In neurons of the medial superior olive (MSO), voltage-gated ion channels control the submillisecond time resolution of binaural coincidence detection, but little is known about their interplay during trains of synaptic activity that would be experienced during auditory stimuli. Here, using modeling and patch-clamp recordings from MSO principal neurons in gerbil brainstem slices, we examined interactions between two major currents controlling subthreshold synaptic integration: a low-voltage-activated potassium current (IK-LVA) and a hyperpolarization-activated cation current (Ih). Both Ih and IK-LVA contributed strongly to the resting membrane conductance and, during trains of simulated EPSPs, exhibited cumulative deactivation and inactivation, respectively. In current-clamp recordings, regular and irregular trains of simulated EPSCs increased input resistance up to 60%, effects that accumulated and decayed (after train) over hundreds of milliseconds. Surprisingly, the mean voltage and peaks of EPSPs increased by only a few millivolts during trains. Using a model of an MSO cell, we demonstrated that the nearly uniform response during modest depolarizing stimuli relied on changes in Ih and IK-LVA, such that their sum remained nearly constant over time. Experiments and modeling showed that, for simplified binaural stimuli (EPSC pairs in a noisy background), spike probability gradually increased in parallel with the increasing input resistance. Nevertheless, the interplay between Ih and IK-LVA helps to maintain a nearly uniform shape of individual synaptic responses, and we show that the time resolution of synaptic coincidence detection can be maintained during trains if EPSC size gradually decreases (as in synaptic depression), counteracting slow increases in excitability.
The principal neurons of the medial superior olive (MSO) serve as the first stage for processing low-frequency binaural acoustic information. They signal the degree of temporal coincidence of inputs to the two ears through changes in their firing rate output (for review, see Grothe, 2003; Joris and Yin, 2007). Apart from specializations in circuitry and synaptic receptors, voltage-gated ion channels play critical roles in establishing a narrow time window over which binaural activity is integrated, enabling the transformation of phase-locked, temporally precise information into cues used for localizing sounds along the azimuth (Svirskis et al., 2002; Scott et al., 2005, 2010).
Low-voltage-activated potassium channels (IK-LVA) and hyperpolarization-activated cation channels (Ih) are the two major conductances in the MSO that are activated throughout the subthreshold voltage range (Svirskis et al., 2004; Scott et al., 2005; Mathews et al., 2010). Ih contributes to the resting membrane conductance of many neurons early in the auditory pathway, in turn sharpening the temporal precision of firing (Banks and Smith, 1992; Golding et al., 1995; Mo and Davis, 1997; Bal and Oertel, 2000; Yamada et al., 2005; K. E. Leao et al., 2006; Hassfurth et al., 2009). IK-LVA is also present in many cell types in early stations of auditory processing, increasing the signal-to-noise ratio and enhancing the precision of phase-locking (Reyes et al., 1994; Rathouz and Trussell, 1998; Bal and Oertel, 2001; Svirskis et al., 2002; Barnes-Davies et al., 2004; Kuba et al., 2005; Scott et al., 2005).
Previous studies have focused on the dynamics of these currents on a short timescale, during the integration of one or few synaptic inputs. However, natural sound presents long trains of synaptic inputs to MSO neurons. Here, with experiments and modeling, we examine the dynamics of Ih and IK-LVA during such ongoing trains of EPSPs and determine how the interplay of these currents affects input integration. Both Ih and IK-LVA change slowly during and after long trains but in a counterbalanced manner. This balancing leads to little change in mean membrane potential and EPSP amplitude during the train and induces rapid repolarization after stimulus termination. Despite the stability of EPSP amplitude, the input trains result in a significant increase of the input resistance that outlasts the stimulus. Although the increase in input resistance is associated with increased spike probability of MSO neurons, high temporal resolution is still retained, thereby enabling the precise coincidence detection of synaptic inputs during ongoing stimuli. The stabilization of EPSP amplitude and mean membrane potential during trains by Ih and IK-LVA may be an important mechanism to help MSO neurons maintain a more uniform integrative window for binaural coincidence detection across stimuli that exhibit different temporal and amplitude characteristics.
Materials and Methods
All experimental procedures followed the guidelines of the National Institutes of Health and were approved by the Institutional Animal Care and Use Committee at the University of Texas at Austin. Both male and female Mongolian gerbils (Meriones unguiculatus, P18–P22) were obtained from Charles River Laboratories or bred at the Animal Resource Center of the University of Texas at Austin. Gerbils were anesthetized with 5% halothane, and the brain removed while submerged in warmed (32°C), oxygenated artificial CSF (ACSF) (in mm: 125 NaCl, 2.5 KCl, 2 CaCl2, 1.0 MgCl2, 20 NaHCO3, 1.25 NaH2PO4, and 25 glucose, pH 7.45 with NaOH). Horizontal sections 200 μm thick were cut using an oscillating tissue slicer (Leica VT-1000S and VT-1200S) and were then transferred to an incubating chamber containing oxygenated ACSF at 35°C. After 30 min, slices were held at room temperature until recording. Individual slices were transferred to a recording stage, bathed with oxygenated ACSF, and maintained at 35 ± 0.1°C during recording.
Whole-cell voltage-clamp recordings.
MSO neurons were visualized using infrared differential interference contrast (IR-DIC) microscopy (Axioskop 2FS; Carl Zeiss) in combination with a Newvicon tube camera (Dage-MTI). Borosilicate patch pipettes (1.65 mm outer diameter; World Precision Instruments) were heat polished and had open tip resistances of 2–4 MΩ when filled with a potassium-based internal solution. For Ih measurements, the pipette solution contained the following (in mm): 127 potassium gluconate, 8 KCl, 10 sodium phosphocreatine, 10 HEPES, 0.5 EGTA, 4 MgATP, and 0.3 NaGTP, pH 7.3, with KOH. Ih was isolated pharmacologically by including the following in normal ACSF (in mm): 1 3,4-diaminopyridine, 10 tetraethylammonium-Cl, 0.2 4-AP, 0.2 BaCl2, 0.001 TTX, 0.05 NiCl2, and 0.2 CoCl2. These drugs block voltage-gated and inwardly rectifying potassium currents as well as voltage-gated sodium and calcium currents. In addition, 10 μm CNQX, 50 μm AP-5, and 2 μm strychnine was included in the ACSF to block AMPA, NMDA, and glycine receptors. In some experiments, 50 μm ZD7288 (4-ethylphenylamino-1,2-dimethyl-6-methylaminopyrimidinium chloride) was added to the bath or 20 μm to the intracellular solution to block Ih. All synaptic blockers were obtained from Tocris Bioscience except for strychnine, which was obtained from Sigma.
IK-LVA was isolated pharmacologically by including the following in the normal ACSF (in mm): 0.05 ZD7288, 0.2 BaCl2, 0.001 TTX, 0.05 NiCl2, and 0.2 CoCl2, along with 10 μm CNQX, 50 μm AP-5, and 2 μm strychnine to block synaptic activity.
Data were recorded with an Axopatch 200B amplifier (Molecular Devices), filtered at 1 kHz for Ih recordings and at 5 kHz for IK-LVA recordings, digitized at 50 kHz, and acquired using custom macros programmed in IgorPro (Wavemetrics). Wrapping electrodes with Parafilm reduced stray electrode capacitance, and the remaining capacitance was further reduced using the electrode capacitance compensation circuitry of the amplifier. Series resistance and whole-cell capacitance were compensated by 85–95%. All voltages reported are corrected for a liquid junction potential of 9 mV. To examine Ih deactivation and IK-LVA inactivation during EPSPs in voltage clamp, a synaptically evoked EPSP recorded in current clamp was scaled to different peak voltages and concatenated with itself to form a stimulus train at 500 Hz. All voltage-clamp recordings were included only if the series resistance was <10 MΩ.
Whole-cell current-clamp recordings.
Whole-cell current-clamp recordings were made from visually identified MSO principal neurons using the same potassium gluconate-based solution used in voltage-clamp recordings and using pipettes with open tip resistances of 2–5 MΩ. The current-clamp recordings were made using Dagan BVC-700A amplifiers in current-clamp mode using bridge balance and capacitance compensation. Recordings were included if the series resistance was <15 MΩ and the resting membrane potential was negative to −55 mV. Data were low-pass filtered at 5 kHz and acquired to computer at 50 kHz. All recordings were corrected for a liquid junction potential of 9 mV. Simulated EPSC waveforms (current injections) were mimicked using an α function with a time constant (τ) of 0.2 ms. Stimulus-induced changes in input resistance were calculated using brief hyperpolarizing pulses (3–5 mV, 10 ms duration) before and after the sEPSC stimulus (150 and 10 ms, respectively).
All analyses were performed using IgorPro. In current-clamp experiments, peak and steady-state I–V plots were generated from peak voltage responses to 100 ms current steps. The input resistance was obtained from the slope of the peak I–V plot between 0 and 10 mV below rest. The membrane time constant was obtained from a single-exponential fit from baseline to the peak of a hyperpolarizing voltage response (3–5 mV from rest). Relative changes in input resistance (RN) during trains of synaptic-like depolarizations were quantified as [(RN(posttrain) − RN(pretrain))/RN(pretrain)] * 100.
In voltage-clamp experiments, the voltage dependence of Ih activation was measured from peak tail currents arising from a step to −100 mV after 1 s prepulses to voltages between −30 and −110 mV in 10 mV increments. These currents were normalized to maximum and minimum values. The normalized g–V curve was fit with a Boltzmann equation of the following form: f(V) = 1/(1 + exp[(V1/2 − V)/k]), where V is the membrane voltage, V1/2 is the half-maximal activation voltage, and k is the slope factor. To measure the reversal potential, Ih was activated with a 1 s pulse to −100 mV, followed by steps to between −100 and −30 mV. Instantaneous tail currents were plotted versus membrane potential, and the reversal potential was calculated from the zero crossing of the linear fit. For group comparisons, means are presented ± SEM and statistical significance was assessed using either a two-way ANOVA or Student's t test at a significance level of 0.05.
We constructed a single-compartment model including the three central subthreshold membrane currents: the voltage-dependent KLVA-type and h-type currents and a leak current. The Ih model was based on our experimental data and fit using Neurofit (Willms, 2002). Its kinetics are described by the sum of a fast (rf) and a slow (rs) gating variable, both using the same activation function r∞. The IK-LVA model with fast activation (w) and slow inactivation (z) was based on whole-cell recordings from MSO cells. We described activation with the model by Mathews et al. (2010). Dynamics of IK-LVA inactivation in our recordings (P. Mathews and N. Golding, unpublished data) was fit well with a sum of two exponentials: for −55, −50, −45, and −40 mV, the fast inactivation time constants (in ms) are 35.4 ± 42.8, 71.7 ± 5.1, 56.1 ± 3.2, and 49.7 ± 3.2, and the slow time constants are 242.0 ± 64.8, 549.5 ± 22.9, 485.5 ± 45.9, and 479.5 ± 33.6, respectively. We described the IK-LVA inactivation time constants with the model from Rothman and Manis (2003a,b), which (when corrected for temperature) agreed well with our measurements. The current balance equation takes the following form: with capacitance Cm = 25 pF, leak conductance gL = 15 nS, peak conductances ḡK-LVA = 190 nS and ḡh = 70 nS, reversal potentials EL = −77.5 mV, EK = −106 mV, and Eh = −37 mV, kr = 0.65, and external input I(t). The cell had a resting membrane potential of −58 mV. Most parameters were based on whole-cell measurements from MSO neurons, whereas the parameters for which we did not have direct experimental data (ḡK-LVA, gL, EL) were set such that we could account for experimental measurements of the input resistance RN (8.5 MΩ), membrane time constant τm (0.34 ms), and the resting membrane potential Vrest (−58 mV) under control conditions and when Ih or IK-LVA was blocked. Gating variables w, z, rf, and rs evolve according to first-order differential equations with steady-state activation or inactivation functions, and voltage-dependent time constants of the gating variables at 35°C, Excitatory synaptic input was modeled by current injections with a time course described by an α function with a time constant of 0.6 ms.
We computed the input resistance RN(t) at V(t) for short (∼10 ms) current pulses by linearizing the current balance equation around the voltage V(t). Because activation of KLVA is fast and KLVA inactivation and Ih activation are relatively slow (∼100 ms), we can write with r(t) = kr rf(t) + (1 − kr) rs(t) and gw(t,V) = 4ḡK-LVAw∞3(V)z(t)(V − EK)w∞′(V), where w∞′ (V) is the derivative of the activation function w∞(V) with respect to V evaluated at V.
To predict the response to input transients that are superimposed on a slowly varying or DC input I(t), we also computed the impedance Z at time t and voltage V(t) for high-frequency sinusoids (>100 Hz). For such frequencies, the dynamics of z(t), rf(t), and rs(t) are too slow to contribute to the impedance, and we can write where ω = 2πf with frequency f. Taking the absolute value of this complex valued expression gives the impedance.
We also computed the afterhyperpolarization (AHP) that follows an EPSC train. We define the variable Vaft at time t as the voltage to which the cell model would immediately relax (within ∼10 ms), if the input I(t) ends at time t. To compute Vaft(t) during a simulated EPSC train, we solved the implicit equation Note that we consider that KLVA activation w(t) reaches its steady-state value w∞(Vaft) shortly (well within ∼10 ms) after the stimulus has stopped, because it has a relatively fast time constant (∼1 ms). To compute the input resistance for 10 ms current pulses immediately after an input train (as we did in the experiments), the membrane potential V(t) in the above equation for RN(t) was replaced by Vaft(t).
We computed the initial and steady-state voltage after a step current input I from Vrest. The instantaneous current–voltage relation was obtained by considering that the slow gating variables z, rf, and rs are still at their resting values associated with Vrest, whereas the fast K-LVA activation has reached its equilibrium at the initial voltage Vinit: For the steady-state current–voltage relation, all gating variables were considered to be in equilibrium at the steady-state voltage Vss: To compute spike probabilities, the dendro-somatic compartment model described above was extended with an axonal compartment that included action-potential-generating currents, a sodium current (INa), and a high-voltage-activated potassium current (IK-HVA), taken from Rothman and Manis (2003a,b). The axonal compartment had a capacitance Cm = 12 pF, leak conductance gL = 24 nS, peak conductances ḡNa = 3000 nS and ḡK-HVA = 150 nS, and reversal potentials EL = −58 mV, ENa = 55 mV, and EK = −106 mV. The (in)activation time constants of the active currents were adjusted for a temperature of 35°C. The somatic and axonal voltages were coupled via an axial conductance gaxial = 50 nS, reproducing the strong attenuation of action potentials from the axon to the soma (Scott et al., 2007). A noise current was added to the somatic compartment, consisting of white Gaussian noise that was low-pass filtered with time constant of 0.2 ms, giving the noise current an SD of ∼167 pA.
Ih and IK-LVA are key determinants of the resting properties of MSO principal cells
We examined the electrophysiological properties of 212 principal neurons of the MSO. Principal neurons were readily distinguishable in current-clamp recordings based on criteria established in previous in vitro patch-clamp studies (Svirskis et al., 2002; Scott et al., 2005), including the bipolar morphology of their dendrites as viewed under IR-DIC optics, the display of strong outward rectification in the voltage range above the resting potential, and the initiation of a single small (<25 mV) action potential in response to all suprathreshold current stimuli (Fig. 1A). MSO principal neurons consistently exhibited low input resistances (<19 MΩ; average, 8.2 ± 0.6 MΩ; n = 9) as was apparent in the voltage–current relationship (Fig. 1A,D). The membrane time constant of MSO neurons was <0.4 ms on average (Fig. 1C). The resting membrane properties were strongly determined by the dual influence of hyperpolarization-activated cationic current (Ih) as well as low-voltage-activated K+ current (IK-LVA). Blockade of h-channels with either 50 μm extracellular ZD7288 or 10 mm cesium hyperpolarized the resting potential by 13 ± 3 mV (n = 6) and 14 ± 4.8 mV (n = 5), respectively, abolished the delayed, depolarizing sag during hyperpolarizing current injections and increased the input resistance and membrane time constant threefold (Fig. 1B–F). Similar results were obtained when h-channels were blocked internally with the inclusion of 20 μm ZD7288 in the pipette solution (RN = 21 ± 3.2 MΩ for internal vs 24.9 ± 5.8 MΩ for external ZD7288; p > 0.5; n = 6 for both groups). IK-LVA also contributed to the resting properties of MSO neurons. Blockade of Kv1.1-containing channels with bath application of 80 nm dendrotoxin K (DTX-K) resulted in a twofold to threefold increase in input resistance and membrane time constant but only produced a slight depolarization of the resting potential (Fig. 1B–F), consistent with previous studies (Scott et al., 2005, 2007; Mathews et al., 2010). Together, these results indicate that Ih and IK-LVA are active at the resting potential and allow for rapid membrane voltage changes via their powerful contributions to the large membrane conductance of MSO principal neurons.
Dynamics of Ih and IK-LVA during EPSP trains
Given that Ih and IK-LVA are partially activated at rest, we asked whether their respective contributions varied during the kinds of repetitive synaptic stimuli typically encountered by MSO neurons during acoustic activity. Voltage-dependent changes in Ih activation and IK-LVA activation and inactivation during trains of synaptic activity could powerfully influence resting membrane properties. Although the brief duration of individual EPSPs in MSO neurons (∼1–2 ms) would not be expected to provide substantial changes in Ih activation or IK-LVA inactivation, both operating on a timescale of ∼100 ms, such changes might accumulate during repetitive synaptic activity. To examine this, we made whole-cell recordings from MSO neurons and determined changes in Ih or IK-LVA during trains of simulated EPSPs in voltage clamp (sEPSPs, 3–15 mV, delivered at 500 Hz from a holding potential of −60 mV). This frequency (500 Hz) was chosen because it approximates the upper range in which bushy cells, which provide excitatory inputs to the MSO, show reliable entrainment (Joris et al., 1994).
For recordings in which Ih was isolated pharmacologically (see Materials and Methods), EPSP trains elicited not only the corresponding and expected leak and capacitive currents but also a slowly developing outward current that outlasted the time course of the stimulus for hundreds of milliseconds (Fig. 2A, left traces and black arrows). The slow outward current was monotonically related to the amplitude of the EPSP voltage commands. In the presence of 50 μm ZD7288, the resting conductance was reduced and the slow outward current was essentially (>91%) blocked (Fig. 2A, middle). These results indicate that Ih contributes to the resting conductance at −60 mV and that a proportion of this current deactivates during trains of depolarizations. To quantify the proportion of Ih deactivation, we performed a tail current analysis at −100 mV and found that up to 40% of gh deactivated during a 15 mV EPSP train relative to the resting conductance at −60 mV (Fig. 2B).
A tail current analysis comparable with that used to describe Ih deactivation (Fig. 2A,B) could not be used during IK-LVA inactivation because of the technical difficulties of accurately subtracting capacitive currents in whole-cell voltage-clamp recordings. When pharmacologically isolating IK-LVA (see Materials and Methods), we observed a slowly developing reduction in IK-LVA during trains of EPSP stimuli, reflecting a cumulative inactivation (Fig. 2C, Control). Because IK-LVA is partially activated at −60 mV, the percentage of IK-LVA inactivation as a fraction of total IK-LVA cannot be measured. Thus, we measured the percentage of IK-LVA inactivation as a fraction of IK-LVA activated as a result of the stimulus train (Fig. 2D). Up to 15% of IK-LVA undergoes inactivation for a 15 mV sEPSP train.
To gain insight into the subthreshold dynamics of the active membrane properties during EPSP trains, we constructed a single-compartment MSO cell model containing the three major channel types that operate in the subthreshold voltage regimen: Ih, IK-LVA, and a passive leak current (IL) (see Materials and Methods). The voltage response during 500 Hz EPSC trains (Fig. 3A) is similar to our experimental current-clamp recordings, which are discussed below (see Figs. 4A, 7A). IK-LVA exhibits rapid activation and deactivation with each cycle of the stimulus, along with a tonic activation after the stimulus onset (Fig. 3B, red trace). Additionally, a progressive inactivation of IK-LVA and deactivation of Ih occurs on a timescale of tens to hundreds of milliseconds (Fig. 3B, magenta and blue traces). These dynamics are reflected in the conductances gK-LVA and gh. Because of the slow inactivation of IK-LVA, the envelope of gK-LVA exhibits a gradual decline (Fig. 3C, red trace). In addition, gh undergoes gradual reduction, without being affected by individual EPSPs attributable to the slow Ih kinetics (Fig. 3C, blue trace). The overall membrane conductance (Gm = gK-LVA + gleak + gh) initially increases with stimulus onset but soon declines below prestimulus state as a result of the cumulative inactivation of IK-LVA and deactivation of Ih (Fig. 3C, black trace). This decline in membrane conductance persists long after the stimulus offset. The cumulative changes in the gating of the two currents are also manifested in the envelopes of the currents (Fig. 3D). The cumulative components of the two currents counteract one another and result in a fluctuating summed outward current that shows little cumulative change over the entire time course of the train (Fig. 3D, light blue trace). The similar time course of recovery from inactivation of IK-LVA and from deactivation of Ih results in a constant total current at the end of the stimulus (Fig. 3D, arrow).
Cumulative effects of Ih deactivation and IK-LVA inactivation on MSO responses
From the cumulative changes in the conductance of the model (Fig. 3C), one would expect that the input resistance of MSO neurons is increased at the end of the stimulus. Stimulus-induced changes in membrane sensitivity were assessed by probing the input resistance 150 ms before and 10 ms after a train of sEPSCs in somatic current-clamp recordings (Fig. 4A). A 1 s 500 Hz train of 9 mV EPSPs in this example resulted in 28% increase in input resistance. To understand what aspects of the stimulus train were critical for regulating membrane input resistance, we manipulated stimulus frequency and amplitude independently of one another (Fig. 4B). In one set of experiments, peak EPSP depolarization and train duration were kept constant (uniform EPSC train, 9 mV, 1 s), and stimulus frequency was varied from 100 to 500 Hz (n = 5). A 6% increase in input resistance was detected at 100 Hz, and these changes increased linearly with frequency up to 23.7%, at a rate of 4.5%/100 Hz (Fig. 4B, top). Alternately, EPSP amplitude was varied while the frequency and duration of the sEPSC train were held constant (500 Hz, 1 s, n = 8). The increase in input resistance varied linearly with EPSP amplitude, up to 60% with 15 mV sEPSPs (Fig. 4B, bottom).
Despite significant Ih deactivation and IK-LVA inactivation, we found that the membrane potential returned quickly to its prestimulus value, only showing a very small AHP (Fig. 4C, top). The AHP after trains of 15 mV EPSPs was <1 mV for stimulus frequencies of up to 500 Hz (n = 5) (Fig. 4C, bottom). The fast return to rest is explained by the similar time course of IK-LVA and Ih after EPSC trains, essentially cancelling their respective hyperpolarizing and depolarizing effects (Fig. 3D). The small, short AHP primarily reflects the rapid deactivation of IK-LVA activated during the stimulus.
The time course of development and duration of input resistance increases was consistent with the slow kinetics of IK-LVA inactivation and Ih deactivation in MSO principal neurons. To observe the time course over which input resistance changes develop, we delivered sEPSC trains of uniform amplitude and frequency (adjusted to elicit 8–10 mV EPSPs at either 250 or 500 Hz) and varied train duration from 10 ms to 2 s (Fig. 4D, inset). The increase in input resistance of MSO principal neurons could be fit well with a dual-exponential function (Fig. 4D). For 500 Hz sEPSC trains, fast and slow time constants averaged 45.1 ± 10.1 and 915.9 ± 215 ms, respectively, whereas for a 250 Hz train, time constants approximately doubled to 74.8 ± 34.7 and 1642.3 ± 1940 ms. Once initiated, input resistance changes were long lasting. The time course of input resistance decay was assessed using either a 200 ms or 2 s stimulus train (9 mV EPSPs at 500 Hz) (Fig. 4E). As with the development of the increase in input resistance, the decay of input resistance followed a dual-exponential time course. The decay of input resistance from the 200 ms train was significantly more rapid than for the 2000 ms train (for 200 ms, τfast = 24.1 ± 5.4 ms, τslow = 231.5 ± 57.3 ms; for 2000 ms, τfast = 36.6 ± 1.9 ms, τslow = 440.9 ± 28.7 ms).
To probe the interactions between Ih and IK-LVA during EPSP trains, we examined the effects of their respective blockers (50 μm ZD7288 and 80 μm DTX-K) on the integration of sEPSC trains (Fig. 4F). In the presence of ZD7288, EPSP responses showed more temporal summation, and cumulative changes in input resistance were sharply reduced (Fig. 4F,G; RN measured as in Fig. 4A). In contrast, when IK-LVA was blocked by DTX-K, initial EPSPs summated briefly before the emergence of a cumulative hyperpolarization, culminating in a large AHP after train offset (Fig. 4F,H). This effect was presumably attributable to the cumulative deactivation of Ih in the absence of a counterbalancing depolarization mediated by IK-LVA inactivation. DTX-K also reduced but did not eliminate the increase in input resistance (Fig. 4F,G). In ZD7288, the cumulative depolarization resulting from IK-LVA inactivation is likely to be partially masked by the fact that greater temporal summation of EPSPs induces greater IK-LVA activation.
Contribution of Ih deactivation and IK-LVA inactivation to input resistance changes
On the basis of the pharmacological experiments (Fig. 4F–H), one may be tempted to assign fractional contributions of Ih and IK-LVA to the cumulative input resistance increases. However, it is important to consider the conditions under which input resistance is measured in assessing how both currents contribute to cumulative changes in RN. In experiments, we measured RN at the membrane potential after halting the EPSC train at various time points (Fig. 4). Using our single-compartment model, we can display the evolution of this after-train potential Vaft during the response to an EPSC train (Fig. 5A, green trace in top left) and compute the buildup and decay of RN at this potential (Fig. 5A, solid black line in bottom left), revealing a similar magnitude and time course of RN increases as in the experiments (compare with Fig. 4D,E). Measurements of RN during the natural afterhyperpolarization of the model cell exceeded measurements made at the resting potential of −58 mV (Vrest, dashed black line), revealing the sensitivity of RN measurements to the conditions under which they are made. The difference, in this comparison, reflects the steep voltage dependence of IK-LVA near rest, as well as the fast kinetics of its deactivation during the AHP. Under conditions of drug application, the membrane may depolarize or hyperpolarize abnormally and standardization of RN measurement is especially meaningful. When blockade of Ih was simulated (Fig. 5A, middle), EPSP trains showed a gradual temporal summation, and Vaft progressively depolarized (green line). In this condition, only a small (12%) change in RN occurred (solid red line), in agreement with the experimental results in Figure 4, F and G. However, when the effects of the depolarizing Vaft are compensated by measuring RN at Vrest (dashed red line), the input resistance increase was 36%, reflecting the fact that increased activation of IK-LVA at Vaft after the EPSP train masked the RN change resulting from the cumulative inactivation of IK-LVA (Fig. 5A–C). Finally, when IK-LVA blockade was simulated, temporal summation of EPSPs was countered by a slow hyperpolarization also reflected in a slowly developing Vaft (Fig. 5A, right). In this case, the strong increase in RN (blue line) was mediated by the deactivation of Ih. Although measurements of RN during the afterhyperpolarization of the model suggest that Ih deactivation makes the strongest contribution to changes in RN (Fig. 5B), when input resistance was calculated at the standardized membrane potential, Vrest, it is apparent that both Ih deactivation and IK-LVA inactivation contribute to cumulative changes in input resistance (Fig. 5C).
Cumulative changes in membrane conductance are insensitive to fine stimulus statistics
Our results demonstrate that an increase in membrane sensitivity during trains develops cumulatively and persists on a timescale of tens to hundreds of milliseconds. To assess the sensitivity of these changes to variable temporal patterns, we constructed trains of brief depolarizations of identical average frequency but differing in their degree of regularity. These trains (0.5 ms step pulses, 350 Hz average frequency, 1 s total duration) were constructed with interspike intervals (ISIs) that randomly varied according to a Gaussian distribution with an SD of 0, 0.5, 1.0, 1.5, or 2.0 ms (Fig. 6A). Ten random train patterns exhibiting each distribution of ISIs were generated and delivered to MSO principal cells in current-clamp mode, and input resistance changes were determined as in Figure 4A. In these experiments, stimulus intensity was adjusted to elicit action potentials, which increased the average membrane depolarization and improved the ability to discriminate stimulus-dependent changes in input resistance. In each cell, neither the mean nor the variance of the input resistance changes was altered by decreases in the regularity of the input trains (Fig. 6B,C) (no statistically significant difference across different SD conditions; p > 0.6, ANOVA). For this analysis, the SDs of the input resistance measurements of different patterns for each cell were normalized to the respective mean values (coefficient of variation). If Ih deactivation or IK-LVA inactivation is sensitive to the short-term temporal structure of the input train, then there should be a systematic increase in the variance of the input resistance measurements with increasing values of ISI SDs. However, no systematic differences were observed in the five cells tested, with the mean SD of increase in input resistance ranging from 3.3 to 4.0% across the different conditions of stimulus regularity (Fig. 6D). These experiments thus show that changes in membrane sensitivity are determined by the average level of synaptic excitation and insensitive to its fine temporal structure.
IK-LVA and Ih interaction during trains maintains nearly constant EPSP amplitude and width
Given the substantial IK-LVA inactivation and Ih deactivation induced by EPSP trains, a significant change in EPSP amplitude would be expected during the trains. However, in whole-cell current-clamp recordings, the EPSP amplitude during the train was surprisingly stable. Responses to 500 Hz trains of sEPSCs (2 s duration) showed a small, transient decrease in amplitude attributable to the activation of IK-LVA, followed by a slow increase close to the original amplitude (Fig. 7A–C). Besides the EPSP amplitude, also the duration of individual EPSPs was stable, showing only a very small frequency-dependent increase (<100 μs) (Fig. 7D).
The nearly uniform response to subthreshold sEPSCs seems at odds with the increase in input resistance that we observed during trains (Fig. 4). In fact, EPSP responses are riding on a gradually developing small hyperpolarization of the resting potential. This hyperpolarization gets occluded during summation of high-frequency inputs but is observable at the termination of the train (Fig. 4C) and was displayed in the model by the after-train potential Vaft (Fig. 5A, green trace).
Alternatively, the constant EPSP amplitude can be easily understood by using the MSO cell model and focusing on the response to a steady current injection representing the mean current during an EPSC train. For example, during a 0.5 nA current step, Ih and IK-LVA and their conductances decrease significantly, whereas V and Ih + IK-LVA vary little (Fig. 8A, solid lines), as seen previously for a 500 Hz EPSC train input (Fig. 3). The decreases in Ih and in the activated IK-LVA during the input step counteract each other, enabling the constant Ih + IK-LVA and constant 4 mV mean depolarization. However, the voltage ranges for gating of Ih and IK-LVA are different, so there is a limit to these balanced changes in current amplitude. For stronger current steps, V evolves to a more depolarized level, as illustrated by using a threefold larger current step (Fig. 8A, dotted lines). After the initial depolarization to −49 mV, Ih and IK-LVA decrease on similar timescales but they are not counterbalanced in amplitude (middle). Although the sum, Ih + IK-LVA, after a small transient (200–300 ms) is nearly constant, Ih is significantly smaller because of its strong deactivation (bottom) and because V approaches the reversal potential for Ih (Eh = −37 mV). The steady-state response is 4 mV more depolarized than just after step onset and is dominated by IK-LVA because gK-LVA does not totally inactivate. These responses to larger steady input currents are predictive of responses to higher-frequency EPSC trains.
The initial and steady voltage responses to steady current inputs are easily predicted from the instantaneous and steady-state current–voltage relations of the membrane (Fig. 8B) (see Materials and Methods). Just after input onset, the membrane potential jumps from Vrest to V on the instantaneous I–V curve (downward pointing triangle) and then slowly evolves to V on the steady-state I–V curve (upward pointing triangle). We see that, for modest current injections (e.g., <1 nA), we can expect a nearly constant mean voltage response, whereas stronger input currents (e.g., 1.5 nA) lead to cumulative depolarization during the input step.
Although this analysis helps us to understand the relative insensitivity of mean voltage alongside significant change in input resistance during a sustained moderate-sized input, it does not speak to the near constant amplitude of EPSP transients. We therefore ask whether small but fast transient inputs are affected by the gradual input resistance changes. By using a linearized approximation (see Materials and Methods), we find that the impedance for high frequencies is barely influenced from the start to the end of the 0.5 nA injection in Figure 8A; above ∼500 Hz, the gain is dominated by the capacitive current (results not shown).
Coincidence detection and temporal resolution during ongoing stimuli
In the MSO neuron model, although V changes little during long, modest input steps, the decreasing conductance of Ih and IK-LVA results in a slowly increasing input resistance RN [measured at V(t)]. For a 1 nA input, the membrane will gradually depolarize by 1.6 mV during the step, whereas RN gradually increases by 46% (Fig. 9A). The initial drop in RN is attributable to the rapid activation of gK-LVA. To address the possible consequences of changing RN for integration of synaptic inputs, we viewed these steady depolarizations as an idealization for an asynchronous background of synaptic currents. How might the adaptation of intrinsic conductances, the slowly increasing RN, affect coincidence detection for two transient inputs that are superimposed on the background? We simulated this condition by superimposing noise on the constant mean 1 nA input along with EPSC pairs separated in time by Δt ms. The resulting firing probability versus Δt at later time points (greater RN) shows an increased excitability (higher firing probability) and a nearly 100% broader half-width of this coincidence detection tuning function (Fig. 9B, “Uniform EPSC ampl.”).
We also determined the firing probability in consideration of an idealized representation of synaptic depression by providing decreasing amplitude EPSC pairs with time of the pulse. We computed the tuning functions by using EPSC amplitudes adjusted so that with Δt = 0 the firing probabilities are matched. This approach resulted in tuning functions that were nearly identical (Fig. 9B, “Adjusted EPSC ampl.”; see inset for adjusted EPSC amplitudes). The same results were obtained when EPSC pairs were incorporated in EPSC trains (data not shown). These results indicate that the temporal precision of EPSPs does not degrade significantly over time and that broadening of the tuning functions for uniform amplitude EPSCs is attributable to an increase in spike probability. Hence, whether the coincidence window broadens or remains constant depends on how synaptic EPSC amplitude evolves over time, which is determined by several factors, e.g., synaptic depression, and presynaptic adaptation affecting the number of activated synaptic inputs.
Finally, we verified the predictions of the model using current-clamp recordings of MSO principal neurons. We provided a square current injection that produced a nearly 7 mV depolarization and added Gaussian noise of 1.6 mV SD. Two sEPSCs separated in time by Δt ms were injected at 50, 250, or 1950 ms after onset of the square current pulse. When all EPSC injections have identical amplitude, we find, as in the model, that the firing probability increased over time, broadening the tuning of coincidence detection (Fig. 9C, “Uniform EPSC ampl.”). Adjusting the EPSC amplitudes such that firing probability at Δt = 0 is matched also shows maintenance of the coincidence window (Fig. 9C, “Adjusted EPSC ampl.”).
Several factors, mediated by the input resistance increase during sustained input, contribute to the enhanced excitability. In addition to modest increases of mean membrane potential and individual EPSPs as seen without noise present, the variance of membrane potential fluctuations increases during a noisy background. The chance occurrence of sequential depolarizing input fluctuations enables the input resistance to influence temporal summation beyond the effect of individual events. These effects together lead to excitability increases that reflect the >50% increase in input resistance.
In MSO principal cells, the encoding of sound localization cues requires the detection of the ongoing temporal registry of binaural synaptic inputs. In this study, we found that, during trains of EPSPs over a range of amplitudes and frequencies, a dynamic interaction between Ih and IK-LVA imparts greater uniformity to the amplitude and shape of EPSPs than would be achieved by the effects of either of the individual currents alone. The nearly stable amplitude of EPSPs during trains occurred in the face of significant increases in input resistance that developed and decayed over hundreds of milliseconds. In both model and experiments, an increase in spike probability mediated by increasing input resistance and modest depolarization during noisy stimulus trains broadened the window for detecting the coincidence of bilateral synaptic stimuli, but this broadening could be eliminated by incorporating a small degree of short-term synaptic depression. We conclude that the interplay between Ih and IK-LVA acts as a homeostatic mechanism during sustained stimulation to preserve an operational mean voltage range and EPSP amplitude; temporal precision of synaptic integration and coincidence detection can be maintained if assisted by some input adaptation, such as short-term synaptic depression.
Interactions between Ih and potassium currents in neurons
In many neurons, Ih gives rise to a non-inactivating, depolarizing current that is partially activated at the resting potential. Given that Ih exhibits reversal potentials between −20 and −40 mV, Ih increases cell excitability by depolarizing the membrane potential toward action potential threshold. However, several studies have shown that the impact of Ih on cell excitability is more complex. In hippocampal and neocortical pyramidal neurons, in which HCN channels are expressed in high density in the distal dendrites (Magee, 1998; Lörincz et al., 2002; Kole et al., 2006), during trains of EPSPs the net outward current from Ih deactivation shortens EPSPs, reduces temporal summation, and decreases the probability of firing (Stuart and Spruston, 1998; Magee, 1999). Similar results have been observed in several cell types in the auditory system, including bushy cells of the cochlear nucleus, principal neurons of the medial nucleus of the trapezoid body, and neurons of the inferior colliculus (Koch and Grothe, 2003; R. N. Leao et al., 2005; K. E. Leao et al., 2006). In CA1 pyramidal neurons, George et al. (2009) have shown that activation of M-type potassium channels can render the influence of HCN channels dependent on the amplitude and time course of EPSPs. Although the resting depolarization of Ih is excitatory, bringing smaller EPSPs closer to firing threshold, larger EPSPs can activate M-current (IM), suppress peak depolarizations, and thus reduce temporal and spatial summation (George et al., 2009). Both Ih and IM affect the amplitude and time course of excitation because of the temporal overlap between EPSPs and the gating of the channels.
The influence of Ih is different in MSO principal neurons compared with the neurons described above because the time course of individual EPSCs is in the submillisecond range (Smith et al., 2000; Magnusson et al., 2005; Couchman et al., 2010), far briefer than the activation and deactivation kinetics of Ih (time constant of ∼100 ms at the resting potential in MSO neurons). As a result, deactivation of Ih occurs only cumulatively during trains of EPSPs. This hyperpolarizing effect is counterbalanced by two factors: the depolarization from cumulative inactivation of IK-LVA and an increase in input resistance, mediated by the inactivation of IK-LVA and deactivation of Ih. Thus, whereas in other neurons interactions between potassium currents and Ih distort the time course of EPSPs over time, in MSO principal neurons EPSP amplitudes are nearly uniform.
The stabilizing influence of Ih and IK-LVA on the amplitude and duration of EPSPs during trains requires that not only must the underlying channels make strong contributions to the overall resting conductance but the magnitudes of the currents must be approximately matched. Simulations with our MSO cell model in which we varied the ratio of gh and gK-LVA over a wide range displayed a gradual transition (results not shown) from the balanced dynamics observed in real MSO neurons to responses that are similar to the experiments in which we blocked either channel. Considerable cell-to-cell variability in the magnitude of Ih and IK-LVA was observed across different MSO neuron recordings, but these experiments do not reveal whether the expression of the two channel types is linked. There is precedent for such a linkage, however. In invertebrate neurons, the expression of Ih has been shown to be coordinated with that of A-type potassium channels to maintain comparable firing patterns (MacLean et al., 2005). It is also important to note that both Ih and IK-LVA are sensitive to a wide range of intracellular modulators (for review, see Kaczmarek et al., 2005; Wahl-Schott and Biel, 2009), which may provide MSO neurons with additional mechanisms by which to adjust the magnitude of resting conductances.
The interactions we have described between Ih and IK-LVA are applicable to other neuron types in the mammalian auditory system. However, the similarities in intrinsic electrical properties are particularly striking in octopus cells of the ventral cochlear nucleus and principal neurons of the lateral superior olive. Both of these cell types integrate high-frequency trains of brief excitatory synaptic inputs, and Ih and IK-LVA make strong contributions to the resting potential (Bal and Oertel, 2000; Hassfurth et al., 2009). Thus, in these neurons, interactions between Ih and IK-LVA could serve to stabilize trains of synaptic stimuli in a similar manner as in MSO principal neurons.
Comparison with avian binaural coincidence detectors
Both Ih and IK-LVA are coexpressed in neurons of the nucleus laminaris, the avian analog of mammalian bushy cells and MSO principal neurons (Reyes et al., 1994; Kuba et al., 2005; Yamada et al., 2005). In these neurons, inactivation of IK-LVA during long synaptic input trains enhances the firing rate, increasing intrinsic gain at the expense of temporal precision (Kuznetsova et al., 2008). In MSO principal neurons, we also observed an increase in intrinsic gain (observed as an increase in firing probability during uniform EPSCs), but changes in the rise time and duration of the underlying EPSPs were relatively subtle. Some of the differences in synaptic integration during trains between birds and mammals may be related to Ih, which is smaller in nucleus laminaris neurons and exhibits a more hyperpolarized activation range (Yamada et al., 2005). These differences would affect synaptic precision because both the conductance underlying Ih reduces the membrane time constant and Ih depolarizes the resting potential into the activation range of IK-LVA. Furthermore, because Ih contributes less to the resting membrane conductance in nucleus laminaris neurons, the inactivation of IK-LVA during long excitatory trains would not be counteracted as strongly by the slow deactivation of Ih, leading to stronger cumulative depolarizations, increased spike probability, and potentially a time-dependent widening of the window for binaural coincidence detection. Together, these findings indicate that, although there are many similar specializations in mammals and birds for achieving submillisecond binaural time resolution, these circuits also exhibit significant differences that likely reflect their independent evolution (Grothe, 2003).
Implications for interaural time-delay coding
Central to sound localization by MSO neurons is their ability to detect coincident inputs. We find that the width of the window for detecting bilateral synaptic coincidence gradually broadens by up to 100% during an ongoing depolarizing stimulus. This effect is mediated by the cumulative increase in input resistance and modest depolarization that can amplify EPSPs that summate or ride on noise, increasing spike probability. When we decreased EPSC amplitudes such that firing probability for precisely coincident EPSCs (Δt = 0) remained constant over time, the width of the coincidence window remained constant during the ongoing stimulus, in both simulations and experiments. This means that, despite the slowly decreasing membrane conductance resulting from cumulative decreases of Ih and IK-LVA, the rise time and duration of individual EPSPs is not altered significantly during the integration of ongoing stimuli.
Importantly, the width of the coincidence window will depend on how the amplitude of synaptic input changes during ongoing stimuli. One important factor determining these changes is short-term synaptic plasticity (Neher, 2008). Studies in the avian auditory system suggest an important role for synaptic depression, which provides an adaptive mechanism for preserving interaural time-delay information independent of sound intensity (Cook et al., 2003; Grande and Spain, 2005). Depression of the synaptic inputs to MSO cells would counteract the increases in excitability and impose a narrower time window for binaural coincidence. However, the magnitude of synaptic depression in time-coding auditory neurons is controversial (Borst, 2010). In MSO principal neurons in vitro, short-term depression of inhibitory and excitatory synaptic currents appears well matched in amplitude and time course and exceeds 50% at frequencies >100 Hz (Couchman et al., 2010). However, these results must be tempered with the finding that short-term depression has been found to be far less prominent in vivo than in unstimulated slices (Lorteije et al., 2009). The balance for MSO principal neurons between the slow dynamics of Ih, IK-LVA, and other adaptation mechanisms, such as synaptic depression, remains a complex but important future issue.
This work was supported by NIH Grants RO1 DC006788 (N.L.G.) and R01 DC008543-01 (J.R.).
- Correspondence should be addressed to Nace L. Golding, Section of Neurobiology, 1 University Station, C0920, University of Texas at Austin, Austin, TX 78712-0248.