A multicompartment model based on available data on lamina I neurons was developed as outlined in the Methods (Fig. 1A). The model neuron was bombarded by synaptic input simulated in a biophysically realistic manner: discrete synaptic events generated inward or outward currents by opening channels in the cell membrane (rather than by simply injecting current) so that synaptic inputs influence the total membrane conductance of the postsynaptic neuron. Simulating synaptic input in this way is crucial for uncovering the role of shunting in firing rate modulation. Three varieties of inhibitory input were tested (Fig. 1B): proportional (to excitation), constant, and feedback. We also tested model neurons with different intrinsic properties (Fig. 1C): basic model containing only fast Na⁺ and delayed rectifier K⁺ channels (i.e. Hodgkin-Huxley or HH channels), tonic-spiking, and single-spiking. Tonic- and single-spiking neurons represent the opposite extremes of physiological cell types in lamina I 54; their responses to somatic injection of constant current are illustrated in Fig. 1C. Using these models, a systematic investigation of the effects of reducing E_anion on firing rate modulation was carried out.

Starting with the basic model neuron, a series of simulations was performed in which the frequency of excitatory synaptic input (f_exc), the frequency of inhibitory synaptic input (f_inh), and E_anion were systematically varied while measuring the frequency of output spiking (f_out). We first posited that both f_exc and f_inh increase with increasingly strong stimulation, and that the increase is proportional though not necessarily equal between excitation and inhibition; the ratio of inhibition to excitation (f_inh/f_exc) is reported as α and was tested at multiple values. Figure 2A shows that reduction of E_anion compromises inhibition's capacity to reduce firing rate. The degree to which firing rate modulation is compromised is most readily understood by comparing the f_out-f_exc curves corresponding to different values of E_anion (colored curves, Fig. 2A) against the f_out0-f_exc curve with no inhibition (i.e. α = 0; black curve, Fig. 2A). A reduction of E_anion to -55 mV completely incapacitated inhibition, as evidenced by the corresponding f_out-f_exc curve (light green) lying very close to the no inhibition curve. Reduction of E_anion to -50 or -45 mV caused paradoxical excitation, as evidenced by the corresponding f_out-f_exc curves (yellow and orange) lying above the no inhibition curve. Even modest reduction of E_anion to -65 or -60 mV caused some disinhibition, as evidenced by the corresponding f_out-f_exc curves (blue and dark green) lying above the curve for E_anion = -70 mV (purple) but below the no inhibition curve. The transition from modest disinhibition to complete disinhibition to paradoxical excitation as E_anion was shifted from -70 mV to -45 mV occurred regardless of the ratio of inhibition to excitation (compare panels showing different values of α in Fig. 2A). The divergence the f_out-f_exc curves was, however, exaggerated as α was increased.

Adding feedback inhibition to proportional inhibition with α = 0.5 had an effect (Fig. 2B) similar to increasing the strength of proportional inhibition (i.e. increasing α in Fig. 2A). In other words, feedback inhibition exaggerated the effects of reducing E_anion, which was manifested on the graphs as increased divergence of the f_out-f_exc curves. Interestingly, the divergence was more exaggerated for large reductions in E_anion (i.e. -45 and -50 mV) compared with small reductions. This is explained by the fact that, when the glycine/GABA_A receptor-mediated input becomes paradoxically excitatory, a positive feedback loop is born, whereas the feedback loop is negative under normal conditions. Positive feedback (i.e. feedback excitation) translates into extreme hyperexcitability.

We then tested the effect of constant inhibition. In contrast to the divergent f_out-f_exc curves seen for proportional inhibition and for feedback inhibition (which is also "proportional" insofar as the feedback neuron's activation is proportional to the output neuron's activity), constant inhibition caused a more parallel shift in the f_out-f_exc curves (Fig. 2C). The vertical separation of those curves was enhanced by increasing f_inh.

Using proportional inhibition, we repeated simulations in a tonic-spiking model neuron (Fig. 2D) and in a single-spiking model neuron (Fig. 2E). While the slopes of the f_out-f_exc curves for these two models were different from those of the basic model (Fig. 2A), the effects of reducing E_anion were very similar: in the tonic-spiking model, reduction of E_anion to -55 mV caused complete disinhibition, the same as in the basic model; the single-spiking model was more resistant, requiring that E_anion be reduced to around -50 mV before disinhibition becomes complete. These data demonstrate that despite the extreme differences in the intrinsic membrane properties of these cell types, firing rate modulation is altered in qualitatively the same way as E_anion becomes reduced.

Data in Figure 2 thus indicate that the degree of reduction in E_anion correlates with the degree to which inhibitory control of spiking is compromised: small reductions (to -65 or -60 mV) cause modest disinhibition, intermediate reductions (to -55 mV) can cause complete disinhibition (i.e. equivalent to completely removing inhibition), and large reductions (to -50 or -45 mV) cause paradoxical excitation. This correlation remains quantitatively true regardless of the circuit connectivity (feedback vs. proportional inhibition), strength of inhibition (magnitude of α or of f_inh), or intrinsic neuronal properties (tonic- vs. single-spiking). In the more detailed investigation that follows, we focus on proportional inhibition in the basic model but, based on the demonstrations in Figure 2, the results can be reasonably extrapolated to other conditions.

The results above demonstrate that reduction of E_anion significantly compromises inhibitory control of firing rate. But although a reduction in E_anion should logically reduce glycine/GABA_A receptor-mediated hyperpolarization, a change in E_anion should not reduce glycine/GABA_A receptor-mediated shunting. The results, therefore, suggest that shunting plays a relatively minor role in the modulation of firing rate, compared with the dominant role of hyperpolarization. This result was unexpected given previous reports on the importance of shunting [e.g. 5556] and therefore required further investigation.

The lack of effect of shunting on firing rate contrasts its known effect on depolarization. To investigate in isolation how shunting modulates depolarization, we modified the basic model by removing HH channels, thereby preventing the model neuron from spiking and allowing us to quantify the underlying depolarization. Figure 3 shows that whereas the depol-f_exc curves for E_anion = -45 and -50 mV lay above the curve for no inhibition at low values of f_exc, they bent downwards at higher values of f_exc so that they eventually lay below the curve for no inhibition (arrow in Fig. 3). This sublinearity in the depol-f_exc curves (i.e. downward bend with increasing input) is precisely what one would expect from shunting, where increasingly more excitatory input is shunted through open glycine/GABA_A channels as excitation increases. These results thereby demonstrate that glycine/GABA_A receptor-mediated shunting remains intact despite reduction of E_anion. As expected, the sublinearity attributable to shunting was absent when there was no inhibition (black depol-f_exc curve in Fig. 3 is linear).

But whereas the effects of shunting are clearly evident in the depol-f_exc curves of Figure 3, they are absent from the f_out-f_exc curves of Figure 2 (i.e. the f_out-f_exc curves with inhibition are only slightly sublinear). If excitatory input drives depolarization, and depolarization drives spiking, then one should look at the relationship between depolarization and firing rate in order to identify why shunting's capacity to modulate firing rate is lost. To do this, we plotted firing rate (f_out) against depolarization (Fig. 4A) rather than against f_exc (as had been down in Fig. 2). Specifically, we plotted f_out generated by a certain value of f_exc (based on simulations in the model neuron with HH channels) against depolarization generated by the same value of f_exc (based on simulations without HH channels).

Figure 4A reveals a rather counterintuitive observation that, for the same amount of depolarization, significantly faster spiking was generated in the presence of synaptic inhibition than in its absence. This was true regardless of the value of E_anion and became more evident as depolarization increased (see below). The most likely explanation for this is modulation of the membrane time constant (τ_membrane), since τ_membrane becomes shorter as membrane conductance increases (Fig. 4B). To test this, we increased the passive leak conductance in the model neuron to reduce τ_membrane by half (open circle on Fig 4B); like inhibitory synaptic input, increasing the passive leak conductance caused f_out to increase (dashed curve on Fig. 4A) compared with the original model neuron (solid black curve). Why does shortening τ_membrane lead to faster spiking? When the model neuron was shunted and therefore had a short τ_membrane, its power spectrum exhibited higher power at all but the lowest frequencies (blue curve in Fig. 4C) compared with the power spectrum for the unshunted neuron with a longer τ_membrane (black curve). The most important consequence of this reduced filtering of high frequencies is illustrated in the inset of Figure 4C: reduced filtering allows the membrane to recharge more quickly between spikes so that higher firing rates can be achieved when the neuron is shunted than when it is not shunted.

Therefore, shunting can reduce the depolarization caused by excitatory input (Fig. 3), which reduces firing rate (Fig. 4A), but it also shortens τ_membrane (Fig. 4B), which can increase firing rate (Fig. 4C inset). Both effects occur regardless of the value of E_anion, but their relative importance for firing rate modulation depends on other factors. It is important to recall here that the depol-f_exc curves with inhibition diverge from the depol-f_exc curve without inhibition only when depolarization becomes suprathreshold or, at least, nearly suprathreshold (Fig. 4A). This indicates that that shortening τ_membrane is only consequential for firing rate modulation when depolarization is suprathreshold, whereas we know from Figure 3 that shunting reduces both sub- and suprathreshold depolarization.

We have previously demonstrated that, when average depolarization is suprathreshold, spikes are generated deterministically whereas, when average depolarization is subthreshold, spikes are elicited by noisy, suprathreshold voltage fluctuations and are therefore generated probabilistically 41. The rate of probabilistic spiking is reduced by shunting because, by reducing depolarization, shunting increases the difference between average depolarization and voltage threshold, which in turn reduces the likelihood of voltage fluctuations crossing threshold. If shunting can reduce suprathreshold depolarization so that it becomes subthreshold, deterministic spiking will become probabilistic and its rate will be reduced by shunting according to the above mechanism. If, on the other hand, excitation is sufficiently strong to cause net depolarization that remains suprathreshold despite shunting, spiking will be deterministic. Under those conditions, rather than being limited by the probability of threshold crossing, the interspike interval is limited by the rate of interspike membrane charging which, as demonstrated above, is sensitive to both depolarization and τ_membrane. Shunting reduces depolarization but it also shortens τ_membrane, where each effect has the opposite impact on the rate of membrane charging. Thus, in regard to firing rate modulation, the dual effects of increased membrane conductance counterbalance each other when spiking is deterministic, whereas the inhibitory effect via reduction of depolarization becomes dominant if spiking is probabilistic. This explanation reconciles the observations in Figures 2 and 3: shunting can reduce depolarization while at the same time having little effect on firing rate.

Since shunting becomes ineffective at modulating firing rate when average depolarization is suprathreshold, one can appreciate that by reducing the hyperpolarization caused by glycine/GABA_A receptor-mediated input or, worse yet, causing that input to become depolarizing, a reduction of E_anion can indirectly compromise shunting's capacity to reduce firing rate (Fig. 4D). Thus, both mechanisms through which inhibitory input normally modulates firing rate (i.e. hyperpolarization and shunting) are both susceptible (directly or indirectly) to changes in E_anion. Furthermore, not only are both inhibitory mechanisms compromised by reduction of E_anion, both mechanisms can contribute to paradoxical excitation if the reduction of E_anion is sufficiently large.

We also tested whether the irregularity of inhibitory synaptic input could compromise control of spiking inasmuch as spikes can occur during inhibitory gaps (i.e. between inhibitory synaptic events). This irregularity may be expected to compromise modulation of firing rate by shunting more than it compromises modulation by hyperpolarization since inhibitory gaps are larger in the former case. The difference in size of inhibitory gaps is a direct consequence of the differential time course of inhibitory postsynaptic currents (IPSCs) and inhibitory postsynaptic potentials (IPSPs): IPSPs have a slower time course because of the low pass filtering caused by the membrane time constant, so that whereas slow IPSPs tend to overlap and produce sustained potentials, faster IPSCs (which directly parallel the time course of the synaptic conductance) overlap less and, therefore, shunting is likely to be intermittent (Fig. 5A). Quantitative testing confirmed that gaps between IPSCs close more slowly than gaps between IPSPs as f_inh increases (data not shown). To test whether inhibitory gaps are functionally significant for firing rate modulation, we replaced the intermittent inhibition associated with irregular synaptic input with constant inhibition equal to the time-averaged synaptic input.

Figure 5B demonstrates that switching from intermittent to constant inhibition had virtually no effect on f_out-f_exc curves except at the most negative values of E_anion. On initial examination, this suggests that inhibitory gaps are relatively insignificant for firing rate modulation. On closer examination however, the fact that irregular inhibition produces larger gaps in shunting than in hyperpolarization (see above and Fig. 5A) suggests that the irrelevance of switching from intermittent inhibition to constant inhibition may simply reflect the relative impotency of shunting to reduce spiking when spiking is generated in a deterministic manner (see above and Fig. 4). Following from this point, the observation that regularizing inhibition improved the effectiveness of inhibition for E_anion values of -65 and -70 mV (stars in Fig. 5B) is significant, as those E_anion values correspond to the same conditions under which depolarization remained subthreshold at high f_exc (Fig. 3). If average depolarization remains subthreshold, then spiking is generated in a probabilistic manner and shunting should retain it capacity to reduce firing rate (see above). In short, Figure 5B shows that regularizing inhibition enhances shunting's capacity to reduce spiking when spiking is probabilistic, but not when spiking is deterministic, consistent with conclusions drawn from Figure 4 regarding the conditions under which shunting can or can not modulate spiking.

Reduction of E_anion does not necessarily occur in isolation. The possibility of compensatory changes complicates the conclusion that disinhibition necessarily follows from reduction of E_anion. Two separate studies suggest that GABA_A transmission may increase following neuropathy 3157. We therefore investigated whether disinhibition develops if reduction of E_anion is coupled with compensatory increases in GABA/glycine transmission.

Under normal conditions with E_anion = -70 mV, even modest amounts of inhibition (e.g. α = 0.5) can reduce firing rate (Fig. 6A, dotted curve). The decrease in firing rate can be quantified by taking the ratio of the response with inhibition to the response without inhibition (f_out/f_out0). The f_out/f_out0 ratio is ~0.6 for α = 0.5, but larger values of α result in greater reduction of that ratio (Fig. 6A, dashed and solid curves). For purposes of illustration, we estimate inhibition conservatively (α = 0.5) and, by extension, consider f_out/f_out0 > 0.6 to represent disinhibition. If E_anion were to decrease to -60 mV, inhibition with α = 0.5 would be incapable of reducing f_out/f_out0 to 0.6 (Fig. 6B, dotted curve), meaning disinhibition would occur under those conditions. But if α was increased to 1.2, the f_out/f_out0 ratio would be returned to 0.6 (Fig. 6B, blue curve). Assuming the network has the capacity to at least double α, this demonstrates that moderate reductions in E_anion cause compensable disinhibition; in other words, the disinhibition that could potentially result from reduction of E_anion can be compensated for by shifting the balance between excitatory and inhibitory input. However, if E_anion were to decrease to -55 mV, even increasing α to 2 could not reduce f_out/f_out0 to 0.6 (Fig. 6C), demonstrating that disinhibition becomes incompensable if reduction of E_anion becomes large. In fact, an increase in α may not only fail to reduce f_out/f_out0 sufficiently (as in Fig. 6C), but may even paradoxically increase f_out/f_out0 as in the case with E_anion = -50 mV (Fig. 6D), resulting in paradoxical excitation. It is interesting to note that paradoxical excitation can occur for values of E_anion below spike threshold, which is approximately -49 mV in the model neuron tested here.

Effects of E_anion on the f_out/f_out0 ratio are summarized in Figure 6E. f_out/f_out0 > 0.6 represents disinhibition based on the conservative estimate of α = 0.5 prior to any compensation, while f_out/f_out0 > 1 represents paradoxical excitation. The relationship between α and the critical value of E_anion beyond which net disinhibition necessarily develops (pink curve on Fig. 6E) shows a ceiling effect wherein increases in α, no matter how large, can not compensate for reductions in E_anion beyond a certain level. For example, assuming α could increase as high as 4, disinhibition would still develop at E_anion ≈ -54 mV (arrowhead in Fig. 6E). Stricter limitation on the increase in α would result in disinhibition occurring for even smaller reductions in E_anion.

In a system capable of compensation, reduction of E_anion does not produce disinhibition until the system decompensates; decompensation occurs when reductions in E_anion outstrip compensatory changes. But although compensatory changes may prevent decompensation from occurring until a large reduction of E_anion has developed, Figure 6F shows that in a system relying on strong compensation (e.g. α = 4 to maintain an f_out/f_out0 ratio of 0.6), small changes in E_anion may cause large changes in the f_out/f_out0 ratio; in other words, decompensation occurs abruptly, which reflects instability within the system. This is evident from the steepness of the f_out/f_out0-E_anion curve where it passes through f_out/f_out0 = 0.6 (long-dashed curve in Fig. 6F). A system relying on less compensation (e.g. α = 1) may decompensate at a lower value of E_anion, but will do so gradually (dot-dashed curve in Fig. 6F), indicating that the system is more stable. Understanding the abruptness of decompensation may help guide therapeutic intervention insofar as it is preferable to reestablish a robust balance between excitation and inhibition rather than an unstable one (see below).

Pathophysiologic changes associated with neuropathic pain also occur outside lamina I. How do those changes influence activity in lamina I neurons? We have heretofore assumed a constant relationship between the strength of peripheral stimulation and the strength of synaptic input to lamina I. As a postsynaptic mechanism, disinhibition resulting from reduced E_anion within lamina I neurons does not affect that relationship; on the other hand, presynaptic mechanisms including peripheral sensitization and presynaptic inhibition do (Fig. 7A): peripheral sensitization steepens that relationship by increasing the frequency of excitatory input elicited by a given stimulus, while presynaptic inhibition reduces the amplitude of individual synaptic events. The distinction between modulation of event frequency and event amplitude is irrelevant for this discussion, insofar as cumulative synaptic excitation (in Siemens per second) equals amplitude per input (in Siemens per event) multiplied by event frequency (in events per second); in short, peripheral sensitization increases cumulative synaptic excitation whereas presynaptic inhibition decreases it. Following the simple logic outlined in Figure 7B, the relationship between f_out and synaptic excitation (which for all intents and purposes is equivalent to the f_out-f_exc relationship) can be combined with the relationship between synaptic excitation and strength of peripheral stimulation to determine the relationship between f_out and strength of peripheral stimulation. Figure 7C illustrates how peripheral sensitization and presynaptic inhibition influence the relationship between f_out and peripheral stimulation; note that the relationship between f_out and synaptic excitation remains unchanged. If the f_out/f_out0 ratio is calculated using f_out from the test condition and f_out0 from the control condition, then the effects of peripheral sensitization and presynaptic inhibition can be visualized as leftward or rightward shifts, respectively, in the relationship between f_out/f_out0 and E_anion (Fig. 7D). Thus, whereas peripheral sensitization will exacerbate the effects of postsynaptic disinhibition, presynaptic inhibition will mitigate the effects. Beyond that, reduced pre- or postsynaptic inhibition within polysynaptic pathways may uncover low threshold input to lamina I neurons 53, which would also alter the relationship between the strength of peripheral stimulation and synaptic input.

It seems logical that if a reduction in E_anion has compromised the strength of inhibition, interventions aimed at reestablishing inhibition's strength would be beneficial for correcting disinhibition. Ideally one would target the primary pathophysiologic cause (e.g. KCC2 expression or its direct effects on chloride extrusion from inside the cell, or upstream events including microglial activation and BDNF release 3142) but with no clinically available drugs to do this, other targets must be considered. For example, the strength and kinetics of GABA_A receptor-mediated input can be modulated by benzodiazepines. We therefore investigated the effects of doubling the strength (w) and τ_decay of GABAergic inputs; parameters of glycinergic input were left unchanged. Figure 8A shows that augmenting individual GABAergic inputs mimics the effects of increasing α (compare with Fig. 6F): it delayed decompensation from occurring until higher values of E_anion, but it did so by steepening the curve relating f_out/f_out0 and E_anion. As explained above, this steepening means that although the intervention may rebalance the system at a normal f_out/f_out0 ratio, that balance is liable to be disturbed by even small changes in E_anion; in other words, the system becomes increasingly unstable. Increasing GABAergic transmission also risks exacerbating paradoxical excitation if reduction of E_anion is particularly large. Furthermore, although endogenous compensation may be expected to occur specifically in neurons affected by changes in E_anion, a drug would not show the same specificity, suggesting the f_out/f_out0 ratio would be inadvertently reduced below 0.6 in normal cells (e.g. with E_anion = -70 mV) exposed to the drug at the same time that the f_out/f_out0 ratio is potentially normalized in affected cells (e.g. with E_anion = -55 mV). Therefore, although a disinhibitory mechanism intuitively suggests that inhibition should be augmented in order to offset the disinhibition, results here suggest that augmenting GABA_A receptor-mediated input (or, similarly, glycine receptor-mediated input) may be unwise when disinhibition occurs through reduction of E_anion. In contrast, disinhibition occurring through a different mechanism (e.g. reduced expression or function of GABA_A or glycine receptors) could be successfully corrected by augmenting inhibition (see Discussion).

Although increasing inhibition ultimately fails to prevent decompensation if the reduction in E_anion grows too large, and at best reestablishes a normal f_out/f_out0 ratio that is easily disrupted, interventions that do not target inhibition are likely to be more robust. NMDA receptors are a common pharmacological target whose blockade can reduce neuropathic pain 58. Figure 8B illustrates that blocking NMDA receptors did not alter the slope of the curve (and thus the stability of the system) and instead caused a uniform reduction in the f_out/f_out0 ratio, which is similar to the effect of presynaptic changes described in Figure 7. Furthermore, reducing excitatory input did not risk exacerbating paradoxical excitation. The magnitude of effects of NMDA antagonism depends on the contribution of NMDA receptor-mediated excitation relative to AMPA receptor-mediated excitation, which is relatively small for conditions tested here (see Methods) but may increase under neuropathic conditions 59. In any case, reducing AMPA receptor-mediated excitation had a similar effect (see below). Reducing sodium channel density, which functionally mimics the postsynaptic effects of local anesthetics and many anti-epileptic medications 60, also resulted in modulation very similar to that described above for NMDA antagonism (data not shown). Insertion of a potassium conductance such as might be activated by opioids 61 also had a similar effect (data not shown). All in all, reducing excitatory input and/or reducing intrinsic neuronal excitability reduces the f_out/f_out0 ratio uniformly across a broad range of E_anion. Combining any of these manipulations with augmentation of inhibition had purely additive effects (Fig. 8C) rather than acting synergistically.

Based on the observation that it may be counterproductive to try to replace inhibition when disinhibition occurs through reduction of E_anion, we explored whether it would be preferable to block inhibitory input altogether and balance the resulting disinhibition with reduction of excitatory input (Fig. 8D). The rationale is that although, on its own, blocking glycine/GABA_A receptor-mediated input would increase the f_out/f_out0 ratio to 1, the appropriate reduction in excitatory input and/or intrinsic excitability could return the ratio to around 0.6 (Fig. 8D, right panel). The benefit of deliberately switching the disinhibitory mechanism (i.e. from reduction of E_anion to blockade of glycine/GABA_A receptors) is that blocking glycine/GABA_A receptor-mediated input would uniformly adjust the f_out/f_out0 ratio to 1, thereby trivializing the variability of E_anion and α between affected and unaffected neurons. Moreover, blocking inhibition would prevent inhibitory input from causing paradoxical excitation in the event that reduction of E_anion was particularly large. One significant requirement is that the distribution and kinetics of the drugs affecting inhibitory and excitatory transmission are similar in order to avoid spatial or temporal mismatches between the two effects. Even if this approach may not be feasible in practice, it illustrates that increasing glycine/GABA_A receptor-mediated input may be counterproductive in certain neuropathic conditions and that alternative approaches, possibly involving non-intuitive drug combinations, deserve consideration.

Glycine and GABA_A receptor-mediated inputs are often thought to act via shunting rather than through hyperpolarization given their large conductance and relatively small driving force. Consequently, even depolarizing glycine/GABA_A receptor-mediated input can have a net inhibitory effect on spike generation by shunting concurrent excitatory input 3839. In the current study, we found that shunting was far less significant than hyperpolarization when it comes to modulation of repetitive spiking. This results from increased membrane conductance having opposing effects: it reduces depolarization by shunting excitatory input (thereby decreasing firing rate) but simultaneously shortens the membrane time constant (thereby increasing firing rate). In terms of firing rate modulation, the first effect predominates when average depolarization is subthreshold and spiking is driven by suprathreshold voltage fluctuations (i.e. probabilistic spiking) but the two effects offset each other when average depolarization is suprathreshold (i.e. deterministic spiking). Shunting therefore becomes ineffective at reducing firing rate when depolarization is suprathreshold, which is especially likely to occur when reduction of E_anion renders glycine/GABA_A receptor-mediated input less hyperpolarizing or, worse yet, depolarizing. Kuhn et al. 62 have previously described how firing rate modulation is complicated by the dual effects of membrane conductance, noting that average depolarization was reduced by shunting while voltage fluctuations became larger because of the reduced filtering associated with a shortened membrane time constant. Their result applies to probabilistic spiking whereas the effect that we have described applies to deterministic spiking and, in that sense, is distinct.

A recent modeling study that investigated the effects of changes in E_anion on firing rate modulation in a neocortical pyramidal neuron 63 concluded that, because of shunting, GABA remained inhibitory despite changes in E_anion. That would appear to contradict our conclusion that shunting fails in the face of large, but physiologically plausible (as reported in Coull et al. 31), reductions in E_anion. However, Morita et al. tested only two values of E_anion. According to our evaluation of the phase-planes shown in Figure 4C of their paper, a Hopf bifurcation would not have prevented repetitive spiking if a slightly lower value of E_anion had been tested. There is therefore no discrepancy between our studies but, simply, a difference in the range of E_anion tested.

Given this new understanding of the biophysical mechanisms, we can predict whether the disinhibition caused by reduction of E_anion can account for the hyperexcitability that is presumably responsible for the allodynia and hyperalgesia associated with neuropathic pain. We estimate that decompensation would start occurring at E_anion ≈ -58 mV (see Fig. 6) assuming that, as compensation, the ratio of inhibitory to excitatory input quadruples relative to the ratio under normal conditions (i.e. α increases from 0.5 to 2). Weaker compensation (α increases to only 1) would result in decompensation starting at E_anion ≈ -61 mV, whereas stronger compensation (α increases as high as 4) would prevent decompensation until E_anion ≈ -54 mV. All of those estimates conservatively assume α = 0.5 under normal conditions (see Results).

Variations in compensation may explain why, with acute manipulations including intrathecal application of BDNF and activated microglia, reduction in E_anion to around -62 mV caused almost an equivalent decrease in withdrawal threshold as that associated with reduction of E_anion to -49 mV following peripheral nerve injury 42: compensation that could have developed in the latter case, may not have had time to develop in the former case; it is also possible, however, that BDNF has other effects 64 that are unaccounted for in this argument. Additionally, we have not taken into account activity-dependent reduction of the chloride gradient 65666768, meaning a much smaller long-term reduction of E_anion (i.e. caused by reduced KCC2 expression) may cause incompensable disinhibition once dynamic, short-term reductions of E_anion (i.e. caused by activity-dependent reduction of the chloride gradient) are taken into account. Activity-dependent potassium accumulation is another fast mechanism that may exacerbate reduction of E_anion leading to incompensable disinhibition 6970. In any case, given that E_anion reduces on average to -49 mV following peripheral nerve injury 31, the disinhibition that results is most likely incompensable; indeed, the observation that ~20% of lamina I neurons were paradoxically excited by GABA under those conditions 31 suggests that an even larger fraction were incompensably disinhibited (given that disinhibition requires less reduction in E_anion than paradoxical excitation).

Regardless of the precise value of E_anion at which it occurs, incompensable disinhibition approximates the conditions of pharmacologically reduced inhibition, which previous work has shown to be sufficient to produce allodynia and hyperalgesia 91011121314151617. It logically follows that incompensable disinhibition resulting from reduced E_anion is sufficient to explain the exaggerated pain perception associated with neuropathic pain. We could not reach that conclusion if disinhibition were compensable (i.e. if compensatory mechanisms could successfully prevent disinhibition) because, in that case, even if the reduction in E_anion could cause allodynia and hyperalgesia, whether or not it did would depend on the success or failure of compensation. Notably, the argument that incompensable disinhibition is sufficient to explain allodynia and hyperalgesia does not exclude other mechanisms from contributing to the aberrant perception; for example, Figure 7 illustrates how peripheral sensitization can exacerbate the hyperexcitability caused by postsynaptic disinhibition. Furthermore, under conditions in which a modest reduction of E_anion occurs, such that some inhibitory capacity remains (e.g. with E_anion <-55 mV), a decrease in GABAergic or glycinergic transmission (either transmitter release or receptor function; see below) would contribute to the disinhibition caused by reduction of E_anion.

Although there is general consensus that disinhibition occurs following neuropathy, the mechanism underlying disinhibition has been controversial. Studies have reported that the number of inhibitory neurons in the spinal dorsal horn decreases following peripheral nerve injury 24262728, but more recent work has argued against this 343536. Other studies have reported a reduction of presynaptic GABA, implicating the GABA transporter GAT1 32 and the GABA synthesizing enzyme GAD65 30, but again this has been contradicted by the demonstration of no change in synaptosomal glycine or GABA 33. In fact, Kontinen et al. 57 reported that GABAergic transmission was increased following neuropathy, presumably as a compensatory change, which would be consistent with the increased GABA contribution to background input to lamina I neurons reported by Coull et al. 31. Disinhibition through reduction of E_anion does not involve reduced glycinergic or GABAergic transmission but instead works at a downstream locus and controls the potency of inhibitory input. Ironically, although the system has built-in redundancy, inasmuch as it uses both glycine and GABA as fast inhibitory neurotransmitters 717273, the reduction in E_anion subverts both glycine and GABA_A receptor-mediated inhibition because of the receptors' common reliance on the transmembrane chloride gradient. This contrasts the mechanism responsible for disinhibition in inflammatory pain, where prostaglandin E2-induced phosphorylation of the glycine receptor decreases glycinergic transmission 7475 without affecting GABAergic transmission. Under those conditions, increased GABAergic transmission can compensate for decreased glycinergic transmission 76.

In addition to reducing E_anion via decreased KCC2 expression, neuropathy leads to other pathophysiologic changes in lamina I and elsewhere in the pain pathway that undoubtedly contribute to the aberrant perception associated with neuropathic pain 13777879. But whereas most other changes perturb a neuron's input-output relationship directly, disinhibition acts indirectly by perturbing a modulatory process. Glycine and GABA_A receptor-mediated inhibition are crucial mechanisms for the endogenous modulation of pain 8081, controlling the inflow of Aδ and C fiber-mediated inputs at the segmental level 325382838485 as well as participating in descending modulation originating from the periaqueductal gray and nucleus raphe magnus 86878889. These control mechanisms are seriously compromised by reduction of E_anion. Disinhibition therefore equates with modulation of a modulatory process, or meta-modulation, and represents a higher order change that not only perturbs the system, but simultaneously compromises the control mechanisms that would otherwise correct that perturbation. This may contribute to the relative intractability of neuropathic pain compared with other types of pain. The ideal therapy would target the primary pathological change and return E_anion to its normal value; this would not only reestablish a normal input-output relationship within the system, but would also restore the system's full capacity to control the input-output relationship. No such therapy currently exists.

The mechanism underlying disinhibition does, nonetheless, have significant implications for reestablishing inhibition through therapeutic interventions. Specifically, disinhibition through reduction of E_anion means increasing glycinergic and/or GABAergic transmission may be inconsequential, and potentially even detrimental, depending on the degree of change in E_anion. However, several studies have reported that allodynia was reduced by applying GABA_A receptor agonists 172022 or by transplantation of GABA-producing cells into the lumbar subarachnoid space 19. This could be explained by an increase in presynaptic inhibition, since primary afferent terminals do not express KCC2 and are therefore not prone to disinhibition by reduced KCC2 expression 31. However, the efficacy of increasing GABAergic transmission is controversial: Stubley et al. 21 reported that transplanted-GABA producing cell could prevent allodynia if transplanted early after nerve injury but could not reverse allodynia once it was established, other studies have reported failure of GABA_A agonists to relieve neuropathic pain after ischemic spinal cord injury 9091. These inconsistencies may be attributable to variation in the model of neuropathic pain, but that implicitly assumes that the underlying mechanisms are qualitatively different depending on the model. The present study suggests that variation can also be explained by quantitative differences in the degree of E_anion reduction, i.e. whether the system was fully decompensated or whether residual inhibitory capacity remained.

Several authors have advocated the benefits of optimizing the treatment of neuropathic pain by choosing treatments targeted towards mechanisms implicated in the pathogenesis of that pain 9293949596. This study has approached the topic of mechanism-based therapies using quantitative modeling (see Fig. 8). By being quantitative, our results highlight how choosing the optimal therapy might not depend solely on what pathogenic mechanism is involved, but on the degree of change that has occurred, e.g. whether the system would benefit from augmenting inhibition depends on how much E_anion is reduced. This may explain the variable efficacy of treatments amongst patients who are suffering from the same neuropathic pain syndrome, where the underlying mechanism is presumably the same but in whom reduction of E_anion may vary.