ICR or Swiss mice (P17–P25) animals were sacrificed after isoflurane inhalation, according to methods approved by the Institutional Animal Care and Use Committee of the University of Pittsburgh and the Committee on Ethics in Animal Experimentation (CETEA) from the University of São Paulo. Coronal slices containing DCN were obtained as in Zugaib et al. (2016). Briefly brains were removed and cut in cold solution whose composition in mM was: NaCl (87), NaHCO₃ (25), KCl (2.5), NaH₂PO₄ (1.25), CaCl₂ (0.5), MgCl₂ (7), glucose (25), sucrose (75), 335 mOsm/kgH₂O, pH 7.4 when bubbled with carbogenic mixture (95% O₂ and 5% CO₂). Before removing the brain from the skull, the vestibulocochlear nerve (VIII cranial nerve) was cut to prevent damage to the DCN. Coronal slices (200 μm thick) containing the three layers of the DCN with its basic circuit (Oertel and Young, 2004) were obtained on a vibratome (Vibratome 1000 Plus) and incubated at 35°C for 45 min and subsequently at room temperature in recording solution [artificial cerebrospinal fluid (aCSF)], whose composition in mM was: NaCl (125), KCl (2.5), NaHCO₃ (25), NaH₂PO₄ (1.25), glucose (10), CaCl₂ (2), MgCl₂ (1), 305 mOsm/kgH₂O, pH 7.4 when bubbled with carbogenic mixture (95% O₂ and 5% CO₂). Alternatively, slices were obtained using a Leica 1000S vibratome in warm (35°C) aCSF, stored at this temperature for 1 h and then at room temperature as in Tzounopoulos et al. (2004). No difference was observed between the protocols or mice strain. Single cells were visualized with IR interference contrast optics and recorded using patch pipettes in either voltage- or current-clamp modes. Fusiform neurons were identified based on their electrophysiological and morphological characteristics (for more details see Tzounopoulos et al., 2004; Zugaib et al., 2016). Pipettes were filled with a K⁺-based internal solution containing (in mM): 113 K-gluconate, 4.5 MgCl₂, 14 tris-phosphocreatine, 9 HEPES, 0.1 EGTA, 4 Na-ATP, 0.3 tris-GTP, 10 sucrose, pH 7.3, ∼300 mOsmol. In some experiments external sodium chloride was replaced by N-methyl-D-glucamine chloride (NMDG-Cl).

Whole-cell recordings were performed at 33–36°C using an inline heating system (Warner Instruments) and perfused with aCSF at a rate of approximately 1 ml/min. Data was acquired at 10 or 20 kHz and low-pass filtered at 3 kHz (Bessel) using a MultiClamp 700B connected to a Digidata 1440A board (Axon Instruments) or an EPC-10 amplifier (HEKA Elecktronics). Voltage clamp experiments were performed at a holding potential of -65 mV, while current-clamp experiments were performed at I = 0 in quiet neurons and after injection of negative DC current (-20 to -200 pA) in active neurons. Acceptable access resistance was considered to be below 20 MΩ and was monitored during the whole experiment.

A single compartment model of the fusiform cell was built using a standard Hodgkin–Huxley formalism. It is based on a previous model reported in Leao et al. (2012) containing the following ionic conductances: I_Na (fast sodium current), I_Kd (delayed rectifier potassium current), I_h, I_NaP, I_Kir, and an I_leak. The kinetics of time and voltage-dependent parameters were determined by activation and inactivation gating variables as described in Leao et al. (2012). The maximal conductance densities of I_Na and I_Kd were adjusted in order to set firing frequencies closer to the experimental observations (Leao et al., 2012), with values of g_Na = 80 mS/cm² and g_Kd = 20 mS/cm². The other conductance densities were: g_NaP = 0.1, g_h = 0.54, and g_leak = 0.15 mS/cm². g_Kir was set at 0.5 mS/cm² for active neurons and at 1 mS/cm² for quiet neurons. The reversal potentials were set at 50 mV for E_Na, -81.5 mV for E_K, -43 mV for E_h, and -51.32 mV for E_leak. The K_IR time constant used was 0.5 ms.

I_h was built on a previous description of the current (Nagtegaal and Borst, 2010). We used two activation variables (A_h1 and A_h2) that were described with same steady state dynamics (A_h^∞) (Leao et al., 2012) but different voltage dependence of time constant (τ_h1 and τ_h2). The two activation time constants were used as in Destexhe and Babloyantz (1993). The kinetic equations were as follows

Based on the experimental data (Leao et al., 2012), the model cell for the quiet versus spontaneously active states differed only in the maximum conductance of I_Kir. The geometry of the model was a cylinder 20 μm of diameter and 20 μm of length. The cell specific capacitance was set at 1 μF/cm². Simulations were run using the NEURON simulator, version7.1, in an 8-core Intel7 processor. The time step was 0.1 ms and the initial membrane potential -65 mV. All measurements were done after waiting 4 s to achieve steady state values. Parameter spaces were obtained varying only two parameters at a time, with the conductance values in the range between 0 and twice their original values. Data was saved and analyzed using MATLAB. In order to determine the regions in parameter space where active and quiet neurons were placed, 1 s of spontaneous activity (i.e., without injected current) was measured. To determine the RMP both sodium conductances (g_NaP and g_Na) were set to 0 and the RMP was measured at the end of a 1 s sweep over the range of values with no injected current.

The model and simulation files are available for public download on the freely available repository ModelDB¹.

We simulated I_h using the Real Time Application Interface for Linux-based (RTAI²) dynamic clamp (Dagostin et al., 2015). Two computers were used, one for data acquisition running PatchMaster (Heka Elecktronics), and a second ‘dynamic-clamp’ computer that reads voltage from the patch-clamp amplifier (EPC-10, HEKA Elecktronics) and generates current commands in real-time every 50 μs. The ‘dynamic-clamp’ computer is an x86 architecture computer (Pentium 4, Intel) with a PCI-6036E data acquisition card (National Instruments) for reading voltage and generating current commands to the clamped neuron. The real-time dynamic clamp software was written (by Dr. R. N. Leao, Federal University of Rio Grande do Norte, Brazil) in GNU-C, and routines for data acquisition were programmed using the Linux Control and Measurement Device Interface (COMEDI³).

All data are corrected for a measured liquid junction potential of 10 mV. Active and quiet neurons were classified as in Leao et al. (2012). Fusiform neurons were classified as active when their spontaneous action potential firing rate was >0.5 Hz. Fusiform neurons that did not display any spontaneous firing or that displayed sparse spontaneous firing, with rates below 0.5 Hz, were classified as quiet. RMP was determined in the presence of TTX. The depolarization sag of the membrane was the difference between the steady state and the hyperpolarization peak (Figure 1A).

The inward rectifying cationic current (I_h) was elicited by 4 s hyperpolarizations from -65 to -120 mV (in some cells we used -20 mV step hyperpolarizations from -60 to -120 mV) and quantified by subtracting the currents before and after the application of ZD7288 (20 μM). I_h was measured at the steady state current at the end of the hyperpolarization pulse. Alternatively, I_h was estimated as the difference between the onset and steady-state current. The conductances obtained using these two approaches were not significantly different (p > 0.05). The activation and deactivation of I_h was measured fitting a double exponential function to the current activation and tail current deactivation. The voltage dependence of g_h was calculated using the peak amplitude of the tail currents elicited after a repolarization to -65 mV and fitted with a Boltzmann function. Leak currents were defined as the currents left after blocking I_h and I_Kir with ZD7288 (20 μM) and Ba⁺⁺ (200 μM), respectively, and I_NaP with TTX (1 μM) (Leao et al., 2012). The slope conductance was determined using the linear part of the subthreshold IV relationship. Membrane input resistance was calculated both in current-clamp mode as the slope of the VI curves in response to -20 pA steps from 0 to -100 pA (Figure 1A), and in voltage-clamp mode as the inverse of the slope of the IV curves from -65 to -80 mV, values close to the RMP of the fusiform neurons (-60 to -80 mV; Leao et al., 2012).

Drugs were prepared from 1000 × stock solutions and diluted before applications. ZD7288 was obtained from Tocris and Ascent Scientific. N-methyl D-glucamine-Cl (NMDG), BaCl₂ and tetrodotoxin (TTX) were purchased from Sigma.

The membrane input resistances were submitted to a normality test (D′Agostino and Pearson) and they were not considered to represent a normal distribution (p < 0.0001, n = 120) so they were analyzed using a non-parametric test (Mann–Whitney). The other parameters had less data than necessary to apply normality tests (<<100) and were treated as having a normal distribution and their means compared with paired and unpaired t-test. However, comparing the data using both parametric and non-parametric tests did not affect our conclusions. Multiple comparisons were performed with one-way ANOVA and a Tukey’s multiple comparison test. Two-tailed significance level was set below 0.05. Correlations were determined using a linear regression fit. Statistics was performed using GraphPad Prism.

Quiet fusiform neurons display increased expression of I_Kir, which would produce a smaller membrane input resistance when compared with the input resistance of active neurons. However, we observed that both quiet and active neurons have similar membrane input resistances when measured both in current clamp (quiet: 77.8 ± 8 MΩ; active: 89.1 ± 9 MΩ; p = 0.36; n = 37 and 36, respectively. Figures 1B,C) and in voltage-clamp mode (quiet: 95 ± 12 MΩ; active 77.1 ± 10 MΩ; p = 0.09; n = 21 and 26, respectively) suggesting the presence of differential expression of compensating conductances that maintain the input resistance constant.

Consistent with this hypothesis, we found that active neurons show bigger hyperpolarization sag of the membrane potential (peak sag: -2.9 ± 0.5 mV, quiet; -6.2 ± 0.8 mV, active; p < 0.01; n = 15 each; Figure 1D). Because this sag is inhibited by the hyperpolarization-activated cationic current (I_h) antagonist ZD7288 (not shown), this suggests the presence of a bigger I_h in these neurons that may normalize the input resistance of quiet and active neurons.

To further test this hypothesis, we measured I_h in active and quiet neurons to compare this conductance in both neuronal types. In accordance with the presence of the h current we observed after applying successive hyperpolarizations, a gradual slow developing inward current that reached a steady state in ∼3 s, which was inhibited by ZD7288 (Figure 2A). The current-voltage (IV) relationship of the ZD-sensitive current of both quiet and active neurons is shown in Figure 2B which shows that the I_h in quiet and active neurons have similar IV relationships. Using the tail currents we calculated the activation curves of I_h and they presented similar parameters (quiet neurons had a V₅₀ of -86.7 ± 4.6 mV and a slope of 8.2 ± 4 while I_h from active neurons had a V₅₀ of -81.5 ± 5 mV and a slope of 7.1 ± 4, p = 0.98). We also calculated the activation and deactivation time constants (fast and slow) of I_h from quiet and active neurons between -100 and -120 mV. Because we did not observe differences of the time constants in these potentials, we averaged the results from these potentials. Except for the fast component of the activation, none of the other parameters was different between quiet and active neurons (Table 1).

While I_h from quiet and active neurons are similar in its kinetics, active neurons presented a bigger slope conductance of h current (measured between -75 and -100 mV) than quiet neurons (quiet: 5.0 ± 0.5 nS; active: 6.9 ± 0.5 nS; p = 0.02, unpaired t-test n = 17 and 18, respectively; Figure 2C). Our data show that on the average active fusiform neurons express a bigger I_h than quiet neurons.

To characterize all conductances affecting membrane input resistance, we looked at the background leak currents of the DCN fusiform neuron, which are traditional regulators of membrane passive properties (Enyedi and Czirják, 2010; Renigunta et al., 2015). After inhibition of I_Kir and I_h with Ba⁺⁺ (200 μM) and ZD7288, and I_NaP with TTX (1 μM), a residual current remains in both quiet and active neurons. This current is linear in the range of subthreshold potentials tested, and will be referred as a leak current (Figure 3A). Remarkably, this current had a depolarized reversal potential (-49.3 ± 4 mV; n = 22). Accordingly, the RMP measured after blockage of I_NaP, I_h, and I_Kir by TTX, ZD, and Ba⁺⁺, respectively, was similarly depolarized (-49.7 ± 1.7 mV; n = 12). These values are considerably above the calculated equilibrium potential of the potassium ions (-84 mV) suggesting that this leak conductance is permeable to cations other than K⁺. Accordingly, perfusion of a low-sodium solution (sodium replaced by NMDG-Cl: [Na⁺]_o = 32 mM, E_rev Na⁺ = 42.6 mV) inhibited the current in all potentials (p < 0.001), shifting the reversal potential of the leak current from -49.7 ± 7.3 to -66.2 ± 2.2 mV (Figure 3B; n = 6) and hyperpolarized RMP from -48.2 ± 3.5 to -60.3 ± 0.9 mV (n = 5; p = 0.012; Figure 3C). We conclude that DCN fusiform neurons express a leak current with Na⁺ permeability that would be capable of depolarizing the membrane potential generating a tonic depolarization if it were not counterbalanced by K_ir currents.

To determine whether variations on this background conductance could offset the effect on membrane input resistance produced by the smaller I_Kir in active neurons, we compared this current in quiet and active neurons. We found that both quiet and active neurons presented leak currents of similar magnitudes and reversal potentials (leak conductance: quiet: 8.0 ± 1.7 nS; active: 7.1 ± 1.5 nS; p = 0.7; I_leak reversal: quiet: -52.7 ± 4.9 mV; active: -46.0 ± 6.2 mV; p = 0.4; n = 13 and 9, respectively; Figure 3D). This shows that these background conductances are similar in both fusiform neuronal types and are probably not compensating the difference in membrane input resistance produced by the differential expression of I_Kir.

So far, our results suggest that active neurons express a more robust I_h in order to compensate for their smaller I_Kir maintaining a similar input resistance than quiet neurons. If this were true, inhibition of I_h would reveal a bigger input resistance in active neurons. Also the more depolarized RMP of active neurons (Leao et al., 2012) could be accountable by their bigger I_h. Therefore, we tested the effect of the application of ZD7288 on the RMP and membrane input resistance of quiet and active fusiform neurons.

We found that application of ZD7288 affected equally the RMP (measured in the presence of TTX) of active and quiet neurons, hyperpolarizing then by the same amount (quiet: -72.1 ± 0.9 to -79.1 ± 1.3 mV; active: -63 ± 1.5 to -69.6 ± 1.8 mV; differences: quiet: -6.79 ± 1.4 mV; active: -7.6 ± 1.05 mV; p = 0.65; n = 10 and 7, respectively), maintaining the same difference in RMP in quiet and active neurons observed originally (Figure 4A). Experiments performed in the absence of TTX showed that inhibition of I_h by ZD7288 is efficient in decreasing the spontaneous firing of active neurons (from 16.2 ± 4.5 to 8.9 ± 7 Hz; n = 10; p < 0.01, paired t-test; Figure 4B), but unable to convert them to quiet neurons. We conclude that despite the differences in g_h in active and quiet neurons it does not participate in setting up the RMP differences observed in fusiform quiet and active neurons, and does not define the firing mode of fusiform neurons.

We then measured input resistance of quiet and active neurons before and after application of ZD7288. Because the VI curve of fusiform neurons has a small rectification around -70/-80 mV and the RMP of active and quiet neurons varied at these potentials and is affected by ZD7288, we performed measurements of input resistance in voltage-clamp mode. We found that in contrast to its effect on RMP, ZD7288 had a differential effect on input resistance on quiet and active neurons. While ZD7288 significantly increased R_input in active neurons (from 121.6 ± 35 to 314.8 ± 8 MΩ; p = 0.007, paired t-test, n = 7; Figure 4Ca), it did not increase significantly membrane input resistance in quiet neurons (from 106.7 ± 22 to 148.5 ± 39 MΩ; p = 0.1, paired t-test, n = 9; Figure 4Cb). We conclude that while I_h has a similar small influence on the RMP of quiet and active neurons, it has, consistent to our prediction, a bigger influence on the membrane input resistance of active neurons.

We previously found that g_Kir correlates positively with RMP in fusiform neurons, in accordance to its major role in regulating membrane potential. If g_h is used to compensate for the increased input resistance created by the smaller g_Kir in active neurons, it is plausible that this conductance would correlate with input resistance in these neurons. In fact, when we correlated g_h and input resistance in quiet and active neurons we found that g_h correlated positively only in active neurons (quiet: r² = 0.01, p = 0.77; active: r² = 0.46, p = 0.02; Figure 4D).

These results show that in active neurons variations in g_h offsets the difference in the input resistance produced by their smaller expression of g_Kir and have a membrane input resistance more sensitive to g_h inhibition than quiet neurons. But despite the difference in g_h seen in quiet and active neurons its inhibition affected RMP equally in both neurons.

The bigger sensitivity of the membrane input resistance of active neurons to ZD7288 suggests they are more sensitive to changes in I_h than quiet neurons. If this were true, the membrane input resistance of active neurons would be more sensitive to increases in I_h than in quiet neurons. To test this hypothesis more directly we roughly doubled g_h by injected an artificial g_h (5 nS) in both quiet and active neurons (Figure 5A) and measured their membrane input resistance before and after artificially increasing g_h in both neuronal types. We found a significant decrease in membrane input resistance in active neurons (Figure 5B; p = 0.0004, Wilcoxon matched-pairs signed rank test; n = 7) while it did not affect significantly the membrane input resistance of quiet neurons (Figure 5C; p = 0.16, Wilcoxon matched-pairs signed rank test; n = 7). No change in input resistance was observed when we measured the input resistance at the onset of the hyperpolarization pulses (Figure 5D) accordingly to what is expected for an effect produced by I_h.

We then tested how further injection of subsequent bigger artificial g_h could affect membrane input resistance of quiet and active neurons. Curiously, doubling g_h to 10 nS was effective in decreasing input resistance in quiet neurons (Figure 5E). When we normalized the input resistance and examined the effect of increasing g_h, we found that the drop in input resistance produced by increasing g_h was similar in quiet and active neurons above 10 nS (Figure 5E), reaching around 70% of the original value at 40 nS of g_h. Interestingly, injection 40 nS of artificial g_h in quiet neurons produced a small depolarization of the membrane potential (from -58.7 ± 2 to -54.2 ± 1 mV; p < 0.05, paired t-test; n = 7), but did not produce spontaneous firing, showing that I_h is not effective in depolarizing the membrane to values sufficient to produce spontaneous firing in fusiform neurons.

We conclude that the membrane input resistance of active neurons is very sensitive to adding 5 nS of g_h, roughly doubling g_h, while this did not affect significantly the membrane input resistance of quiet neurons. On the other hand, membrane input resistance of quiet and active neurons is equally sensitive to further applications of increasing artificial g_h.

We found that the difference of g_h of quiet and active neurons is not very big and its inhibition affected their RMP similarly, but membrane input resistance after ZD7288 is considerably bigger in active neurons. This is in accordance with a bigger sensitivity of membrane input resistance of active neurons to variations in g_h. Accordingly, g_h only correlated with input resistance in active neurons, suggesting that variations in this conductance are used by active neurons to compensate for their smaller g_Kir and maintain homeostatic control of membrane input resistance. Additionally, this difference in g_h seems to not to affect the RMP on quiet and active neurons differentially. It seems that the effects of variations of g_h on membrane properties depend on the level of other conductances differentially expressed in quiet and active neurons. To understand how concerted variations in these currents affect subthreshold membrane properties and the transition quiet to active and membrane input resistance, we used a computer model containing the identified subthreshold conductances (g_Kir, g_h, g_leak) of the fusiform cell (Figure 6A).

We found previously (Leao et al., 2012) that RMP of fusiform neurons is very sensitive to I_Kir inhibition by Ba⁺⁺ 200 μM, and that the differences in its magnitude create the differences of RMP which creates the firing modes of the fusiform neuron. On the other hand, even with a bigger I_h found in active neurons, its inhibition was not sufficient to change differently the RMP of active and quiet neurons. We then compared how changing g_h and g_Kir in our model influenced RMP. In Figure 6B we see the effect on RMP of the changing g_Kir and g_h. It is clear that RMP is much more sensitive to changing in g_Kir than in g_h. For instance, for a given g_h (0.5 mS cm^-2), RMP changes from -52.1 to -63.4 mV varying g_Kir from 0 to 1 mS cm^-2, while varying g_h from the same amount only changed RMP from -58.5 to -55.6 mV from a g_Kir of 0.5 mS cm^-2. We also can see that accordingly to its effect on RMP, g_Kir affects strongly the transition to quiet to active (blue line) in contrast to g_h. Interestingly, it can be seen that the impact of g_h on RMP is bigger in quiet than active neurons (compare the area above and below the blue line), which is different from what we observed experimentally by inhibiting I_h with ZD7288 (Figure 4A). In Figure 6C we analyzed the variations of g_leak and g_h (keeping g_Kir at 0.5 mS cm^-2). Again, variations of g_h are less effective in affecting RMP when compared with variations of g_leak, especially in active neurons (region above the blue line, with bigger values of g_leak). Finally we compared the impact of varying g_leak and g_Kir on the RMP and quiet-active transition (Figure 6D). We see that while increasing g_Kir can hyperpolarize the RMP, g_lleak is very effective in depolarize RMP, because we needed around 4–5 times more g_Kir to counteract the effect of g_leak, and produce a quiet neuron (above the blue line).

Our model showed that the depolarizing g_leak has a strong depolarizing effect on RMP. To evaluate the interaction of the reversal potential of the leak current and its conductance in RMP we varied both conductance and reversal potential of g_leak in model neurons with values of g_Kir typical of an active and a quiet neuron. Figure 7 shows that only with a reversal potential around -50 mV we were able to reach the values of activity threshold set by the I_NaP (-59/-57 mV). Also at values of E_rev below -65 mV the RMP becomes almost insensitive to variations of g_leak, especially in quiet neurons. Although a bigger I_Kir, as seen in quiet neurons, reduces the impact of g_lleak on depolarizing RMP, it does not prevent its effect on creating active firing in high conductances of g_leak (Figure 7B). We concluded that the presence of a sodium component that increases the reversal potential of g_leak is fundamental to depolarize the membrane allowing spontaneous firing in DCN fusiform neurons.

We then studied the relationship of variations of g_h and g_Kir on the membrane input resistance of fusiform neurons (Figure 8A). The model showed that, similarly to what we observed experimentally, the bigger g_Kir, the smaller the effect of g_h on membrane input resistance (Figure 8B). Figure 8C shows the relationship of membrane input resistance and g_h in two situations: with a low g_Kir typical of active neurons, and a big g_Kir typical of quiet neurons. In accordance to what was observed experimentally, g_h has a more pronounced impact in the membrane input resistance in the model active neuron than in the model quiet neuron. We also observed a smaller depolarizing sag of the membrane potential after hyperpolarization in quiet neurons. This might be caused by a reduced g_h in these neurons, but because the differences observed in g_h between quiet and active neurons were not very pronounced, we decided to test if the bigger g_Kir of quiet neurons dampens the depolarization sag in these neurons. In fact, our model shows that the influence of g_h in producing the sag is diminished when g_Kir is bigger (Figures 8C–E). Our model and experimental data show that the g_h and g_Kir interaction not only controls the membrane input resistance, but also affects dynamic responses of the membrane during hyperpolarization.

Our model predicts that in a neuron with more prominent g_Kir, g_h has less impact on membrane input resistance. Accordingly, we found that the membrane input resistance of quiet neurons, which had been shown to express a bigger g_Kir, is less sensitive to inhibition and enhancement of g_h. However, we do not know how exactly both conductances interact in a single cell to produce their effects in the RMP and input resistance. In order to evaluate how these individual conductances, plus g_leak, behave in a single neuron, we compared the subthreshold conductances g_Kir, g_h, and g_leak in the same neurons (six quiet and six active), by applying in sequence ZD7288 and Ba⁺⁺ in order to compare the proportions of these conductances in the same neuron.

We found, as previously, that g_Kir was significantly different in quiet and active neurons (Figure 9A). g_h was bigger in active neurons, but the value did not achieve significance (Figure 9A). Surprisingly, the absolute values of g_Kir and g_h (or g_leak) did not correlate inversely as would be expected if g_h (or g_leak) increased as g_Kir decreased in order to keep input resistance similar in the two types (Figures 9B,C). However, we found that the proportion of the total subthreshold conductances (g_Kir + g_h + g_leak) of g_Kir and g_h varied inversely significantly both in quiet and active neurons while g_Kir and g_leak did not (Figures 9D,E). Accordingly, when we analyzed the proportion of the subthreshold hyperpolarizing conductance (g_Kir) and the depolarizing conductances (g_h + g_leak), we found that when g_Kir is responsible for 50% or more of the total subthreshold conductances, the neurons is quiet, while when g_Kir represents 50% or less of these conductances the neuron is active (Figure 9F). We conclude that while the absolute individual values of g_h and g_Kir are not inversely correlated in an individual fusiform neuron, their individual proportions vary inversely in order to keep membrane input resistance constant in quiet and active neurons.