We characterized the morphology and electrophysiology of spiral ganglion neurons (SGN) using whole cell patch-clamp recordings combined with single-cell labeling from the middle turn of rat cochleae ranging in age from post-natal day (P) 1 through P16. Labeled SGN were classified in the XZ plane of the organ of Corti, where both sides of the inner hair cell, the tunnel of Corti, and three rows of outer hair cells (OHCs) are identifiably organized for classification (schematized in Figure 1A). The dendritic morphology of individual SGN was characterized by introducing biocytin into the soma via the patch pipette (Figure 1B &C). The biocytin diffused to fill the peripheral terminal (Figure 1B). The biocytin filled neuron was visualized after fixation and immuno-processing using fluorophore conjugated streptavidin (Figure 1B; see Materials and methods).

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We identified two subtypes of SGN based on their connectivity to cochlear hair cells. Type I SGNs contacted inner hair cells (Figure 1D–F; n = 50), while type II SGNs (Figure 1G; n = 9) projected underneath the inner hair cells, turned toward the cochlear base and made multiple contacts under the outer hair cells (ranging from 6 to 15 contacts). Of the type I afferents, many reconstructed afferent fibers had terminal branches that did not touch on any hair cells but projected into neighboring areas, proximal to the hair cells (Figure 1D .2, 1E.2, 1F.2). These fibers project on areas that are not visualized with Myosin VI signaling. In other cases (n = 2), type I SGN terminals extend to a neighboring inner hair cell. Finally, in one case, the fiber projected into the outer hair cell layer but did not turn. This fiber was also negative for peripherin (see Materials and methods). We did not encounter any other examples of putative Type I fibers extending out to the OHC region such as observed in other studies (e.g. Huang et al., 2007). However, because peripherin is not a definitive marker for Type II fibers, especially in early development, we excluded this fiber from further analysis.

In this age range, the branching patterns of Type I fibers are highly polarized to either the modiolar or pillar face of a hair cell. For those fibers that contact the modiolar face, nearly all the branches of the fiber are also located on the modiolar side of the hair cell and vice-versa (See Figure 1—figure supplement 1 and Appendix 1). Whether this indicates the presence of selective guidance cues for modiolar versus pillar-contacting fibers remains to be tested. Although the polarization of fibers allowed us to confidently assign fibers as being either modiolar- or pillar-contacting, we moved away from this bimodal classification in preference for a more continuous scale as described below.

We defined a continuous position scale, which we refer to as ‘Normalized Basal Position’ (NBP), to quantify where SGN terminals contact the inner hair cells (Figure 1H). The ‘modiolar’ and ‘pillar’ halves of the hair cell were first defined by drawing a bisecting plane from the basal pole to the cuticular plate of the hair cell in the XZ plane of the confocal scan. The origin (NBP = 0) was set at the basal pole of the bisected inner hair cell. To determine NBP we first computed the fractional distance of the contact position along the radial axis of the hair cell (c) relative to the length of the hair cell (L) (see Figure 1H). The normalization by hair cell length standardized the position scale across preparations and controlled for possible changes in hair cell length with age. This value was multiplied by +1 if the contact position was on the modiolar face and by −1 if the contact position was on the pillar face.

NBP measurements were only made when the preparation was in relatively pristine condition after electrophysiological manipulations and immunostaining. Therefore, only a subset of the data had this measurement (n = 38 of 50). If there were multiple branches that contacted the inner hair cell, we used the most extreme contact position relative to the basal pole for our analyses. NBP values ranged from −0.32 to +0.52 (n = 38) (Figure 1I). In the preparations where we could not measure the NBP, we could classify the position on a bimodal system as either modiolar-contacting (NBP >0) or pillar-contacting (NBP <0). In total, we classified 34 fibers as modiolar-contacting, 16 fibers as pillar-contacting, and nine as type II SGN. The non-uniform distribution between Type I, Type II and subtypes of Type I fibers is in line with the pattern of innervation previously reported in rat and cat animal models, where the vast majority of SGN fibers appear to land on the modiolar-face of the inner hair cell (Liberman and Oliver, 1984; Kalluri and Monges-Hernandez, 2017).

As we showed in the previous section, we found significant correlations between several biophysical properties and normalized basal position. In this section, we generate prediction models for normalized basal position based on a linear combination of multiple biophysical features. The full details of the model building can be found in the methods. Briefly, the process began by pooling all the current-clamp and voltage-clamp features that are significantly correlated with basal position. To prevent overfitting, the number of variables retained into the model was reduced using a backward stepping process, with highly collinear (i.e. redundant) variables removed. By analyzing the collinearity between biophysical properties, the model building process also pointed at the underlying relationships between variables. In Figure 5, we show four prediction models corresponding to the four ways in which the data were divided in different subsets. The first model is based only on the subset of neurons that spiked in response to current steps. These neurons were pooled across a wide age range (from P3-P10). The second model is over the same age range but also includes non-spiking neurons. By including non-spiking neurons, the model limits the current-clamp variables to those that can be measured in the absence of action potentials. The third and fourth models include spiking and non-spiking neurons but filter the data into narrow age bins. By looking at narrow age ranges, we test if spatial gradients are present at multiple developmental time points.

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Next we examined age-dependent trends in SGN biophysics (Figure 6). The three key predictors for NBP change significantly with age; g_max becomes larger (r(136) = 0.50, p<0.0001), current thresholds increase (r(79)=0.42, p<0.0001), and average latencies become shorter (r(133)=-0.40, p<0.0001). Note that all recordings between P1 and P16 are included in this analysis of age dependence, even those SGN that did not label to the terminal. To illustrate the range of responses at any particular age range and age dependent changes in biophysics, in Figure 6A we plot the size of the near steady-state outward current (at 400 ms) for individual cells as a function of the command voltage. The data are binned into three age groups (P1-5, n = 67; P6-9, n = 57; and P10-16, n = 13). Although the average current is smaller at younger ages, the overall range in current amplitudes is large, even within any particular age group. For example, many SGN at older ages have currents as small as those at younger ages.

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Figure 6—source data 1

Maximum conductance versus age for Figure 6C.

Conductance values are in microSiemens.

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Figure 6—source data 2

Current threshold versus age dataset for Figure 6E.

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Latency versus age dataset for Figure 6G.

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Pruning of terminal branches is faster in modiolar-contacting SGN

Next, we describe fiber morphology as supporting evidence for modiolar-contacting neurons developing at a faster rate than pillar-contacting neurons. Our results suggest that morphological maturation parallels biophysical maturation. The afferent terminals of SGN are highly branched during early development and are pruned during maturation to form a single bouton connection between the SGN and inner hair cell (Druckenbrod and Goodrich, 2015, Huang et al., 2007, Echteler, 1992). Consistent with previous reports, we also found that the number of terminal branches decreases as a function of maturation (r(53) = −0.79, p<0.0001) (Figure 7A and B). We observed mature one-to-one connections as early as P5 on the modiolar face. In contrast, none of the pillar-contacting fibers had mature terminal morphology, even by P10 (Figure 7C). We quantified differences in the pruning rate of modiolar- and pillar-contacting fibers from P5-P10 and found that modiolar-contacting fibers’ have fewer branches than do pillar-contacting fibers (1.9 +/- 0.24, n = 12 vs. 3.2 +/- 0.32, n = 7, respectively) (p=0.030, t-test) (Figure 7C, inset). Since, modiolar-contacting fibers appear to prune at a faster rate than pillar-contacting fibers, these data are consistent with the biophysics in suggesting that neurons on the modiolar face are changing faster with post-natal than those on the pillar face.

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In mature auditory nerve, fiber diameters are larger for high-SR fibers, which are the fibers primarily found on the pillar side of the inner hair cell (Merchan-Perez and Liberman, 1996). We measured fiber diameters of fluorescently labeled SGN as the average diameter of the last 10–20 µm of the parent fiber just before the branching begins near the inner hair cells (Figure 7A, see bracketed area). Consistent with previous in vivo labeling studies, we found that type I SGN have significantly larger fiber diameters than do type II SGN (1.28 +/- 0.05 µm, n = 37 vs. 0.59 +/- 0.12 µm, n = 6; p<0.0001, t-test) (Figure 7D). Fiber diameters are not significantly different between modiolar-contacting SGN and pillar-contacting SGN (1.25 +/- 0.29 µm vs. 1.11 +/- 0.22 µm; p=0.25, t-test) (Figure 7D). These results are consistent with reports in mice where fiber diameters begin to differentiate around the onset of hearing (Coates, personal communication).

Our results show striking correlations between the biophysical properties of SGN somata and the position where peripheral dendrites contact hair cells. Within the type I population, current thresholds decreased, first-spike latencies increased, and the size of net outward conductance decreased in a gradient as as a function of contact position along the base of inner hair cells. Although the ion channel properties of SGN somata are known to be diverse in vitro, this is the first clear demonstration that such diversity is systematically organized about the auditory nerve’s effective map for ‘intensity-coding’. Specifically, the more excitable neurons with low current thresholds and long membrane time constants in vitro are found on the pillar side of inner hair cells, where in vivo auditory nerve fibers have high spontaneous rates and low-intensity thresholds (Kiang et al., 1965; Liberman, 1978). The direction of in vitro biophysical gradients qualitatively aligns with mature in vivo physiology and hints at a possible post-synaptic contribution to sound-driven thresholds and excitability.

Type II SGN represent ~5% of the SGN population, make connections with multiple outer hair cells, and have a yet unknown role in the neuronal encoding of sound (Spoendlin, 1969; Kiang et al., 1984; Liberman and Dodds, 1984). In this study, type II SGN were 9 of 59 labeled fibers ranging in age from P3 to P8. The small number of neurons over a wide age range limits our ability to analyze and attribute a statistically significant biophysical phenotype to type II. Also, there may be more than one subtype of type II fibers (Vyas et al., 2019), making the scarcity of type II’s even more limiting for statistical evaluation. However, we found two biophysical trends that distinguish type II SGN from the majority of type I SGN. Type II fibers tended to be on the extreme end of the distribution in having small steady-state outward potassium currents that inactivated rapidly (Figure 4). The values of both of these voltage-clamp features have a large variance, with type II SGN positioned at the extrema of the two distributions. That the currents of type II fibers inactivate faster than for type I fibers is consistent with the previous reports of Jagger and Housley, 2003. Our results extend those previous results by showing that the inactivation time constant of type I SGN varies as a gradient from the pillar to modiolar face. Although the voltage-clamp responses showed a trend relative to type II and type I SGN, we did not find significant differences in response latencies in current clamp for the type II SGN. The latencies of type II SGN were not significantly different from the mean latencies of type I SGN. Because of this overlap, we were not able to use these variables to predict differences between type I and type II SGN.

The spike initiation zone for auditory neurons is on their peripheral neurites under inner hair cells, not at their somata where we are recording. It remains to be tested whether ion channels are found in spatial gradients at the peripheral neurites. Such gradients are possible since similar groups of ion channels and neurotransmitter receptors are seen at the soma and peripheral neurite (Rutherford et al., 2012; Yi et al., 2010; Hossain et al., 2005). Non-uniform sampling due to difficulty in accessing terminals with patch-electrodes may prevent such studies from seeing the full biophysical diversity seen in the SGN somata (Rutherford et al., 2012). Thus, whether spontaneous rate and threshold are defined exclusively by pre-synaptic mechanisms or further shaped by post-synaptic mechanisms remains an unresolved issue. Indeed, the presence of lateral olivocochlear efferents on the terminals of auditory neurons has long made the possibility of post-synaptic modulation of spiking activity highly likely (Wu et al., 2020).

How would variations in post-synaptic biophysics shape auditory nerve responses? Neurons with differences in current thresholds and temporal integration properties are likely to respond differently to the heterogeneity in synaptic input that inner hair cell synapses are known for. Specifically, excitatory post-synaptic currents (EPSCs) at individual inner hair cell synapses are remarkably heterogeneous in amplitude and kinetics (e.g., Grant et al., 2010). Some EPSCs are monophasic (temporally compact EPSCs with fast onset kinetics and typically large amplitudes) while others are multiphasic EPSCs (broad, slow onset EPSCs with smaller amplitudes). One proposal is that the relative prevalence of monophasic/multiphasic EPSCs at different synapses may contribute to diversity in the responses of auditory afferents (e.g. Grant et al., 2010). However, whether the prevalence of mono- and multi-phasic EPSCs varies with synaptic position remains to be determined. Our results suggest an additional level of post-synaptic processing that could further shape the responses of auditory neurons. Pillar-contacting SGN likely have low-current thresholds and longer temporal integration windows. These neurons will be more likely to reach spike threshold in response to a larger variety of EPSC amplitudes and shapes. The lower current threshold means that these neurons will spike in response to small and large EPSCs and the longer temporal integration means that these neurons can also reach threshold by integrating over the slow onset kinetics of multi-phasic events. Since intermediately accommodating firing patterns were more prevalent on the pillar face (Figure 2), supra-threshold multiphasic EPSCs may also produce more than one action potential. Ectopic spiking has been noted in pre-hearing auditory afferents (Wu et al., 2016). In contrast, fibers with larger current thresholds and shorter temporal integration times are more likely to respond to large-amplitude, rapid onset EPSCs. Such fibers would presumably also experience more spike failure in response to sub-threshold events and the slower depolarizations that would result from multiphasic EPSCs. Whether such spike failure occurs in this system remains unclear given the difficulty of terminal recordings; some studies report that each EPSC faithfully produces an action potential (e.g., Rutherford et al., 2012), while a recent study reported that in some fibers many EPSCs do not produce action potentials (e.g. Wu et al., 2016). Our results suggest that post-synaptic heterogeneity could dove-tail with pre-synaptic heterogeneity to shape diversity in auditory neuron responses.

Somatic ion channels may also have a function in and of themselves. According to models, the expression of ion channels on the SGN soma may be helpful for preventing spike failure. The impedance mismatch between the peripheral dendrite and the large soma can dramatically slow down and attenuate spikes, thereby increasing the probability of spike failure (e.g. modeling by Rattay et al., 2013; Hossain et al., 2005). In this scenario, the soma could independently filter spike trains as they sweep towards the brainstem (Davis and Crozier, 2015), and the nature of that filtering would be determined by somatic ion channels.

The observed link between in vitro cellular biophysics with putative SR-subgroups opens new opportunities for exploring and reevaluating mechanisms driving SGN function, regardless of the ultimate functional consequence of gradients in somatic ion channel properties. We have described a prediction model which uses easily measured biophysical properties such as current threshold and first-spike latency to classify SGN into putative SR-subgroups. Moreover, the modeling strategy systematically identified covariant/redundant variables among a larger group of easily measured biophysical variables. This identified gradients in potassium conductance as the most parsimonious explanation for the group of biophysical gradients observed (Figure 5). We argue that systematic variation in net-conductance accounts for the gradients in current threshold and response latencies reported here. As a result, highly covariant variables such current threshold and latency can interchangeably predict basal position. By combining non-redundant biophysical variables (such as current threshold and outward current inactivation), our regression models predict basal position to within a +/- 9% margin of error. This is a remarkable resolution given that the inputs to the model use relatively simple biophysical measurements. The success of the model is a reflection of the strength of these underlying relationships.

A final practical outcome of these results is that we can apply the prediction model to study other properties of SR-subgroups by using technically favorable dissociated somatic preparations. These would include studies focused on understanding the specific ion channels expressed by different SGN subgroups, the sensitivity of these neurons to different efferent neurotransmitters and the vulnerability of SGN subgroups to degeneration (Furman et al., 2013). This work complements the search for molecular markers for SGN subgroups because these approaches are feasible in neonatal animals before molecular expression has matured and in non-mouse species where transgenic models are not readily available.

Data were collected from spiral ganglion somata in semi-intact cochlear preparations from Long-Evans rats on post-natal day (P)one through P16. Animals were handled in accordance to the National Institutes of Health Guide for the Care and Use of Laboratory Animals and all procedures were approved by the animal care committee at the University of Southern California.

Temporal bones were dissected in chilled and oxygenated Liebovitz-15 (L-15) medium supplemented with 10 mM HEPES (L-15; pH 7.4,~315 mmol/kg). The semi-circular canals were removed, as was the bone surrounding the cochlea’s sensory epithelium. The cochlea was then cut into three turns, with the middle turn used for all experiments. The middle turn was further prepared by removing the Reissner’s membrane, stria vascularis, and tectorial membrane. The cochlear turn was then mounted under two stretched nylon threads on a glass coverslip. The entire coverslip with cochlea so mounted was incubated in an enzyme cocktail containing L-15, 0.05% collagenase, and 0.25% trypsin for 15–20 min at 37°C. The digested tissue was washed with fresh L-15 and mounted under the microscope objective. The preparation was then continually perfused with fresh oxygenated L-15.

Somatic visibility was best in the layers closest to the objective. As a result, mounting direction was sometimes flipped (with hair cells oriented to the coverslip) to target neurons in other areas of the ganglion. Angle of electrode approach was also varied to target SGN that were close to the modiolar core and those closer to the organ of Corti.

All data were analyzed with pClamp 10.7 software. In current-clamp mode, we measured various whole-cell properties of the neuron including the resting potential, current threshold for spikes, action potential latency, and the after-hyperpolarization time constant. In voltage-clamp mode, we measured the approximate steady-state value of outward currents (~taken 400 ms after stimulus onset) in response to a family of voltage steps. In many cells, the outward current inactivated for long-duration voltage step. We quantified the time-course for inactivation, ${\tau }_{inact}$, by fitting a single exponential curve from the peak outward current to end of the 400 ms. This was computed in all cells for the largest command voltage applied (+ 70 mV) (Figure 4C, inset). In some neurons (n = 39 of 128), a single exponential curve did not provide a good fit or the 400 ms protocol was too short to adequately estimate the time course; these cells were not included in subsequent multiple variable regression analyses.

Cell capacitance (7.4 +/- 0.36 pF) and series resistance (13.9 +/- 1.85 MOhms) were estimated using the membrane-test protocol on pClamp and/or by analyzing a recording of the capacitive transient in response to small hyperpolarizing voltage steps. No online series resistance correction was applied during recordings. All whole-cell currents and stimulus voltages in the main text and figures are reported without correcting for series resistance and without normalizing by cell capacitance. As we discuss in the supplement section, these corrections do not change our interpretations.

Recordings were made between one and five hours after dissection. Preparations were viewed at X630 using a Zeiss Axio-Examiner D1 microscope fitted with Zeiss W Plan-Aprochromat optics. Signals were driven, recorded, and amplified by a Multiclamp 700B amplifier, Digidata 1440 board and pClamp 10.7 software.

Recording and cleaning pipettes were fabricated using filamented borosilicate glass. Pipettes were fired polished to yield an access resistance between 5 and 7 MΩ. The tip of each recording pipette was covered in a layer of parafilm to reduce pipette capacitance. Large bore cleaning pipettes were used to mechanically remove excess tissue debris surrounding the somatic area. A second cleaning pipette was used to apply suction to remove myelinating glial cells and layers of myelin from the spiral ganglion neuron.

Recording pipettes were filled with the following standard internal solution (in mM): 135 KCl, 3.5 MgCl₂, 3 Na₂ATP, 5 HEPES, 5 EGTA, 0.1 CaCl₂, 0.1 Li-GTP, and titrated with KOH to a pH of 7.35. This yielded a total potassium concentration of 165 mM with a total osmolality of 300 mmol/kg. Voltages are reported without correcting a junction potential of approximately 3.8 mV (calculated by JPCalc as implemented in pClamp 10.7, Barry 1994).

In this study, we only used recordings in which the neuron formed a giga-ohm seal and presented a stable resting potential. After recording whole-cell currents and voltage responses in current clamp, we stimulated the cell with current pulse trains which we empirically determined helped drive the biocytin toward the peripheral terminal. Neuronal terminals were successfully filled in ~50% of recordings. Some neurons did not fill if the soma lysed after the recording pipette was pulled away. We found that pipette resistances of 5–7 MΩ were best for successfully sealing, driving biocytin, and cleanly pulling away from the soma.

Following the electrophysiology, the preparation was processed to immunohistochemically label hair cells and to attach a fluorescent label to the biocytin filled peripheral processes. The preparations were fixed in 4% paraformaldehyde for 15 min at room temperature followed by three rounds of washing in 5% phosphate-buffered saline (PBS) for 10 min each on a shaker. The preparations were placed for one hour in a blocking buffer consisting of 16% normal goat serum, 0.3% Triton-X, 450 mM NaCl, and 20 mM phosphate buffer. Next, preparations underwent three rounds of wash in 5% PBS for 5 min each. The preparation was then sequentially incubated in the following primary and secondary antibodies dilutions. Primary antibodies were added and incubated for 12–18 hr at room temperature. Secondary antibodies were added and incubated for 1 hr. Following both primary and secondary incubations, we washed the samples for three 15-min rounds in 1x PBS.

Primary antibodies included (1) anti-myosin-VI-rabbit polyclonal to label the cytoplasm of hair cells, (2) streptavidin Alexa Fluor 488 conjugate to label biocytin filled neurons, and (3) anti-peripherin to label type II spiral ganglion neurons. Secondary antibodies included Alexa Fluor 594 anti-rabbit.

The immunolabeled preparations were mounted under a glass coverslip and onto glass slides with the fade-protectant medium Vecta-shield. Hardened nail polish dots were placed under the coverslip to prevent it from crushing the cochlear sections. We generated z-stack images of each preparation on one of the following two confocal microscopes: (1) Olympus FV1000 laser scanning confocal microscope and (2) Zeiss LSM 800 with a 10-60x, 1.42 numerical aperture, oil immersion objective, and a threefold zoom (on IHC-SGN synapse). The scanning format was set to collect 1024 × 1024 pixels yielding a sampling of 0.069 µm/pixel in the lateral (XY) dimension. Sections were acquired with z-steps of 0.49 µm with pinholes set at 1 Airy unit. We scanned the different fluorescent signals in separate channels in sequence to ensure optimal imagining of each structure.

Images were processed using Imaris software in order to analyze the connectivity pattern of the SGN afferent projection and the hair cells. In the XY plane of the z-stack images, SGN were primarily classified based on whether the afferent projection contacted the inner hair cell region or projected past the inner hair cells, turned radially and projected into the outer hair cell area. Three-dimensional reconstructions of the afferent projection were produced in Imaris by using the FilamentTracer tool in Imaris. The tool reconstructs the fluorescent signal by tracing the fiber (and branches when present) and fills the area with sequential spheres whose diameters best fit the diameter of the fiber at a specific point. Imaris provides multiple measurements of the fiber including the length, diameter, and volume of the afferent fiber on average and/or at a region of interest. The number of branches were counted manually by counting the number of projections extending from the initial parent fiber. The diameter varied along the length of the extending branch from the soma to hair cell. We measured and reported the average diameter of the last 10–20 μm of the parent fiber just before the branching begins near the inner hair cells. In fibers with multiple branches contacting the hair cell, we took the contact point that was closest to the cuticular plate as the primary contact.

For our statistical analysis, we used a combination of pClamp, Matlab, JMP, Origin Pro, and Prism eight software packages. pClamp software was used to gather and quantify raw data from electrophysiological recordings. Imaris and MATLAB were used to quantify the morphology of the SGN. All variables were confirmed as being normally distributed using a Shapiro-Wilk test for small datasets. Equivalence of variance was tested using Levene’s test. To compare the means of two distributions, we used a Student’s t-test. For multiple comparisons, we used one-way ANOVA followed by Tukey’s HSD post-hoc analysis (for groups with equal variances) or Welch’s ANOVA and Games-Howell HSD post-hoc tests (for groups with unequal variances). The relative dispersion in distributions was quantified by the coefficient of variation (CV) which is the ratio between the standard deviation and the mean of the distribution. We used 2-way ANCOVA to compare between groups when one covariate was a continuous variable (e.g. when comparing non-spiking vs spiking groups as a function of normalized basal position or comparing modiolar vs. pillar groups as a function of age). The results of the ANCOVA analyses and slope analysis of regressions are shown in Table 1 and Table 4, and the individual data points with regressions are shown in figures. The strength of correlations between two continuous variables is reported by Pearson’s r. We used an alpha-level of 0.05 for all statistical tests. In most cases, the full distribution of data is displayed by graphing individual points.

We built models based on multiple-linear-regressions to predict normalized-basal position based on the biophysical properties of type I SGN (see Results). Given their small numbers, type II SGN were excluded from the data set used for modeling. The regressions computed a predicted basal position (${\widehat{y}}_i$) based on a linear combination of multiple input variables (i.e. biophysical features from current clamp and voltage clamp):

The input variables ${(x}_{\mathrm{1,2},3,\dots ,n})$ contributing to the regression were those with the most significant correlations with normalized basal position (Table 2). Next, the regression coefficients and intercepts (${\beta }_{\mathrm{1,2},3,\dots ,n}and{\beta }_o$) were optimized to minimize the sum of the squared error between the predicted basal position (${\widehat{y}}_i$) and the actual basal position ($y_i$):

To test for redundancy across variables we used Equation 6 to compute the variable inflation factors ($vif$):

where $R_n^2$ is the $R^2$ obtained when the n^th variable ($x_n$) is regressed against the remaining variables.

Variables with $vifs$ greater than 4.0 were deemed to be highly collinear and thus were eliminated as containing redundant information. We used a backward stepping procedure to successively eliminate input variables such that the fewest possible input variables provided the optimal adjusted-R² and root-mean-squared error (RMSE). This method of variable elimination is an especially aggressive method for minimizing overfitting. Power analysis was performed in JMP for each statistical test to determine observed power and minimum sample size with a significance level (alpha) of 0.05. Power and least significant number were determined by the significance level, error standard deviation (sigma), and effect size (delta). The identity of the variables $x_i$, coefficients ${\beta }_i$ and $vif$ values for four models corresponding to four data subsets are reported in Table 3.

We tested for non-isopotential behavior by analyzing high resolution recordings of capacitive transient currents (I_CV) in voltage clamp. These measurements were only made in a subset of recordings. The capacitive transient current was measured by hyperpolarizing the neuron from −60 mV to −65 mV (Figure S.B). This produced a small inward current that decayed. The capacitive portion of the current was isolated by first removing the steady-state current (shaded area under the current). In non-isopotential cells, the decay of the capacitive current can best be described by a sum of exponential decays (e.g. Equation (7)).

For example, the capacitive currents in retinal bipolar cells and the Purkinje cells are best fitted with a bi-exponential function, with each exponent term representing the sequential decay across two compartments representing the soma and neurite (Golowasch et al., 2009; Taylor, 2012; Rall, 1969). In contrast, the decay from an iso-potential cell is adequately described by a single exponential term.

Here we fit the capacitive transient currents with Equation (7) and compared the coefficients (A₁, and A₂) of the two exponential terms where τ₂ < τ₁ (Figure 4—figure supplement 1.C). The ratio between the fast and slow terms (A₂/A₁) shows that the fast component represented more than 80% of the transient current in 11 out of 16 neurons and was observed in both pillar- and modiolar-contacting SGN (Figure 4—figure supplement 1.D). Since the fast component dominates, this suggests that our recordings are largely isopotential.

We estimated the extent of the plasma membrane clamped under voltage-clamp by computing the effective capacitance (Taylor, 2012). Capacitance values averaged at 7.8+/- 0.35 pF (n = 35) and were not correlated with normalized basal position (r = 0.05, p=0.85) (Figure 4—figure supplement 1.E). These measurements suggest that there was no systematic modiolar to pillar gradient in the cell surface area clamped by the recording electrode.

Based on confocal scans in the ganglion, we estimate that the SGN in our preparation had an average diameter of around 12.7 +/- 0.3 µm, n = 28. This observation is consistent with measurements made in other mammalian species where somatic diameters range between 10–15 µm (Tsuji and Liberman, 1997; Berglund and Ryugo, 1991; Romand and Romand, 1987; Nadol et al., 1990). Assuming an unmyelinated spherical soma (with a specific capacitance around ~1 µF/cm²), the somatic capacitance would be around 5.1 +/- 0.2 pF. Based on the similarities in values between the capacitance as estimated from voltage clamp and from estimated cell diameters, we conclude that we are largely clamping and measuring the currents local to the SGN somata.

In this study, we were not able to measure the extent of the myelin that may be present on the neuron, and therefore cannot assess how differences in myelination and consequent variations in specific capacitance influence our measured capacitance. Because we remove myelinating satellite cells before recording from the SGN soma, we can assume that there is some myelination of the cell bodies and/or neurite. However, we cannot account for SGN having differences in the extent of their myelination which would affect the specific capacitance and total surface area of the neuron. Furthermore, myelination of the cell bodies and/or the neurite may increase the length constant of voltage changes along the neuron and could effectively make the neuron display isopotential behavior. Further studies accessing the passive membrane properties of SGN in the acute semi-intact preparation are needed to determine whether the measured capacitance of the SGN changes when different degrees of myelin are present.

Note that the capacitance or membrane surface area of a passive membranes can also be measured in current-clamp; however, SGN have voltage-dependent conductances that activate near resting potential (~−60 mV). The distortions caused by the activation of these conductances make it difficult to accurately estimate capacitance in current clamp.

Differences in biophysical behavior measured in voltage-clamp did not arise from differences in the axial conductance, where neurons with larger diameters would have larger axial conductance. Based on our fiber diameter measurements (Figure 7), the axial resistance of type I SGN does not change significantly as SGN contact position moves along the modiolar-pillar axis. In contrast, type II SGN had significantly smaller fiber diameters than type I SGN but had similar net conductance values as that of pillar-contacting type I SGN, suggesting that variations in axial diameter did not translate into significant variations in input conductance.

Series resistance estimates were not significantly different in SGN along the modiolar-pillar axis, suggesting that there were negligible errors in measuring the magnitude of currents in voltage-clamp. Series resistance estimates of identified type I SGN ranged from 2.6 to 11.0 MΩ with an average of 6.6 +/- 2.3 MΩ (n = 20). This series resistance estimate was measured via the Multiclamp 700B membrane seal test by analyzing the capacitive transient current. In some cases, these estimated series resistances were less than the pipette resistance, which lead to us question the accuracy of the measurement. This possible inaccuracy of estimating the series resistance led to our decision to report our voltage-clamp measurement uncorrected for series resistance. Series resistance estimates as a function of basal position displayed a slight negative linear trend (Figure 4—figure supplement 1.F). However, when we performed series resistance corrections on our voltage-clamp measurements, our initial assessment is maintained with maximum magnitudes of steady-state currents significant correlated with basal position (R² = 0.29, p=0.0003) (Figure 4—figure supplement 1.F, red trace). To further assess how much error in the series resistance estimation is needed to collapse the trends of steady-state currents with basal position, we simulated increasing levels of correlations of the series resistance estimations to the normalized basal position scale (Figure 4—figure supplement 1.G, blue and black traces). Our analysis shows that there would need systematic errors six times stronger than the amount we measured in our dataset to collapse these trends (Figure 4—figure supplement 1.F, black trace). Because series resistance of a patched SGN was not correlated with whether the neuron contacted the modiolar- or pillar-face of the inner hair cell, magnitude of currents measured in the voltage-clamp were not significantly impacted to cause concern for our biophysical assessment.

Here we did not compensate for or correct voltage errors resulting from the series resistance as we are accustomed to do in isolated neurons. We chose to report raw whole-cell currents to avoid inadvertently adding variability from cell to cell that may result from incorrect estimates of series resistance. Our decision stemmed from our initial concerns that space-clamp errors in the semi-intact preparations would make it difficult to accurately estimate series resistance using the built-in capacitance neutralization function in the Multiclamp 700b. The neutralization procedure assumes a single exponential decay for an iso-potential cell, as would be reasonable for the compact morphology of small isolated somata (see above). We were concerned that imperfect neutralization of capacitance transients would produce errors in both series resistance and membrane capacitance estimates. To avoid adding additional sources of variability to our voltage-clamp estimates of currents, we chose not to apply series resistance corrections or to normalize currents by cell capacitance.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We acknowledge the excellent technical support provided by Ms. Maya Monges-Aviles. We thank Ruth Anne Eatock, Christopher Shera, and members of the Kalluri laboratory and the Caruso Department of Otolaryngology for their valuable comments at various stages of this work.

Animal experimentation: Animals were handled in accordance to the National Institutes of Health Guide for the Care and Use of Laboratory Animals and all procedures were approved by the animal care committee at the University of Southern California (protocol number 20704).

© 2020, Markowitz and Kalluri

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