Combined Changes in Chloride Regulation and Neuronal Excitability Enable Primary Afferent Depolarization to Elicit Spiking without Compromising its Inhibitory Effects

The central terminals of primary afferent fibers experience depolarization upon activation of GABAA receptors (GABAAR) because their intracellular chloride concentration is maintained above electrochemical equilibrium. Primary afferent depolarization (PAD) normally mediates inhibition via sodium channel inactivation and shunting but can evoke spikes under certain conditions. Antidromic (centrifugal) conduction of these spikes may contribute to neurogenic inflammation while orthodromic (centripetal) conduction could contribute to pain in the case of nociceptive fibers. PAD-induced spiking is assumed to override presynaptic inhibition. Using computer simulations and dynamic clamp experiments, we sought to identify which biophysical changes are required to enable PAD-induced spiking and whether those changes necessarily compromise PAD-mediated inhibition. According to computational modeling, a depolarizing shift in GABA reversal potential (EGABA) and increased intrinsic excitability (manifest as altered spike initiation properties) were necessary for PAD-induced spiking, whereas increased GABAAR conductance density (ḡGABA) had mixed effects. We tested our predictions experimentally by using dynamic clamp to insert virtual GABAAR conductances with different EGABA and kinetics into acutely dissociated dorsal root ganglion (DRG) neuron somata. Comparable experiments in central axon terminals are prohibitively difficult but the biophysical requirements for PAD-induced spiking are arguably similar in soma and axon. Neurons from naïve (i.e. uninjured) rats were compared before and after pharmacological manipulation of intrinsic excitability, and against neurons from nerve-injured rats. Experimental data confirmed that, in most neurons, both predicted changes were necessary to yield PAD-induced spiking. Importantly, such changes did not prevent PAD from inhibiting other spiking or from blocking spike propagation. In fact, since the high value of ḡGABA required for PAD-induced spiking still mediates strong inhibition, we conclude that PAD-induced spiking does not represent failure of presynaptic inhibition. Instead, diminished PAD caused by reduction of ḡGABA poses a greater risk to presynaptic inhibition and the sensory processing that relies upon it.


Introduction
Synaptic inhibition regulates transmission of sensory signals through the spinal cord. Importantly, numerous chronic pain conditions are associated with diminished inhibition [1][2][3][4][5] and pharmacological blockade of inhibition at the spinal level has been shown to reproduce many features of those chronic pain conditions [6][7][8][9]. Decreased transmitter release, reduced GABA A /glycine receptor function, and altered chloride regulation are all potential disinhibitory mechanisms, but pre-and postsynaptic inhibition are not equally susceptible to certain pathological changes; for instance, the potassium-chloride co-transporter KCC2 is not expressed in primary afferent neurons, meaning disinhibitory effects of KCC2 downregulation [10] are attributable entirely to reduced postsynaptic inhibition, in cells that express KCC2. KCC3 is expressed in some primary afferents and can extrude chloride under isosmotic conditions [11,12] but it remains unknown whether KCC3 is altered under pathological conditions. Yet selective disruption of presynaptic inhibition can cause mechanical and thermal hypersensitivity [13] and presynaptic expression of the α2 GABA receptor subunit is necessary for the antihyperalgesic effect of diazepam [14]. These observations affirm that presynaptic GABA A Rmediated inhibition also plays a key role in nociception.
Pre-and postsynaptic inhibition in spinal cord are mechanistically distinct. Postsynaptically, in mature spinal neurons, the reversal potential associated with GABA A R (E GABA ) is normally around -70 mV [10], meaning GABA A R activation reduces depolarization caused by concurrent excitatory input. Presynaptically, in the central terminals of primary afferents, E GABA is normally around -35 mV because chloride is actively loaded into primary afferents by the sodium-potassium-chloride co-transporter NKCC1 [13,[15][16][17], thus GABA A R activation causes depolarization. Contrary to the presumed excitatory effect of depolarization, primary afferent depolarization (PAD) mediates inhibitory effects via sodium channel inactivation and shunting [18][19][20][21]. However, PAD can sometimes trigger spikes that conduct antidromically, thus producing what is referred to as a dorsal root reflex (DRR) [22]. One theory holds that antidromically conducted spikes mediate an inhibitory effect by colliding with and blocking othrodromically conducted spikes originating in the periphery [23,24]; however, collisions are unlikely since the latency to travel the full length of the nerve is short relative to the interspike interval at realistic spiking rates. PAD-induced spikes are unlikely to trigger synaptic release from the PAD-affected branch because spike amplitude is attenuated, but PAD-induced spikes that manage to propagate to adjacent, PAD-free branches may trigger synaptic release [25]. The experiments required to test these model predictions are prohibitively difficult. The above theory was formulated for large myelinated proprioceptive afferents involved in locomotion; in contrast, within smaller afferents responsible for nociception, the prevailing view is that PADinduced spikes occur only under pathological conditions and that DRRs contribute to neurogenic inflammation and hypersensitivity [22,26]. Within this context, PAD-induced spiking is thought to represent conversion of PAD from an inhibitory process to an excitatory one [22].
With respect to biophysical mechanisms, PAD-induced spiking requires GABA A R activation [27] and NKCC1-mediated chloride loading [28]. Enhanced chloride loading and the consequent depolarizing shift in E GABA has been hypothesized to facilitate PAD-induced spiking [29,30]. Nerve injury increases NKCC1 protein levels and PAD [13,31], and although total NKCC1 expression is not altered by inflammation [32,33], NKCC1 membrane trafficking and phosphorylation are affected by painful stimuli [34]. Notably, inflammation causes a depolarizing shift in E GABA [35] and promotes DRRs in C and Aδ fibers [36]. Increased GABA A R density and reduced low-threshold potassium channel density have also been hypothesized to promote DRRs [35,37] but the full set of requirements for PAD-induced spiking remains unclear. We sought to identify which biophysical changes, alone or together, enable PADinduced spiking and how such changes impact PAD-mediated inhibition.

Results
Changes in GABA conductance density ḡ GABA , its associated reversal potential E GABA , and intrinsic excitability have all been implicated in PAD-induced spiking, as outlined above. To account for whether a neuron spikes transiently or repetitively, and whether spike threshold is sensitive to the rate of depolarization, we discuss excitability in terms of spike initiation dynamics [38]. Rather than characterize further how excitability and GABAergic signalling are pathologically altered, we sought to decipher how known pathological alterations contribute to PAD-induced spiking. To this end, we took an approach distinct from previous studies to determine how isolated and combined changes in each factor-ḡ GABA , E GABA , and excitabilityaffect PAD-induced spiking. We began with a minimalist conductance-based computer model to generate predictions that we then tested experimentally in acutely dissociated dorsal root ganglion (DRG) neurons using dynamic clamp. Intracellular recording/stimulation in most axons is prohibitively difficult but sustained depolarization of the soma or axon by optogenetic-based photostimulation evokes transient spiking, although photostimulation of peripheral axon terminals can evoke repetitive spiking in some DRG neurons [39]. It remains unclear how central axon terminals respond to sustained depolarization. We assume here that somatic and axonal spike initiation properties are qualitatively similar, but if axons were more excitable (i.e. more prone to repetitive spiking) than somata, they would operate farther to the right along the "excitability" axis described below. We applied virtual GABA conductances rather than assuming the soma and axon have equivalent GABA A R densities. As a final step, we confirmed our results in a multicompartment axon model.

PAD-induced spiking in a model neuron
Starting with computer simulations, we co-varied E GABA and intrinsic excitability (controlled by β w ; see Methods) while keeping ḡ GABA fixed at 2 nS/pF. The light grey and dark grey regions of the resulting 2-D bifurcation diagram (Fig 1A) show the E GABA and β w combinations that produce transient and repetitive spiking, respectively. Spiking pattern was determined by the response to GABA conductance "steps". To more accurately simulate different forms of synaptic transmission, other conductance waveforms were tested: phasic inhibition via intrasynaptic GABA A R was modeled by a "fast" synaptic waveform (τ rise = 2 ms; τ decay = 20 ms; see Eq 6); tonic inhibition corresponds to the sustained component of the conductance step, but we also tested a "slow" synaptic waveform with intermediate kinetics to simulate spilled-over GABA asynchronously activating extrasynaptic GABA A R (τ rise = 20 ms; τ decay = 200 ms).  Sample responses to a fast synaptic waveform (τ rise = 2 ms, τ decay = 20 ms), a slow synaptic waveform (τ rise = 20 ms, τ decay = 200 ms) and a conductance step for parameter combinations labeled in A. Slow-onset conductance requires stronger ḡ GABA (3.5 nS/pF, grey trace in c) to elicit transient spiking than a fast-onset conductance; all black traces are for ḡ GABA = 2 nS/pF. (C) 2-D bifurcation analysis described in A was repeated for different ḡ GABA values. Dashed and solid lines show borders for the transient and repetitive spiking regions, respectively. Increasing ḡ GABA 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 ḡ GABA confers increased spiking only to a certain point, beyond which further increase actually reduces spiking. and β w = -20 mV; point b), GABA conductance caused depolarization but no spiking. PADinduced repetitive spiking required a combined depolarizing shift in E GABA and β w (point e) whereas transient spiking required a smaller increase in β w (point c) and could result solely from a large change in E GABA . By comparison, an isolated change in β w could not enable PADinduced spiking. As illustrated in panel c of Fig 1B, slow-onset GABA A R input required stronger input to elicit spiking because transient spiking involves a spike initiation mechanism that is sensitive to the rate of depolarization [40].
Next, we repeated the 2-D bifurcation analysis for different ḡ GABA values to produce a family of curves (Fig 1C). The dashed curve demarcating the minimum requirements for transient spiking shifted downward as ḡ GABA was increased. The solid curve demarcating the minimum requirements for repetitive spiking also shifted downward for an initial increase in ḡ GABA but shifted rightward as ḡ GABA was increased further, indicating that GABA A R activation is maximally excitatory at intermediate densities. Somatic recordings have demonstrated somatic ḡ GABA between 0.2 and 0.5 nS/pF [35] and the absolute ḡ GABA values reported by Chen et al. [13] correspond to approximately 0.1 nS/pF after conversion to densities based on estimated surface areas. Axonal ḡ GABA may differ from somatic ḡ GABA (given precedents for differential ion channel distribution [41]) but measuring ḡ GABA in central axon terminals is prohibitively difficult. Our experimental approach does not rely on measuring axonal ḡ GABA but, instead, was designed to determine the minimum ḡ GABA required (for different E GABA and intrinsic neuronal excitability) to enable PADinduced spiking; comparing this value against measured ḡ GABA (in the soma) reveals whether the density of native GABA receptors is sufficient to evoke spiking under different conditions. It remains unclear what ḡ GABA would be necessary to evoke spiking in central axon terminals.

PAD-induced transient spiking in DRG neurons
To test the simulation predictions described above, we conducted experiments in acutely dissociated DRG somata using an approach distinct from previous studies. Rather than activating native GABA A Rs by puffing GABA (which would produce a current whose conductance, reversal potential and kinetics are not easily measured or independently manipulated), we used dynamic clamp to apply a virtual conductance whose parameters are precisely and independently controllable. In this way, we quantified the minimum virtual ḡ GABA required to elicit spiking under different conditions. Importantly, because virtual ḡ GABA can be higher than native ḡ GABA , the density of native GABA A R does not limit our studies; indeed, failure of GABA puffs to evoke spikes in previous studies [13,35,42] suggests that somatic ḡ GABA is normally too low to produce spikes, but ḡ GABA may be higher in central axon terminals. In dynamic clamp, the voltage recorded from a neuron is passed to a computer, which, in real time, uses voltage to calculate current that is injected back into the patched neuron, thereby introducing a virtual conductance [43]. This approach allows manipulations to be applied like in computer simulations but to real neurons, such that we can avoid modeling the neuron (and making any assumptions about intrinsic excitability) and test directly how virtual GABA A R input affects native voltage-gated channels controlling spike initiation. Notably, photostimulation-based testing of axonal excitability has revealed transient spiking comparable to that observed in somata [39] but the excitability of central axon terminals remains uncertain. If central axon terminal and somatic excitability are similar, then the requirements for PAD-induced spiking ascertained for the soma can be extrapolated to those terminals; on the other hand, if those terminals are more excitable, they would operate farther to the right on the excitability axis depicted in the inset of Fig 2A. To begin, we tested virtual GABA conductances in neurons from naïve animals before and after reproducing the hyperexcitability associated with nerve injury by blocking K v 1-type potassium channels with 4-AP [44,45]; this corresponds in the model to setting β w to less negative values. Testing with different E GABA and stimulus waveforms, we systematically increased ḡ GABA to try to elicit spiking. As illustrated for a typical cell in Fig 2A, PAD was most likely to produce spiking after application of 4-AP and a depolarizing shift in E GABA to -20 mV. Fig 2B summarizes the proportion of cells in which PAD-induced spiking was observed under each test condition. For cells from naïve animals tested with E GABA = -35 mV, 4-AP increased the proportion exhibiting PAD-induced spiking but not significantly (p = 0.079; Fisher's exact test) whereas the 4-AP effect was highly significant for E GABA = -20 mV (p = 0.004). Shifting E GABA from -35 mV to -20 mV significantly increased the proportion of cells exhibiting PAD-induced spiking both before and after 4-AP (p < 10 −3 and 10 −4 , respectively), consistent with the NKCC1 hypothesis of DRR generation [29,30]. But as predicted by our simulations, the proportion of cells with PAD-induced spiking was most significantly increased by the combination of 4-AP and a depolarizing shift in E GABA (p < 10 −9 ). Within this data set, two cells were subsequently identified as outliers based on analysis of the A total of 29 neurons from naïve rats were tested before and after 4-AP and for each E GABA . A total of 10 neurons from nerve-injured rats were tested for each E GABA . The proportion of spiking/non-spiking cells was compared between conditions using Fisher's exact tests (see Results). (C) Left panel summarizes the minimum ḡ GABA required to elicit spiking in cells that spiked both before and after 4-AP for E GABA = -20 mV. Minimum ḡ GABA 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 ḡ GABA . As illustrated in S1 Fig, this revised model shows the same relationship between E GABA and excitability (β w ) as seen in Fig 1. Right panel shows minimum ḡ GABA plotted against soma diameter. Soma diameter, which correlates with fiber type, did not significantly affect minimum ḡ GABA or the effect of 4-AP (p = 0.61 and 0.29, respectively; two-way repeated measures ANOVA). (D) Summary of the minimum ḡ GABA required to elicit spiking in cells that spiked for each E GABA value after 4-AP. The depolarizing shift in E GABA 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 g GABA steps and ramps. The minimum ḡ GABA 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. E GABA = -20 mV.
Based on cells that exhibited PAD-induced spiking before and after 4-AP for E GABA = -20 mV, the minimum ḡ GABA needed to elicit spiking was significantly reduced from 0.49 ± 0.07 nS/pF (mean±SEM) to 0.16 ± 0.03 nS/pF by 4-AP (p = 0.005, Tukey test following ANOVA described below) (Fig 2C left). Plotting the same data against soma diameter revealed a trend towards higher minimum ḡ GABA for smaller cells, but soma diameter did not have a significant effect (p = 0.61) and nor did it interact significantly with the 4-AP effect (p = 0.29; two-way repeated measures ANOVA) (Fig 2C right). Notably, we report all conductances as densities to correct for the direct effect of membrane surface area on our measurements; however, soma diameter is known to correlate with fiber type [46], and so the insignificant effect of cell size (after normalization by surface area) argues that minimum ḡ GABA does not differ significantly between myelinated (A) and unmyelinated (C) neurons. Of the cells that exhibited PADinduced spiking for both E GABA values after 4-AP, the minimum ḡ GABA needed to elicit spiking was significantly reduced from 0.30 ± 0.07 nS/pF to 0.11 ± 0.02 nS/pF by shifting E GABA from -35 mV to -20 mV (p = 0.022, paired t-test) (Fig 2D). Of the 10 cells tested with both fast and slow g GABA waveforms at E GABA = -20 mV after 4-AP, 7 responded to both stimuli with transient spiking and 2 responded with repetitive spiking. Among transient spiking cells, the slow waveform required higher ḡ GABA than the fast waveform to elicit transient spiking (0.46 ± 0.09 nS/pF vs 0.27 ± 0.09 nS/pF) which, although not a statistically significant difference (p = 0.25; paired t-test), is consistent with a spike initiation mechanism sensitive to the rate of depolarization. By comparison, the two repetitive spiking cells required exactly the same minimum ḡ GABA for the fast and slow waveforms, consistent with a spike initiation mechanism sensitive only to the amplitude of depolarization [40]. Comparing the responses to g GABA steps and ramps illustrates that the latter are far less effective in eliciting transient spiking (Fig 2E). All of these experimental data are consistent with simulation results in Fig 1

PAD-induced repetitive spiking in DRG neurons
Testing with current injection (I stim ) confirmed that 4-AP had the intended effect of increasing excitability yet, despite responding to I stim steps with repetitive spiking, most neurons responded to g GABA steps with transient spiking, as illustrated in Fig 3A. Specifically, PADinduced repetitive spiking was not observed in any nerve-injured neurons and was seen in only two neurons after 4-AP application. All neurons were tested with a broad range of ḡ GABA to confirm that repetitive spiking could not eventually be achieved by applying a stronger conductance. Increasing ḡ GABA above the minimum required to elicit transient spiking consistently caused attenuation of the spike height and clamped the subsequent voltage near E GABA (Fig  3B). Based on our simulation results (see Fig 1A), we reasoned that the lack of repetitive spiking was due to 4-AP or nerve injury not causing a sufficient increase in excitability. To test this hypothesis, we further increased excitability by using dynamic clamp to introduce a virtual sodium conductance like that upregulated after nerve injury [45]. As predicted, PAD-induced repetitive spiking was made possible by this additional manipulation (Fig 3C). Although we managed to reproduce PAD-induced repetitive spiking, the extent of the required manipulations suggests that naturally occurring pathological changes cause few neurons to become sufficiently hyperexcitable that PAD will induce repetitive spiking. That said, if the central terminals of axons are more excitable (i.e. more prone to repetitive spiking) than the soma, PAD would be more likely to elicit repetitive spiking than suggested by our data.

PAD-mediated inhibition in a model neuron
The above results demonstrate that depolarizing GABA current can induce transient spiking under conditions associated with nerve injury. This does not, however, exclude PAD from Responses from another neuron showing that increasing ḡ GABA 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 E GABA after the initial spike. (C) To further increase excitability, dynamic clamp was used to insert a virtual voltage-dependent sodium conductance (ḡ Na = 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 g GABA waveform or g GABA step induced repetitive spiking. The result was observed in 2 of 2 neurons tested.
doi:10.1371/journal.pcbi.1005215.g003 retaining its inhibitory effects, especially given that inhibition stems from sodium channel inactivation and shunting. In fact, although PAD may induce a single spike at its onset, shunting effects persist as long as GABA A R are activated. This raises the important question of whether more spikes (arising in the periphery or ectopically in the soma or a neuroma) are blocked by PAD than are induced by PAD in the central axon terminals.
Our initial model did not include sodium channel inactivation for the sake of simplicity; therefore, our next step was to modify the model so that a certain proportion of sodium channels, controlled by parameter p, experience inactivation (Eqn. 7). Using this new model, we set β w to 0 mV to facilitate repetitive spiking and conducted 2-D bifurcation analysis to determine the p and E GABA combinations associated with different effects of PAD (Fig 4A). The grey region shows parameter combinations for which a g GABA step (2 nS/pF) applied alone elicits spiking (sample traces a and d in Fig 4B). The green region shows parameter combinations for which the same g GABA step inhibits spiking induced by I stim steps (sample traces c-e in Fig 4B). Importantly, the green and grey regions overlap, thus demonstrating that PAD can induce spikes yet nonetheless block spikes originating by other means.  unchanged (not illustrated) but the region of PAD-mediated inhibition expanded as ḡ GABA was increased, suggesting that stronger GABA A R activation manages to terminate spiking despite a smaller proportion of inactivatable sodium channels.

PAD-mediated inhibition in DRG neurons
To measure PAD-mediated inhibition in real DRG neurons, we combined g GABA and I stim steps as done for simulations in Fig 4B. Fig 5A shows a typical neuron in which I stim elicited repetitive spiking. Interposing a g GABA step during the I stim step caused reduction or complete cessation of repetitive spiking depending on ḡ GABA and E GABA . Note that spikes occurring during the g GABA step were shorter than those occurring outside the g GABA step, consistent with the shunting effect of the virtual GABA conductance. Applying the g GABA step before the onset of I stim confirmed that the former could elicit transient spiking yet still inhibit the repetitive spiking otherwise driven by I stim (Fig 5B). Using the same stimulus sequence, we measured rheobase (i.e. the minimum I stim required to elicit spiking) for each level of ḡ GABA (Fig 5C). Rheobase was significantly increased by increments in ḡ GABA (p = 0.013, two-way repeated measures ANOVA) but was not significantly affected by E GABA (p = 0.52) (Fig 5D). These data confirm that PAD elicited in the cell body of DRG neurons mediates shunting inhibition even under conditions in which it can induce spiking.
Possible involvement of calcium-activated chloride channels in PAD Activation of the calcium-activated chloride channel ANO-1 in primary afferent neurons can evoke or exacerbate pain, especially under inflammatory or neuropathic conditions [47][48][49][50]. Notably, intracellular chloride tends to be elevated under those conditions (see Introduction), which may explain why ANO-1 activation is excitatory rather than inhibitory. Consistent with this, ANO-1 modulation of spiking evoked by current injection is sensitive to intracellular chloride level [51] but demonstration that ANO-1 itself evokes spiking was based on a chloride reversal potential of -18 mV [49]. Given its activation requirements [52], we predicted that ANO-1 channels would not be activated by the GABAergic input underlying PAD; recall that GABA A R activation is necessary for PAD [22]. Nonetheless, to rule out a contribution by ANO-1, we repeated virtual PAD experiments (like in Fig 2) before and after blockade of ANO-1 channels by bath-applied 10 μM T16Ainh-A01 (A01) (Fig 6). Based on the pipette solution, the chloride reversal potential for ANO-1 was -20 mV but E GABA for virtual g GABA was set to -35 or -20 mV in dynamic clamp. As predicted, ANO-1 blockade had no significant effect on the minimum ḡ GABA needed to evoke spiking for E GABA = -20 mV (p = 1.0, paired ttest; Fig 6A) and nor did it significantly affect the depolarization evoked by different ḡ GABA for E GABA = -35 mV (p = 0.77, two-way repeated measures ANOVA; Fig 6B) or have any effect on rheobase, input resistance, or resting membrane potential (p > 0.05, paired t-tests). The data above are based exclusively on capsaicin-responsive cells (see Fig 6C) since ANO-1 channels are expressed primarily in cells that express TRPV1 [47]. Notably, the response to capsaicin was reduced by ANO-1 blockade (Fig 6D), consistent with Takayama et al. [49] and thus verifying the efficacy of our A01. Based on these results, we conclude that ANO-1 channels are not activated and, therefore, do not contribute to PAD under our experimental conditions.

PAD-mediated inhibition of spike propagation in a multicompartment model neuron
All simulations described thus far were conducted in a single compartment model. This adequately simulates spike initiation occurring in proximity to the recording electrode, as occurs when recording from an isolated DRG soma. Although spontaneous or PAD-induced spiking may arise at the site of PAD, an important inhibitory effect of PAD in the intact fiber is to block the orthodromic propagation of spikes originating in the periphery. To test for conduction block, we converted our single-compartment model into a 3-compartment model (Fig  7A). Although still very simple compared with past models used to study this topic [e.g. 19,25,53], this model suffices to qualitatively illustrate key points relevant for the present study. Each compartment was further subdivided into equipotential segments. Based on its small diameter and the absence of nodes, this model simulates continuous propagation in an unmyelinated fiber. By applying GABA conductance to the middle compartment, we tested if that conductance can induce spikes (originating within that compartment) and/or block the propagation of other spikes (evoked at the far end of adjacent compartment).
For an E GABA value of -35 mV, g GABA never evoked spiking (consistent with the single-compartment model) but it did block spike propagation (Fig 7B, left column). Interestingly, blocked propagation could occur even in the absence of sodium channel inactivation, therein supporting claims that shunting mediated by g GABA mediates an inhibitory effect. When E GABA was shifted to -20 mV, g GABA evoked a single spike that propagated in both directions away from the center compartment (Fig 7B, right column). Yet despite this excitatory effect, propagation of other spikes was blocked in two of the three conditions illustrated. Sample traces were chosen to illustrate that large g GABA could block propagation in the absence of sodium channel inactivation but a smaller g GABA could achieve the same effect when combined with sodium channel inactivation. Fig 7C demonstrates that sodium channel inactivation can accumulate over time, thus eventually blocking spikes traveling as part of a train. These results confirm that PAD does not abruptly lose its inhibitory effects once able to induce its own spikes.

Discussion
Using computer simulations and an experimental approach distinct from previous studies, we have identified which pathological changes are necessary and sufficient to enable PAD-induced spiking. We determined that a depolarizing shift in E GABA is necessary yet insufficient to enable PAD-induced spiking in most DRG neurons. An increase in intrinsic excitability (i.e. altered spike initiation properties) is also necessary, especially to enable PAD-induced repetitive spiking. Neurons may experience both changes after nerve injury or inflammation, meaning PADinduced spiking could occur in certain pathological conditions [22,26,29]; however, other factors such as the requirement for fast depolarization suggest that PAD-induced spiking is probably rare (see below), but this depends on the excitability of central axon terminals, which still remains uncertain. Intriguingly, our data also suggest that PAD continues to mediate presynaptic inhibition under conditions in which it can induce transient spiking. Although seemingly spike under all three combinations of ḡ GABA and p that were tested, where p represents the proportion of sodium channels susceptible to inactivation. The g GABA step did not elicit its own spiking in any condition. On the other hand, for E GABA = -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 ḡ GABA relies on sodium channel inactivation to block spike propagation, whereas stronger ḡ GABA 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 ḡ GABA 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. Primary Afferent Depolarization-Induced Spiking paradoxical, the co-existence of excitatory and inhibitory effects has been observed previously in studies of presynaptic inhibition in crayfish [54] and is consistent with the biophysical mechanisms responsible for each effect. This is unlike what happens postsynaptically in spinal neurons, where paradoxical excitation develops only after inhibition fails [10,55]. Our data argue that increased PAD has a net inhibitory effect, meaning paradoxical excitation via enhanced PAD poses less risk to somatosensory processing than disinhibition caused by reduced PAD.
The GABA conductance density required for PAD-induced spiking under normal conditions is evidently quite high, so much so that we were able to elicit spiking in only 2 of 29 neurons despite testing with virtual ḡ GABA several times greater than the typical density measured in somata [13,35]. This is consistent with previous failures to elicit spikes by puffing GABA on the soma [13,35,42]. Puffed GABA also failed to elicit calcium signals when applied to the central terminals of GCaMP-expressing primary afferents [13], and Verdier et al.
[56] observed GABA-induced spiking in only 4 of 77 neurons tested in the trigeminal nucleus. The value of ḡ GABA in central axon terminals remains an open question but evidence points to reduced expression of presynaptic GABA A Rs following nerve injury [13,57,58], which suggests that presynaptic inhibition is weakened by reduction of ḡ GABA rather than ḡ GABA becoming strong enough that PAD induces spiking. That said, the minimum ḡ GABA needed for PAD-induced spiking is reduced by increased neuronal excitability (Fig 2C) and by a depolarizing shift in E GABA (Fig 2D). Unlike an increase in ḡ GABA , which increases inhibitory effects due to shunting, increased neuronal excitability and depolarized E GABA can encourage PAD-induced spiking without enhancing PAD-mediated shunting. Studying transient spiking cells in the chick cochlear nucleus, Monsivais and Rubel [59] found that depolarizing GABA A R input could elicit spiking after blockade of the low-threshold potassium current known to be responsible for transient spiking [60]. The same GABA A R input normally inhibited stimulus-evoked spiking by activating the low-threshold potassium current and thereby elevating spike threshold [59]. Those data are entirely consistent with results presented here. Notably, PAD-induced spiking would be more likely in central axon terminals if those terminals are more excitable that we have assumed based on extrapolation from somatic data. Intracellular chloride could be depleted during PAD if chloride uptake via NKCC1 became saturated (at least transiently) and thus failed to keep pace with chloride efflux via activated GABA A channels. The potential for altered chloride concentration is exacerbated by the small caliber of central axon terminals, especially C fibers, since intracellular volume is small compared to surface area [61]. Chloride depletion, if it occurred, would cause an activity-dependent hyperpolarizing shift in E GABA , the implication being that E GABA may be near -20 mV only at the onset of GABA A R activation. Given that PAD-induced spiking depends on a depolarized E GABA value, a hyperpolarizing shift would discourage PAD-induced repetitive spiking. That said, the transient spiking observed in our dynamic clamp experiments was not due to chloride depletion since the virtual GABA current is mediated by current injection through the patch pipette rather than by chloride efflux across the cell membrane. In effect, PAD-induced repetitive spiking may be more difficult to evoke under natural conditions, and transient spiking may rely even more heavily on abrupt depolarization than our experiments suggest.
Following on the above points, both simulations and experiments demonstrated that smaller pathological changes in E GABA and/or excitability are required to enable PAD-induced transient spiking than are required for PAD-induced repetitive spiking. This has important implications. Even if sustained, PAD is likely to produce only one spike at its onset (if it produces any spikes at all) and will likely not produce any spikes unless its onset is abrupt. This is because transient spiking involves a spike initiation mechanism that is sensitive to the rate of depolarization [40]. Sensitivity to g GABA onset kinetics would be inconsequential if presynaptic inhibition was phasic, which is to say that the GABA A Rs are clustered within the synaptic cleft and therefore receive an abrupt pulse of GABA upon its vesicular release [62], but evidence points toward a more tonic mode of action (unlike the phasic inhibition studied in the crayfish neuromuscular junction [63]) as outlined below. Recording from mammalian primary afferent terminals to measure the activation kinetics (and density) of the GABA A R current is prohibitively difficult, but immunocytochemical evidence argues that C fiber terminals are devoid of gephyrin [64]. Since gephyrin is usually necessary for GABA A R clustering [65], its absence suggests that GABA A Rs are distributed more diffusely. Electrophysiological evidence for highaffinity GABA A Rs in primary afferent neurons [37] supports this view since such receptors have a δ subunit [66] in place of the γ subunit that is necessary for clustering [62,67]. If primary afferent GABA A Rs are indeed distributed extrasynaptically, and are thus activated asynchronously as GABA diffuses beyond the synaptic cleft, then g GABA will have slow onset kinetics and is unlikely to elicit transient spiking. Only the most hyperexcitable fibers (i.e. those capable of PAD-induced repetitive spiking) are likely to exhibit any PAD-induced spiking. And whereas PAD-induced transient spiking relies on abrupt GABA A R activation, PAD-mediated inhibition does not; instead, PAD-mediated inhibitory effects will last throughout the duration of the PAD. In other words, slow activation of extrasynaptic GABA A Rs-arguably the most likely scenario at least for C fiber terminals (see above)-will not cause PAD-induced spiking but will cause PAD-mediated inhibition.
Notably, dorsal root reflexes (DRRs) have typically been studied using electrical stimulation of a nerve or dorsal root to synchronously activate a large number of afferent fibers [e.g. 68]. Notwithstanding differential conduction latencies, such input will evoke a large burst of GABA release, causing GABA A R activation that is ideally suited for PAD-induced transient spiking. It is not obvious that those same fibers would exhibit PAD-induced spiking under more natural conditions (i.e. less synchronous inputs). However, Dubuc et al. [69] observed antidromic spiking in 19% of cat dorsal root fibers during fictive locomotion. It has long been recognized that dorsal root reflexes are more common in certain afferents (e.g. stretch receptors) with direct evidence for DRRs being weakest in C fibres [22]. However, Lin et al. [36] reported spontaneous and von Frey-evoked antidromic spiking in all fiber types and, moreover, found that intradermal capsaicin selectively increased antidromic spiking in C and Aδ fibers. Based on more recent observations, including data presented here, one may suspect that chloride regulation, GABA receptor clustering and/or intrinsic excitability differ between afferent types. Somatic recordings suggest that important differences do indeed exist [70] but definitively resolving this requires comparison of axon terminals (rather than somata) and is therefore technically difficult. Notably, Dubuc et al. [69] observed repetitive antidromic spiking, as have others [e.g. 71], which argues that the excitability of certain afferent terminals is quite high. The role of axonal excitability warrants closer attention in future studies. Observation that cooling increases DRRs [72] likely holds important clues. Please see [5] for a recent review of other factors.
As already explained, PAD-induced spiking does not equate with failure of presynaptic inhibition. The resilience of presynaptic inhibition is best appreciated by comparing how pre-and postsynaptic inhibition fail. As KCC2 is downregulated postsynaptically, E GABA undergoes a depolarizing shift that directly compromises the inhibitory effect of GABAergic input [61]. The same shift in E GABA that reduces postsynaptic inhibition is what eventually results in paradoxical excitation. This shift from inhibition to paradoxical excitation is evidently not what happens presynaptically. In primary afferent terminals, the changes required for paradoxical excitation-a shift in E GABA and increased excitability-do not undermine the inhibitory effect; in fact, the relatively high ḡ GABA required for PAD-induced spiking also encourages PAD-mediated inhibition. This conclusion contradicts past assumptions on this matter. Furthermore, whereas the risk of paradoxical excitation increases postsynaptically during sustained GABAergic input (because of chloride accumulation), presynaptically, the balance shifts towards inhibitory effects over time as sodium channel inactivation accumulates and if intracellular chloride is depleted. The greatest risk to presynaptic inhibition is reduced PAD rather than enhanced PAD.
To conclude, we have demonstrated that combined changes in E GABA and intrinsic excitability enable PAD-induced transient spiking. However, unless neurons become so hyperexcitable that PAD can induce repetitive spiking, slow (asynchronous) activation of extrasynaptic GABA A Rs is unlikely to elicit any spiking. On the other hand, PAD will continue to mediate presynaptic inhibition. In practical terms, our results suggest that presynaptic inhibition is a viable therapeutic target whose enhancement carries little risk of causing paradoxical excitation.

Ethics Statement
All experiments were approved by the University of Pittsburgh IACUC and by The Hospital for Sick Children Animal Care Committee.

Computer simulations
Starting from a previously published model [45,73], our single compartment, conductancebased model is described as follows: where activation variable m changes instantaneously with voltage V according to whereas w changes more slowly according to t w ðVÞ ¼ 1 Neuronal excitability was varied by changing parameter β w [38]. Injury-induced hyperexcitability can be reproduced by shifting β w from its normal value of around -20 mV to less negative values [73]. Setting β w to less negative values reflects a multitude of potential injuryinduced molecular changes including reduced K V 1-type potassium current, which we model experimentally using 4-AP application, and increased sodium current, which we model experimentally using dynamic clamp (see below); the effect of such changes, occurring alone or together, is to alter spike initiation [45]. All other neuronal parameters were fixed as reported previously [38] at the following values: C = 2 μF/cm 2 ; sodium conductance ḡ Na = 20 mS/cm 2 , E Na = 50 mV, β m = -1.2 mV, γ m = 18 mV; potassium conductance ḡ K = 20 mS/cm 2 , E K = -100 mV, ϕ w = 0.15, γ w = 10 mV; leak conductance g leak = 2 mS/cm 2 , E leak = -70 mV.
Stimulating current I stim was not applied unless indicated. Maximal GABA conductance density ḡ GABA and reversal potential E GABA were varied. Units for ḡ GABA were converted to nS/ pF for comparison with experimental measurements. The normal E GABA value in primary afferent is around -35 mV based on measurements using different techniques [12,13,35,42]. GABA conductance was activated as a step or as a synaptic waveform described by which comprises an exponential rise to maximum (with time constant τ rise ) followed by an exponential decay back to baseline (with τ decay ). The peak is normalized to 1 by factor x before being scaled by ḡ GABA . Kinetics are reported in the Results section. For simulations reported in Figs 4 and 7, sodium channel inactivation h was applied to a proportion of sodium channels defined by p, thus giving the following current balance equation g Na m 1 ðVÞhðV À E Na Þ À ð1 À pÞ " g Na m 1 ðVÞðV À E Na Þ À " Changes in h are described by the same equations used to describe w (Eq 3-5) where β h = -28 mV, γ h = -14 mV, and ϕ h = 0.005.
All simulations in single compartment models were conducted in XPP. Bifurcation analysis was conducted using AUTO via the XPP interface. The multicompartment model was built in NEURON. Ion channels were modeled as above except that both ḡ Na and ḡ K were increased to 30 mS/cm 2 . Additional parameters were as follows: axial resistivity R a = 150 OÁcm, diameter = 1 μm, compartment length = 1 mm, d_lambda = 0.01. GABA conductance ḡ GABA was modeled as a uniform density throughout the middle compartment.

Dorsal root ganglion (DRG) neuron preparation and electrophysiology
All experiments were carried out on adult (200-340 g) male Sprague-Dawley rats (Harlan, Indianapolis, IN and Charles River, Montreal, Quebec). A subset of animals received spinal nerve ligation (SNL) 2-5 days before terminal experiments [74]. Under isoflurane anesthesia, the paraspinal muscles were separated to access the L6 process, which was carefully removed. The L5 spinal nerve was tightly ligated with 6-0 silk suture. All nerve-injured animals maintained motor function but developed neuropathic pain as inferred by guarding of the affected paw.
To collect DRG neurons, rats were deeply anesthetized by subcutaneous injection of anesthetic cocktail (1 ml/kg of 55 mg/ml ketamine, 5.5 mg/ml xylazine, and 1.1 mg/ml acepromazine) or by isoflurane (4% for induction; 2.5% for maintenance). DRG (L4 and L5 in naïve animals; L5 in nerve-injured animals) were surgically removed to chilled MEM-FBS culture media and desheathed. DRG were then enzymatically treated for 45 minutes in culture media composed of 89% MEM, 370 units/ml penicillin and 370 μg/ml streptomycin, 1% MEM vitamin solution (all from Life Technologies), and 1.2 mg/ml collagenase Type 4 (Worthington Biochemical Corp). DRG were mechanically dissociated by trituration with a fire-polished Pasteur pipette, and further enzymatically treated for 5 minutes in Ca 2+ -and Mg 2+ -free Hanks' balanced salt solution (HBSS; Life Technologies Inc), containing 2.5 mg/ml trypsin (Worthington Biochemical Corp) and 0.02% sterile ethylenediaminetetraacetic acid (EDTA; Sigma-Aldrich Canada Ltd). Trypsin activity was subsequently inhibited by the addition of MEM-FBS supplemented with 0.625 mg/ml MgSO 4 (Caledon Labs). Dissociated cells in MEM-FBS were plated on glass coverslips previously coated by a solution of 0.1 mg/ml poly-D-lysine, and incubated in MEM-FBS at 37°C, 5% CO 2 , and 90% humidity for 2 h. Coverslips were then transferred to a HEPES-buffered Leibovitz's L-15 media containing glutamine (Life Technologies Ltd), 10% FBS, 100 units/ml of penicillin and 100 μg/ml streptomycin, and 5 mM D-glucose (Caledon Labs) and stored at room temperature until used for experiments for 2-28 hours later. Spiking properties do not change appreciably over this period and nor do neurites develop based on storage at room temperature, omission of laminin from coverslips, and the growth factor-free culture medium used.
Coverslips with cultured cells were transferred to a recording chamber constantly perfused with room temperature, oxygenated (95% O 2 and 5% CO 2 ) artificial cerebral spinal fluid containing (in mM) 126 NaCl, 2.5 KCl, 2 CaCl 2 , 2 MgCl 2 , 10 D-glucose, 26 NaHCO 3 , 1.25 NaH 2 PO 4 . Cells were recorded in the whole-cell configuration with >70% series resistance compensation using an Axopatch 200B amplifier (Molecular Devices; Palo Alto, CA). Electrodes (2-5 MO) were filled with a recording solution containing (in mM) 125 KMeSO 4 , 5 KCl, 10 HEPES, 2 MgCl 2 , 4 ATP, 0.4 GTP as well as 0.1% Lucifer Yellow; pH was adjusted to 7.2 with KOH and osmolality was between 270 and 290 mosmol/L. For experiments on the contribution of ANO-1 channels, KMeSO 4 was reduced to 67 mM and KCl was increased to 63 mM to give E Cl = -20 mV. Data were low-pass filtered at 2 KHz, digitized at 20 KHz using a CED 1401 computer interface (Cambridge Electronic Design, Cambridge, UK), and analyzed offline. Virtual GABA conductance was applied via dynamic clamp using Signal 5 software (CED). The virtual conductance was modeled as a step or as a synaptic waveform described by Eqn. 6. To express the virtual conductance as a density and thus exclude direct effects of cell size, we normalized absolute conductance values by membrane capacitance C because C is proportional to the surface area of the cell. Capacitance was measured for each cell based on responses to small (50 pA) hyperpolarizing current steps, where C = τ membrane / R in . To increase cellular excitability in neurons from naïve animals, potassium channels were blocked with bath applied 4-aminopyridine (4-AP). In a subset of experiments with 4-AP, a virtual voltagedependent sodium conductance was also inserted via dynamic clamp using the equations and parameters reported by Ratté et al. [45]. Neurons from nerve-injured animals are already hyperexcitable and were not, therefore, subject to manipulations (i.e. 4-AP or virtual sodium conductance) intended to increase excitability.
All data and computer code are available from the corresponding author upon request.