Postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents: A simulation study

Abstract

Postinhibitory excitation is a transient overshoot of a neuron's baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron's firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation's strength correlates with the inhibitory stimulus's amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition.

Fig 1. Postinhibitory excitation in human motor units.

(a): Motoneurons (MNs) receive multiple, typically unknown synaptic inputs (green). Particularly, reciprocal inhibition is mediated by interneurons (gray). In humans, the recording of motor unit spike trains (black) allows for studying the function of motoneurons. (b): The integration of synaptic inputs in motoneurons is determined by ion channels (blue). (c): Peristimulus frequencygram (PSF) of three exemplary tibialis anterior motor units in response to reciprocal inhibition, elicited by electrical stimulation of the tibial nerve during sustained isometric contractions. Moving average is shown in blue, data from [7]. It is unclear if the observed postinhibitory excitation is caused by neural pathways or intrinsic motoneuron properties.

Fig 2. Peristimulus analysis for an exemplary selected tibialis anterior motor unit.

(a): Peristimulus frequencygram (PSF). (b): Cumulative summation of PSF (PSF-cusum). The electrical stimulus to the tibial nerve was applied at time zero. Solid horizontal lines show prestimulus mean values and dashed lines mark the significance threshold for reflex responses. Arrows show the distance between manually determined turning points in PSF-cusum, i.e., inhibition and excitation amplitude. The period of postinhibitory excitation is highlighted with gray color. Data from [7].

Fig 3. Peristimulus analysis for simulated motoneurons.

(a): Peristimulus frequencygram (PSF) for a simulated neuron with h-current. (b): PSF for a simulated neuron without h-current. In (a) and (b), the injected inhibitory postsynaptic current (IPSC, amplitude -10nA) and the schematic trajectory of the induced inhibitory postsynaptic potential (IPSP) are depicted in gray and blue color, respectively. The actual time course of the membrane potential depends on the membrane potential value and the size of other inputs at IPSC application time. (c): PSF cumulative summation (PSF-cusum) for a simulated neuron with h-current. (d): PSF-cusum for a simulated neuron without h-current. Solid horizontal lines show prestimulus mean values and dashed lines mark the significance threshold for reflex responses. Arrows show the distance between two manually determined turning points in PSF-cusum, i.e., inhibition and excitation amplitude.

Fig 4. Postinhibitory excitation in different simulation settings.

Excitation amplitudes in relation to inhibitory postsynaptic current (IPSC) amplitude and for three different baseline discharge rates (low (△), medium (o), and high (x) drive) and with three different amounts of noise (standard deviation 0% (a), 12.5% (b) and 25% (c) of mean drive). Gray lines show linear regressions.

Fig 5. Analysis of history-dependent interspike interval duration in simulated motoneurons.

Top row: model with h-current, bottom row: model without h-current. Baseline frequency 10 Hz, no noise, inhibitory postsynaptic current (IPSC) amplitude -10 nA. (a, c): Membrane potential trajectory without stimulus (black, undisturbed interval) and with stimulus applied at two exemplary time points (blue, green). Dashed arrows mark IPSC application time with respect to the last discharge (t_stim) and solid arrows mark change of interspike interval with respect to the undisturbed interval (Δ ISI). Insert in (a) shows h-current for the shown interspike intervals between 40 ms and 100 ms. Here, a positive sign indicates current flux into the cell. (b, d): Change of interspike interval duration (Δ ISI) over time of IPSC application with respect to the last discharge (t_stim). Intervals shown in (a) and (c), respectively, are marked with asterisks. Dashed lines separate prolonged interspike intervals (inhibition) from shortened interspike intervals (excitation).

Fig 6. Cluster-based analysis of peristimulus frequencygram (PSF).

PSF and PSF cumulative summation (PSF-cusum) for one experimentally recorded motor unit and a simulated neuron with and without h-current (data from Figs 2 and 3). The blue boxes in panels (a, b, c) cluster the first postinhibitory spikes that fire at least one standard deviation above the mean baseline frequency (black line). Accordingly, the green boxes cluster all first postinhibitory spikes that fire with at least one standard deviation below the mean baseline frequency. (d, e, f): Clusters of spike trains from which the first poststimulus spikes appear in the blue or green box, respectively. (g, h, i): PSF-cusum of all spike trains (black) and clusters of spike trains (blue, green).

Fig 7. Characteristic behavior of the computational motoneuron model.

(a): Membrane potential time course of the simulated motoneurons without (black) and with h-current (blue) in response to injection of the current step shown in (b). Membrane potential is given relative to the resting potential. (c): Steady-state membrane potential (V_step) vs. overshoot membrane potential (V_overshoot) of the simulated neuron (x) compared to data obtained from [26] (o) and [12] (△). (d): Equivalent electric circuit of the motoneuron model. Blue color highlights components added compared to the previous version of the model [18]. (e): Current-frequency relation for the model without (black) and with (blue) h-currents.