The dendritic location of the L-type current and its deactivation by the somatic AHP current both contribute to firing bistability in motoneurons

Abstract

Spinal motoneurons may display a variety of firing patterns including bistability between repetitive firing and quiescence and, more rarely, bistability between two firing states of different frequencies. It was suggested in the past that firing bistability required that the persistent L-type calcium current be segregated in distal dendrites, far away from the spike generating currents. However, this is not supported by more recent data. Using a two compartment model of motoneuron, we show that the different firing patterns may also result from the competition between the more proximal dendritic component of the dendritic L-type conductance and the calcium sensitive potassium conductance responsible for afterhypolarization (AHP). Further emphasizing this point, firing bistability may be also achieved when the L-type current is put in the somatic compartment. However, this requires that the calcium-sensitive potassium conductance be triggered solely by the high threshold calcium currents activated during spikes and not by calcium influx through the L-type current. This prediction was validated by dynamic clamp experiments in vivo in lumbar motoneurons of deeply anesthetized cats in which an artificial L-type current was added at the soma. Altogether, our results suggest that the dynamical interaction between the L-type and afterhyperpolarization currents is as fundamental as the segregation of the calcium L-type current in dendrites for controlling the discharge of motoneurons.

Keywords: afterhyperpolarization; bistability; dynamic clamp; modeling; persistent calcium current.

Figure 1

The strong coupling model. The two compartments have similar passive properties, and they are coupled via a symmetrical conductance ten times larger than in the BRK model. The soma is endowed with spike generating currents and an AHP current. A L-type calcium current is present in the soma (somatic variant of the model) or in the dendrites (dendritic variant). The dendritic component of the N-type calcium current was eliminated from the BRK model, and the activation curve of the somatic component is steeper (see text). Dendrites are endowed with a calcium sensitive potassium conductance. Input consists in either a current injected in the soma or synaptic excitation of the dendrites.

Figure 2

Response of the strong coupling model (G_c = 1 mS/cm²) to excitatory input. (A) Voltage response to a triangular current ramp. Dendritic G_Ca−L is 0.33 mS/cm² as in the BRK model. From bottom to top: current injected in the soma, soma voltage and dendritic voltage. The discharge is symmetrical, the recruitment current on the ascending ramp and the derecruitment current on the descending ramp differing by less than 1.5% (50.2 and 49.4 mV, respectively). (B) Same as A but G_Ca−L increased to 0.45 mS/cm². The discharge is clearly asymmetrical. A dendritic plateau potential of 16 mV sets in at firing onset (I_S = 38 μA/cm²). On the descending ramp, firing persists down to 20 μA/cm². (C) F-I curves. Current ramp from 0 to 120 μA/cm² and back. F-I curves (solid lines) are displayed for G_Ca−L = 0.33 (right), and 0.45 mS/cm² (left). For this latter value,firing stops when the injected current reaches 70 μA/cm² because of spike blockade. Decreasing the dendritic G_K(Ca) from 0.7 to 0.25 mS/cm² (with G_Ca−L kept at 0.33 mS/cm², dashed line) has the same effect as increasing G_Ca−L from 0.33 to 0.45 mS/cm² [with G_K(Ca) kept at 0.7 mS/cm²]. (D) Synaptic excitation of dendrites. F-G_syn curves are shown for G_Ca−L = 0.1 (right) and 0.3 mS/cm² (left). No dendritic potassium conductance G_K(Ca). Triangular conductance ramp from 0 to 0.5 mS/cm² (i.e., equal to the leak conductance of dendrites) and back, velocity of 0.01 mS/cm²/s. Note that frequency plateaus are present near firing onset for G_Ca−L = 0.1 mS/cm² as in the subprimary firing range of mouse motoneurons (Manuel et al., 2009). We showed that they are due to mixed mode oscillations in a previous paper (Iglesias et al., 2011). The ascending (upward pointing arrows) and descending branches (downward pointing arrows) of the hysteresis loops are indicated on panels (C,D) and on the following figures.

Figure 3

Control of the firing pattern by the AHP conductance. (A) F-G_syn curves for G_{Ca − L} = 0.2 mS/cm². Somatic AHP conductance G_AHP = 0.0, 3.14, and 10 mS/cm² (see labels) but no potassium conductance in dendrites. For G_AHP = 3.14 mS/cm² (the same value as in the BRK model), the F-G_syn curve is graded and displays only a tiny range of bistability below recruitment (thin arrow). When the AHP is suppressed, firing starts at 137 Hz, and the size of the bistability range considerably increases. In contrast, bistability disappears when G_AHP is increased to 10 mS/cm². (B) Somatic I–V curves. Same conditions as in (A). The curves obtained without AHP and for G_AHP = 10 mS/cm² (solid lines, see labels) differ only above −33 mV. In contrast, increasing the dendritic G_K(Ca) to 0.7 mS/cm² (in the absence of somatic AHP) suppresses the negative slope region of the I–V curve in the subthreshold voltage range [dashed line labeled G_K(Ca)]. The curves are not hysteretic because a dendritic compartment strongly coupled to the soma cannot account for the distal dendritic component of the L-type current. This departure from realism is of little significance as we focus here on the interaction between the proximal component of the L-type current and the somatic AHP. (C) F-G_syn curves for G_{Ca − L} = 0.35 mS/cm². G_AHP = 10, 20, 30, and 40 mS/cm² (see labels). At variance with panel A, the F-G_syn curves display a primary range of firing when G_AHP is large enough to counterbalance the L-type current and has then a strong regulatory effect on the discharge. (D) F-I curves for G_{Ca − L} = 0.35 mS/cm². Same as in D but current is injected in the soma. Note that the large AHPs at play create a wide primary firing range, in keeping with the traditional role of the AHP in firing rate control.

Figure 4

Model with somatic L-type current and passive dendrites. (A) F-I curves for G_{Ca − L} = 1.0 mS/cm². Triangular ramp of current injected in the soma from 0 to 100 μA/cm² and back (velocity: 10⁻⁴ μA/cm².s). Increasing values of G_AHP from top to bottom, see labels). α_N = 0.0045 mol/nA.cm as before, but α_L is set to 0. When G_AHP = 10 mS/cm² (top curve), firing starts at 54 Hz at the recruitment threshold (32 μA/cm²), and the F-I curve shows a large domain of quiescence/firing bistability, derecruitment occuring only for a negative current of −15 μA/cm² on the descending ramp. Firing bistability is observed for between 15 and 25 (middle curve, G_AHP = 20 mS/cm²). When G_AHP is increased beyond 25 mS/cm², bistability disappears and the F-I curve becomes graded (bottom curve, G_AHP = 30 mS/cm²). Note that the recruitment threshold remains unchanged. (B) Effect of α_L on firing. F-I curves for G_{Ca − L} = 1 mS/cm² and G_AHP = 20 mS/cm² and α_N = 0.0045 mol/nA.cm. Increasing values of α_L from top to bottom (see labels). The firing bistability displayed in A (top, α_L set to 0) persists when α_L is increased to 2% of α_N, but the firing frequency is strongly reduced. When α_L is doubled, to 4% of α_N, the abrupt transition to the low frequency state on the down ramp is replaced by a series of frequency plateaus reflecting mixed mode oscillations. (C) F-I curve for G_{Ca − L} = 0.5 mS/cm². α_L set to 0 and α_N = 0.0045 mol/nA.cm as in A. Increasing values of G_AHP (see labels). Quiescence/firing bistability occurs for G_AHP smaller than 10 mS/cm² (top), and the F-I curve is graded for larger G_AHP. No firing bistability takes place. (D) Membrane currents. G_{Ca − L} = 1 mS/cm² and G_AHP = 20 mS/cm² (regime of firing bistability, see A). Top: L-type current (positive); bottom: sum of the leak and AHP currents (negative); dashed line: sum of the three currents. All currents are time averaged over the interspike interval and plotted as a function of the current injected in the soma. The zero current line is displayed in gray. The ascending current ramp is indicated by rightward pointing arrows and the descending branch by leftward pointing arrows.

Figure 5

An artificial L-type current injected in the soma can elicit a counterclockwise hysteresis in a spinal motoneuron. CP motoneuron (axonal conduction velocity: 80 m/s, input conductance: 0.5 μ S). (A) No dynamic clamp current (control case). (A1) Ramp of current applied to the soma (bottom) and intracellular recording of soma voltage (top). (A2) F-I curve. The ascending branch (increasing current) is indicated by diamonds (upward arrow) and the descending branch (decreasing current) by crosses (downward arrow). (B) Same as A but a dynamic clamp current mimicking the L-type current was injected in the soma. Parameters of this current were the following. Conductance: 100 nS, half activation voltage: −35 mV, steepness of the activation curve: 2 mV, activation time constant: 50 ms, reversal potential: 80 mV.

Figure 6

Transitions between states elicited by current pulses. (A) Quiescence/firing bistability. CP motoneuron (axonal conduction velocity: 90 m/s, input conductance: 1.0 μS). The current pulse (24 nA, 1 s) elicited an accelerating discharge that started with a frequency of 14 Hz and reached 50 Hz at the end of the pulse. After the pulse, the motoneuron kept firing at a lower frequency (5 Hz) instead of going back to rest. A hyperpolarizing current pulse (−24 nA) terminated firing. Artificial L-type current conductance: 350 nS, half-activation voltage: −50 mV, steepness of the activation curve: 2 mV, activation time constant: 400 ms. (B) Firing bistability. CP motoneuron (axonal conduction velocity: 90 m/s, input conductance: 1.1 μS). A 31 nA bias current was applied, which made the neuron steadily discharge at the mean frequency of 19 Hz. A pulse of 10 nA lasting 1.5 s was then superimposed to shift the motoneuron toward its up state (57 Hz, three times more than before the pulse). After the pulse, the motoneuron kept firing at a mean frequency of 30 Hz, about half more than the before the pulse. Two different firing states were thus obtained for the same injected current. The discharge in the up state (during and after the pulse) was more irregular than in the down state (before the pulse). L-type conductance: 820 nS, half-activation: −58 mV, steepness: 1 mV, activation time constant: 400 ms, reversal potential: 20 mV.