Mechanics of Hearing 2024 Discussion 2

Discussion 2: Hair bundle mechanics II, Nonlinear dynamics of the cochlea, Cochlear processing, and Cochlear mechanics: methods and results Moderators: Anthony Peng1, Renata Sisto2, Sebastiaan Meenderink3and Jong-Hoon Nam4 1Department of Otolaryngology, Head, and Neck Surgery, Eberhard Karls University of Tübingen, Elfriede-Aulhorn-Strasse 5, Tübingen 72076, Germany. 2Department of Otolaryngology-Head and Neck Surgery, Stanford University, Stanford, CA. 3Picker Engineering Program, Smith College, Northampton, 01063, MA, USA COCHLEAR MECHANICS: METHODS AND RESULTS SESSION [Karl Grosh]: We start the discussion with the last session first. [Sunil Puria]: So you started by the Karavitaki and Mountain data with the tunnel crossing fibers move. And we talk about that data a lot in our lab apparently. So I’m curious. But then you ended up saying that the fluid in the tunnel doesn’t move a lot, the inner tunnel and the outer tunnel compared to the scala media, which makes me think you think that the tunnel crossing fibers shouldn’t move so I want you to reconcile that for me, please. [Anders Fridberger]: Yes, so I think the difference can be explained by difference in the stimulation. Karavitaki and Mountain used electrical stimulation, we used sound and because we’re not restoring the endocochlear potential, the preparation is sort of in passive mode also. [Sunil Puria]: Do you think it was high electrical and that’s why it’s moving, because it’s charged [. . . ] [Anders Fridberger]: Well, actually, those fibers are attached to the outer hair cells at one end so if the cell is contracting, then I suppose it would produce some sort of motion in the fiber also. [Sunil Puria]: Oh, you think it’s not fluid then? It could be just mechanical. [Anders Fridberger]: I’m not saying either way. I’m just highlighting different possibilities. [Sunil Puria]: That’s a good thought. Thank you. [John Guinan]: Yeah, in the Karavitaki-Mountain preparation, they distinctly looked at the possibility that it was the outer hair cells moving. And their focus of the electric activity was narrow, and they saw the motion going outward both ways from that. And so it does not fit with the idea that the outer hair cells are pulling on the fibers. They distinctly looked at that possibility. It’s presumably the outer hair cells contract and squeeze that space and squirt the fluid along. [Aleksander Zosuls]: So I repeated a lot of Domenica’s experiments using mechanical stimulation and I could confirm what John was saying. If you stimulate, you get an antiphasic motion almost as if the MOC fibers are getting dragged, which is kind of indicating fluid flow. It’s a lot faster. It’s almost instantaneous compared to the traveling wave, slow wave velocity. [Anders Fridberger]: Yeah, I suppose another difference is the location of measurement. We are in the apex, and Karavitaki and Mountain was in the middle turn, I think. [Aleksander Zosuls]: They were the 2nd turn. [Elisabeth Olson]: I’m going to talk about the fluid pressure, because you were speculating it that it was maybe too small to actually be driving motion. But I know it can drive Reissner’s membrane motion because people like Nigel Cooper and Wei Dong, I think have measured that. And way back I measured pressure in that compartment, but it wasn’t very good measurement. But there was definitely sizable fluid pressure sort of similar to the, you know, in the base. So I think that speculation is very speculative. [Anders Fridberger]: Yes, and we do see movement of Reissner’s membrane also. And in fact, we see the largest fluid movements at the center of scala media, and as you approach any of the structures, the movements become smaller. Whatever that means. [Jong-Hoon Nam]: Regarding your nano-ear, the second method, what is the focal volume of that optical trap? [Anders Fridberger]: Actually, we didn’t measure the focal volume of the optical trap, but it’s the same lens as we used in FCS. But the wavelength is 1,064 nanometers, so presumably I think the volume would be a bit larger than what we get at the shorter wavelength. [Jong-Hoon Nam]: And it is like a two watt laser power, very high laser power. Aren’t you worried about the heat in the small focal volume? [Anders Fridberger]: Well, you could be worried about that, but on the other hand we have the fluid around which cools things down quite efficiently. And an infrared laser beam does not heat the tissues very much because they are basically optically transparent. [Jong-Hoon Nam]: Okay, thanks. [Christopher Bergevin]: I just want to make a quick anecdotal comment. There’s a long history of lizard research at the research laboratory of electronics at MIT. So I wanted to make a plea to Scott and Denny to make a video like they did for a lizard as well. And maybe John will do it at USC as well. [John Oghalai]: A question for Scott. It’s really about how to visualize the movements. I mean, your movies, it’s kind of simulated because you only can move it in the optical axis, but it could have actually, I mean, it’s probably a real 3D motion. And then we’ve seen pseudo-colored overlays on top of OCT pictures to try to show magnitude and then another one for phase. Any ideas? I want to hear your comments about what’s the best way to present data in a way that’s easily understandable in a paper, because you can’t put a movie in a paper. What should be the standard? [Scott Page]: So with the first question, so we can do 2D two-beam and we built a system that’s fiber based for two beam. This research is kind of old for me. I meant to present it in 2020, but something happened and then so here we are. The second question is interesting. My movies were all grayscale. So I’m used to doing the color overlays like you guys but try to present the movies in grayscale so that things like looked uniform. How to present that on paper I’m not exactly sure. I’m not even sure that the paper that I’m publishing as a result of this conference is really going to convey what I was trying to say. I guess that would be a great question I have for you guys. I mean, is it supplemental material? I don’t know. I did show some of these at a poster presentation and it was the same thing. I was kind of standing there with a laptop and people did ask to put it on YouTube and things like that. I think now I feel comfortable with that. [Sunil Puria]: I mean when we do final model simulation you get all those and sometimes we do these quiver plots where you show the angle of the of the motion and the magnitude and that I think is a good way of capture it in a single snapshot. [Sebastiaan Meenderink]: I have a quick question for Anna. Thank you, first of all, for your beautiful presentation. I really liked and enjoyed it. It’s very exciting that we are moving from 1D to 3D. I was wondering, could you say something about sort of the fundamental limitations of your method in terms of how big are the motions that you can track? Is that limited by your pixel size and also the speed of the motion that you measure. Is that like how fast you can image the Bscans or are there other limitations or can you overcome those limitations? [Anna Wisniowiecki]: The speed, it’s definitely based on the scan rate. The speed or the vibration frequencies we can measure is based on how high we can scan our MEMS mirror. We’re working on doing that above resonance so that we can get into the kilohertz range. We actually saw they sell some MEMS mirrors that go into the tens of kilohertz. So we expect that we can find a solution to that. For the limitations on vibration amplitude, I mean, we need to resolve the speckle. Our window size is microns because of our optical resolution. I think usually we don’t expect motions that are micron scale. So as long as it’s contained in that window size, we should be able to track it. [Sebastiaan Meenderink]: So can you make your B-scans smaller, like only 100 A-lines and then be 10 times as fast? Or is that the rate limitation? You need the full B-scan with 1,000 A-lines or 10,000 A-lines? Or is it just per A-line, scan time per A-line? [Anna Wisniowiecki]: It’s true that the number of A-lines in a B-scan is kind of the ratio between our sweep rate and our scan rate. Our ability to capture a large field of view at one time is going to shrink as we push the scan rate up. Yeah, so we do have to take that into consideration as well. [Brian Frost]: I had two things. One is with the visualization thing, I still think the best way is what actually JongHoon does, which is to draw the little ellipses with varying aspect ratios and sizes, because that gets across that. And then you could do it if you did 3D at two orthogonal planes. And I forgot my second thing, so that’s all I wanted to say. [Dáibhid Ó Maoilèidigh]: Can I make a suggestion related to that? Is there any concept that we could break it into its eigenmodes? So in other words, it’s a complex motion with many, many small motions and large motions. And in principle, if you break it into its eigenmodes at each individual level, maybe we can decompose it. [Jong-Hoon Nam]: That was the idea of what our poster, Wei-Ching Lin present the basilar membrane over the radial span vibrations decomposing to different eigenmode. And we did a similar thing over the tectorial membrane. Regarding the image visualization, depending on your presenting purpose, there could be different ways we are experimenting, different to a cube plot, like an elliptical plot, or to test the area of motor theory, like the entire area, how it changes, I think, depending on the purpose of what you try to present your idea, the way, different way of a presentation will be useful, I think. [Anes Macic]: I have two questions for Anna. First question is the phantom that you used for testing. What kind of motion was that? Was that a rigid body motion or was there any strain? I’m wondering if like strain induced de-correlation of your signal can influence, can you still do it if there is significant strain? [Anna Wisniowiecki]: So the phantom, as far as we know, it’s just a piezo stack. It’s supposed to move along one axis. But I don’t, I’m not sure exactly what you mean by the strain. It’s bonded, so we expect it to just be a rigid motion. [Anes Macic]: Okay, and my second question was, so when we do just vibration measurements from phase, we sort of don’t process reflectivity, but do you think that we could sort of have, if we do observe some modulation in reflectivity, we can say, oh, this is more likely to be a vector that’s pointing more along our optical axis than if we don’t see any modulation, we can sort of say, oh, this is likely to be something that’s more perpendicular to it. Do you think it can be combined with sort of 1D phase sensitive OCT? [Anna Wisniowiecki]: That’s actually the plan for vibration amplitude at the moment to get the amplitude from the normal axial measurements. But in the end, that method is, by choosing to use that, we’re still not sensitive to lateral motion. So we might be able to get the vibration. We’ll see that there’s motion from the vibration angle measurement in the perpendicular plane, but we won’t know the amplitude from our current method. [Anes Macic]: I think that’s still very useful. Thank you. [Anna Wisniowiecki]: Thank you. [Jong-Hoon Nam]: Okay, let us conclude this session. Let’s thank Anna, Anders and Scott again. COCHLEAR PROCESSING SESSION [Sebastiaan Meenderink]: Let’s move to the previous session, John’s talk, Karolina’s talk and Harry’s talk. Are there any questions coming up right now? People have, there were long lines at the microphones when I cut you all off, so there must be some lingering questions. They lingered away. [Dáibhid Ó Maoilèidigh]: I have a silly question. John, you mentioned that brain state doesn’t affect the answer, but isn’t the brainstem part of the brain, or am I mistaken? So a reflex is brain state. I know what you were getting at. It’s not attention. [John Oghalai]: So yeah, the way the auditory cortex people think about it, that’s the brain. [Sunil Puria]: I have a question for Hari. I noticed that your damaged chinchilla hypersensitivity tails were way hypersensitive. Usually, it’s like 6 dB in cats at least that I’ve seen, but they were like 30, 40 dB hypersensitive. I didn’t quite understand why that happened. [Hari Bharadwaj]: So, some of the tip to tail ratios that is in the data is in fact close to zero or even negative. And it seems to happen. And Mike, you should feel free to jump in. For a whole range of frequencies, one kilohertz and above. Yeah, so the, with noise-induced hearing loss in particular, the tip-to-tail ratios do go pretty low. [John Guinan]: The classic Liberman data showed 30 dB. And a typical kind of explanation was that he’s wiped out the outer hair cell stereocilia connection to the tectorial membrane. And so the stiffness is way down and the motion moves everything. And the phase is also reversed from the normal phase. Anyhow, 30 dB is a typical increase in the tail sensitivity. [Christopher Bergevin]: I also had a question for Hari. Thank you for the very nice talk earlier. When you’re talking about cochlear hearing loss, you referred to it as a complex mix. And I was kind of curious how that applied to the definition of the distorted tonotopy. So, two questions: Do you have a precise definition of what distorted is? And then the second question was, does that kind of, is that just applied to say kind of the basilar membrane or something? Or do you distinguish between something, or do you distinguish between, say, cochlear, basilar membrane tonotopy versus, say, brainstem versus cortical distortions in that regard? [Hari Bharadwaj]: So, the mention of the complex sensorineural hearing loss it was just to make sure that is clear that this distorted tonotopy, which I will try to define again, may not happen in all forms of sensory neural hearing loss, and it’s been observed primarily with noise-induced hearing loss in the chinchilla models, which seems to be associated with outer hair cell injury, either the outer hair cell loss or outer hair cell stereocilia damage. And when we say distorted tonotopy, we really just mean that a fiber whose characteristic frequency is such and such a number, it seems to be primarily coding temporal information that’s more than an octave below the CF. So that’s, it’s a functional definition and it’s at the auditory level. So it’s at the output of the cochlea. It’s not brainstem or anything else. [Karolina Charaziak]: I also have a question to Hari. I was wondering if you guys have also had a chance to collect any neural tuning curves in chinchillas but at lower frequencies, like below 2 kHz, where we know the tuning curves flip their shape, and they don’t have the low-frequency tail but they do seem asymmetric in the other way, and whether there was any change in the map at this weird, apical end of chinchilla cochlea. [Hari Bharadwaj]: I might pass this to Mike Heinz. [Michael Heinz]: I think, Hari showed the sort of population plot and below 1.5 kHz, there’s sort of like a half octave shift downward, which I think is sort of the classic sort of half octave shift. It’s the tip diminishing and shifting a little bit. I think our data set, this one at least, is sort of lacking maybe what you’re asking about, the even further like 500 Hz CFs and things like that. So I think certainly in this data set, it’s not there. I’m forgetting if we have some that really address your question of the really low frequencies. But I think to add onto the definition of distorted tonotopy, I think there’s the tip diminishing, which we all think about. That’s sort of the classic. And there’s a half octave, up to a half octave shift related to cochlear amplifier, cochlear non-linearity. But this is something, this is really a shift from tip-to-tail listening. And that’s sort of the point of this is that when we’ve tried to quantify the local Q10 effect on the neural coding, on the speech perception, that’s not as much able to explain the big effects as this tip-to-tail ratio. So, we’re trying to separate those two mechanisms and get people to think about the tip-to-tail shift. [Karolina Charaziak]: Thank you. I have one more question, maybe the answer is obvious and I am just not remembering, do we know what causes such a huge hypersensitivity at the tail? [Hari Bharadwaj]: I don’t know but I think John Guinan just had an explanation. [Hari Bharadwaj]: So, the hypersensitive tails are correlated with the loss of stereocilia between the outer hair cells and the tectorial membrane. That was established anatomically by Charlie Liberman in his classic study. It’s presumably reducing the stiffness and also reducing the drive to the outer hair cells. So there’s no drive to the outer hair, there’s no cochlear amplification, and there’s also less stiffness of the cochlear partition. [Dáibhid Ó Maoilèidigh]: Can I just ask then, is there a loudness perception deficit at super threshold levels for people that have this distorted tonotopy because they’re missing cells or damaged? I mean, obviously it’s hypersensitive, but if you go above their new thresholds, because loudness is related to the spread of the traveling wave. [Sunil Puria]: That’s supposedly what causes recruitment. But I don’t think it’s more hypersensitive than normal. It catches up to loudness at the high level. [Hari Bharadwaj]: In sensorineural hearing loss broadly, loudness perception does grow very rapidly. So, this might have something to do with that. And just to clarify one thing, so this distorted tonotopy phenomenon, to the extent that we can measure it in psychophysical tuning curves in humans, it seems very widespread. So it’s not a couple of people with distorted tonotopy. This is basically sensorineural hearing loss. [Sunil Puria]: Going back to the stereocilia damage, I don’t think that can explain 30 dB, that would mean that stereocilia is 30 times greater than the entire organ of Corti when you damage it. Does the amplifier get damaged and reduced? [John Guinan]: The idea is explained in my 2012 paper, what drives the inner hair cell stereocilia. When you detach the tectorial membrane from the rest of the organ of Corti, the motion of the organ of Corti then squeezes the space between the tectorial membrane and the reticular lamina, and that causes a longitudinal, a radial flow of fluid that drives the inner hair cell stereocilia. So it’s not that the motion, that the transverse motion has gotten much bigger. It’s that the radial motion across the inner hair cells has gotten much bigger. [Sunil Puria]: So it’s not a stiffness change. [John Guinan]: It’s not specifically a stiffness change of the organ of Corti. [Sunil Puria]: That helps me, thank you. [John Oghalai]: Two comments. So on that topic, we do have these Tecta mice where the tectorial membrane is lifted off the epithelium. And the passive mechanical vibration that they have because their outer hair cells aren’t stimulated is identical to a dead wild type mouse. So, there is no, it doesn’t vibrate more. Second thing was about loudness recruitment. I mean, yeah, that’s the classic thinking that it’s, you’ve got kind of a broader passive basilar membrane wave, you’re stimulating more inner hair cells and then the brain responds. Some of our data are suggesting maybe there is some increased cochlear amplification there too. So, we will see, we need to be testing that. [Sebastiaan Meenderink]: Sorry, I think it’s time that we move on to maybe the previous section from this morning. NONLINEAR DYNAMICS OF THE COCHLEA SESSION [Renata Sisto]: I’m here to elicit questions about nonlinear dynamics of the cochlear session five of this morning. Any question for our speakers? [Brian Frost]: I have a question for Henri. I thought it was interesting, and I know that we were talking about it earlier, that you have this best frequency sort of goes down in your model as you increase level, right? The peak frequency, I should say. And the first time you fixed that was by increasing longitudinal coupling. And then you almost, I don’t want to use too mean a word, you almost ruined what you fixed by adding in your energy pumping. But in my head, I was thinking, why can’t you just go increase longitudinal coupling again or add in, I don’t know, a third order or second order longitudinal coupling term on top of it to go fix that problem. I mean, obviously, eventually you’re just going to chase something. But it felt like that was all that was really missing for your model to fit data. [Henri Ver Hulst] So basically, when I added coupling, so it corrected for the shift in sensitivity. But yeah, I mean, the issue is that I introduced a linear regime, and obviously then I lose the compressive non-linearity that is characteristic of the cochlear non-linearity. I basically I cannot fix both the peak sensitivity and still have the compressive nonlinearity. So this is why like energy pumping was required to boost sensitivity to weak stimuli. [Brian Frost]: I guess my confusion is then what role in your final version, which has longitudinal coupling and the energy pumping, let’s say, what role is longitudinal coupling playing? If you take away the longitudinal coupling, what does that look like with the energy pumping still? Because it felt like what the longitudinal coupling fixed was then removed by the last term. You know what I mean? [Henri Ver Hulst]: So there are two things. The first thing, it’s very practical. It fixed a numerical instability, because basically, if I had only the energy pumping with 2D, I had numerical instability. I don’t know for sure that it was like, whether it was the numerical scheme that was unstable, or it was the model itself. But that’s unsure. And but second thing that I wanted to say was, coupling helps shaping the curve. So if I want to fine tune, you know, the comparative match between the curve in experiment and in the model, I needed to add coupling. And actually, it was dissipative coupling and I could also add elastic coupling, in which case I was also able to better capture the shape of the experiment. [Renata Sisto]: I also have a comment about that. Also, in my model I have to introduce a friction force due to viscosity to avoid instability when the fluid focusing is added in the model. It’s just a question of what you would prefer. They are preferring a longitudinal coupling between oscillators, I would prefer to speak about viscosity and interaction with viscoelastic elements. I have a stabilizing force proportional to the wave number and you to the wave number squared. Other question? [Yi-Wen Liu]: I have a question for Bastian. In your talk, you’re calculating the mutual information across different oscillators. And so my question is, how do we read it? So is an increase in mutual information always a good thing? Does that imply that the model is really doing a good job in processing the stimuli? [Bastian Epp]: Good question. The motivation behind using mutual information was to kind of say, is there anything that’s been going from the stimulus to the system. I would assume that having a high amount of mutual information is probably a good thing because there’s something that’s available. But how to map that one to one, I don’t know. And maybe mutual information is not the best way, maybe transfer entropy might be a better way because it’s like a unidirectional way, but I don’t know. It was just a way of trying to not make too many assumptions about information. [Yi-Wen Liu]: Thank you. [Stefanie Gutschmidt]: For Bastian or me, or anyone that is doing fluid interaction, fluid coupling. Has anyone modeled the fluid parameters from the base to the apex, including the dimensions of the organ of Corti, and do you see, or what are the changes of properties, this effective mass and effective damping properties, or viscosity properties, and can this somehow explain the two parameter ranges that we see, the linear response and the one third force response. That’s my question. [Henri Ver Hulst]: I’m not sure that I have properly understood your question, but what’s clear is that we don’t model the full organ of Corti, we consider only two degrees of freedom. And so it’s like a thin membrane. And concerning the fluid, I mean, it is assumed that it doesn’t depend on properties that vary with the anatomy, because obviously, like it’s a homogeneous fluid. [Stefanie Gutschmidt]: The fluid is Reynolds number dependent, that highly depends on the space. And so when you have oscillators in a fluid that are bound by boundary conditions, moving boundary conditions, you definitely have viscous layers and what have you that influence the properties. That’s the underlying question. [Renata Sisto]: They did not include. They did not include the viscosity and the viscous fluid. [Henri Ver Hulst]: Yeah, it’s not included in the fluid, but I mean, so basically the tonotopic properties appear in the, I mean, for example, if you put viscous force, you will have a Laplacian V term, yes? And basically, in that derivative of the fluid velocity field, you will have mechanical properties of the interface that will appear somehow. But this does not mean that the property of the fluid vary with the position. [Dáibhid Ó Maoilèidigh]: I have a question for Henri. Did you consider keeping the non-isynchronous term to help with the phase change that you need for the active energy pumping? Maybe that’s an alternative strategy. It seemed like you needed to shift phase so that you get energy pumping and you have a phase in the non-linear term that you haven’t taken advantage of? [Henri Ver Hulst]: Yes, that’s correct. Energy pumping arise at position that are basal to the peak. And basically, near the peak where the imaginary part of the non-linear parameter you wouldn’t have like, it’s too close to the peak sensitivity to have an effect on energy pumping of the traveling wave. I’m not sure. Okay, maybe Pascal. [Pascal Martin]: The imaginary part of the non-linear coefficient has nothing to do with the energy pumping. It will control the level dependence of the natural frequency of the oscillator, as Dolores has explained. If you have an imaginary part in your non-linear coefficient, then when you drive harder, the resonance, the peak of the resonance shifts. Depending on the sign of this imaginary part, it will shift towards higher frequency or towards lower frequencies. So, we could indeed use that to shape the resonance so that we can control how it shifts with level using that thing, but we didn’t want to go too much into that because we don’t want to do data fitting, really. We want to identify generic properties that will come onto our models, not details, and that’s a detail to us. And energy pumping is controlled by the phase relation between the driving pressure and the variable z. There’s this phase term there that comes from the transformation that brings the system into normal form. If this value is different than π/2, then all those, except when πis precisely equal to π/2, then all these critical oscillators will pump energy when they are driven at a frequency lower than the natural frequency. That’s a generic property. You get that for free. So something that people see in cochlear models, I don’t know if everybody agrees on that, but this is a property that’s generic to any critical oscillator. Any critical oscillator driven at the frequency that is lower than the natural frequency, frequency pumps energy into the environment. If it’s driven above, it sucks energy from the environment. [Dáibhid Ó Maoilèidigh]: So it has to do with the interpretation of [...] and it’s relation to observed [. . . ] [Pascal Martin]: Yes, yes, yeah, there’s a phase down there. [Jont Allen]: I think what I’m about to say is relevant to this, but I’m not absolutely positive. But the outer hair cell was extracted from, I can’t remember, was it a cat? And by Peter Dallos and his student, He. And they measured the longitudinal stiffness as a function of the membrane voltage. And what they very clearly showed is about a factor of two in the stiffness as you increase the voltage, then the cell becomes less stiff. And if the cell is sitting there perpendicular to the reticular lamina and it becomes left stiff, then the basilar membrane CF moves because the outer hair cell, I believe, we’ve got three rows of outer hair cells and they are controlling the basilar membrane stiffness. Now, if that’s true, and I don’t see how it can be avoided, then as the voltage changes, as the cell depolarizes, the outer hair cell becomes less rigid, turgor drops, the stiffness goes down, and that causes the CF to shift towards the high frequency region, towards the base. And that is a very important possibility, and I’ve written at least one detailed paper about how this all plays out in my poster out there. And the poster session explicitly delivers that. So I see this as inevitable. And it’s clearly, so please ask me, I’d be happy to share the paper with you. You can go look at the poster, talk to me. [Alessandro Altoè]: I have a question for Henri. You are looking at this coupled model through the point of view of oscillators. Have you tried to compute wave numbers? Can you get a wave number description from the Hopf point of view? [Henri Ver Hulst]: Once you have your model and you have your waves, you can analyze the data coming out from the model the way you analyze experimental data. So the question you ask is, can you extract a wave number from data? It’s the same question. And we can using stuff that you do. And when we do, we get a complex wave number with a real and imaginary part. And we indeed see that in the case where this phase parameter that we put in the model is different than π/2, I always forget which one is which, the sign of the imaginary part, is consistent with energy pumping basal to the best place, as you see in data. [Alessandro Altoè]: You use like this simple equation of the oscillator to actually describe the wave number other than the vibration in a way that helps interpreting the experiment? [Henri Ver Hulst]: So, we get it after the fact, right? We don’t get it a priori. We put the normal form, we couple the oscillators, so then we get the waves, and then from the waves, we measure the wavelength, and therefore the wave number. So we don’t get a priori. There’s not an analytical expression of the wave number a priori. [Alessandro Altoè]: What I’m getting at is that in short wave region or long wave region, you can use the oscillator equation to predict the wave number and might be actually cool. [Renata Sisto]: I suggest continuing the discussion during the dinner and move to the other session. HAIR BUNDLE MECHANICS II SESSION [Anthony Peng]: We’ll move back to the morning session, the first session this morning. So we had a bunch of talks about hair bundle stiffness and as well as energy consumption within the hair bundle. So if there are people who have questions for, it was Shefin, Jamis, Alexander, Dáibhid, and Rob. I’m going to start things off then and actually ask Alexander. You showed that there was this kind of gap or this kind of loss of force, or let’s say jump in displacement, let’s say, right? And so what do you think that’s actually caused by? [Alexander Cartagena]: That is a great question. I think the jumps are a combination of slippage combined with plane of the bundle and also the coherent motion of the bundle itself, hopefully on the opening of the MET channels because it does happen in one. So, the behavior depending on the two different conditions that I looked at seems to happen differently. [Anthony Peng]: Are you saying then that you think it’s gating compliance you’re seeing? [Alexander Cartagena]: Combination of. So I’m not totally sure because I haven’t been able to look at MET activity during deflections. So I think that will be the data that will be key in order to make sure and prove if that’s the case or not. If that’s not the case, then I am measuring some kind of bundle loss of cohesion and probably explained have been amplified during deflection. [Christopher Bergevin]: This is a question for Shefin. It’s a very naive basic question, but I was just wondering if you could comment on how fluid the membrane is and if things like lipid rafts or anything like that are kind of useful conceptually for thinking about what’s going on with regard to how the channels and the bilayer interact. [Shefin George]: Right, yeah. The concept of raft is kind of going around basically domains forming where specific lipids come together and basically helping the signaling of proteins. So with our technique, we do see, I mean, so domains are generally can range from like nanometer size to like maybe a couple of hundred nanometers, but usually they generally form less than 20 nanometers or 10 nanometer range. So with our technique, we can obviously see that at this moment. It’s been really coming up that it’s really important for the protein or channel activation, specific interactions with lipids. So yeah, that’s something that we would be interested in looking, but right now we don’t have that kind of resolution to see. [Robert Fettiplace]: I had a question for Alexander. I didn’t really understand how any of these data had any bearing on the cooperativity of the mechano-electrical transducer channels. Really the only way to work that one out is to actually record from the cells and look at the channels themselves. Does he have any comment on that? [Alexander Cartagena]: I completely agree. I mean the only thing that I am trying to convey to the audience is that, if we look that when if we look at the deflections at the nanometer scale, when I do this and I track the deflections, I do see that knowing that in one case we have absence of interconnections that I do see that the force curves show you different domains or I call them displacements or jumps that could be in that could be indicative of either splain of the stereocilia or it could have some kind of implication towards the cooperative gating. [Robert Fettiplace]: Can you explain what you mean by cooperative gating? So there’s no evidence for cooperative gating? [Alexander Cartagena]: No, no, there’s none. I agree. So to me, cooperative gating is that channels will open at the same time or channels will open in series when deflected. [Varun Goyal]: I have a question to Alexander as well. Just a curious question. I may have missed this information on your slides. So when you got rid of the top connectors, how much was the reduction in the bundle stiffness compared to when they were there? [Alexander Cartagena]: So the reduction is about 60 or 65%. So it’s quite significant. So when you compare bundles that have connectors with bundles without connectors, you have, or I calculated by AFM, the stiffness around five to six micronewtons over nanometers. I need to remind the units, but then I get like one to two. [Varun Goyal]: And just to, just to confirm, the tip links were intact in that case, right? [Alexander Cartagena]: Yes. [Dáibhid Ó Maoilèidigh]: I’ve just got a quick question for Rob. You’re talking about the amount of ATP that you needed to basically run the bundle. Can you compare that energy consumption to the amount of ATP is required to maintain the silent current? Because that’s another huge energy expenditure. So how do they compare in terms of how much ATP you’re consuming per second? [Rob Raphael]: [. . . ] it will just scale linearly. [Dáibhid Ó Maoilèidigh]: No, no, what I mean is if we compare how much energy it takes to maintain the calcium and proton gradient in a stereocilium with, let’s say, bundles in a section of the cochlea, is that 5% of the amount of energy it takes to maintain the silent current? Is it the same amount of energy to maintain the silent current? I mean, in other words, the cochlea is very metabolically active, there are mitochondria. Are the mitochondria equally working to maintain resting potential, recycled calcium? Is there a concentration? I know the stria vascularis is very vascularized. [Rob Raphael]: The silent current calculation is a little [. . . ] because that’s the energy up in the marginal cells to get the potassium back in. It’s also the energy of the sodium potassium also ATP and the fibrocytes so I would need to do some math I cannot do it in my head, and get back to you. Do you expect it, you are asking as a physicist? [Dáibhid Ó Maoilèidigh]: No, just wondering because you were talking about sizes. I’m just trying to get an intuition about how much energy is being expended where. And I just, maybe you knew the number. I don’t know. [Rob Raphael]: I will get back to you on that. [Ondrej Tichacek]: I have a question to Dáibhid. So I hope this is not too naive understanding, but you showed that basically if you compare your very detailed V-shaped model of the bundle with the idealized bundle, you don’t see actually so much effect of the V-shape. You see more effect of the angle. And I was wondering whether you have any take on what is actually the role of the V-shape because we see the V-shape and we don’t see it in the inner hair cell stereocilia for example. [Dáibhid Ó Maoilèidigh]: So there was a previous publication that talked about how for net flow across in the subtectorial space, the V-shape would help to reduce the drag associated with this net flow. So it is true, it creates a slight decrease, about 50% decrease, but the drag is still quite high for net flow. So what we were wondering is, is there a consequence of, you know, if you have a V-shape and then you stimulate the stereocilia with a given stimulus, presumably it’s going to create some negative consequences because it’s not idealized. But how large are those negative consequences? They didn’t seem to be that large. I was surprised that it didn’t deviate from ideal as much as I expected it to deviate. So maybe it’s a way to pack stereocilia and retain three rows. It’s a speculative reason. If there’s a good reason to have three rows, but you want to have as many stereocilia within a given cross-section that you have for a single outer hair cell. But I don’t know yet. [Jont Allen]: it’s a trade-off! [Dáibhid Ó Maoilèidigh]: It may be a trade-off. Yeah. [John Oghalai]: Could I speculate too? I mean, a lot of our experiments with bundles are keeping the reticular lamina flat and you deflect the bundle. But in the mammalian cochlea, that isn’t how it really works, right? And especially with the outer hair cells, the whole reticular lamina is bending. And a lot of the measurements that we’re seeing now show a lot of longitudinal movement, radial movement. That bundle, if it’s a straight line, might be really tilting quite a bit. But if it’s at an angle, it might give it more support and be able to maintain its integrity. [Dáibhid Ó Maoilèidigh]: That’s absolutely right. Maybe it’s a structural issue that prevents it from. [John Oghalai]: I mean, I think it was your talk where you showed there was a lot of potential bundles that never really sprouted. Or they sprouted in the progress. [Dáibhid Ó Maoilèidigh]: That’s right. The stereocilia retract. So it could just be a structural stability issue. Yeah, that’s true. [Francesco Gianoli]: I have a question for Dáibhid. Since we are wildly speculating, how independent are the two sides of the V-shape. So, we know that the motion in the cochlea is not exactly radial, longitudinal process that are a bit slanted, so how much it could be an independent motion of the two sides? [Dáibhid Ó Maoilèidigh]: That’s an interesting idea. I mean, yeah. Yeah, no, that’s a really interesting idea. What we saw is the left and right wing were moving anti-symmetrically. So they were moving to the center at the same time and away from the center at the same time. So they were gating approximately in sync. And there was about a 10% to 15% variability in the timing relative to the mean time, you looked at the standard deviation. So there wasn’t that much timing variability, which I was really surprised about because all of the channels are being gated with very different amplitudes. So it’s not impossible, and as I mentioned, some of the bundles have very short wings, and some of those bundles, the radial fibrous to my knowledge, and the tectorial membrane extend longitudinally a little bit. So it may be that the bundle orientation is following the radial fibers to some degree and this asymmetry creates a preferred direction of stimulus that’s not along that notch column but is displaced from the notch column. So we’re going to check that out and we’re going to check for those shapes. [Sunil Puria]: And the angle changes from base to apex of the weighing. We showed that with Philip Joris, with Tony. Yeah, that’s also interesting. [Jont Allen]: I think it’s important to think about the distance between outer hair cells, which I think is like 10 or 12 microns, and the wavelength locally. So, you should compute a dimensionless number of the wavelength over the 12 microns or the reciprocal of that. And that is an important consideration when you’re actually trying to do any analysis because it has to do with sampling. And the one thing that I wanted to say from before is frequency times the wavelength is equal to the speed of the wave. And the reciprocal of the wavelength is the wave number. So that’s the formula you want to use to get relationships between wave numbers. And k, the wave number, which is a reciprocal wavelength, is ekt or something like that. [Dáibhid Ó Maoilèidigh]: So the wavelength to my knowledge is much larger than the diameter of a hair bundle. So approximately speaking, all of the hair bundles in a near the peak even are being deflected approximately the same amount in the same direction. It’s a much bigger scale. The wavelength is 200 microns at the peak and it’s much larger than the scale we’re looking at. CLOSING [Anthony Peng]: Okay. Thank you, guys. So, thank you all again. Thank you, all the speakers.