Hair cells with heterogeneous transfer characteristics encode mechanical stimuli in the lateral line of zebrafish

Ribbon synapses of hair cells transmit mechanical information but the transfer characteristics relating deflection of the hair bundle to glutamate release have not been assessed directly. Here we have imaged glutamate to investigate how hair cells encode information in the lateral line of zebrafish. Half the hair cells signalled cupula motion in either direction from rest, achieving maximum sensitivity for deflections of ~40 nm in the preferred direction. The remainder rectified completely and were less sensitive, extending the operating range of the neuromast beyond 1μm. Adaptation was also heterogeneous, with some hair cells generating sustained synaptic outputs and others transient. A unique signal encoded a return to rest: a transient burst from hair cells unresponsive to the initial stimulus. A mixed population of hair cells with these various transfer characteristics will allow a neuromast to encode weak stimuli as well as the amplitude and duration of stronger deflections.


Introduction
An increasingly important context for the study of mechanotransduction is the lateral line of larval zebrafish (Graydon et (Nicolson, 2015). Understanding the transfer characteristics of these synapses is therefore fundamental to understanding how mechanical information is encoded within the lateral line.
All the hair cells within a neuromast act as a population to encode a single mechanical stimulus -the deflection of the cupula into which they all project. The direction of deflection is encoded by a "push-pull" system in which half the hair cells are depolarized by motion in one direction and the other half by motion in the opposite, with segregation of these two populations onto separate afferent fibers (Faucherre et al 2009). A number of fundamental questions about signalling in the lateral line remain unanswered. How does the output of individual hair cells encode deflections of the cupula? What is the dynamic range over which signalling occurs? And how does the output from the synaptic ribbon adapt? It is equally important to understand how these properties might vary between hair cells to determine how the population acts to encode the amplitude and duration of a stimulus.
Direct answers to these questions require assaying the release of glutamate from individual hair cells while deflecting the hair bundle by known amounts. The output of hair cells has been studied by measuring capacitance changes (Beutner et al 2001;Brandt et al 2005;Ricci et al 2013;Olt et al 2014) or by recording synaptic currents in the afferent fiber (Keen & Hudspeth 2006;Li et al 2009;Weisz et al 2012), but both these techniques require the synapse to be activated by direct injection of current which bypasses the normal process of mechanotransduction. We therefore developed an all-optical approach in which deflections of the cupula and release of glutamate from multiple hair cells were imaged within one neuromast. Monitoring synaptic transmission using the glutamate sensor iGluSnFR (Marvin et al 2013) allowed us to investigate the transfer characteristics of both individual hair cells and the population.
Here we show that the output of a neuromast is determined by a heterogeneous population of hair cells. About 40% signal deflections of the hair bundle less than 100 nm, while the remainder are less sensitive and extend the dynamic range of the neuromast to encode deflections beyond 1 µm. These heterogeneous transfer characteristics extend to the dynamics of adaptation, enabling the generating of a population code that signals weak stimuli while maintaining the ability to encode the amplitude and duration of stronger deflections.

An all-optical approach to measuring the transfer characteristics of hair cell ribbon synapses in vivo
The lateral line system has been studied intensively but the input-output relation of hair cells within neuromasts is still unclear. To observe the output in larval zebrafish we used the Sill promoter to drive expression of the fluorescent glutamate sensor iGluSnFR in the surface membrane of primary afferents postsynaptic to hair cell ribbons (Pujol-Martí et al 2012;Marvin et al 2013;Figs. 1A-C). Neuromasts in the posterior lateral line were stimulated using a narrow pipette that applied positive and negative pressure steps, generating iGluSnFR signals at distinct hotspots ( Fig. 1D-F). To test if these hotspots coincided with presynaptic ribbons we used fish co-expressing iGluSnFr with Ribeye-mCherry (Odermatt et al 2012). Figs. 1D and E home in on four varicosities from two afferents: two of the ROIs were contacted by one ribbon (amber and blue ROIs) while the other two were not (red and green ROI). iGluSnFR signals were only observed in areas that were not in close apposition to a ribbon synapse (Fig. 1F), and this was the rule in all three neuromasts in which this test was made. This example also demonstrates how synapses of opposite polarity could be monitored simultaneously: while the blue ROI was activated by positive deflections towards the head the amber ROI was activated by negative deflections towards the tail (Fig. 1F).  Figure 1E). Fig. 1I shows images of the cupula at z = 15 µm, from which the x translation was estimated from the movement of the centre of mass of the fluorescence. At any single pressure, the x translations at different z gave consistent estimates of the angle of rotation confirming that the lower part of the cupula behaves as a beam pivoting around its base ( Supplementary Fig. 1D). We were therefore able to 4 calibrate the relation between applied pressure and rotation of the cupula for each experiment, which in turn allowed us to control for variables such as the diameter of the pipette delivering the stimulus or its location relative to the neuromast (  Figure 1F).

Ribbon synapses in the lateral line can signal deflections less than 100 nm
What is the mechanical sensitivity of hair cells in the lateral line? Relating spikes in the afferent nerve to estimates of cupula deflection, Haehnel-Taguchi et al (2014) report that deflections below 8 µm cannot be encoded. In contrast, calcium imaging in the hair cells themselves indicate that robust responses can be elicited by deflections of about 2-3 µm (Sheets et al 2012;Kindt et al 2012). Imaging glutamate release we found that many hair cells were at least an order of magnitude more sensitive than these estimates, signalling deflections less than 100 nm.

Figure 2 near here
The traces in Fig. 2A show iGluSnFR signals from two nearby hair cells in response to positive and negative pressure steps of increasing amplitude, each lasting 1 s. It can be immediately seen that hair cell 1 (black trace) was more sensitive to small deflections from rest, generating changes in glutamate release at stimulus strengths that did not elicit glutamate release from hair cell 2 (red trace). The mechanical tuning of these receptors was characterized as the peak amplitude of the iGluSnFR signal (R) as a function of angular rotation of the cupula (X), as plotted in Fig. 2B. A good description of this relation was provided by a two-state Boltzmann equation of the form: Where R max is the saturating response in the preferred direction, R min is the maximum change in the null direction, X 1/2 is the rotation that half-activates and X S is the slope factor.
Notably, this equation also provides a good description of the relation between hair bundle displacement and mechanotransducer current in hair cells of a number of species, where it has been interpreted as reflecting the transition of the mechanotransducer channel between an open and a closed state (Holton & Hudspeth 1986;Crawford et al 1989).
The two synapses in Fig. 2B differed most significantly in X 1/2 (arrowed), which is the point at which the gradient of the input-output relation is at its steepest and the sensitivity 5 of the receptor at its maximum (Dayan and Abbott, 2001

Heterogeneous transfer characteristics of hair cells within individual neuromasts
The input-output relation of hair cells within a neuromast also varied significantly in their working range (WR) -the deflection required to increase the response from 10% to 90% of maximum (Markin & Hudspeth 1995). The hair cells featured in Fig. 2A and B operated over relatively broad working ranges of 490 nm (5.6°) and 790 nm (9.1°), respectively.
Other receptors, however, operated with much narrower working ranges of 90 nm (~1°), as shown by the black trace in Fig Fig. 2E, which displayed an initial peak followed by a long tail. The initial peak contained about 60% of synapses and was centred at ~1.5°, which is equivalent to deflections of 130 nm. These estimates fall within the range of measurements (20-400 nm) made in auditory and vestibular hair cells of a number of species (Fettiplace & Kim 2014). The other 40% of synapses, however, signalled much larger deflections, with working ranges between 5° and 30° (0.5 -2.5 µm).

Figure 3 near here
The variety of input-output relations measured using iGluSnFR was not expected and we wondered if it might reflect an unexpected property of the reporter. We therefore also assessed the signal transmitted from hair cells by imaging the calcium in the post-synaptic afferent using GCaMP6f under the pan-neuronal HuC (elavl3) promoter (Experimental Procedures).

Individual hair cells can encode opposing directions of motion
The two populations of hair cells polarized to opposite directions allow the neuromast to encode the direction of a stimulus using a "push-pull" system, similar in principle to the ON and OFF channels in the retina (Ghysen & Dambly-Chaudière 2007;Masland 2012). It is less clear whether individual hair cells also encode opposing directions of motion.
Afferents leaving the neuromast spike spontaneously and this activity is driven by the release of glutamate from hair cells at rest, which is in turn dependent on the activity of the mechanotransducer channel (Trapani & Nicolson 2011). Can this activity be reduced by deflection in the non-preferred direction? The red trace in Fig. 4A shows an example where this is indeed the case: deflections of the cupula in the non-preferred direction caused a decrease in glutamate release and the input-output relation in Fig. 4B shows that this synapse used 40% of its dynamic range to signal motion in the null direction. In contrast, another hair cell in the same neuromast was completely rectifying, only modulating release in the preferred direction (black trace in Fig. 4A).

Figure 4 near here
The ability of individual hair cells to signal opposite directions of motion was quantified as the "relative set-point" for glutamate release -the fraction of the total dynamic range of the synapse modulated by deflections from rest in the preferred direction. The distribution of relative set-points across a sample of 67 hair cells is shown by the histogram in Fig. 4C.
In 27% of synapses this fraction was less than 0.7, i.e more than 30% of the dynamic range was used to signal deflections in the null direction as a decrease in the rate of glutamate release. These results demonstrate that while the output from most hair cells in the posterior lateral line rectify strongly, the large majority can encode deflections of the cupula both towards the head and away. This property will allow for larger differential signals in the two afferents, whereby an increase in the spike rate of one occurs simultaneously with a decrease in the rate of the second to below the spontaneous rate in the absence of a stimulus.

A mixed population of high-and low-sensitivity hair cells
How do hair cells with different transfer characteristics act as a population to encode a deflection of the cupula? To obtain an overall picture of how the neuromast operates we estimated the total input to a single afferent by averaging the stimulus-response relation 7 from 67 hair cells, assuming that hair cells of opposite polarity were, on average, mirrorimages of each other (Fig. 5A). This assumption was based on the observation that the stimulus-response relations of hair cells signalling deflections towards the head were not significantly different from those signalling deflections towards the tail. The tuning curve averaged over all hair cells could be described as the sum of two sigmoid functions with significantly different slope factors and half-angles (X S(1) = 0.4 ± 0.1, X S(2) = 1.9 ± 0.9, X 1/2(1) =0.6 ± 0.09° and X 1/2(2) = 6.1 ± 1.1°). The distribution of half-angles shown in Fig. 3C also indicated two basic populations of hair cells, separable either side of X 1/2 = 2°, so we also averaged the stimulus-response relations for hair cells above and below this threshold, as shown in Fig. 5B. The slope factors and half-angles describing the transfer function of these two populations were X S(<2°) = 0.5 ± 0.04, and X 1/2(<2°) = 0.7 ± 0.04 (red trace) and X S(>2°) = 1.8 ± 0.3, and X 1/2(>2°) =5.0 ± 0 (blue trace). Separating these populations according to X 1/2 revealed another important functional difference: hair cells of low sensitivity were completely rectifying with a relative set point of one while cells of high sensitivity had a relative set point of 0.8.

Figure 5 near here
The sensitivity of a sensory system can be quantified as the change in response per unit change in stimulus i.e the first derivative of the stimulus-response relation (Dayan & Abbott 2001). The dashed line in Fig. 5C shows this function for the average output of all 67 hair cells, from which three features stand out. First, the neuromast achieves maximum sensitivity at deflections of just ~40 nm at the tip of the hair bundle. Second, deflections from rest can be signalled with a sensitivity about 63% of maximum, either as an increase or a decrease in glutamate release, and this is made possible by the relative set-point of the high-sensitivity population of hair cells. Third, the high-sensitivity population saturates at deflection of ~220 nm, but the dynamic range of the neuromast as a whole is extended up to about 1 µm by the low-sensitivity population. Acting together, these two groups of hair cells will make the neuromast very sensitive to small deflections of the cupula while maintaining a large dynamic range.

Heterogeneous adaptive properties of hair cells within individual neuromasts
A second strategy by which sensory systems prevent saturation is adaptation, a timedependent change in gain that adjusts the working range in response to the recent history of stimulation (Wark et al 2007).  (Howard & Hudspeth 1987;Shepherd & Corey 1994;(Holt et al., 2002); (Kennedy et al., 2003)), reviewed by (Ricci & Kachar 2007) and depression at the ribbon synapse (Schnee et al 2005;Schnee et al 2011;Goutman 2017). These two processes have been studied in isolation, but little is known about how they act together to adjust the input-output relation of the hair cell.
To investigate the adaptive properties of the neuromast we applied saturating or nearsaturating pressure steps of 2 s or more. In 61 of 65 hair cells adaptation was apparent as synaptic depression but there was a large degree of variability within the same neuromast.
For instance, Fig. 6A shows an example in which glutamate release fell to about 30% of peak in one hair cell (red) but only to 70% of peak in another (black). We quantified the reduction in glutamate release as an adaptation index (

Hair cells sensitized by small deflections
Adaptation in sensory systems is usually thought of as a reduction in gain acting to prevent saturation (Wark et al 2007), but in 3 cells a strong deflection caused the rate of glutamate release to increase over periods of a few seconds, as shown by the red trace in qualitatively similar mechanism appears to operate in the neuromast where depressing synapses most clearly signal a deflection away from rest and sensitizing synapses signal a deflection back to rest.

Population signalling of a return to rest
Here we have shown that push-pull signalling within a neuromast is facilitated by the highsensitivity population of hair cells with relative set-points below 1 (Fig. 4A) and by a mixture of sensitizing and desensitizing hair cells (Fig. 6). A third and distinctive property of the population signal is shown by the pair of synapses in Fig. 7A, which were of opposite polarity and completely rectifying such that a deflection in the non-preferred direction did not generate a response (green boxes). A return to rest from the non-  we discuss how these variations contribute to the information that can be transmitted as well as the cellular mechanisms by which they might arise.

Sensitivity, working range and set-point
The high-sensitivity group of hair cells operated with half-angles around 1.5° (Fig. 2F), which corresponds to a displacement of 130 nm at the tip of the stereocilia and is comparable to the sensitivity of auditory and vestibular hair cells in mice and other species (Fettiplace & Kim 2014). This group saturated at deflections of ~220 nm (Fig. 5B), which is much narrower than the working range of the neuromast as a whole (Haehnel-Taguchi et al 2014). The difference can be accounted for by the second, low-sensitivity population of hair cells that extended the dynamic range of the neuromast beyond 1 µm. A strategy for detecting stimuli with high-and low-sensitivity receptors allows the neuromast to encode weak stimuli effectively without saturating.
An important feature of the high-sensitivity hair cells was a relative set-point that allowed small deflections in either direction to modulate glutamate release (Figs. 4 and 5).
The sensitivity to deflections from rest achieved 63% of the maximum measured at ~40 nm ( Fig. 5C) so it seems likely that deflections less than 50 nm will be transmitted to targets in the hindbrain. The behavioural significance of detecting such small deflections is, however, harder to judge and would require one to measure (or perhaps calculate) deflections of the cupula in a motile fish. One possibility is that the high-sensitivity group of hair cells are involved in the sensing of flow velocity gradients around the body of the fish that have recently been shown to underly rheotaxis in the absence of visual input (Oteiza et al 2017). Low-sensitivity hair cells would then be available to encode stronger stimuli triggering reflexes such as the escape response.
What are the mechanisms that underly these variations in sensitivity? One potential locus is the transduction process within the hair bundle. The relationship between displacement from rest and the MET current has also been found to vary in different hair

Adaptation
We also found a large variability in the adaptive properties of hair cells within individual neuromasts, in terms of the degree, speed and even direction (Fig. 6). Such a mixture of responses will help the population within a neuromast to signal both sustained stimuli, such as water flow (Voigt et al 2000), Adaptation of the MET current varies strongly between hair cells but can generally be described by two time constants, τ fast in the ms range and τ slow in the tens of ms range (Shepherd & Corey 1994;Holt et al 1997;Vollrath & Eatock 2003;Stauffer & Holt 2007).
These processes are, however, orders of magnitude faster than the kinetics of adaptation that we were able to observe at the output of the synapse (Fig. 6), indicating that the ratelimiting process is downstream of the MET channel. A strong possibility is depletion of releasable vesicles at the ribbon synapse. Indeed, capacitance measurements of exocytosis in hair cells of the lateral line demonstrate that a strong step depolarization stimulates release that decays with time constants of ~500 ms (Lv et al 2016;Eatock 2000), while optical measurements at ribbon synapses in the retina demonstrate that these can also depress with time-constants of a few seconds (Nikolaev et al 2013).
An intriguing finding was that a small number of hair cells sensitized during small deflections by gradually increasing the rate of glutamate release over periods of hundreds of milliseconds (Fig. 6). As well as signalling weak but continuous stimuli, sensitization will cause the offset to be signalled more strongly than the onset. Both these phases of the output may play a role in behaviours such as rheotaxis, where constant but slow flows of water deflect the neuromasts for prolonged period, and deviations from this flow orientation trigger a righting behavior (Oteiza et al 2017). Studies of the MET channel do not usually test its modulation over these longer time-scales, so it is difficult to assess if these might be the cause of sensitization. A stronger candidate for the intracellular signal 13 integrating these weak stimuli is the accumulation of calcium in the cytoplasm, which has been shown to accelerate the trafficking of vesicles for release (Castellano-Muñoz & Ricci 2014) as well as exocytosis itself (Pangršič et al 2015). This replenishment process will likely also determine the degree of adaptation achieved in the steady state (Baden et al 2014).
A second process that signalled the offset of a stimulus was so-called "negative adaptation" to hair bundle deflections away from the kinocilium, which primed the hair cell to generate a transient burst of glutamate release when the cupula returned towards rest (Fig. 7). The amplitude of this signal was a function of both the amplitude and duration of the deflection and therefore encoded the integrated stimulus. A signal that specifically informs upstream circuits of the cessation of an input might be used to, for instance, readjust the gain with which incoming signals control motor behaviour.
14 Experimental Procedures

Fish husbandry
Adult zebrafish (Danio rerio) were maintained in fish water at 28.5°C under a 14:10 hour light:dark cycle under standard conditions (Brand et al 2002). Fish were bred naturally and fertilized eggs were collected, washed with distilled water and transferred into 50 ml of E2 medium (concentrations in mM: 0.05 Na2HPO4, 1 MgSO4 7H2O, 0.15 KH2PO4, 0.5 KCl, 15 NaCl, 1 CaCl2, 0.7 NaHCO3, pH7-7.5). At 24 hours post fertilisation (hpf) 1-phenyl2thiourea (pTU) was added to yield a final concentration of 0.2 mM to inhibit pigment formation. All procedures were in accordance with the UK Animal Act 1986 and were approved by the Home Office and the University of Sussex Ethical Review Committee.

Fish Lines
The This line allowed us to image the iGluSnFR signal in afferent neurons while visualising synaptic ribbons in hair cells. All fish were maintained in a nacre mutant background (Lister et al 1999).

Mounting and Cupula Staining
All experiments were performed at room temperature (20°C -25°C) using larvae at 7-10 days post fertilisation (dpf). At 4 dpf, embryos were screened for the strongest expression of the appropriate. Larvae were anaesthetised by immersion in 0.016% tricaine (MS-222), diluted in E2. They were then placed side-down into a 'fish-shaped' pit carved into a thin (~1mm) layer of PDMS (Sylgard184, Dow Crowning) on a coverslip. Mechanical stability was provided by a 'harp' (Warner Instruments) placed on top of the larva. The pressure applied by the nylon strings was adjusted to allow normal blood flow while maintaining enough pressure to hold down the larvae. The larva was then paralyzed by injection of 0.25mM alpha-Bungarotoxin (αBTX; Tocris) into the heart. To avoid damaging the cupula, special care was taken not to touch the upward-facing side of the fish during the mounting procedure. The cupula was then stained by incubating the fish in a 1:500 dilution of 1mg/ml WGA AlexaFluor-594 or WGA AlexaFluor-350 (Life Technologies) for 2 minutes followed by thorough washing with E2. When counter-staining hair cells with FM4-64 (Synaptored, Biotium) larvae were incubated in a 1 µM solution for 1 minute and then washed with E2.

Mechanical stimulation
Pressure steps were applied to a neuromast through a glass pipette attached to a high speed pressure clamp (HSPC-1, APA scientific) (Trapani et al 2009). The output pressure was controlled and recorded using mafPC software (courtesy of M. A. Xu-Friedman) running in IgorPro (Wavemetrics) and synchronised to image acquisition. The micropipette was pulled to a diameter of ~30 µm and the tip bent through 30° using a micro forge (Narishige) to allow liquid flow parallel to the body of the larva. The tip was positioned ~20 µm above the body, ~100 µm from the neuromast. This study was confined to neuromasts of the posterior lateral line with an 'anterior-posterior' axis of sensitivity. The direction of the pipette (pointing towards the tail or towards the head) was changed during the course of some experiments but did not affect measurements.

In Vivo Two-Photon Imaging
Fish were imaged on a custom built two-photon microscope driven by a mode-locked Titanium-sapphire laser (Chameleon 2, Coherent) tuned to 915 nm. Excitation was delivered through a 40x water immersion objective (Olympus, 40x LUMIPlanF, NA: 0.8) and emitted photons were collected both through this objective and an oil condenser (NA 1.4, Olympus) below the sample. Green and red fluorescence was separated by a 760dcxru dichroic and filtered through 525/70 nm and 620/60 nm emission filters before being focused onto GaAsP photodetectors (Hamamatsu). The microscope was controlled by ScanImage v3.8 (Vidrio Technologies) and image acquisition was synchronised with the stimulus. Movies were acquired at 10-50 Hz.

Measuring deflections of the cupula
The angular deflection of the stained cupula was assessed by measuring its translational displacement in multiphoton images in planes at different z distances from the surface of the hair cells. These measurements were made at a variety of stimulus pressures and repeated in 3-4 planes 5 µm increments. The central position of the cupula within each frame was extracted by first thresholding the image and then fitting an ellipse to estimate the centre of mass. Next, the translational deflections induced by the applied pressure steps in each plane were calculated: these were consistent with the proximal regions of the cupula (z < 15-20 µm) behaving as a pivoting beam (McHenry & van Netten 2007). In this way, a calibration of the angular deflection of the cupula for each stimulus pressure was obtained for each experiment (Fig. S1). This calibration was repeated if, for instance, the pipette was moved.

Image Analysis
Images were analysed in Igor Pro (Wavemetrics) using custom-written software including the SARFIA toolbox (Dorostkar et al 2010). Movies containing small drifts in the x-y dimension were registered but movies mages with large drifts, including potential zmotions, were discarded. Regions of Interest (ROIs) were determined using an algorithm that began by identifying pixels with both large signals and high degrees of temporal correlation. Pixels surrounding thee ROI "seeds were added to the ROI until the correlation value fell below a threshold. Background fluorescence was then subtracted and baseline fluorescence (F o ) was defined as the average fluorescence preceding the first stimulation interval. The change in fluorescence relative to baseline (∆F/F o ) was calculated and used for further analysis.
The adaptation index (AI) was calculated as: Where R peak is the instantaneous peak response after stimulus onset R sustained is the average responses during the last 100 ms of stimulus presentation. Therefore, an AI close to 0 indicates no adaptation, an AI close to 1 indicates complete adaptation and a negative AI indicates sensitization.

Figure Legends
(C) Responses of two hair cells from another neuromast, which differ more significantly in their working range.  neuromasts. In Neuromast 1 the red and blue traces in (B and C) have an X 1/2 of 3.5° and 6.6° and a working range of 6.6° and 5.5°, respectively. In neuromast 2 (D-F) X 1/2 ranges from 1.4° to 3° and the working range spans from 1.7° to 3°.
(B) The average stimulus-response relation of hair cells separated into two groups based on half-angle with a threshold of 2°. The two subsets had average half-angles of 0.7° (red) and 5° (blue). The high-and low-sensitvity groups of hair cell also differed significantly in R min , the maximum change in the null direction, with values of -0.11 ± 0.01 and -0.02 ± 0.02, respectively. The working rages of these populations were 2.3° and 8° respectively and overlapped between 1° and 1.9°.
(C) The sensitivity of the whole population calculated as the derivative of the fit in (A).
Small deflections (below 2°) are encoded with high sensitivity by the large population of hair cells whereas the second smaller population extends the dynamic range significantly to also capture larger cupula deflections, ranging beyond 10°. (C) Distribution of adaptation index from 65 hair cells stimulated with a 5 s step.
(D) Distribution of the decay time constants from the 55% of cells that could be fit with tau < 2 s. In the remainder of cells tau was greater than 2 s and could not be estimated.
(E) A series of iGlusnFr signals from one hair cell. Large deflections cause glutamate release to rapidly reach a peak and then depress while small deflections do not generate a detectable signal for ~0.5 s after which glutamate release accelerates.
(F) Two hair cells from the same neuromast responding to negative deflections. Cell 1 shows sensitization to small deflections but cell 2 does not.
(G) The adaptation index as a function of deflection angle for cell 1 (red) and cell 2 (black) from B. Dashed lines are fits to the points.

(B)
The relationship between angular deflection in the null direction and amplitude of the rebound response. Data is averaged from 33 hair cells in which the largest rebound response exceeded 20% of the maximum response in the preferred direction (R max = 0.32 ± 0.01, R min = 0 ± 0.01, X 1/2 = -0.56 ± 0.05 and X s = 0.3 ± 0.05). displacements to positive and negative pressure steps of increasing magnitude (black, green and red, corresponding to stimuli delivered boxes shown in D). Note that x displacement is directly proportional to z at any pressure, indicating that the cupula moved through a fixed angle, acting as a beam. The angular deflection was calculated as tan -1 (Δ/z), where (Δx) was the translation in the centre of mass of the staining in C.
(F) A calibration curve relating the stimulus pressure to the angular deflection from the measurements in C-D (grey shading is the s.e.m). The relation is roughly linear.