Effects of Ih and TASK-like shunting current on dendritic impedance in layer 5 pyramidal-tract neurons

Abstract

Pyramidal neurons in neocortex have complex input-output relationships that depend on their morphologies, ion channel distributions, and the nature of their inputs, but which cannot be replicated by simple integrate-and-fire models. The impedance properties of their dendritic arbors, such as resonance and phase shift, shape neuronal responses to synaptic inputs and provide intraneuronal functional maps reflecting their intrinsic dynamics and excitability. Experimental studies of dendritic impedance have shown that neocortical pyramidal tract neurons exhibit distance-dependent changes in resonance and impedance phase with respect to the soma. We, therefore, investigated how well several biophysically detailed multicompartment models of neocortical layer 5 pyramidal tract neurons reproduce the location-dependent impedance profiles observed experimentally. Each model tested here exhibited location-dependent impedance profiles, but most captured either the observed impedance amplitude or phase, not both. The only model that captured features from both incorporates hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and a shunting current, such as that produced by Twik-related acid-sensitive K⁺ (TASK) channels. TASK-like channel density in this model was proportional to local HCN channel density. We found that although this shunting current alone is insufficient to produce resonance or realistic phase response, it modulates all features of dendritic impedance, including resonance frequencies, resonance strength, synchronous frequencies, and total inductive phase. We also explored how the interaction of HCN channel current (I_h) and a TASK-like shunting current shape synaptic potentials and produce degeneracy in dendritic impedance profiles, wherein different combinations of I_h and shunting current can produce the same impedance profile.NEW & NOTEWORTHY We simulated chirp current stimulation in the apical dendrites of 5 biophysically detailed multicompartment models of neocortical pyramidal tract neurons and found that a combination of HCN channels and TASK-like channels produced the best fit to experimental measurements of dendritic impedance. We then explored how HCN and TASK-like channels can shape the dendritic impedance as well as the voltage response to synaptic currents.

Keywords: Twik-related acid-sensitive K+(TASK) channels; h-current (Ih); impedance; pyramidal tract neurons; resonance.

Graphical abstract

Figure 1.

Inductance influences neuronal impedance and the response to synaptic stimulation. A: a simple, passive neuron model (soma and dendrite with membrane capacitance) was connected to a series circuit with an inductor (L = 1 MH or 100 MH), resistor (R = 25 MΩ), and battery (E = −70 mV) to illustrate some of the effects of inductance on impedance and synaptic potentials. We computed impedance between the center of the dendrite and the soma with this circuit attached (blue and red lines) and without it (black lines). B: the inductive circuit combined with membrane capacitance from the neuron produces resonance. When L = 100 MH, resonance frequency (∼7 Hz) is comparable with those seen in PT dendrites (13, 27). They are much higher when L = 1 MH. In the passive neuron alone, impedance amplitude falls off with frequency. Resonance frequencies are indicated with vertical dashed lines. C: the inductive circuit also increases impedance phase, with positive inductive/leading phase (voltage peak precedes current peak for an oscillatory input) seen at low frequencies. The horizontal dotted line indicates 0 radian phase shift between the stimulating current in the dendrite and voltage response at the soma (i.e., synchrony). D: effects of increased inductance on EPSPs measured at the soma: When L = 1 MH, peak EPSP voltage is earlier compared to the passive neuron due to higher impedance phase across the power spectrum of the synaptic current stimulus, but it produces much more undershoot that seen in PTs (32, 33). Conversely, when L = 100 MH, there is little change in peak EPSP time, but EPSP shape is more in line with that observed experimentally (32, 33). Time of peak synaptic conductance is indicated by the vertical dotted line. EPSP, excitatory postsynaptic potential; PT, pyramidal tract neuron; V_memb, neuronal membrane potential; Φ_c, transfer impedance phase.

Figure 2.

Impedance responses in dendrites of model 5. A: constant amplitude, linear chirp, current waveform which is applied to different points along the apical dendrite. B: stimulated locations along the apical trunk: proximal (blue), central (red), and distal (green). We recorded membrane potentials at the stimulated compartments (C, E, and G) and at the soma (D, F, and H). I: Z_c was computed from the changes in the membrane potential at the soma and the current stimulus applied to the dendrites. J: from the transfer impedance amplitude, |Z_c|, we compute the transfer resonance frequency, which is indicated by the vertical dashed line for the most distal recording site. K: from the transfer impedance phase Φ_c, we compute the synchronous frequency, again indicated by a vertical dashed line for the most distal site.

Figure 3.

Resonant frequencies and synchronous frequencies of five PT models compared with experimental data. A: four of the five models show transfer frequencies along the apical trunk within the experimentally observed range. The fifth produced transfer frequencies above this range. Experimental values of transfer frequencies were extracted from Ulrich (27) and Dembrow et al. (13). B: only two models exhibit synchronous frequencies along the apical trunk which are within the experimental range. The other three models produce synchronous frequencies below this range. Experimental values of synchronous frequencies were extracted from Dembrow et al. (13). PT, pyramidal tract neuron.

Figure 4.

The impedance phase in PT models and its implications for synaptic potentials. A: model 5 exhibits much greater total inductive phase along the apical trunk compared with the other models. B: comparison of two models’ transfer impedance phase profiles from halfway along the apical trunk (136.4 μm from the soma) showing Φ_cis greater in model 5 than in model 4 for all frequencies probed. Inset shows somatic V_memb response to 2 Hz and 10 Hz sinusoidal stimuli in the time domain from both models. At 2 Hz, V_memb leads the stimulating current by roughly 17 ms in model 5, whereas they are nearly synchronous in model 4. At 10 Hz, lag in V_memb is reduced in model 5 compared with model 4. Dotted black lines indicate the stimulating current waveform. C: somatic EPSP in response to synaptic stimulation in both models at the same point along the apical trunk. Peak V_memb occurs more than 1 ms earlier in model 5 than in model 4. EPSP, excitatory post-synaptic potential; PT, pyramidal tract neuron.

Figure 5.

A model of HCN including a TASK-like shunting current best approximates experimentally observed impedance profiles. Resulting impedance features when using three different models of HCN channels in the same model neuron. A: compared with the original PT model which uses the HCN and TASK-like channel models from Migliore and Migliore (41), the mechanisms developed by Kole et al. (48) and Harnett et al. (51) reduced transfer frequency along the apical trunk, but the values remain well within the experimental range. B: they led to dramatic reductions in synchronous frequency, however. HCN, hyperpolarization-activated cyclic nucleotide-gated; PT, pyramidal tract neuron; TASK, Twik-related acid-sensitive K⁺.

Figure 6.

Selective blockade of I_h and shunting current differentially modulates dendritic impedance. A and B: example transfer impedance amplitude and phase profiles between the distal end of the apical trunk and the soma 288.9 μm away, respectively, under baseline conditions (red) and when either I_h (green) or the shunting current (red) have been blocked. We also observe how resonance strength (C), total inductive phase (D), transfer frequency (E), and synchronous frequency (F) are attenuated along the apical trunk under those same conditions.

Figure 7.

Selective blockade of I_h and shunting current reduces transfer impedance phase and effects timing and shape of EPSPs. A: model 5 was stimulated with a 20-s long, subthreshold white-noise stimulus roughly halfway along the apical trunk (136.4 μm from the soma), and V_memb was measured at the soma following blockade of HCN (green) and TASK-like channels (blue), as well as under control conditions (red). Transfer impedance phase was reduced by blockade of the shunting current and further reduced by blockade of I_h. The y-axis on the left shows transfer impedance phase. Since the reduction of transfer impedance phase influences the timing of somatic response to synaptic stimulation in the dendrite, the normalized power spectrum of a single AMPA-like excitatory synapse is superimposed (black dashed line), with the y-axis on the right showing normalized synaptic power. The frequencies with the highest synaptic power overlap with the frequency ranges in which the downward transfer impedance phase shifts cause by I_h and shunting current blockade are most prominent. B: model 5 was stimulated with a single excitatory AMPA-like synaptic stimulus at the same location. Maximal synaptic conductance was tuned to produce a ∼1 mV EPSP at the soma, and peak synaptic current occurred at 1 ms (black, vertical dashed line). Maximal EPSP V_memb lagged 3.7 ms behind peak synaptic under control conditions, 4.8 ms after blocking TASK-like shunting current, and 6.3 ms after blocking I_h. EPSPs narrow in accordance with decreasing resonance strength seen in Fig. 6. AMPA, α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid; EPSP, excitatory post-synaptic potential; HCN, hyperpolarization-activated cyclic nucleotide-gated; I_h, h-current; TASK, Twik-related acid-sensitive K⁺.

Figure 8.

Using a model of HCN channels including a shunting current in model 1 produces realistic impedance amplitude and phase response, comparable with model 5. A: morphologies of model 1 and model 5. B: distribution of g_Ih, which affects both I_h and TASK-like shunting current, in the two models. Distances are normalized to the farthest compartment from the soma in each cell. C: transfer frequencies increase but remain within experimental range as originally. D: synchronous frequencies along the apical trunk are greatly improved compared to the experimental data (red). *Experimental values for transfer and synchronous frequencies. E: total inductive phase between model 5 and the adjusted model 1 are similar. Note that distances in C–E are normalized to the length of each model’s apical trunk. HCN, hyperpolarization-activated cyclic nucleotide-gated; I_h, h-current; TASK, Twik-related acid-sensitive K⁺.

Figure 9.

Combined effects of modulating HCN and TASK-like channel density on dendritic impedance. HCN density (ΔI_h) and/or TASK-like channel density (ΔI_lk) were modulated by ±90% in 10% increments across the entire neuron, which altered resonance strength (A), transfer frequency (B), synchronous frequency (C), and total inductive phase (D). Parameters are presented in percent change from baseline. HCN, hyperpolarization-activated cyclic nucleotide-gated; I_h, h-current; TASK, Twik-related acid-sensitive K⁺.