A modelling study of locomotion-induced hyperpolarization of voltage threshold in cat lumbar motoneurones

Abstract

During fictive locomotion the excitability of adult cat lumbar motoneurones is increased by a reduction (a mean hyperpolarization of approximately 6.0 mV) of voltage threshold (Vth) for action potential (AP) initiation that is accompanied by only small changes in AP height and width. Further examination of the experimental data in the present study confirms that Vth lowering is present to a similar degree in both the hyperpolarized and depolarized portions of the locomotor step cycle. This indicates that Vth reduction is a modulation of motoneurone membrane currents throughout the locomotor state rather than being related to the phasic synaptic input within the locomotor cycle. Potential ionic mechanisms of this locomotor-state-dependent increase in excitability were examined using three five-compartment models of the motoneurone innervating slow, fast fatigue resistant and fast fatigable muscle fibres. Passive and active membrane conductances were set to produce input resistance, rheobase, afterhyperpolarization (AHP) and membrane time constant values similar to those measured in adult cat motoneurones in non-locomoting conditions. The parameters of 10 membrane conductances were then individually altered in an attempt to replicate the hyperpolarization of Vth that occurs in decerebrate cats during fictive locomotion. The goal was to find conductance changes that could produce a greater than 3 mV hyperpolarization of Vth with only small changes in AP height (< 3 mV) and width (< 1.2 ms). Vth reduction without large changes in AP shape could be produced either by increasing fast sodium current or by reducing delayed rectifier potassium current. The most effective Vth reductions were achieved by either increasing the conductance of fast sodium channels or by hyperpolarizing the voltage dependency of their activation. These changes were particularly effective when localized to the initial segment. Reducing the conductance of delayed rectifier channels or depolarizing their activation produced similar but smaller changes in Vth. Changes in current underlying the AHP, the persistent Na(+) current, three Ca(2+) currents, the "h" mixed cation current, the "A" potassium current and the leak current were either ineffective in reducing Vth or also produced gross changes in the AP. It is suggested that the increased excitability of motoneurones during locomotion could be readily accomplished by hyperpolarizing the voltage dependency of fast sodium channels in the axon hillock by a hitherto unknown neuromodulatory action.

Figure 1. Single cell models and initial properties

A, three types of single cell models (S, FR and FF) with five compartments (axon, initial segment (IS), soma, proximal dendrite and distal dendrite) were built that retained the macro structure of cat lumbar motoneurones important for the generation of anti- and orthodromic action potentials. B, overlap of the SD and initial segment spikes produced by the S-type model motoneurone. The amplitude of the SD spike is ≈67 mV and the initial segment spike ≈30 mV. C, frequency-current (f-I) relation produced by step current injection into the soma compartments of the three types of model cell (S, FR and FF). The frequency was calculated by dividing the number of spikes by the duration (500 ms) of each step current. The slopes of the primary range for the three models are 3.4, 1.8 and 3.6 Hz nA⁻¹, respectively (below the horizontal dotted line), and the slopes of the secondary range are 12, 13 and 11 Hz nA⁻¹ (above the dotted line). D, truncated SD spikes taken from the antidromic single spikes produced by the three types of the model cell. Spikes were overlapped on the alignment of their resting membrane potentials. The afterhyperpolarization (AHP) durations are 100, 85 and 80 ms for the S, FR and FF type models, respectively, and the amplitudes of the AHP are 4, 3 and 2 mV, respectively. E, passive responses of the models to an injection of −2 nA of current into the soma compartment. The voltage trajectories are aligned on the resting membrane potentials. The membrane hyperpolarizations produced by a −2 nA current injection were −3.2 mV for the S-type model cell, −2.0 mV for the FR-type and −1.2 mV for the FF-type.

Figure 2. Intracellular recording from a cat lumbar motoneurone (Krawitz et al. 2001)

Spikes were evoked by injecting triangular currents (not shown) into the motoneurone before (A) and during fictive locomotion (B). The averaged spikes made from the firing in A and B, respectively, were overlapped in C to show the differences in voltage threshold (Vth), AP height and AP width between control (dotted line) and fictive locomotion (dark line). In this example, the mean Vth, averaged spike height and averaged spike width were −27.4 mV, 52.2 mV and 2.0 ms, respectively, in control and −34.6 mV, 55.9 mV and 2.3 ms, respectively, during fictive locomotion. The motoneurone showed a 7.2 mV hyperpolarization in mean Vth, 3.7 mV increase in AP height and 0.3 ms increase in AP width during fictive locomotion. The distribution of Vth hyperpolarization from 38 motoneurones (Krawitz et al. 2001) is shown in D. Sixteen per cent of the cells displayed a Vth hyperpolarization of 1-3 mV, 47 % of the cells within 3-9 mV, 29 % of the cells within 9-12 mV and 8 % of the cells over 12 mV. Hyperpolarization of Vth measured from eight motoneurones in both the excitatory (open bars) and inhibitory phase (hatched bars) of the LDPs is shown in E (see text for detail). The measurement of Vth and action potential amplitude and width is described in the Methods section. Voltage calibration bar for A and B is shown in A.

Figure 4. Altering somatic I_Na alters Vth

The S-type model cell was made to fire under two conditions (B and C) by injecting triangular current (the same as that used in Fig. 3) into the soma compartment. Vth for each spike shown in panels Ba and Ca was plotted as a dot in Bb and Cb, respectively. The first four spikes in each condition were averaged and then overlapped on the averaged spike of control taken from Fig. 3C (insets in Ba and Ca, dotted-line spike for control). The dotted line crossing panels Ba and Ca represents the resting membrane potential of −65 mV, and the dotted line crossing panels Bb and Cb represents the mean value of the Vth of −47.2 mV for the S-type model cell in the control condition. A, curves of the state variable m and h were shifted to the hyperpolarizing direction by 4 and 6 mV, respectively (left panel). This resulted in a left-ward shift of product of hm³ (right panel). Dotted lines stand for control and dark lines for shifted curves. B, Vth could be hyperpolarized by unevenly shifting the state variables of g_Na (shown in A) with small changes in spike height and width. C, increasing the somatic max g_Na resulted in a large increase in spike height and width.

Figure 3. Reducing I_K(AHP) does not affect Vth

Triangular currents (15 nA, 5 s, starting from −2 nA; shown at the bottom in A and B) were injected into the soma compartment of the S-type model cell to make the cell fire in two conditions (A and B). Each dot in the middle panels of A and B is the Vth for the corresponding spike in the top panels. A, in control, the mean Vth was −47.2 ± 0.3 mV (dotted lines in top and middle panels in A and B). B, a decrease in the maximum conductance of the I_K(AHP) by 50 % resulted in a reduction in the amplitude of the AHP by ≈25 % (reducing ≈1.0 mV) with little hyperpolarization (< 0.3 mV) of Vth (dark line in the middle panel of B) and no changes in spike height or width. C, the first four spikes from A and B were averaged and then overlapped. The dotted line is for the averaged control spike, and the dark line for the averaged spike where g_K(AHP) was reduced by 50 %.

Figure 5. Hyperpolarization of Vth could be produced by increasing the initial segment I_Na or decreasing the initial segment I_K(DR)

Triangular currents (as used in Fig. 3) were injected into the soma compartment of the S-type model cell to make the cell repetitively fire in four conditions (A, B, C and D). Vth for each spike shown in Aa, Ba, Ca and Da are plotted in Ab, Bb, Cb and Db, and the average of the first four spikes in each condition is superimposed on the control spike (dotted line) in Ac, Bc, Cc and Dc. The dotted line crossing the top panels represents the resting membrane potential of −65 mV, and the dotted lines crossing the middle and bottom panels represent the mean value of the Vth of −47.2 mV for the S-type model cell measured in control. A, increasing the maximum initial segment g_Na hyperpolarized the Vth by 5.5 mV with moderate increases in AP height (8.0 mV) and width (0.7 ms). B, shifting the initial segment g_Na state variables m and h to the hyperpolarizing direction lowered the Vth by 5.6 mV and resulted in a 7.0 mV increase in AP height and 1.2 ms increase in AP width. C, reducing the max initial segment g_K(DR) produced a hyperpolarization of the Vth by 3.1 mV and caused a small increase in AP height (5.3 mV) and width (0.5 ms). D, shifting the state variable of initial segment g_K(DR) in the depolarizing direction hyperpolarized the Vth by 3.0 mV with little increase in AP height (4.2 mV) and width (0.3 ms).

Figure 6. Altering g_NaP affects Vth and spike shape

Repetitive firing of the S-type model cell was evoked by a triangular current injection as shown in Fig. 3. Averaged spikes (dark line) from each condition (A-D) are superimposed on the control spike (dotted line). The straight dotted line crossing panels A-D represents the mean value of Vth (−47.2 mV) measured in control. A, addition of g_NaP to both the initial segment compartment with g_NaP= 12 mS cm⁻² (≈5 % of initial segment g_Na) and soma compartment with g_NaP= 6 mS cm⁻² (≈1.5 % of somatic g_Na) hyperpolarized the Vth by 1.7 mV and resulted in a 4.1 mV increase in AP height and 1.0 ms increase in width (middle trace). Increasing the initial segment g_NaP by 150 % lowered the Vth by 2.9 mV with a 6.9 mV increase in AP height and a 1.3 ms increase in width. B, negatively shifting the activation curve of the initial segment g_NaP by 5 mV hyperpolarized Vth by 3.2 mV and increased the spike height (6.6 mV) and width (1.6 ms). C, increasing the somatic g_NaP by 150 % hyperpolarized the Vth by 2.2 mV with a 7.7 mV increase in AP height and 4.1 ms increase in AP width. D, shifting the activation voltage of somatic g_NaP to the left by 5 mV hyperpolarized the Vth by 2.2 mV and resulted in a double spike with a 5.7 mV increase in the AP height and a 3.6 ms increase in AP width.