase-lock (Bialek and Wit, 1984; Wit 1986; Van Dijk and Wit, 1988) of SOAEs by an externally supplied tone are wellknown properties of self-sustained oscillators. So, experimental results indicate that SOAEs are generated by self-sustained oscillators inside the inner ear. Good candidates for these oscillators are the sensory cells, especially since it has been shown that haircells can have a motor function. (Brownell et al, 1985; Zenner, 1986; Ashmore, 1987). This motor function is thought to play a role in the feedback loop that sharpens frequency selectivity of the inner ear. (For a recent review see: Dallos, 1988) If positive feedback becomes too large the system starts to oscillate and this may produce SOAEs (Gold, 1948). In the mammalian organ of Corti outer haircells have the properties to fullfil a motorfunction task, and in models in which positive feedback is incorporated this motor function drives inner hair cells (Zwicker, 1979; Neely, 1988). Inner haircells
are supposed to be involved in forward transduction only. In this respect the discovery of SOAEs from frog ears (Palmer and Wilson, 1981) may be of importance. Frogs have rather primitive hearing organs with only type II haircells, that have the characteristics of mammalian outer haircells (Lewis et al., 1985). SOAEs from frogs have properties similar to those of human SOAEs; the only observed difference is a smaller frequency stability (broader spectral peaks) for frog SOAEs (Van Dijk and Wit, 1987). Some years ago it was discovered by W~tehead et al. (1986) that body temperature has a strong influence on SOAE frequency in frogs. And recently we discovered that also DC injection into the inner ear of the frog has a strong influence on SOAE frequency. These findings have consequences for models of the inner ear transduction process in which positive feedback is incorporated. In this paper we give results for DC injection in the green frog (Rana esculentu) and try: to give an explanation for these results based on known properties of frog haircells. Mater&
Direct current was supplied to the inner ear fluids through the implanted electrode and a skin needle electrode. Current was delivered by a battery powered home built constant current source and measured with a moving coil meter integrated in the instrument. SOAEs were recorded on videotape after pulse code modulation for different current values (both positive and negative; current was said to be positive if the inner ear electrode was positive with respect to the skin electrode). SOAE signals were monitored during recording and analyzed off-line with a PAR/U~gon type 4512 real-time FFT spectrum analyzer. Results The results presented in this paper are part of the results of an investigation of the properties of t
I
I
I
I
-
-----k-
and Methods
Experiments were performed in 4 green frogs (Rana esculenta). Under anaesthesia with MS 222 a small hole was pierced in the upper part of the skull, about halfway between the tympanic membrane and the skull midline. A 0.3 mm diameter platinum wire with teflon coating (removed at the tip) was fixed into this hole with dental cement. The electrode tip contacted the outside of the membraneous inner ear encapsulation; close to the utricle. After this preparation the frog had an antenna-like electrode protruding from the skin over a few m&meters length. With such a permanent electrode the frog lived among other frogs in a terrarium and could be used for several experiments. During an experiment the frog was again lightly anaesthetized with MS 222. SOARS were measured with a sensitive condenser microphone (Wit et al., 1981), acoustically coupled to the tympanic membrane with 1 cm of PVC tubing. Measurements were performed inside a soundproof box.
I
B __(
-20
L I
0.6
I
I
0.8 frequency
-
I
40
I
1.0
1 1.2
( kHz )
Fig. 1. Frequency spectra of a spontaneous otoacoustic emission from a frog for different values of injected direct cuTrent (expressed in PA, current is positive if the inner ear electrode is positive with respect to the skin reference electrode).
201
--L--
-80
-40
direct Fig. 2. Frequency function of direct
80
cu;rent (:A)
of spontaneous otoacoustic emission as a current through the inner ear. Results are given for 4 frogs.
the electrical correlate of spontaneous otoacoustic emissions in frogs (Wit et al, 1989). All frogs in which an electrode was implanted had one relatively strong SOAE with a frequency between 1.0 and 1.2 kHz. Fig. 1 shows for one frog that DC alters both amplitude and frequency of this SOAE. For sufficiently strong positive current the emission could even be made to disappear. As far as this could be judged from the FFT analyzer display, SOAE frequency and amplitude followed a current change instantaneously. Fig. 2 gives SOAE frequency for different current values for all 4 frogs. The average slope of the curves in this figure is approximately 2 HZ/PA. Discussion Positive current through the inner ear of the frog causes a decrease of SOAE amplitude (fig. 1). The same effect can be observed when body temperature of the frog is lowered (Van Dijk and Wit, 1987). In terms of a Van der Pol-oscillator model for SOAE generation this means that the positive feedback force decreases and/or that the damping force and the negative feedback force increase (see Appendix). The best explanation for the observed amplitude decrease is a reduction of the positive feedback force. The power supplied to the oscillator by the feedback force may even become too small to compensate for the losses in the resistive
elements of the oscillator, which results in complete extinction of the oscillation. (This situation occurs if the feedback force parameter becomes smaller than the damping constant; see Appendix). How positive current or temperature decrease can reduce the positive feedback force remains obscure until more is known about the actual feedback mechanism. Also not known yet are the elements that determine frequency of a frog SOAE. In a mechanical model these elements would be mass and stiffness. It is unlikely that current or temperature will influence mass. So the observed frequency changes through DC injection (fig. 2) or change of body temperature (Van Dijk and Wit, 1987) have to be explained by a stiffness change. This stiffness change has to be large, and it is not known whether there are inner ear structures that exhibit the necessary large stiffness change. Very speculative is the thought that tectorial structures might change their stiffness, as has been observed for gels if temperature or ion concentration is changed (Tanaka, 1981). In a mechano-electrical model for SOAE generation (Weiss, 1982) the frequency determining elements could also be in the electrical domain. (The model cannot be purely electrical; it has to have a mechanical part, because SOAEs are mechanical oscillations). Support for such a type of model comes from the observation in the frog of an electrical counterpart of SOAEs (Wit et al., 1989). Electrical resonances can be evoked in haircells of the amphibian papilla of the frog (Pitchford and Ashmore, 1987). If haircells are the generators of SOAEs (for which no direct proof has been given yet), then recently constructed models for electrical tuning of haircells (Crawford and Fettiplace, 1981; Ashmore and Attwell, 1985; Lewis and Hudspeth, 1989) are of help to explain changes of frog SOAE frequency. In these models tuning frequency for a hair cell is determined by cell membrane capacity and ion channel inductance. The inductive behaviour of an ion channel is caused by the fact that ion current through the channel is time delayed with respect to a voltage change across the channel. Hair cell resonances can be reproduced by a model that incorporates two active conductances: a voltage activated Ca2+ conductance and a Ca2+
activated K’ conductance (Lewis and Hudspeth, 1989). The SOAE frequency change introduced by current injection into the inner ear, as we observe it (fig. 2), may be caused by a change of the properties of these actived conductances. In current-clamped haircells from the amphibian papilla of the bullfrog Roberts et al. (1986) found that the resonant frequencies of the cells increased monotonically with the amplitude of the depolarizing pulse. The only parameter that could explain these results to some extend was the time constant for the onset of potassium current after a voltage step. So it might be that current injection into the inner ear of the frog changes in some way the time constants of ionic channels, which in turn would lead to a change in resonance frequency. If SOAEs are produced by hair cells this would then also lead to a change of SOAE frequency. In a model for electrical tuning in hair-cells Ashmore and Attwell (1985) show that a voltage gated current alone cannot account for the high Q values of the resonance behaviour of the cells, but that a calcium gated current could account for the observed sharp tuning. In this model different resonance frequencies for cells at different locations in the inner ear sensory epithelium can best be explained by a different number of calcium pumps in the cell membrane, leading to a different pump rate for different cells. For individual cells. with a fixed number of calcium pumps, pump rate will change if parameters that determine pump rate are changed. For a higher resonance frequency a higher pump rate is needed. Ion pumps are medium- to large sized membrane spanning proteins. They may be considered as channels that go through a cycle of conformational transitions, during which an ion is taken up from one side, is temporary trapped inside the protein, and is released to the other side. The calcium pump is such a type of pump, driven by ATP-ase (Haynes and Maudveno, 1987). The pump rate of ATP-driven ion pumps depends on temperature and membrane voltage (Lauger, 1987). So if direct current injection into the inner ear of the frog would change hair cell membrane voltage, a mechanism to explain change of ion channel time constant (leading to an inductance change) has been found. The temperature dependence of Ca transport in
human red cells was studied by Lee and Shin (1969) and by Schatzmann and Vincenzi (1969). From the numbers given by the authors an activation energy of approximately 20 kcal/mole for active calcium transport by CaZ’ activated ATPase in human red cells can be derived (Sehatzmann, 1975). For an Arrhenius temperature dependence of pump rate this number yields a 12% increase of pump rate per Kelvin (of centigrade). In the model by Ashmore and Attwell (1985) hair cell resonance frequency is proportional to the square root of Ca pump rate. So a 6% increase of resonance frequency per degree would be predicted. It is interesting to note that temperature effects of this magnitude have been reported for the frequency of voltage ringing in hair cells isolated from the chick cochlea (Fuchs et al.. 1988). A 6% increase per degree corresponds well with the highest value found for the temperature dependence of frog SOAEs: 50 Hz/centigrade at 7 kHz (Whitehead et al., 1986; Van Dijk and Wit, 1987). Direct current injection and temperature both influence SOAE amplitude as well as SOAE frequency. With current injection an amplitude decrease is accompanied by a frequency increase (Figs. 1 and 2). Lowering of body temperature, however, causes a frequency decrease, together with an amplitude decrease (Van Dijk and Wit, 1987). This means that the mechanism that controls SOAE frequency is different from the mechanism that controls its amplitude. Acknowledgements
We thank Ms. Willy Kanis for typing the manuscript. This study was supported by the Heinsius Houbolt Fund and the Netherlands Organization for the Advancement of Research (NWO). Appendix
Consider a mechanical system of mass m on a spring with stiffness K. The differential equation for the displacement x(t) of the mass is: mX+
[y+X(X)]i+KX=o
(1)
203
yi is the damping force and A( force (Bialek and Wit, 1984). For h(x)=
-_,+X,x’
the system tion:
and
is a feedback
Xi>y
is a Van der Pol oscillator
with equa-
To this oscillator energy is supplied for small values of x, while power is dissipated for large x. The result is a limit-cycle oscillation. In order to calculate the amplitude of this oscillator, we start from the mathematical form of the differential equation for a Van der Pol oscillator:
i’+a(z2-
+ cd;z= 0
l)i
with amplitude a = 2 (Hanggi 1982). Substitution of
d
z=x
(4) and
Riseborough,
x2
&-u
A, -Y
Ly=-
m
2,L
w”
m
in eq. (4) gives eq. (3) after some calculation. So, the (physical) Van der Pol oscillator has an amplitude
A=2
A, -
J x
Y
2
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