Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency

Abstract

Network oscillations typically span a limited range of frequency. In pacemaker-driven networks, including many central pattern generators (CPGs), this frequency range is determined by the properties of bursting pacemaker neurons and their synaptic connections; thus, factors that affect the burst frequency of pacemaker neurons should play a role in determining the network frequency. We examine the role of membrane resonance of pacemaker neurons on the network frequency in the crab pyloric CPG. The pyloric oscillations (frequency of approximately 1 Hz) are generated by a group of pacemaker neurons: the anterior burster (AB) and the pyloric dilator (PD). We examine the impedance profiles of the AB and PD neurons in response to sinusoidal current injections with varying frequency and find that both neuron types exhibit membrane resonance, i.e., demonstrate maximal impedance at a given preferred frequency. The membrane resonance frequencies of the AB and PD neurons fall within the range of the pyloric network oscillation frequency. Experiments with pharmacological blockers and computational modeling show that both calcium currents I(Ca) and the hyperpolarization-activated inward current I(h) are important in producing the membrane resonance in these neurons. We then demonstrate that both the membrane resonance frequency of the PD neuron and its suprathreshold bursting frequency can be shifted in the same direction by either direct current injection or by using the dynamic-clamp technique to inject artificial conductances for I(h) or I(Ca). Together, these results suggest that membrane resonance of pacemaker neurons can be strongly correlated with the CPG oscillation frequency.

Figure 1.

Membrane resonance measurement of the pyloric pacemaker neurons AB and PD. Simultaneous recordings of the AB (A1) and PD (A2) neuron oscillations during the ongoing pyloric rhythm. B1,. The voltage response of the AB neuron to a 60 s ZAP current injection (top trace) that sweeps a frequency range between 0.2 and 3 Hz indicates a maximum amplitude at a preferred resonance frequency (f_max, indicated by arrowhead). B2, The voltage trace of the PD neuron in response to a similar ZAP current also shows a resonance frequency f_max (arrowhead). The small horizontal dashed lines in A and B show the −50 mV level. C1, The impedance profile of the AB neuron in the frequency domain. The cross bar shows the resonance frequency and the maximum impedance value (f_max = 0.69 ± 0.05 Hz; Z_max = 23.5 ± 2.3 MΩ; n = 6). The resting membrane potentials for the AB trace was −49.2 ± 2.2 mV. The shaded region indicates 1 SE. C2, The impedance profile of the PD neuron (f_max = 0.92 ± 0.04; Z_max = 10.1 ± 0.7 MΩ; n = 7). The resting membrane potentials for the PD trace was −52.7 ± 2.4 mV. Note that the f_max and Z_max values shown in C1 and C2 do not exactly match the peak of the mean impedance profile (solid line) attributable to the fact that the peak of the mean impedance profile is determined not only by the peak of the profiles in individual experiments but also by their slopes and amplitudes.

Figure 2.

Ionic current contributing to membrane resonance properties of the PD neuron. A, The voltage response of the PD neuron to a ZAP current injection (bottom trace) in control (Ctl) and after superfusion with Cs⁺ to block I_h or Mn²⁺ to block I_Ca. The vertical arrowhead in Ctl indicates the resonance frequency. The small horizontal dashed lines show the −50 mV level. The baseline of the ZAP current is 0 nA. The resting membrane potentials for the control trace, after superfusion with Cs⁺ and after superfusion with Mn²⁺, were −51.2 ± 0.65, −53 ± 1.1, and −52.5 ± 3.9 mV, respectively. In neither Cs⁺ nor Mn²⁺ saline, the resting membrane potential was not significantly different from control saline (Student's t test, p > 0.5). B, The impedance profile of the PD neuron in control and after superfusion with Cs⁺ (n = 4). Note the shift of f_max from 0.96 to 0.41 Hz. C, The impedance profile of the PD neuron in control and after superfusion with Mn²⁺ (n = 4), which abolishes resonance. The shaded regions in B and C indicate 1 SE.

Figure 3.

I_h shapes the lower envelope of the voltage profile of the PD model neuron. All ionic currents other than I_leak, I_h, I_Ca, and I_K(Ca) have been removed. A, The voltage response of the model PD neuron to a ZAP current injection in control (black) and after blocking I_h (dotted gray). The dashed curves mark the lower envelope of the voltage profiles (slightly displaced for clarity), indicating the effect of I_h in shaping the voltage response of the PD model neuron. B, The voltage response (dotted gray) with the maximum conductance of I_h set to one-half of the control value of 0.2 nS (black). C, The voltage response with the maximum conductance of I_h set to 0.3 nS (dotted gray). The control trace is shown in black. D, The impedance profile of the traces shown in A–C. Note that increasing the maximum conductance of I_h shifts the resonance frequency to a slightly higher value. The small horizontal line in A shows the −60 mV level in A–C.

Figure 4.

I_h and I_Ca, respectively, shape the lower and upper envelope of the voltage profile of the PD model neuron. A, Same as Figure 3A, showing the effect of blocking I_h (dotted gray) on the voltage response of the model neuron. Black trace is control. Dashed curves show the lower envelope of the voltage profile, and the bars on the right indicate the voltage range at the highest frequency. B, A constant DC bias current (0.32 nA) was applied after blocking I_h to counteract the hyperpolarized voltage attributable to blocking I_h. Even with the depolarizing bias current, the effect of blocking I_h (dotted gray) was mainly visible in shaping the lower envelope of the voltage profile (dashed curves). Note that the upper envelope still shows a local maximum. The bars on the right indicate the voltage range at the highest frequency. C, The voltage response of the model PD neuron after blocking I_Ca (dotted gray). Note the role of I_Ca in shaping of the upper envelope of the resonance envelope indicated with the dashed curves. D, Blocking both I_Ca and I_h removes the resonance property by reshaping both upper and lower envelopes (dashed curves) of the voltage profile. E, The impedance profile of the model PD neuron in control and the cases shown in A–D. Note when either the upper or lower envelopes of the voltage profile are reshaped, the resonance peak and f_max in the model neuron is abolished. The small horizontal line in A shows the −60 mV level in A–D.

Figure 5.

The effect of blocking potassium currents on the resonance profile. A, An example of the effect of TEA (which blocks both the delayed rectifier and calcium-dependent potassium currents) on the voltage response of the PD neuron to a ZAP current injection (amplitude of ∼1 nA) shows sporadic spikes at lower frequencies. The resting membrane potentials was −50 ± 1 mV. B, When the conductance of the potassium currents is reduced to 20% of its original value in the computational model of the PD neuron (see Materials and Methods), in response to a ZAP current injection, it produces calcium spikes in a range of frequencies, similar to that observed in the biological neuron (A). C, Reducing the amplitude of the injected ZAP current in TEA, in some cases, enabled us to measure the impedance despite the presence of small spike-like responses in the voltage profile (C1; TEA panel). In these cases, when the TEA impedance was compared with control (C2), there was no large difference in the resonance frequency despite the larger impedance values, in TEA, at most frequencies. The resting membrane potentials for the TEA trace was −50 mV. Dashed lines in A, B, and C1 denote −50 mV.

Figure 6.

The resonance frequency f_max of the PD neuron is correlated with its ongoing oscillation frequency f_pyloric. A, Negative or positive DC injection in the PD neuron decreases or increases f_pyloric (left). After superfusion with TTX to abolish activity, the voltage traces of the same PD neuron are shown (right) in response to the injection of a ZAP current plus the same bias current as the left column. The arrowhead shows the resonance frequency of the PD neuron. The small horizontal dashed lines show the −50 mV level. The resting membrane potentials for the PD traces in response to ZAP injection were −46, −51, and −60 mV from top trace to the bottom, respectively. B, The f_max of the PD neuron plotted versus f_pyloric when both values are changed by injection of the same DC bias currents. The dashed line shows the linear fit of the data points (y = 0.315 x + 0.835; R² = 0.77 ± 0.12; p < 0.007; n = 7 experiments; 2–4 data points per experiment).

Figure 7.

Alteration of the oscillation frequency (f_pyloric) of the PD neuron by shifting its membrane resonance frequency f_max using the dynamic-clamp technique. A, Adding or subtracting g_Ca shifts both f_max and f_pyloric. A1, Voltage traces of the PD neuron during ongoing oscillations in normal saline (top traces) and in response to a ZAP current applied in TTX (bottom traces). The left column shows the effect of subtracting a dynamic-clamp artificial I_Ca, and the right column shows the effect of adding I_Ca (see Results). The resting membrane potentials for the traces were −55, −48, and −39 mV, respectively. A2, Impedance profiles measured from traces in A1, shown as a function of frequency. B, Adding or subtracting g_h shifts both f_max and f_pyloric. B1, As in A1, the left column shows the effect of subtracting a dynamic-clamp artificial I_h, and the right column shows the effect of adding I_h (see Results). The resting membrane potentials for the traces were −57, −48, and −41 mV, respectively. B2, Impedance profiles measured from traces in B1, shown as a function of frequency. C, Normalized changes in f_pyloric induced by changing either I_Ca or I_h are correlated to normalized changes in f_max corresponding to the subtraction or addition of the same dynamic-clamp artificial currents. The dashed line shows a linear fit of data points (R² = 0.57 ± 0.088; p = 0.001; n = 5 experiments; up to 6 negative and 6 positive conductance values were done in each experiment). The filled circle (−g_dyn) shows the average change obtained by the subtraction of dynamic-clamp artificial currents (Δf_pyloric/f_pyloric = −0.035 ± 0.016 and Δf_max/f_max = −0.36 ± 0.072), and the open square (+g_dyn) shows the average obtained by the addition of dynamic-clamp artificial currents (Δf_pyloric/f_pyloric = 0.081 ± 0.016 and Δf_max/f_max = 0.581 ± 0.115) for both I_Ca and I_h.