Essential role of the persistent sodium current in spike initiation during slowly rising inputs in mouse spinal neurones

Abstract

Spinal motoneurons, like many neurons, respond with repetitive spiking to sustained inputs. The afterhyperpolarization (AHP) that follows each spike, however, decays relatively slowly in motoneurons. The slow depolarization during this decay should allow sodium (Na+) channel inactivation to keep up with its activation and thus should prevent initiation of the next spike. We hypothesized that the persistent component of the total Na+ current provides the mechanism that generates a rate of rise sufficiently rapid to generate a spike. In large cultured spinal neurons, presumed to be primarily motoneurons, inhibition of persistent sodium current (NaP) by the drug riluzole at low concentrations resulted in a loss of repetitive firing. However, cells remained fully capable of producing spikes to transient inputs. These effects of riluzole were not due to insufficient depolarization, enhancement of the AHP, or sustained Na+ channel inactivation. To further test this hypothesis, computer simulations were performed with a kinetic Na+ channel model that provided greater independent control of NaP relative to transient Na+ current (NaT) than that provided by riluzole administration. The model was tuned to generate substantial NaP and exhibited good repetitive firing to slowly rising inputs. When NaP was sharply reduced without significantly altering NaT, the model reproduced the effects of riluzole administration, inducing failure of repetitive firing but allowing single spikes in response to sharp transients. These results strongly support the essential role of NaP in spike initiation to slow inputs in spinal neurons. NaP may play a fundamental role in determining how a neuron responds to sustained inputs.

Figure 1. Kinetic model of the Na⁺ channel used in the computer simulations

Values for all the constants shown are given in Table 1. Based on the model developed by (Taddese & Bean, 2002) but adapted to match the transient behaviour for young rat motoneurons (Safronov & Vogel, 1995).

Figure 2. Frequency–current (F–I) and current–voltage (I–V) relations

A, the cell responded to a slow-depolarizing current ramp (bottom trace) with sustained repetitive firing (top trace). B, the F–I relation (ascending ramp only) is plotted for the cell in A. The slope of the linear regression (black line) defined the F–I gain for the cell. C, a slow-depolarizing voltage-ramp command (bottom trace) was used for all voltage-clamp protocols. The current response in control conditions (black line) and in the presence of 1 μm TTX (grey line) is shown. D, the I–V relations (ascending ramp only) for the control (black trace) and TTX (grey trace) trial are shown. Na_P was measured as the difference between these two I–V functions.

Figure 3. Reduction of Na_P with riluzole

The I–V relations for Na_P are shown for control conditions and for riluzole at three different doses (0.1, 1.0 and 5.0 μm) (thick grey line, thin grey line, dotted line), and after TTX administration (thick dotted line). A, Raw I–V functions. B, The control and riluzole currents after subtraction of the TTX I–V function. Increasing riluzole concentrations dose-dependently inhibited Na_P.

Figure 4. Restoration of firing from transient inputs

A, under control conditions (top panel, thin black trace), a motoneuron responded to a depolarizing current ramp injection (bottom panel, black trace) with repetitive firing. The addition of 10 μm riluzole (top panel, thick black trace) inhibited all firing to the same amplitude current injection, even at voltages depolarized compared to spike threshold. However, superimposing a 5 Hz current step on top of the current ramp (bottom panel, grey trace) resulted in a spike at the onset of virtually all superimposed pulses (middle panel, grey trace). B, in a different cell than in A, sustained repetitive firing was again observed to a current ramp injection (top panel, thin black trace). In the presence of 2 μm riluzole, all firing was inhibited (top panel, thick black trace). However, superimposition of current noise on the current ramp injection (bottom panel, grey trace restored significant firing (middle panel, grey trace).

Figure 5. Effect of increased current amplitude on firing

A, in control conditions, repetitive firing (top panel, black trace) was observed to a current step (bottom panel, black trace). Riluzole (10 μm) blocked all firing to the current step except at its onset (top panel, thick black trace). Increasing the current amplitude (bottom panel, grey traces) did not restore firing (middle panel). B, the first 50 ms of the step from A is shown. Riluzole (10 μm) did not increase the AHP (upper panel, compare thick and thin black traces), and increased step sizes depolarized the cell well beyond spike threshold without restoring repetitive firing (middle panel, grey traces).

Figure 6. Dose-dependent riluzole inhibition of excitability and Na_P

A, the F–I relations and linear regressions are shown for control (•), 0.1 mm riluzole (□), and 1.0 mm riluzole (▵). The F–I gain is reduced and the current threshold for the onset of firing is increased with increasing riluzole concentrations. B, the dose–response curve for all cells is shown for the effect of riluzole on the F–I gain (grey circle) for 0.1 mm riluzole (n = 11), 0.5 mm riluzole (n = 10), 1 mm riluzole (n = 8), 2 mm riluzole (n = 5), 5 mm riluzole (n = 5), and 10 mm riluzole (n = 5). The effect of riluzole on for NaP (▪) is also shown 0.1 mm riluzole (n = 6), 0.5 mm riluzole (n = 5), 1 mm riluzole (n = 7), 2 mm riluzole (n = 5), 5 mm riluzole (n = 5) and 10 mm riluzole (n = 5). The EC₅₀ for riluzole inhibition of the F–I gain (grey arrow) was 1.1 mm and Na_P (black arrow) was 1.8 mm. Riluzole also dose-dependently increased the current threshold for firing (right side, bars; mean ±s.e.m. shown for B). Threshold amplitudes could not be measured above 2 mm riluzole because spiking behaviour became very irregular.

Figure 7. Inhibition of voltage upswing

In control conditions (thin trace), repetitive firing was generated from a depolarizing current ramp injection (spikes are shown truncated). Prior to spike initiation, an upswing the membrane potential was observed (arrow). The addition of 1 mm TTX (bold trace) blocked all firing and the voltage upswing to the current stimulus, strongly suggesting that the upswing was due to Na_P.

Figure 8. No negative slope region

A, in control aCSF, repetitive firing (top panel) was observed to a current step injection (bottom panel). B, in control aCSF (thick trace), no negative slope region was observed to a voltage ramp command, even though sustained repetitive firing was observed. The addition of 1 mm TTX (thin trace) inhibited all Na⁺, and a larger outward current was observed.

Figure 9. Effect of the rate of rise of the voltage command

A, the I–V relations are shown for trials with rates of rise of 9 mV s⁻¹ (thin grey trace), 18 mV s⁻¹ (thick grey trace), 90 mV s⁻¹ (thin black trace), and 180 mV s⁻¹ (thick black trace). A single breakthrough spike (shown truncated) was observed with the trial using a voltage command of 180 mV s⁻¹. B, the traces from A are shown leak- and TTX-subtracted to reveal the effect of rate of rise on Na_P. By increasing the rate of rise of the voltage command, Na_P was markedly increased, suggesting that Na_P does slowly inactivate.

Figure 10. Effect of voltage upswing on Na_P

In the presence of 0.5 mm riluzole, repetitive firing (A, green trace) was observed in response to a depolarizing current ramp injection. In response to a voltage-clamp ramp command (A, red trace) that approximated the subthreshold rate of rise to the current ramp command, no negative slope region was observed in the I–V relation (B, red trace). However, prior to spike initiation, an upswing in the membrane potential (inset and Figure 7) was observed. (The inset shows the boxed region in A.) A voltage-clamp command that approximated this upswing (A, blue trace) generated a robust persistent inward current (B, blue trace). Therefore, during current-clamp conditions, the voltage transitions from the slow voltage command (A, bold red trace) to the fast voltage command (A, bold blue trace) when the voltage upswing begins. The current response to the voltages transitions from the bold red trace (B) to the bold blue trace (B) and the negative slope region to generate a spike is now present. The thin red lines (A and B) represent the slow voltage command and current response after the voltage upswing. The thin blue lines (A and B) represent the fast voltage command and current response before the voltage upswing.

Figure 11. The behaviour of the Na⁺ channel model in response to a series of voltage steps

A, Na⁺ currents generated by steps from −120 mV to −60 mV, −50 mV, −40 mV, and −10 mV. The dashed line shows the behaviour of the reduced Na_P version of the model to the step to −10 mV. At this and all other voltage steps, the Na⁺ current of the reduced Na_P model was virtually superimposed on the standard model for the first few milliseconds. The lower level of Na_P is evident after the decay of the most of Na_T. B, same as A, but on an expanded vertical scale to more clearly reveal differences in Na_P. C, steady-state activation and inactivation curves for the standard (▾) and reduced (×) Na_P models.

Figure 12. Repetitive firing behaviour of the model motoneuron

A, with a linearly rising ramp, the model with the standard level of Na_P exhibited good repetitive firing (thin black trace) to a ramp of injected current. The reduced Na_P model failed to generate any spike to this same input (thick black trace). However, adding a series of transient current pulses on top of the ramp, generated spikes in the reduced Na_P model (grey trace), showing it was still capable of initiating spikes to transient inputs. B, behaviour to step inputs: good repetitive firing in the standard model (thin black trace), loss of all but the initial spike in the reduced Na_P model (thick black trace), and failure to restore repetitive firing by increasing the amplitude of the step (grey trace). These simulation results parallel the experimental results for riluzole administration.

Figure 13. Effect of varying amplitude of Na_P on the rate of rise of input required for repetitive firing

In the model motoneuron, varying the rate constant O_off (see Fig. 1) from 0.015 (reduced Na_P model) to 0.03 (standard model) decreased the rate of rise of a linear current ramp needed to generate repetitive firing. The minimal rate of rise that produced at least five spikes is plotted versus Na_P expressed as a percentage of Na_T for a step from −120 mV to −10 mV.