The outer-hair-cell RC time constant: A feature, not a bug, of the mammalian cochlea
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Evaluation Summary:
This paper proposes that specializations in the outer hair cells' biophysical properties along the cochlea may allow them to amplify the reduced receptor potentials in a manner sufficient to explain all present experimental results. Moreover, the filtering provided by the hair cells may be beneficial for hearing soft high-frequency sounds because it decreases noise and harmonic distortions. Importantly, the amplitude of the relevant motions, even with the low-pass-filtered attenuation, are as large as those measured in the high frequency regions of the cochlea. The authors provide insights and suggestions but the paper lacks strong supportive experimental data to definitively resolve the claimed "apparent" membrane time constant conundrum.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #3 agreed to share their name with the authors.)
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Abstract
The cochlea of the mammalian inner ear includes an active, hydromechanical amplifier thought to arise via the piezoelectric action of the outer hair cells (OHCs). A classic problem of cochlear biophysics is that the long resistance-capacitance ( RC ) time constant of the hair-cell membrane produces an effective cut-off frequency much lower than that of most audible sounds. The long RC time constant implies that the OHC receptor potential—and hence its electromotile response—decreases by several orders of magnitude over the frequency range of hearing. This “ RC problem” is often invoked to question the role of cycle-by-cycle OHC-based amplification in mammalian hearing. Here, we use published data and simple physical reasoning to show that the RC problem is, in practice, a relatively minor physical issue whose importance has been unduly magnified by viewing it through the wrong lens. Indeed, our analysis indicates that the long RC time constant is actually beneficial for hearing, reducing noise and distortion while increasing the fidelity of cochlear amplification.
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Author Response
Reviewer #1 (Public Review):
The paper correctly identifies two biophysical properties that may impact an OHC contribution to cochlear amplification. These are the membrane RC time constant and prestin kinetics. The RC problem was identified by Santos-Sacchi 1989 (1) based on measures of OHC membrane capacitance, electromotility (eM) and published OHC resting and receptor potential data. At issue was a 20 dB disparity between threshold BM measures and eM when the resting potential (RP, ~ -70 mV)) is displaced from the voltage at maximal eM gain or peak NLC (Vh; ~ -40 mV). If RP were actually at Vh then the problem would not have been identified, assuming that prestin's voltage-responsiveness were frequency-independent, which was not in question at that time. Over the last two decades several groups have found prestin …
Author Response
Reviewer #1 (Public Review):
The paper correctly identifies two biophysical properties that may impact an OHC contribution to cochlear amplification. These are the membrane RC time constant and prestin kinetics. The RC problem was identified by Santos-Sacchi 1989 (1) based on measures of OHC membrane capacitance, electromotility (eM) and published OHC resting and receptor potential data. At issue was a 20 dB disparity between threshold BM measures and eM when the resting potential (RP, ~ -70 mV)) is displaced from the voltage at maximal eM gain or peak NLC (Vh; ~ -40 mV). If RP were actually at Vh then the problem would not have been identified, assuming that prestin's voltage-responsiveness were frequency-independent, which was not in question at that time. Over the last two decades several groups have found prestin performance to be low pass. Isolated OHCs, macro-patch and OHCs in situ cochlear explants all show this low pass behavior. To date, no manipulations of load have pushed the voltage responsiveness to frequency-independent. This manuscript tries to avoid the kinetics issue and attempts to focus on the RC problem that has been dealt with extensively since 1989, including at that time a suggestion that the RC problem points to the dominance of the stereocilia bundle (2).
The authors suggest that kinetics of prestin is not addressed in the current manuscript, but this is not the case. In ignoring the paper from Santos-Sacchi and Tan 2018 (3), reliance on Frank et al.'s (4) data explicitly utilizes their kinetic results. OHC84 (so-called short cell, 51 um long) is essentially frequency-independent after microchamber voltage roll-off correction. The authors choose 1 nm/mV gain at 50 kHz to work with in their arguments. As it turns out, the corrected eM of OHC84 is wrong since it does not fix the reported 23 kHz microchamber voltage roll-off. While OHC65 is appropriately fixed, OHC84 is over compensated. Gain at 50 kHz should be about half the chosen gain. This is not the most problematic issue for their arguments, however.
In Santos-Sacchi and Tan 2018 (3) we show that low frequency (near DC) eM gain for OHCs averaging 55.3 um long is about 15 nm/mV. This indicates, as noted in that paper, that the resting potential of OHC84 was far shifted from Vh, accounting for its wide-band frequency response. If indeed, the authors still maintain that OHC eM is frequency-independent, ala Frank et al. (and in disregard to other publications where, to the contrary, eM gain would be far less at 50 kHz - see (5, 6)), then the eM gain at 50 kHz should be closer to 15 nm/mV; large enough, I think, to make their RC problem exercise overkill. That is, even in 1989 such a gain would not have suggested an RC problem. This is assuming that the normal resting potential is at Vh. Of course, at Vh membrane capacitance would be about twice that of linear capacitance (due to peak NLC) - the cell time constant does not discriminate against source of capacitance. All in all, isolated OHC biophysics that provides the voltage dependence and the kinetics of prestin cannot be ignored to deal with the RC problem in isolation. Doing so will give a false sense of how the cochlea works, and will encourage others to neglect, without rationale, published pertinent data, as with the Sasmal and Grosh 2019 (7) model where the OHC is treated as a frequency-independent PZE device.
Finally, to scorn the significance of component characteristics comprising the whole cochlea, e.g., based on isolated OHC biophysics or prestin's cryo-EM structure, as a fallacy of composition suffers itself from hasty generalization. Of course, knowing the biophysics of single OHCs informs on the system response. Otherwise, the prestin KO would have been an unfunded goal, never allowed to pass beyond a system modeler's review. Indeed, the authors would have none of the "carefully" chosen data to present their RC counter argument. Pertinent, published biophysical characteristics must be included in any critical discussion on OHC performance. For that matter, cochlear modelers must follow the same rule.
We thank reviewer #1 for the suggestions on the kinetics of prestin and previous literature.
Although there is no data (to our best knowledge) for electromotilty (eM) in isolated basal murine OHCs, a more thorough review of the existing literature on the topic suggest that the assumed parameters are indeed a reasonably conservative estimation of eM in situ.
Additionally, the OHC parameters are pessimistic enough to account for a doubling of effective capacitance due to NLC.
Regarding the fallacy of composition, we are puzzled that the reviewer interpreted it as a “scorning” of the OHC biophysics, obviously important for cochlear function. The raised point is simple and rather obvious: a system built with low-pass filters doesn’t mean that the system is a low-pass filter. This is elucidated with the analogy, familiar to electrical engineers, that high- and band-pass filters are often built by cascading and mixing the response of low-pass filters. The “fallacy of composition” therefore lies in the conclusion that since eM is “low-pass”, it can’t possibly contribute to high frequency amplification. Strikingly, this conclusion is often based on measured vibrations near the OHCs showing transfer functions with >30 dB peak-to-tail ratio, and that are somewhat consistent with the inner working of cochlear models. That is, we are criticizing one specific interpretation of the biophysical data, not certainly suggesting that collecting and analyzing the data in the first place is unimportant.
Reviewer #2 (Public Review):
In the inner ear, the cochlea transforms sound-induced vibrations into electrical signals that are sent to the brain. Cochlear outer hair cells (OHCs) are thought to amplify these vibrations, but it is unclear how amplification works. Sound-induced vibrations modulate the current entering an OHC, which drive its receptor potential, causing the OHC to change length. The change in length owing to the receptor potential variation, known as the OHC's electromotile response, depends on the size of the receptor potential. However, the receptor potential decreases with increasing sound frequency, because of the resistance (R) and capacitance (C) of the OHC's membrane. This paper addresses the RC problem, limitations on high-frequency amplification owing to the OHC's receptor potential decreasing with frequency.
The authors use a well-known simplification of the RC problem and some back-of-the-envelope calculations to argue that OHCs can amplify sufficiently well at high frequencies to match experimental data, despite the decrease in their receptor potentials. They argue that changes to OHC properties along the cochlea allow them to amplify at high frequencies and that OHCs reduce noise and distortion. They argue against OHCs as being cochlear impedance regulators and that OHCs do not limit cochlear tuning.
Figure 1 and Equations 1-6 are useful teaching tools but are not novel. The back-of-the-envelope calculations use these equations and a limited number of data points from the literature. There are many prior models that show amplification despite the RC problem, but they are not analyzed or discussed in much detail.
How RC OHC filtering reduces noise without reducing the signal is not explained. The type of noise calculation done in Appendix 1 is well-known and the application is again a rough back-of-the-envelope calculation. Most of the statements about noise are not fleshed out or supported by calculations.
The discussion about tonotopic variations has little new data. Fig. 2 uses two data points from the literature and an unpublished data point from a colleague. The fact that BM displacement is smaller at the base than at the apex is well known. There is speculation that reduced OHC motion is "effectively counteracted" by gradients in OHC capacitance and MET current, but no evidence is presented.
The discussion about distortions is pedagogical but is again speculation without new or strong-supporting evidence. Fig. 3 argues that OHCs might reduce high-frequency distortions, but don't limit the cochlear amplifier. The plots shown are either well-known consequences of filtering or a summary of the authors' previous model data.
The arguments against OHCs as regulators and that they don't limit tuning are not well flushed out, speculative, and unsupported by new calculations or data.
This paper does not clarify OHC operation or the RC problem, because it mixes speculation, limited data, and topics that are not clearly related to the problem.
We agree with reviewer #2 that there are no new physics principles elucidated here, and that most of the discussion relies on simple calculations. But we believe that such simple calculations are the missing piece (absent in the literature) that allow one to appreciate the magnitude of the problem under exam—magnitude typically inflated by focusing on quantities whose physical significance is uncertain. In other words, we believe that the simplicity of the calculations and physical reasoning is not a bug, but a feature of the paper.
We believe that in his criticism regarding various topics of discussion presenting little or speculative new evidence, this reviewer might not have fully considered that most of the evidence provided here is fundamentally a physics-based review of the recent experimental data, incidentally the same type of data previously employed to argue that the RC problem is dramatic in the first place. Likely we didn't convey this message clearly enough in the manuscript.
While the arguments against OHCs as regulators are not all new, they are often ignored (or perhaps forgotten) and we believe there is a value in synthesizing them all in one place. The support for these arguments comes from fundamental hydrodynamic principles, previous modeling studies, and most importantly from OCT data collected over the last 6 years. Of course, the discussion on the plausibility of suggested mechanisms lacking a concrete proposal cannot be 100% “analytic”.
About noise and signal amplification, the missing piece perhaps is that distributed internal noise sources (e.g., thermal and shot noise) are independent of each other and hence spatially incoherent. While the manuscript doesn’t specifically deal with signal vs. noise amplification in cochlear models, spatially distributed amplification is known to boost signals more than internal noise—a principle universally used in telecommunications and addressed in >60-year-old literature.
Reviewer #3 (Public Review):
This paper discusses the effect of the low-pass filtering between outer hair cell transducer current and receptor voltage. The filter's cut-off frequency (where the response is down by a factor of 0.71 of its maximum) can be quantified by the resistance and capacitance of the cell hair cell's basolateral membrane. The capacitance value is determined mainly by the lipid membrane and is augmented by the charge movement of the piezoelectric prestin molecule, which endows the OHC with its electromotile properties. The OHC's capacitance (C) value is pretty well known. The resistance (R) is determined mainly by K+ channels in the basolateral membrane, a value that is also known reasonably well. The low-pass cut-off frequency is equal to (2pi*RC)^-1 and has a value of a ~1 to a few kHz - a value that has both experimental and theoretical support. The low-pass filtering of membrane voltage is important because the cell responds to membrane voltage by shortening and lengthening - this electromotility is thought to be key to the cochlea's operation and in particular to cochlear amplification, the process that enhances the magnitude and tuning of the cochlea's passive response to sound. However, the auditory system works to 80 kHz and even higher in some animals. Thus, it has been posed (let's say by team A) that the RC cut-off frequency value of a few kHz makes electromotility too slow to operate "cycle-by-cycle" up to several 10s of kHz. The article under review, representing team B, supports "cycle-by-cycle" action, arguing that the several kHz cut off frequency is not a problem and is even an advantage.
The arguments put forward in favor of cycle-by-cycle action are:
- The size of the motions, even with the low-pass-filtered attenuation are as large or larger as those measured in the cochlea at high frequencies.
- Noise is often increasing as frequency decreases, thus low-pass-filtering is actually good, to reduce the predominantly low frequency noise.
- Harmonic distortion is at supra-CF frequencies, so it's good if the hair cell is low-pass-filtering to reduce harmonics.
These three points are reasonable, and the quantification relating to statement 1 is convincing. However, the quantification associated with point 2 is muddled. The hair cell voltage signal is expressed in volts, but the noise value is given in terms of the current mediated by 1-5 channels. A quantitative comparison should be made, with signal and noise expressed in the same units, preferably volts and volts/root(Hz), with a bandwidth estimated. The appendix attempts to be more quantitative and something like that short appendix should be incorporated into the paper. If a quantitative comparison in standard units is not possible with current data, that can be stated and underscores that we really don't know whether the noise is a problem for cycle-by-cycle amplification. Point 3 is reasonable and nicely illustrated in Fig. 3B. I did not get anything from Fig. 3A and the corresponding discussion on page 8 lines 320-335. Panels C and D were under-explained and could be removed, and the caption's reference to "short wave hydrodynamics" was also under-explained.
The arguments put forward to challenge gain control mechanics, which employ DC shifts to set effective operating conditions:
- Operation based on DC and quasi-DC operating points is sensitive to noise, which as noted above is often increasing as frequency decreases.
- Operation that employs a DC shift for operating point is likely to work in such a way to reduce stiffness, which has been shown to be inconsistent with active cochlear responses. For example, stiffness reduction would reduce traveling wave wavelength and thus alter the response phase and timing to a degree that has not been observed experimentally. This has long been known and relevant papers are cited.
Point 4 was not convincing to me because the motions related to setting operating conditions could be larger than the nanoscale cycle-by-cycle response motions - thus these operating point motions could be above the noise values that seem limiting to cycle-by-cycle amplification. Point 5 is a nice reminder of the conclusion that, based on experimental findings and physics-based basic cochlear models, the cochlear amplifier must work by means of energy injection. This point was made clearly by Kolston (well cited in this paper) and later supported by other work.
The present paper is informative in many ways and offers useful insights for further exploration. It is nicely written and illustrated. Because the signal and noise values are not quantified, the basic claim, that the cochlea amplifier can amplify a noisy signal effectively, is not convincing and that basic question is still unsettled. Overall, the paper would be improved if the claims and arguments were presented more tightly, with fewer digressions, and more modestly.
We thank reviewer #3 for the many comments and suggestions.
We agree that plotting the spectral density of a “near-threshold” OHC signal vs. inherent electric noise results in much simplification. Regarding noise and signal amplification, previous work on transmission lines points out that amplification is the way to increase SNR along the line.
We believe that part of the undergoing confusion is that the problem is not how OHC can amplify a “noisy signal” —the cochlea amplifies “noisy” sounds similarly as it amplifies pure tones— but how OHCs can amplify signals in presence of internal noise. Amplification and detection are two distinct things, and signal amplification does not rely on detection. Detection is an intrinsically nonlinear decision process (e.g., signal present/absent). Amplification in relevant frequency ranges is what allows to detect signals in the real world (e.g., radio receivers). The cochlea (as portrayed by classic theories) does not seem exceptional in this regard.
We agree that the effect of noise on DC responses is not very clear in the manuscript. Although it is difficult to make quantitative statements on a hypothesis that lacks a concrete mechanistic proposal, ~63% of (inherent) electric noise power is confined below the RC corner frequency, i.e, the frequency band of the regulatory OHC. In presence of (unavoidable) flicker and brown noise (e.g., Brownian motion of stereocilia), this percentage can only increase. Conversely, in the frequency band of OHC cycle-by-cycle amplification, the noise power is only a tiny fraction of the total.
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Evaluation Summary:
This paper proposes that specializations in the outer hair cells' biophysical properties along the cochlea may allow them to amplify the reduced receptor potentials in a manner sufficient to explain all present experimental results. Moreover, the filtering provided by the hair cells may be beneficial for hearing soft high-frequency sounds because it decreases noise and harmonic distortions. Importantly, the amplitude of the relevant motions, even with the low-pass-filtered attenuation, are as large as those measured in the high frequency regions of the cochlea. The authors provide insights and suggestions but the paper lacks strong supportive experimental data to definitively resolve the claimed "apparent" membrane time constant conundrum.
(This preprint has been reviewed by eLife. We include the public reviews from …
Evaluation Summary:
This paper proposes that specializations in the outer hair cells' biophysical properties along the cochlea may allow them to amplify the reduced receptor potentials in a manner sufficient to explain all present experimental results. Moreover, the filtering provided by the hair cells may be beneficial for hearing soft high-frequency sounds because it decreases noise and harmonic distortions. Importantly, the amplitude of the relevant motions, even with the low-pass-filtered attenuation, are as large as those measured in the high frequency regions of the cochlea. The authors provide insights and suggestions but the paper lacks strong supportive experimental data to definitively resolve the claimed "apparent" membrane time constant conundrum.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #3 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
The paper correctly identifies two biophysical properties that may impact an OHC contribution to cochlear amplification. These are the membrane RC time constant and prestin kinetics. The RC problem was identified by Santos-Sacchi 1989 (1) based on measures of OHC membrane capacitance, electromotility (eM) and published OHC resting and receptor potential data. At issue was a 20 dB disparity between threshold BM measures and eM when the resting potential (RP, ~ -70 mV)) is displaced from the voltage at maximal eM gain or peak NLC (Vh; ~ -40 mV). If RP were actually at Vh then the problem would not have been identified, assuming that prestin's voltage-responsiveness were frequency-independent, which was not in question at that time. Over the last two decades several groups have found prestin performance to be …
Reviewer #1 (Public Review):
The paper correctly identifies two biophysical properties that may impact an OHC contribution to cochlear amplification. These are the membrane RC time constant and prestin kinetics. The RC problem was identified by Santos-Sacchi 1989 (1) based on measures of OHC membrane capacitance, electromotility (eM) and published OHC resting and receptor potential data. At issue was a 20 dB disparity between threshold BM measures and eM when the resting potential (RP, ~ -70 mV)) is displaced from the voltage at maximal eM gain or peak NLC (Vh; ~ -40 mV). If RP were actually at Vh then the problem would not have been identified, assuming that prestin's voltage-responsiveness were frequency-independent, which was not in question at that time. Over the last two decades several groups have found prestin performance to be low pass. Isolated OHCs, macro-patch and OHCs in situ cochlear explants all show this low pass behavior. To date, no manipulations of load have pushed the voltage responsiveness to frequency-independent. This manuscript tries to avoid the kinetics issue and attempts to focus on the RC problem that has been dealt with extensively since 1989, including at that time a suggestion that the RC problem points to the dominance of the stereocilia bundle (2).
The authors suggest that kinetics of prestin is not addressed in the current manuscript, but this is not the case. In ignoring the paper from Santos-Sacchi and Tan 2018 (3), reliance on Frank et al.'s (4) data explicitly utilizes their kinetic results. OHC84 (so-called short cell, 51 um long) is essentially frequency-independent after microchamber voltage roll-off correction. The authors choose 1 nm/mV gain at 50 kHz to work with in their arguments. As it turns out, the corrected eM of OHC84 is wrong since it does not fix the reported 23 kHz microchamber voltage roll-off. While OHC65 is appropriately fixed, OHC84 is over compensated. Gain at 50 kHz should be about half the chosen gain. This is not the most problematic issue for their arguments, however.
In Santos-Sacchi and Tan 2018 (3) we show that low frequency (near DC) eM gain for OHCs averaging 55.3 um long is about 15 nm/mV. This indicates, as noted in that paper, that the resting potential of OHC84 was far shifted from Vh, accounting for its wide-band frequency response. If indeed, the authors still maintain that OHC eM is frequency-independent, ala Frank et al. (and in disregard to other publications where, to the contrary, eM gain would be far less at 50 kHz - see (5, 6)), then the eM gain at 50 kHz should be closer to 15 nm/mV; large enough, I think, to make their RC problem exercise overkill. That is, even in 1989 such a gain would not have suggested an RC problem. This is assuming that the normal resting potential is at Vh. Of course, at Vh membrane capacitance would be about twice that of linear capacitance (due to peak NLC) - the cell time constant does not discriminate against source of capacitance. All in all, isolated OHC biophysics that provides the voltage dependence and the kinetics of prestin cannot be ignored to deal with the RC problem in isolation. Doing so will give a false sense of how the cochlea works, and will encourage others to neglect, without rationale, published pertinent data, as with the Sasmal and Grosh 2019 (7) model where the OHC is treated as a frequency-independent PZE device.
Finally, to scorn the significance of component characteristics comprising the whole cochlea, e.g., based on isolated OHC biophysics or prestin's cryo-EM structure, as a fallacy of composition suffers itself from hasty generalization. Of course, knowing the biophysics of single OHCs informs on the system response. Otherwise, the prestin KO would have been an unfunded goal, never allowed to pass beyond a system modeler's review. Indeed, the authors would have none of the "carefully" chosen data to present their RC counter argument. Pertinent, published biophysical characteristics must be included in any critical discussion on OHC performance. For that matter, cochlear modelers must follow the same rule.
1. J. Santos-Sacchi, Asymmetry in voltage-dependent movements of isolated outer hair cells from the organ of Corti. J. Neurosci. 9, 2954-2962 (1989).
2. A. J. Hudspeth, How the ear's works work. Nature 341, 397-404 (1989).
3. J. Santos-Sacchi, W. Tan, The Frequency Response of Outer Hair Cell Voltage-Dependent Motility Is Limited by Kinetics of Prestin. J. Neurosci. 38, 5495-5506 (2018).
4. G. Frank, W. Hemmert, A. W. Gummer, Limiting dynamics of high-frequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. U. S. A. 96, 4420-4425 (1999).
5. J. Santos-Sacchi, D. Navaratnam, W. J. T. Tan, State dependent effects on the frequency response of prestin's real and imaginary components of nonlinear capacitance. Sci. Rep. 11, 16149 (2021).
6. J. Santos-Sacchi, W. Tan, Complex nonlinear capacitance in outer hair cell macro-patches: effects of membrane tension. Sci. Rep. 10, 6222 (2020).
7. A. Sasmal, K. Grosh, Unified cochlear model for low- and high-frequency mammalian hearing. Proc Natl Acad Sci U S A 116, 13983-13988 (2019). -
Reviewer #2 (Public Review):
In the inner ear, the cochlea transforms sound-induced vibrations into electrical signals that are sent to the brain. Cochlear outer hair cells (OHCs) are thought to amplify these vibrations, but it is unclear how amplification works. Sound-induced vibrations modulate the current entering an OHC, which drive its receptor potential, causing the OHC to change length. The change in length owing to the receptor potential variation, known as the OHC's electromotile response, depends on the size of the receptor potential. However, the receptor potential decreases with increasing sound frequency, because of the resistance (R) and capacitance (C) of the OHC's membrane. This paper addresses the RC problem, limitations on high-frequency amplification owing to the OHC's receptor potential decreasing with frequency.
The …
Reviewer #2 (Public Review):
In the inner ear, the cochlea transforms sound-induced vibrations into electrical signals that are sent to the brain. Cochlear outer hair cells (OHCs) are thought to amplify these vibrations, but it is unclear how amplification works. Sound-induced vibrations modulate the current entering an OHC, which drive its receptor potential, causing the OHC to change length. The change in length owing to the receptor potential variation, known as the OHC's electromotile response, depends on the size of the receptor potential. However, the receptor potential decreases with increasing sound frequency, because of the resistance (R) and capacitance (C) of the OHC's membrane. This paper addresses the RC problem, limitations on high-frequency amplification owing to the OHC's receptor potential decreasing with frequency.
The authors use a well-known simplification of the RC problem and some back-of-the-envelope calculations to argue that OHCs can amplify sufficiently well at high frequencies to match experimental data, despite the decrease in their receptor potentials. They argue that changes to OHC properties along the cochlea allow them to amplify at high frequencies and that OHCs reduce noise and distortion. They argue against OHCs as being cochlear impedance regulators and that OHCs do not limit cochlear tuning.
Figure 1 and Equations 1-6 are useful teaching tools but are not novel. The back-of-the-envelope calculations use these equations and a limited number of data points from the literature. There are many prior models that show amplification despite the RC problem, but they are not analyzed or discussed in much detail.
How RC OHC filtering reduces noise without reducing the signal is not explained. The type of noise calculation done in Appendix 1 is well-known and the application is again a rough back-of-the-envelope calculation. Most of the statements about noise are not fleshed out or supported by calculations.
The discussion about tonotopic variations has little new data. Fig. 2 uses two data points from the literature and an unpublished data point from a colleague. The fact that BM displacement is smaller at the base than at the apex is well known. There is speculation that reduced OHC motion is "effectively counteracted" by gradients in OHC capacitance and MET current, but no evidence is presented.
The discussion about distortions is pedagogical but is again speculation without new or strong-supporting evidence. Fig. 3 argues that OHCs might reduce high-frequency distortions, but don't limit the cochlear amplifier. The plots shown are either well-known consequences of filtering or a summary of the authors' previous model data.
The arguments against OHCs as regulators and that they don't limit tuning are not well flushed out, speculative, and unsupported by new calculations or data.
This paper does not clarify OHC operation or the RC problem, because it mixes speculation, limited data, and topics that are not clearly related to the problem.
-
Reviewer #3 (Public Review):
This paper discusses the effect of the low-pass filtering between outer hair cell transducer current and receptor voltage. The filter's cut-off frequency (where the response is down by a factor of 0.71 of its maximum) can be quantified by the resistance and capacitance of the cell hair cell's basolateral membrane. The capacitance value is determined mainly by the lipid membrane and is augmented by the charge movement of the piezoelectric prestin molecule, which endows the OHC with its electromotile properties. The OHC's capacitance (C) value is pretty well known. The resistance (R) is determined mainly by K+ channels in the basolateral membrane, a value that is also known reasonably well. The low-pass cut-off frequency is equal to (2pi*RC)^-1 and has a value of a ~1 to a few kHz - a value that has both …
Reviewer #3 (Public Review):
This paper discusses the effect of the low-pass filtering between outer hair cell transducer current and receptor voltage. The filter's cut-off frequency (where the response is down by a factor of 0.71 of its maximum) can be quantified by the resistance and capacitance of the cell hair cell's basolateral membrane. The capacitance value is determined mainly by the lipid membrane and is augmented by the charge movement of the piezoelectric prestin molecule, which endows the OHC with its electromotile properties. The OHC's capacitance (C) value is pretty well known. The resistance (R) is determined mainly by K+ channels in the basolateral membrane, a value that is also known reasonably well. The low-pass cut-off frequency is equal to (2pi*RC)^-1 and has a value of a ~1 to a few kHz - a value that has both experimental and theoretical support. The low-pass filtering of membrane voltage is important because the cell responds to membrane voltage by shortening and lengthening - this electromotility is thought to be key to the cochlea's operation and in particular to cochlear amplification, the process that enhances the magnitude and tuning of the cochlea's passive response to sound. However, the auditory system works to 80 kHz and even higher in some animals. Thus, it has been posed (let's say by team A) that the RC cut-off frequency value of a few kHz makes electromotility too slow to operate "cycle-by-cycle" up to several 10s of kHz. The article under review, representing team B, supports "cycle-by-cycle" action, arguing that the several kHz cut off frequency is not a problem and is even an advantage.
The arguments put forward in favor of cycle-by-cycle action are:
1. The size of the motions, even with the low-pass-filtered attenuation are as large or larger as those measured in the cochlea at high frequencies.
2. Noise is often increasing as frequency decreases, thus low-pass-filtering is actually good, to reduce the predominantly low frequency noise.
3. Harmonic distortion is at supra-CF frequencies, so it's good if the hair cell is low-pass-filtering to reduce harmonics.These three points are reasonable, and the quantification relating to statement 1 is convincing. However, the quantification associated with point 2 is muddled. The hair cell voltage signal is expressed in volts, but the noise value is given in terms of the current mediated by 1-5 channels. A quantitative comparison should be made, with signal and noise expressed in the same units, preferably volts and volts/root(Hz), with a bandwidth estimated. The appendix attempts to be more quantitative and something like that short appendix should be incorporated into the paper. If a quantitative comparison in standard units is not possible with current data, that can be stated and underscores that we really don't know whether the noise is a problem for cycle-by-cycle amplification. Point 3 is reasonable and nicely illustrated in Fig. 3B. I did not get anything from Fig. 3A and the corresponding discussion on page 8 lines 320-335. Panels C and D were under-explained and could be removed, and the caption's reference to "short wave hydrodynamics" was also under-explained.
The arguments put forward to challenge gain control mechanics, which employ DC shifts to set effective operating conditions:
4. Operation based on DC and quasi-DC operating points is sensitive to noise, which as noted above is often increasing as frequency decreases.
5. Operation that employs a DC shift for operating point is likely to work in such a way to reduce stiffness, which has been shown to be inconsistent with active cochlear responses. For example, stiffness reduction would reduce traveling wave wavelength and thus alter the response phase and timing to a degree that has not been observed experimentally. This has long been known and relevant papers are cited.Point 4 was not convincing to me because the motions related to setting operating conditions could be larger than the nanoscale cycle-by-cycle response motions - thus these operating point motions could be above the noise values that seem limiting to cycle-by-cycle amplification.
Point 5 is a nice reminder of the conclusion that, based on experimental findings and physics-based basic cochlear models, the cochlear amplifier must work by means of energy injection. This point was made clearly by Kolston (well cited in this paper) and later supported by other work.The present paper is informative in many ways and offers useful insights for further exploration. It is nicely written and illustrated. Because the signal and noise values are not quantified, the basic claim, that the cochlea amplifier can amplify a noisy signal effectively, is not convincing and that basic question is still unsettled. Overall, the paper would be improved if the claims and arguments were presented more tightly, with fewer digressions, and more modestly.
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