Robustness of burst firing in dissociated purkinje neurons with acute or long-term reductions in sodium conductance

Abstract

Cerebellar Purkinje neurons often generate all-or-none burst firing in response to depolarizing stimuli. Voltage-clamp experiments using action potential waveforms show that burst firing depends on small net inward currents that flow after spikes and reflect the net balance between multiple large currents. Given this, burst firing is surprisingly robust in the face of changes in the magnitude of the underlying currents from cell to cell. We explored the basis of this robustness by examining the effects of reducing the sodium current, the major contributor to the postspike inward current. Burst firing persisted in concentrations of tetrodotoxin that produced half-block of sodium current. This robustness of bursting reflects an acute feedback mechanism whereby waveform changes from the reduced sodium current (reduced spike height and a hyperpolarizing shift in postspike voltage) cause compensatory decreases in postspike potassium currents. In particular, reduced spike height reduces calcium entry and subsequent calcium-activated potassium current, and the hyperpolarizing shift in postspike voltage speeds deactivation of Kv3-like potassium channels. Other experiments examined bursting in Na(v)1.6-/- mice, in which sodium current density is reduced in the long term. Under these circumstances, there was upregulation of both T-type and P-type calcium current and a change in the balance of calcium current and calcium-activated potassium current such that their net influence shifted from being inhibitory during bursts in wild-type neurons to excitatory during bursts from Na(v)1.6-/- mutant neurons. Thus, Purkinje neurons have both acute and long-term feedback mechanisms that serve to maintain burst firing when voltage-dependent sodium conductance is reduced.

Figure 1.

Inward currents underlying bursts in two dissociated Purkinje neurons. A, Top, All-or-none burst elicited by short (1 ms) injection of depolarizing current from a steady holding voltage near -90 mV (established by steady hyperpolarizing current to stop spontaneous firing). The second panel shows the first interspike interval on an expanded time scale and illustrates the period over which interspike voltage and current was measured (shaded box). The two bottom panels show sodium current elicited by this waveform (in the same cell in which the waveform was recorded), obtained by subtracting the current measured before and after 500 nm TTX (using reduced external sodium to improve voltage control), and calcium current elicited by the waveform (bottom), obtained by subtracting currents before and after replacement of 2 mm Ca²⁺ by 2 mm Mg²⁺, both solutions containing 130 mm TEA to block potassium currents. B, The same as A but for a different neuron. In A and B, the sodium current axis has been expanded 6.18-fold relative to the calcium current axis based on the expected scaling factor from the Goldman-Hodgkin-Katz current equation when scaling the sodium current measured in 25 mm sodium to that expected in physiological (155 mm) sodium. Currents were averaged over a 1.3 ms time window starting 1.5 ms after the peak of the first action potential (gray boxes). Although the burst waveforms are very similar in the two cells, for the cell in A the interspike sodium current was much bigger than the calcium current (when adjusted for sodium concentration), whereas the opposite was true in B. Vcmd, Command waveform.

Figure 2.

Inward current profiles during the first interspike interval of bursts in six different Purkinje cells are shown. The bursts from different Purkinje cells are displayed (left) along with bars showing the magnitude of the sodium, calcium, and net ionic current (calculated from -C × dV/dt) during the first interspike interval of each cell (right). A, Three cells that fired similar bursts consisting of three spikes. B, Three cells that fired two-spike bursts. Across both populations, some cells had a dominant sodium current, some had a dominant calcium current, and some had comparable sodium and calcium currents. In all cases, the dominant current was many-fold larger than the net inward ionic current driving depolarization toward the second spike. Sodium currents were recorded in either 25 or 50 mm sodium and have been scaled up to those expected with 155 mm sodium based on the Goldman-Hodgkin-Katz current equation.

Figure 3.

Effect of calibrated reduction in sodium conductance on bursting in Purkinje neurons. A, Dose-response relationship for TTX inhibition of sodium current in Purkinje neurons. Sodium current was measured as the peak current elicited using a voltage step from -75 to -10 mV. Each point in A shows current relative to control averaged over five cells, except for 100 nm TTX (complete block in 2 cells). The solid line is drawn according to 1/(1 + [TTX]/2.7 nm). The external solution consisted of the following (in mm): 50 NaCl, 105 TEACl, 4 KCl, 2 CaCl₂, 2 MgCl₂, and 10 HEPES, pH 7.4 with ∼5 NaOH. B, Effects of increasing degrees of sodium current block on all-or-none burst firing in a Purkinje cell. Concentrations of TTX were selected to produce 25, 50, and 75% block of sodium current. The external solution consisted of the following (in mm): 155 NaCl, 4 KCl, 2 CaCl₂, 2 MgCl₂, and 10 HEPES, pH 7.4 with ∼5 NaOH.

Figure 4.

Interspike currents between the first and second spikes of all-or-none bursts elicited by control burst waveforms (solid bars) and waveforms recorded (in the same cells) in the presence of 2.7 nm TTX to block sodium current by 50% are shown. The calcium current was measured over the first interspike interval as in Figure 1. Potassium currents were measured over the same interval. The total potassium current was determined by subtracting currents before and after replacing the external sodium (155 mm) by equimolar TEA, with a background of normal (2 mm) calcium. The purely voltage-dependent potassium current (I_Kv) was determined by the same manipulation but with a background of zero calcium (replaced by magnesium). The calcium-activated potassium current (I_KCa) was calculated by subtracting I_Kv from the total potassium current. Bars and error bars represent mean ± SD for measurements in six cells for calcium current and four cells for potassium currents. ^*p < 0.05; paired t test.

Figure 5.

Evaluation of effect of changing spike height or postspike voltage on postspike ionic currents. A, Changes in spike height were approximated by changing the height of a 0.5 ms step to voltages between +50 and +20 mV (in 5 mV increments, from -90 mV), followed by repolarization to -66 mV. Currents after the short depolarization are shown for “spike” heights of +50, +40, +30, and +20 mV. Solution changes as in Figure 4 were used to determine currents carried by purely voltage-dependent potassium channels, by calcium channels, and by calcium-activated potassium channels. B, A current during repolarization to -66 mV as a function of preceding spike voltage. Currents integrated over the period shown were normalized to the largest current (which followed a step to +50 mV in all cases) in each cell. The mean ± SD is shown for experiments in seven cells. C, Ionic currents after spike repolarization to different voltages. In this case, a more realistic artificial spike was used (constructed by piecewise approximation), followed by repolarization to various fixed voltages. Currents are shown for repolarizations to -58, -66, -74, and -82 mV (currents were determined at 4 mV intervals, but not all are shown). D, Current as a function of repolarization voltage, integrated over the period shown. Currents were normalized to the current during repolarization to -58 mV. Bars and error bars represent mean ± SD for experiments in nine cells.

Figure 6.

All-or-none bursting in Purkinje neurons from Na_v1.6^-/- mice compared with neurons from wild-type mice (homozygous normal littermates). A, Two-spike (top) and three-spike (bottom) bursts from Na_v1.6^+/+ mice. B, Two-spike (top) and three-spike (bottom) bursts from Na_v1.6^-/- mice. C, Distribution of the number of spikes per burst for cells from Na_v1.6^+/+ and Na_v1.6^-/- mice.

Figure 7.

Interspike currents between the first and second spikes of all-or-none bursts in action potential clamp experiments in cells from Na_v1.6^+/+ animals (filled bars) versus Na_v1.6^-/- animals (open bars) are shown. Inset, Example of a command waveform showing the window over which currents were averaged (gray box). Contributions of individual currents determined by ionic and pharmacological subtraction as in Figures 1 and 4. Sodium current was measured in reduced sodium (50 mm) to reduce clamp errors and scaled up to expected values for 155 mm sodium. Bars and error bars show mean ± SD. I_Na, n = 14 for wild type and n = 11 for mutants; I_Ca, n = 14 wild type and n = 14 mutants; I_Kv, n = 13 wild type and n = 11 mutants; I_KCa, n = 13 wild type and n = 9 mutants; I_Ca + I_KCa, n = 13 wild type and n = 9 mutants. ^*p < 0.05; ^**p < 0.01; ^***p < 0.001.

Figure 8.

Relative magnitude of inward current from sodium channels and calcium channels between the first two spikes in bursts in individual cells from Na_v1.6^+/+ animals and Na_v1.6^-/- animals. The y-axis plots the fraction of total inward current in the interspike interval carried by sodium channels. The sodium current and calcium current during the first interspike interval were determined in each cell in action potential clamp experiments using the action potential of each cell as in Figure 1. Filled circles, Cells from series of experiments using Black Swiss mice; closed triangles, cells from wild-type littermates of Na_v1.6^-/- mice (CH3 strain background); open triangles, cells from Na_v1.6^-/- animals.

Figure 9.

Densities of various ionic currents determined by voltage steps in Purkinje neurons from Na_v1.6^+/+ (filled bars) and Na_v1.6^-/- (open bars) animals are shown. Currents were activated with voltage steps from a steady holding potential of -95 mV. Sodium currents were measured with steps to -25 mV in reduced sodium (25 or 50 mm) and scaled using the Goldman-Hodgkin-Katz equation to the current expected in 155 mm sodium. Calcium and potassium currents were measured with steps to -10 mV; calcium currents were also measured using steps to -40 mV to obtain currents with a higher fractional contribution from T-type channels. All currents were recorded using normal physiological solutions using the same subtraction procedures as for action potential clamp experiments to isolate individual currents. Bars and error bars show mean ± SD. I_Na, n = 16 for wild type and n = 17 for mutants; I_Ca, n = 14 wild type and n = 15 mutants; I_Kv, n = 13 wild type and n = 13 mutants; I_KCa, n = 12 wild type and n = 12 mutants. ^*p < 0.01; ^**p < 0.001.

Figure 10.

Comparison of calcium current elicited in a single cell (from Na_v1.6^+/+ animal) by burst waveforms characteristic of Purkinje neurons from Na_v1.6^+/+ (black traces) and Na_v1.6^-/- (gray traces) animals is shown. The gray box indicates the time over which interspike current was measured.

Figure 11.

Kinetics and voltage dependence of the components of calcium current in Purkinje neurons from Na_v1.6^+/+ animals and Na_v1.6^-/- animals. A, Comparison of ω-Aga- IVA-sensitive and mibefradil-sensitive components of calcium current in a wild-type cell (left column) and in an Na_v1.6-null cell (right column). Note the identical voltage sensitivity and kinetics for each component of current in mutant versus wild-type cells. B, Comparison of mibefradil-sensitive calcium current elicited by a pulse protocol designed to highlight channel deactivation kinetics. Tail currents are fitted by smooth single-exponential curves with the indicated time constants.

Figure 12.

Effects of calcium removal on bursting in cells from wild-type and Na_v1.6^-/- animals. A, All-or-none bursts in a Purkinje neuron from an Na_v1.6^+/+ animal recorded in control Tyrode's solution containing 2 mm calcium and 2 mm magnesium (left) and after moving the cell to a solution in which calcium was replaced by equimolar magnesium (right). B, Same for a Purkinje neuron from an Na_v1.6^-/- animal.