Fig 1.
PAD-induced spiking in a neuron model.
(A) 2-D bifurcation diagram showing the combinations of EGABA and βw that allow a GABA conductance step (ḡGABA = 2 nS/pF) to elicit repetitive or transient spiking (dark and light grey regions, respectively). Labels a-f indicate parameter combinations for which sample responses are shown in B. Normal conditions correspond to EGABA = -35 mV and βw = -20 mV (point b). (B) Sample responses to a fast synaptic waveform (τrise = 2 ms, τdecay = 20 ms), a slow synaptic waveform (τrise = 20 ms, τdecay = 200 ms) and a conductance step for parameter combinations labeled in A. Slow-onset conductance requires stronger ḡGABA (3.5 nS/pF, grey trace in c) to elicit transient spiking than a fast-onset conductance; all black traces are for ḡGABA = 2 nS/pF. (C) 2-D bifurcation analysis described in A was repeated for different ḡGABA values. Dashed and solid lines show borders for the transient and repetitive spiking regions, respectively. Increasing ḡGABA from 1 to 2 nS/pF (cyan → black) caused a downward shift in both borders but further increases (black → green) caused little change in the former and a rightward shift in the latter, indicating that increased ḡGABA confers increased spiking only to a certain point, beyond which further increase actually reduces spiking.
Fig 2.
PAD-induced transient spiking in DRG neurons.
(A) Sample responses to virtual GABA conductance applied via dynamic clamp. Labels a-d on cartoon indicate testing conditions and are referred to in all subsequent panels. Most neurons, like the typical one illustrated here, spiked only for EGABA = -20 mV and after being made hyperexcitable by exposure to 2.5 mM 4-AP (point c). (B) Summary of the proportion of neurons responding with or without spikes to virtual PAD. Numbers inside each bar indicate the number of cells. A total of 29 neurons from naïve rats were tested before and after 4-AP and for each EGABA. A total of 10 neurons from nerve-injured rats were tested for each EGABA. The proportion of spiking/non-spiking cells was compared between conditions using Fisher’s exact tests (see Results). (C) Left panel summarizes the minimum ḡGABA required to elicit spiking in cells that spiked both before and after 4-AP for EGABA = -20 mV. Minimum ḡGABA was significantly reduced from 0.76 ± 0.19 to 0.20 ± 0.05 nS/pF (mean ± SEM) by 4-AP (p = 0.005, two-way repeated measures ANOVA and Tukey test). These values are lower than observed in simulations in Fig 1; therefore, we adjusted the neuron model to reproduce this higher sensitivity to ḡGABA. As illustrated in S1 Fig, this revised model shows the same relationship between EGABA and excitability (βw) as seen in Fig 1. Right panel shows minimum ḡGABA plotted against soma diameter. Soma diameter, which correlates with fiber type, did not significantly affect minimum ḡGABA or the effect of 4-AP (p = 0.61 and 0.29, respectively; two-way repeated measures ANOVA). (D) Summary of the minimum ḡGABA required to elicit spiking in cells that spiked for each EGABA value after 4-AP. The depolarizing shift in EGABA from -35 mV to -20 mV caused a significant reduction (p<0.022, paired t-test) from 0.30 ± 0.07 nS/pF to 0.11 ± 0.02 nS/pF. (E) Sample responses from a typical neuron tested with gGABA steps and ramps. The minimum ḡGABA required to elicit transient spiking when applied as a step was 40 nS (or 0.96 nS/pF after normalization by membrane capacitance) but a ramp with 2.5x greater peak amplitude failed to elicit spiking. EGABA = -20 mV.
Fig 3.
PAD-induced repetitive spiking in DRG neurons.
(A) Sample traces from a typical neuron showing that 4-AP had the intended effect of enabling repetitive spiking in response to current injection (Istim, top traces), yet virtual GABA conductance continued to elicit only transient spiking (bottom traces). EGABA = -20 mV. Scale bar for gGABA in all panels show nS before and after normalization by membrane capacitance of the recorded cell. (B) Responses from another neuron showing that increasing ḡGABA across a very broad range (an order of magnitude greater than required for transient spiking) failed to eventually induce repetitive spiking. Instead, spike amplitude was attenuated and membrane potential was effectively clamped near EGABA after the initial spike. (C) To further increase excitability, dynamic clamp was used to insert a virtual voltage-dependent sodium conductance (ḡNa = 0.2 nS/pF) after applying 4-AP. The effectiveness of this manipulation is clear from the development of spontaneous spiking (right panels). Under these conditions, a slow gGABA waveform or gGABA step induced repetitive spiking. The result was observed in 2 of 2 neurons tested.
Fig 4.
PAD-mediated inhibition in a neuron model.
(A) 2-D bifurcation diagram showing the combinations of EGABA and p associated with PAD-induced spiking (grey region) and PAD-mediated inhibition of other spiking (green region), where p represents the proportion of sodium channels susceptible to inactivation. Simulations here are based on a neuron model with sodium channel inactivation (Eq 7) with βw = 0 mV and ḡGABA = 2 nS/pF. Note that the green and grey regions overlap, indicating that PAD can initiate its own spikes yet still inhibit spikes initiated by other means (e.g. by stimulating current Istim). Labels a-e indicate parameter combinations for which sample responses are shown in B. (B) Responses to gGABA steps occurring alone or during Istim steps are shown down the left and right columns, respectively. (C) Boundary between inhibitory and non-inhibitory region (as in A) re-plotted for different ḡGABA. Higher ḡGABA enables GABA to be inhibitory despite less inactivating sodium current (i.e. smaller p) and more depolarized EGABA.
Fig 5.
PAD-mediated inhibition in DRG neurons.
(A) Sample responses from a typical neuron made hyperexcitable by 4-AP and virtual sodium conductance (ḡNa = 0.3 nS/pF). The repetitive spiking elicited by the Istim step was reduced by application of a small gGABA step (middle row) and was altogether stopped by larger gGABA steps (top row). For equivalent ḡGABA, stronger inhibition was evident with EGABA = -35 mV than with EGABA = -20 mV (compare left and right columns). (B) Sequence of Istim and gGABA steps was changed to verify that the latter could elicit transient spiking yet still inhibit the repetitive spiking driven by Istim. Note that repetitive spiking starts after the gGABA step ends and lasts until the Istim step ends. (C) PAD-mediated inhibition of transient spiking was assessed using the same protocol as in B but we varied the amplitude of the Istim step to determine rheobase (i.e. the minimum Istim required to evoke spiking). Only responses to rheobasic stimulation are shown. Note that rheobase increases with increases in ḡGABA, whereas spike height decreases. (D) Change in rheobase (mean ± SEM) is plotted against ḡGABA for EGABA = -35 mV (blue, n = 3 cells) and -20 mV (red, n = 4 cells). Rheobase was significantly increased by ḡGABA (p = 0.013, one-way repeated measures ANOVA; p = 0.013 (*), p = 0.002 (**), Holm-Sidak post-hoc tests vs no gGABA) but EGABA did not have a significant effect (p = 0.52).
Fig 6.
ANO-1 channels do not contribute to PAD.
For all panels, responses in the presence of the ANO-1 antagonist T16Ainh-A01 (A01) are shown in red for comparison against responses in normal aCSF shown in black. (A) Traces show responses in a typical neuron to the minimum virtual ḡGABA required to evoke spiking based on a fast synaptic waveform and EGABA = -20 mV before and after ANO-1 blockade. Summary data show that the minimum ḡGABA to evoke spiking was not significantly changed by A01 (p = 1.0; paired t-test) based on all TRPV1+ neurons (n = 5) that spiked in response to virtual GABA. (B) Traces show responses in a typical neuron to different ḡGABA based on slow synaptic waveform and EGABA = -35 mV. Summary data show mean (± SEM) depolarization at different ḡGABA for all (n = 7) TRPV1+ neurons tested. Blockade of ANO-1 did not significantly affect depolarization (p = 0.77; two-way repeated measure ANOVA). (C) At the end of each experiment, the recorded cell was stimulated with capsaicin. Traces show typical data from a responsive (TRPV1+) and unresponsive (TRPV1-) neuron. Because ANO-1 is expressed predominantly in TRPV1+ neurons, only data from capsaicin-responsive neurons were included for analysis in panels A and B. (D) To confirm the efficacy A01, we verified that it reduced the response to capsaicin, consistent with Takayama et al. [49].
Fig 7.
PAD-mediated inhibition of spike propagation in a multi-compartment axon model.
(A) Cartoon depicts our three-compartment axon model. One or more spikes were initiated by current injection applied to the left end of the axon. Voltage was measured at the midpoint of each compartment; color of traces in B and C correspond to compartment colors shown in A. GABA conductance was distributed uniformly throughout the middle (blue) compartment. (B) For EGABA = -35 mV (left column), gGABA blocked the propagation of the evoked spike under all three combinations of ḡGABA and p that were tested, where p represents the proportion of sodium channels susceptible to inactivation. The gGABA step did not elicit its own spiking in any condition. On the other hand, for EGABA = -20 mV (right column), PAD-induced transient spiking was observed for all three conditions yet propagation of the stimulus-evoked spike was blocked in two of the three conditions. Comparing the top and middle panels shows that modest ḡGABA relies on sodium channel inactivation to block spike propagation, whereas stronger ḡGABA could block propagation without any contribution from sodium channel inactivation. (C) During a spike train, sodium channel inactivation accumulates between spikes such that spikes early in the train can propagate whereas later spikes do not. Comparing with combinations of ḡGABA and p required to block propagation of a single spike (see B), these results show that partial blockade during a spike train can be mediated by even comparatively weak PAD.