Single I_h Channels in Pyramidal Neuron Dendrites: Properties, Distribution, and Impact on Action Potential Output

Fluctuation analysis of I_h in cell-attached recordings

To examine the properties of single I_h channels, we used NSFA of macroscopic I_h currents (Conti et al., 1980; Sigworth, 1980; Alvarez et al., 2002). I_h currents in these experiments were activated by 400 ms hyperpolarizations to maximize the number of possible repetitions. Filtering of individual sweeps (Fig. 1D, top) was performed with a digital Gaussian filter at 100 Hz and the current variance (σ²) calculated from the difference between 100 consecutive sweeps (Fig. 1D, bottom). The plot of the current σ² versus time had a peak coinciding with half-maximal activation at ∼25 ms (Fig. 1E). Plots of the current σ² against mean I_h current amplitude could be well fit with a parabolic function, from which the single-channel amplitude (i), the total number of channels (N), and open probability (P_o) can be estimated (Fig. 1F). On average, at dendritic sites ∼500 μm from the soma, NSFA gave estimates of i of 88 ± 9.9 fA, N of 342 ± 24, and P_o of 0.92 ± 0.03 (n = 5) during hyperpolarizing voltage steps of 100 mV from an estimated patch holding potential of approximately −50 mV.

Accuracy of parameters extracted using NSFA

How accurate are the values for i, N, and P_o obtained from NSFA? To assess this, we simulated I_h channels and performed NSFA on simulated macroscopic I_h currents. These simulations used I_h channels with activation kinetics similar to that observed experimentally (single exponential kinetics with τ of 50 ms). Two different channels were simulated, one without flicker (Fig. 2A, C–O) and one with channel flicker (Fig. 2B, C–C–O). In both cases, i was 100 fA and N was 500. In the case of the nonflickering channel, P_o was 1 (Fig. 2A), whereas P_o was 0.5 in the flickering channel (Fig. 2B, forward and backward rates, δ, into and out of the open state were equal). Simulated macroscopic I_h current traces were generated by adding 500 single-channel traces (Fig. 2A,B) and realistic recording noise. These currents were digitally filtered at frequencies ranging from 2 Hz to 10 kHz and subjected to NSFA. An example of the effect of filtering on variance-mean plots for simulated I_h channels using a model with 1 kHz flicker is shown in Figure 2C after filtering at 100 Hz or 10 kHz. A full analysis of the impact of filtering on the parameters extracted with NSFA for the nonflickering and flickering models is shown in Figure 2D. These plots indicate that, in the nonflickering model, i is underestimated during filtering at less than ∼20 Hz or more than ∼1 kHz (Fig. 2D, left), leading to overestimations of N (data not shown), whereas P_o increased monotonically with filter cutoff frequency (Fig. 2D, right). These simulations suggest that, in a situation in which there is no channel flicker, the best estimates of single I_h channel parameters are obtained after filter at ∼100 Hz. The situation was reversed in models with channel flicker, with the estimated value of i increasing monotonically with cutoff frequency (Fig. 2D, left), whereas P_o increased and then decreased with increasing cutoff frequency and only converged to its appropriate value (0.5) at the highest cutoff frequencies tested (Fig. 2D, right). Thus, under conditions of high-frequency channel flickering, NSFA will only be accurate when the cutoff frequency is set at or above 10 kHz.

With these theoretical relationships in mind, we tested the impact of filtering on the parameters extracted with NSFA for native I_h currents. Macroscopic I_h currents recorded at 10 kHz bandwidth were off-line digitally filtered at cutoff frequencies ranging from 2 Hz to 10 kHz. Variance-mean plots of recorded I_h currents after filtering at 100 Hz and 10 kHz are shown in Figure 2E. Figure 2F shows the estimated parameters obtained with NSFA for all cutoff frequencies tested. Similar to the nonflickering model, with increasing cutoff frequency i increased and then decreased, whereas P_o increased monotonically (similar results were observed in four other datasets). The impact of filtering on the single-channel parameters extract using NSFA of native I_h currents is therefore similar to that observed in the nonflickering model, suggesting that native I_h channels do not undergo significant flickering in the frequency range below ∼ 5 kHz. Given this, these findings suggest that a cutoff filter frequency of ∼100 Hz is optimal for obtaining the best estimates from NSFA. This is also consistent with theoretical work indicating that errors attributable to filtering will occur if the time constant of filtering (τ_filter) is more than $$mathtex$$\( \raisebox{1ex}{1$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$$\)$$mathtex$$ of the time constant of channel activation (Alvarez et al., 2002). In neocortical dendrites, I_h has a weighted time constant of activation of ∼50 ms. Thus, in our case, τ_filter should not be >5 ms, corresponding to a low-pass cutoff frequency (f_c) of 1/(2πτ_filter) or ∼30 Hz.

Finally, we investigated the accuracy of the parameters extracted with NSFA under a large range of different signal-to-noise conditions in our nonflickering model filtered at 100 Hz by varying i and N systematically (supplemental Fig. S3, available at www.jneurosci.org as supplemental material). From these simulations, we found that, if the amplitude of macroscopic I_h currents is <1 pA or i is <10 fA, the errors in i, N, and P_o are large (> 50%) and thus highly inaccurate. However, if the macroscopic I_h current is >10 pA, as typically found in this study, the errors are <20%. Together, these simulations indicate that NSFA has sufficient precision to accurately estimate the single-channel parameters of I_h channels under our recording conditions.

Dependence of I_h single-channel properties on voltage

Does NSFA of macroscopic I_h currents accurately describe the voltage-dependent properties of I_h? To address this, hyperpolarizing pulses of −100 and −60 mV amplitude were alternated at 1 s intervals, and NSFA was performed on the obtained variance-mean relationships (Fig. 3A) (six patches ∼570 μm from the soma). Because the total channel number N cannot be estimated precisely when channels are not fully activated, we fixed N during fitting of variance-mean plots for −60 mV steps to the value estimated during NSFA of −100 mV steps in the same patch. From this analysis, P_o was estimated to be, on average, 0.94 ± 0.03 during −100 mV steps and 0.55 ± 0.05 during −60 mV steps (n = 6). These estimates of P_o follow a voltage dependence similar to that obtained for the I_h activation curve determined from tail currents (Fig. 3B). The unitary amplitude, i, was significantly smaller during −60 mV steps compared with −100 mV steps (Fig. 3C, left) (p < 0.001), as expected because of the reduced driving force, whereas the unitary conductance, γ, was not statistically different (Fig. 3C, right) (p > 0.13). In conclusion, the results above indicate that NSFA of macroscopic I_h currents accurately describes the voltage-dependent properties of single I_h channels.

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Figure 3.

Voltage-dependent properties of I_h obtained with NSFA. A, Top, I_h currents evoked by hyperpolarizing steps to −150 mV (left) and −110 mV (right). Bottom, Fitting variance versus mean of the plots (black line) yielded a P_o of 1.05 with 889 channels and i of 109 fA during steps to −150 (left), whereas P_o was reduced to 0.51 and i to 91 fA during steps to −110 mV (right). N was fixed to that obtained during steps to −150 mV (889) during fitting of the NSFA data for steps to −110 mV (black line). B, Pooled data (n = 5) of P_o during steps to −150 mV (0.94 ± 0.03) and −110 mV (0.54 ± 0.05; filled circles) is consistent with the activation curves obtained from I_h tail-current amplitudes (open circles; same data as in Fig. 1C). C, Histogram of single-channel current amplitude i (left) and conductance γ (right) extracted with NSFA during steps to −150 and −110 mV. **p < 0.001 (n = 6).

Dependence of I_h single-channel properties on location

Previous studies on I_h in layer 5 pyramidal dendrites have reported a significantly higher current density at distal dendritic locations (Williams and Stuart, 2000; Berger et al., 2001). Because the macroscopic I_h current is determined by the product of i, N, and P_o, we can now separate which of these factors underlies the highly nonuniform subcellular distribution of I_h in these neurons (Fig. 1B). Three examples of variance-mean plots obtained from recordings 270, 400, and 740 μm from the soma are shown in Figure 4A. Figure 4B shows that, when P_o is plotted as a function of recording location, for distances from ∼120 to 900 μm from the soma, no clear dependence exists on dendritic site. Similarly, the I_h single-channel conductance, γ, was independent of the dendritic recording location (Fig. 4C). Plotting γ as a histogram indicates that γ represents a single population with average amplitude of 676 ± 35 fS (Fig. 4C, inset) (n = 18). In contrast, N was found to rise steeply with distance from the soma (Fig. 4D). An exponential fit to this data indicates that N increases e-fold for a 240 μm path length along the main apical dendrite of layer 5 pyramidal neurons, similar to the e-fold change in current density (Fig. 1B). At the most distal dendritic locations examined (900 μm from the soma), we observed as many as ∼2500 I_h channels per dendritic patch, whereas at the most proximal sites (120 μm from the soma), as few as 40 channels per patch were observed. This gradient is essentially identical to the reported 60-fold increase in immunogold-labeled HCN1 particles in layer 5 dendritic membrane (Lorincz et al., 2002). These data correspond to I_h channel densities of 9–550/μm², assuming a membrane patch area of ∼4.5 μm² (Engel and Jonas, 2005). The high density of I_h in the distal dendrites of layer 5 pyramidal neurons is comparable with the density of voltage-activated Na⁺ channels found at nodes of Ranvier (Hille, 2001). In conclusion, these data indicate that the nonuniform scaling of I_h current density is generated by an exponential increase in channel number per dendritic membrane area, leading to high channel densities in distal dendrites.

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Figure 4.

NSFA reveals a distance-dependent increase in N. A, Superimposed examples of variance-mean plots for three dendritic locations (270, 400, and 740 μm from the soma) with the variance-mean fits (black lines). B, Plot of open probability P_o versus recording distance from the soma. Data were fitted with a regression (slope of −0.015; n = 18). C, Plot of single-channel conductance γ versus distance from the soma. Data fitted with a linear regression (slope of +0.11; n = 18). Inset shows a histogram of γ revealing a single population well fitted with a Gaussian function (n = 18). D, Plot of the number of channels per patch (N) versus distance (d) from the soma. The data are well described by a single-exponential function of the form: 49 × exp(d/240) + 47, indicating that the I_h channel number increases e-fold for a 240 μm change in distance.

Contribution of stochastic I_h channel gating to membrane noise

The results above indicate that I_h channels have a very small single-channel conductance yet can be expressed at very high densities. Why is the single-channel conductance of I_h so small? Clearly, it would be energetically more efficient to increase single-channel conductance, for example by 10-fold to 6.8 pS, thereby reducing channel number by a factor of 10 for the same current density. One possible explanation for the small single-channel conductance of I_h is that there are other constraints on the system, such as voltage noise. Previous work indicates that the stochastic opening and closing of voltage-dependent channels can generate fluctuations in membrane potential, which could be a significant source of voltage noise in excitable cells (DeFelice, 1981; White et al., 2000). To directly address whether the stochastic gating of single I_h channels contributes to membrane noise, we recorded voltage noise at the resting membrane potential in the presence of blockers for NMDA, AMPA, GABA_A, and Na⁺ channels. In Figure 5, an example is shown of control membrane potential fluctuations at the soma with an SD, σ_V, of 122 μV (Fig. 5, black trace). To isolate the contribution of I_h channels to these voltage fluctuations, we bath applied 50 μm ZD 7288 (BoSmith et al., 1993). This led to a hyperpolarization of the somatic resting membrane by 11 mV (average change, −10.3 ± 0.5 mV; n = 6), which was corrected for by positive DC injection to obtain a similar resting membrane potential as in control (−77.9 mV). Under these conditions, σ_V was reduced to 89 μV (Fig. 5, gray trace). Spectral analysis of traces before and after ZD 7288 showed that I_h noise is particularly dominant in the low-frequency range (Fig. 5, left). On average, application of ZD 7288 lead to a reduction of σ_V by 33 ± 7 μV (Fig. 5, right) (n = 6; paired t test, p < 0.01), showing that native I_h channels contribute significantly to voltage noise at resting membrane potentials.

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Figure 5.

Impact of I_h channel gating on somatic voltage noise. Whole-cell somatic voltage recordings before (top trace; black) and after (bottom trace; gray) I_h channel block by bath application of ZD 7288 (50 μm). All data were recorded in the presence of synaptic blockers and TTX. DC injection was used to maintain the same membrane potential in control and ZD 7288. Left, Power spectrum of the same traces indicating that ZD 7288 attenuates voltage fluctuations in the low-frequency range. Right, Population data of the average SD, σ_V, of the somatic voltage noise in control (black bar) and ZD 7288 (gray bar).

Impact of I_h single-channel conductance on membrane noise

Next we investigated the impact of I_h single-channel properties on membrane voltage noise using a model in which single-channel conductance and number could be varied in a controlled manner. A stochastic Hodgkin–Huxley model of I_h based on our experimental data (Fig. 6A) was introduced into a morphologically realistic model of a layer 5 pyramidal neuron (Fig. 6B). The model contained voltage-activated Na⁺, K⁺, and Ca²⁺ conductances distributed uniformly throughout the dendritic tree, together with a stochastic I_h channel model distributed exponentially to mimic the experimentally observed increase in I_h current density with distance from the soma (Fig. 1B). Addition of I_h depolarized the soma by 10 to −79 mV and set the membrane potential in the very distal tuft branches to −65 mV. This effect of I_h on the resting membrane potential was quantitatively similar to experimentally observed changes in membrane potential with distance from the soma (supplemental Fig. S1, available at www.jneurosci.org as supplemental material).

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Figure 6.

Impact of I_h channel single-channel conductance on voltage noise in a model. A, Modeling of I_h kinetics using Hodgkin–Huxley (H–H) formalism. Steady-state voltage-activation curve (top) and the voltage dependence of activation (weighted single time constant; filled circles, bottom) and deactivation (open circles) together with the predictions from the Hodgkin–Huxley I_h model (lines). B, Left, Morphology of the compartmental layer 5 neuron. Conductance densities at the soma and a distal dendritic location, together with representative examples (right) of the resting membrane potential at the soma (−79 mV; bottom trace) and distal dendrites (−63 mV; 1000 μm from the soma; top trace) using a model with single-channel conductance γ of 680 fS. C, The power of somatic membrane potential fluctuations versus frequency for models with γ of 680 fS (black) and 6.8 pS (gray). Data fitted with a Lorentzian function (see Materials and Methods) from 1 to 30 Hz giving a cutoff frequency f_c of 6.0 and 4.2 Hz, respectively, in the models with γ of 680 fS and 6.8 pS. D, The SD of the resting membrane potential σ_V plotted against γ and total N used in the simulations. The squares represent σ_V at the soma and the circles σ_V at a dendritic position 1000 μm from the soma. The lines are the predicted relationship between σ_V and γ (see Materials and Methods).

We first performed simulations using I_h channels with a single-channel conductance of 680 fS, the experimentally determined value. Figure 6B shows that, using this model, small fluctuations in somatic membrane potential occur with a σ_V of 40 μV (Fig. 6B, bottom trace). As expected, because of the higher density of I_h in distal dendrites, as well as their small diameter, fluctuations in membrane potential at distal dendritic locations (1000 μm from the soma) were significantly larger than at the soma, with σ_V being 129 μV (Fig. 6B, top trace). We next performed simulations with a single-channel conductance of 6.8 pS, 10-fold greater than observed experimentally while maintaining the same current density by scaling down N. Note that 6.8 pS is still in the low range compared with the single-channel conductance of most other ion channels (Hille, 2001). Increasing the I_h single-channel conductance, γ, to 6.8 pS increased σ_V to 129 μV at the soma (Fig. 6C, bottom, gray trace) and up to 408 μV in dendritic compartments ∼1000 μm from the soma (data not shown). Analysis of the PSD of voltage fluctuations indicated that this increase in membrane noise was similar at all frequencies of the power spectrum (Fig. 6C). The cutoff frequency of the PSD was slightly lower at the soma than in the dendrites (∼5 vs ∼8 Hz), presumably because of greater “filtering” of voltage fluctuations at the soma by the larger somatic capacitance (data not shown).

To compare the voltage noise introduced by I_h with that generated by channel noise from voltage-activated Na⁺ channels, we performed simulations using a stochastic Na⁺ channel model with γ_Na = 10 pS. In these simulations, we used a deterministic I_h model to allow us to isolate the contribution of voltage-activated Na⁺ channels to membrane noise independent of I_h channel noise. At resting membrane potentials, stochastic Na⁺ channels generated membrane noise with σ_V = 7.3 μV at the soma, significantly smaller than the observed σ_V = 40 μV in models with stochastic I_h channel (γ = 680 fS). In dendritic compartments ∼1000 μm from the soma, σ_V increased to 47 μV (compared with 129 μV for I_h channels). These data indicate that, at resting membrane potentials, the voltage noise attributable to stochastic gating of I_h channels is significantly larger than that mediated by Na⁺ channels.

Despite the uniform dendritic Na⁺ channel density in the model, the Na⁺ channel voltage noise was greatest at distal dendritic locations. Given recent experimental evidence that Na⁺ channel noise is greater at depolarized potentials (Jacobson et al., 2005), we reasoned that the larger membrane fluctuations at distal dendritic locations were generated by increased activation of voltage-dependent Na⁺ channels as a consequence of the depolarizing action of nonuniform I_h (supplemental Fig. S1, available at www.jneurosci.org as supplemental material). Consistent with this idea, when the I_h density in our model was set to be low and uniform, leading to a homogeneous resting potential of −83 mV, the σ_V of Na⁺ channel-induced membrane noise was 2.7 μV in both distal dendritic and somatic compartments. This suggests a dual role for I_h on membrane noise in the distal dendrites: increasing membrane noise via the high density of distal dendritic I_h channels, as well as via depolarization-induced activation of dendritic Na⁺ channels.

The relationship between γ, N, and σ_V is depicted in a log–log plot in Figure 6D. Previous theoretical work indicates that the current variance, σ_I², is proportional to N and the square of γ (White et al., 2000; Diba et al., 2004). Consistent with this idea, the observed change in σ_V was well predicted by the expected change in current noise, with σ_V proportional to the square root of γ (Fig. 6D). These simulations indicate that the impact of I_h single-channel conductance on voltage noise follows known theoretical descriptions of the contribution of single-channel properties to current noise. From this, it follows that, for a given current density, reducing I_h single-channel conductance, rather than channel number, is the most effective means to reduce the impact of stochastic gating of I_h on membrane noise.

Impact of I_h channel noise on action potential fidelity

To assess the functional implications of I_h channel noise, we first analyzed the probability and timing of AP generation in response to weak periodic suprathreshold inputs. A small sinusoidal current (3 Hz; 4 pA peak-to-peak) was injected into the soma together with a larger DC adjusted to elicit one AP per sine-wave cycle in models with deterministic I_h. These current injections elicited, on average, one AP per sine-wave cycle in models with stochastic I_h with a single-channel conductance, γ, of 680 fS (Fig. 7A). The ability to detect the sinusoidal signal (the SNR) was quantified from the 3 Hz peak in the PSD (see Materials and Methods). The temporal precision of AP output was quantified from the SD of the temporal jitter in AP timing (σ_t) (Fig. 7A). Increasing γ 10-fold to 6.8 pS led to an increase in AP failures and spontaneous APs not phase locked to the peak of the weak input signal (Fig. 7B), leading to a decrease in both the SNR (Fig. 7C, black diamonds) and temporal precision (Fig. 7C, blue diamonds). Systematic variation of γ between 0.4 and 400 pS showed that, as γ increases, there is an ∼100-fold decrease in SNR and a qualitatively similar decrease in temporal precision (Fig. 7C, diamonds).

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Figure 7.

Impact of I_h single-channel noise on the fidelity of AP output in the model. A, Somatic injection of a small suprathreshold sinusoidal current signal (I_sin = 4 pA; 3 Hz; top trace) elicited, on average, one AP per sine-wave cycle (bottom trace) in a model with γ of 680 fS. Right, Superimposed responses on an expanded time scale. Bottom, Histogram of AP onset latency relative to the phase of the sine wave for 400 consecutive sine-wave cycles. Data were fitted with a Gaussian function (green line) with SD σ_t. B, Corresponding plots as in A but with increased γ to 6.8 pS. Note the threefold increase in AP jitter. C, SNR determined from the 3 Hz peak in the power-spectrum density, and temporal precision (blue diamonds, 1/σ_t) are plotted as a function of γ (range, 0.4–400 pS). Subthreshold sinusoidal current injections (red; I_sin = 4 pA) and suprathreshold injections (black; I_sin = 4 pA) were analyzed for stochastic resonance. The dotted lines are fits according to stochastic resonance theory (see Materials and Methods). D, Superimposed sweeps of APs evoked by a simulated excitatory synaptic conductance (g_dend; left trace; calibration bar, 60 nS) injected 400 μm from the soma in models with single-channel conductance γ of 680 fS (top) and 6.8 pS (bottom). Note the larger trial-to-trial variability (jittering) in models with large γ. E, Spike precision defined as 1/σ and plotted versus the change in amplitude of the excitatory synaptic conductance in models with γ of 680 fS (black diamonds) and 6.8 pS (blue circles). For comparison, a model with deterministic I_h and stochastic Na⁺ channels with γ_Na = 10 pS is shown (open circles). F, Input–output relationship showing the probability of AP generation versus the change in amplitude of the excitatory synaptic conductance in models with γ = 680 fS (black line; steepness of the sigmoid fit, s = 0.31 nS) and γ = 6.8 pS (blue line; s = 0.68 nS). For comparison, a model with deterministic I_h and stochastic Na⁺ channels with γ_Na = 10 pS is shown (open circles; s = 0.59 nS).

Can the detection of subthreshold periodic signals, however, be facilitated by membrane noise via stochastic resonance (Wiesenfeld et al., 1994; Wiesenfeld and Moss, 1995; Stacey and Durand, 2000)? To examine the impact of I_h channel noise on stochastic resonance, the amplitude of DC injected into the soma was adjusted so that small sinusoidal currents (3 Hz; 4 pA peak-to-peak) were just subthreshold in models with deterministic I_h. In models with stochastic I_h, these current injections elicited stochastic resonance, with the SNR dependent on the amplitude of the I_h single-channel conductance, γ (Fig. 7C). In the example shown in Figure 7C (red circles), the SNR peaked in I_h models in which γ was ∼10 pS. According to classical stochastic resonance theory (Wiesenfeld and Moss, 1995), the SNR peak is expected at half of the threshold barrier height (ΔU). Consistent with this expectation, reducing ΔU by using larger DCs, which brings subthreshold sinusoidal currents closer to AP threshold, led to SNR peaks at smaller values of γ (e.g., <1 pS; data not shown). Decreasing the amplitude of sinusoidal currents from 4 to 1 pA with identical values of ΔU resulted in SNR peaks at approximately the same value of γ but smaller SNR amplitude. These findings indicate that, although detection of small periodic signals can be improved by voltage noise from stochastic gating of I_h channels, the optimal I_h single-channel conductance critically depends on the characteristics of the signal that is to be detected.

We also investigated the impact of I_h channel noise on AP output during EPSPs of varying amplitude located 400 μm from the soma (Fig. 7D–F). For all EPSP amplitudes, ∼25 trials were repeated while changing only the values for the random number generator used to generate stochastic gating of simulated I_h channels. In models with γ of 680 fS, the variance in spike timing was small (σ_t ≤ 1 ms), and the precision (1/σ_t) increased linearly with synaptic strength (Fig. 7E, black diamonds). In comparison, considerable more jittering in AP latency was observed in models with γ of 6.8 pS, and precision increased only weakly with EPSP amplitude (Fig. 7E, blue circles). Simulations with stochastic Na⁺ channels, but deterministic I_h channels, indicated that stochastic gating of Na⁺ channels introduces similar reductions in temporal precision to that seen in models with stochastic I_h with γ of 6.8 pS (Fig. 7E, open circles).

The reduced precision of AP generation in models with larger I_h channel noise was associated with a shallower slope of the input–output relationship of EPSP amplitude versus the probability of AP generation (Fig. 7F). A change in slope of this input–output function indicates that models with higher I_h single-channel conductance have a larger threshold uncertainty (White et al., 2000). Simulations with stochastic Na⁺ channels but deterministic I_h channels also showed a larger threshold uncertainty (Fig. 7F, open circles). Note that the change in the input–output function during EPSPs in models with stochastic I_h did not translate into a change in slope of the AP firing frequency (f) versus input current (I) relationship (f/I curve) during long (1 s) pulses (data not shown). This was presumably the case because the level of background noise generated by stochastic gating of I_h (SD < 1 mV) was too small to cause a change in f/I gain, as observed by others during balanced synaptic noise (Chance et al., 2002).

Comparisons with previous studies

Although our data provide compelling evidence for small-conducting I_h channels, a recent study in acutely dissociated CA1 pyramidal neurons using excised patches from the soma has proposed a >10-fold higher single-channel conductance of 10 pS (Simeone et al., 2005). Such large single-channel openings (∼1 pA), however, were not observed in previous cell-attached studies of native I_h currents in CA1 pyramidal neurons (Magee, 1998). In addition, it is also unclear how I_h currents were observed at all in the study of Simeone et al. (2005), given the evidence that I_h is very sensitive to enzymatic procedures for acute dissociation (Budde et al., 1994). Our findings in brain slices are also at odds with estimates of HCN single-channel conductance based on heterologously expressed HCN subunits (2.5–35 pS) (Johnson and Zagotta, 2005; Michels et al., 2005). Although the explanation for these discrepancies are also unclear, a number of proteins are known to interact with HCN subunits, such as Filamin A or TRIP8b (Gravante et al., 2004; Santoro et al., 2004). Additional experiments will be needed to address whether interaction of these proteins with HCN channels leads to modification of channel properties, such as single-channel conductance. Given this possibility, it is worth noting that the studies that used cell-attached recording configuration (the present study) (DiFrancesco, 1986) consistently observed a small single-channel conductance <1 pS. This may suggest that excised patch-clamp recordings disturb the single-channel properties of I_h, perhaps via removal of accessory or loss of interactions between HCN channels and critical cytosolic proteins.

I_h channel noise

Given the wide spectrum of observed unitary conductances for voltage-dependent channels (from ∼1 to 300 pS) (Hille, 2001), we asked why is the single-channel conductance of I_h so small? A growing number of studies indicate that noise generated by random channel opening limits neuronal response reliability (Schneidman et al., 1998; White et al., 2000), influences the energy efficiency of channels (Schreiber et al., 2002), and constrains the physical dimensions of axon diameters (Faisal et al., 2005). Conversely, noise can have a beneficial role by enhancing the detection of weak periodic signals via a stochastic resonance mechanism (Wiesenfeld and Moss, 1995) or via enhancing subthreshold oscillations (Dorval and White, 2005). Based on these studies, it seems likely that the magnitude of channel noise is under evolutionary pressure in biological systems seeking energy-efficient coding systems (Laughlin and Sejnowski, 2003). We show here that native I_h channels generate between ∼40 and 130 μV of voltage noise (rms) spatially distributed from the soma to distal dendrites, with most of the power below 10 Hz (Figs. 5, 6). Although most recent studies have focused on the role of stochastic openings of Na⁺ channels (Schneidman et al., 1998; Diba et al., 2004; Dorval and White, 2005; Faisal et al., 2005; Jacobson et al., 2005), we propose that I_h is also likely to be an important source of intrinsic channel noise in neurons. This would be expected to be the case for a number of reasons. First, channel noise is greater for voltage-dependent channels, like I_h, that have slow activation kinetics (Diba et al., 2004). Second, channel noise increases linearly with channel number (Diba et al., 2004), and, as we show, I_h channel densities can be very high, particularly at distal dendritic locations (Fig. 4). Third, channel noise would be expected to lead to larger voltage noise in smaller compartments in which I_h channel densities are maximal. Finally, the depolarizing gradient generated by I_h will enhance Na⁺ channel noise. These observations indicate that the dynamic interplay between I_h and Na⁺ channel noise will need to be considered in future studies investigating the impact of membrane noise in neuronal computation.

Functional implications of I_h channel gating on action potential output

We asked whether I_h noise is large enough to impact on AP output. This was shown to be the case both for perithreshold weak periodic stimuli and single EPSPs (Fig. 7). In models with high I_h single-channel conductance (6.8 pS), larger AP jitter and lower phase reliability were observed compared with models with the experimentally observed I_h single-channel conductance of 680 fS. In contrast to these negative aspects of I_h noise, models with stochastic I_h also showed stochastic resonance for very weak (1–4 pA) oscillatory inputs. Whether such noise-enhanced signal detection is functionally relevant in cortical layer 5 pyramidal neurons is presently unclear, because, under in vivo conditions, it seems likely that voltage noise will be dominated by the large fluctuations of ongoing, spatially distributed, synaptic activity at dendritic sites (Destexhe et al., 2003). Furthermore, although I_h noise could improve detection of weak sinusoidal signals, the optimal single-channel conductance was critically dependent on the characteristics of the input signal to be detected. Thus, it seems unlikely that stochastic resonance mechanisms have worked as a selection factor for I_h single-channel conductance. Rather, our results suggest that such selection, favoring small-conducting I_h channels, is more likely to depend on the influence of stochastic channel noise on the reliability of spike timing (Fig. 7C, top, E, F).

Although our studies concentrate on cortical layer 5 pyramidal neurons, which express I_h channels primarily in their dendrites, many of the results can be generalized in other neuronal and cell types. For example, expression of I_h in small-diameter compartments such as axons (Notomi and Shigemoto, 2004) would be expected to increase channel noise and limit the axonal conduction reliability (Faisal et al., 2005). In addition, because the magnitude of channel noise is further increased by slower channel activation kinetics (Diba et al., 2004), it seems likely that spike-time jitter will be even greater in cells in which HCN activation is slower, such as in the cardiac cells (DiFrancesco, 1984) and thalamic relay neurons (McCormick and Pape, 1990). Such predictions remain to be tested.

Given that theoretical relationships indicate that current noise is linearly dependent on single-channel number but changes with the square root of channel conductance (White et al., 2000; Diba et al., 2004), reducing single-channel conductance is an efficient means to reduce membrane noise attributable to stochastic channel gating. This result may well explain the small single-channel conductance of I_h channels in the brain and suggests that the single-channel conductance of I_h is evolutionarily constrained to be small to reduce its impact on both membrane noise and AP output.

In conclusion, our results indicate that native I_h channels in the brain have a small single-channel conductance, comparable in size with the single-channel conductance of I_f in the heart, which is likely to be critical for reducing membrane noise attributable to stochastic gating, thereby maintaining the fidelity of temporal patterns of AP output.