Using dynamic clamp to quantify pathological changes in the excitability of primary somatosensory neurons

Key points Primary somatosensory neurons normally respond to somatic depolarization with transient spiking but can switch to repetitive spiking under pathological conditions. This switch in spiking pattern reflects a qualitative change in spike initiation dynamics and contributes to the hyperexcitability associated with chronic pain. Neurons can be converted to repetitive spiking by adding a virtual conductance using dynamic clamp. By titrating the conductance to determine how much must be added to cause repetitive spiking, we found that small cells are more susceptible to switching (i.e. required less added conductance) than medium–large cells. By measuring how much less conductance is required to cause repetitive spiking when dynamic clamp was combined with other pathomimetic manipulations (e.g. application of inflammatory mediators), we measured how much each manipulation facilitated repetitive spiking. Our results suggest that many pathological factors facilitate repetitive spiking but that the switch to repetitive spiking requires the cumulative effect of many co‐occurring factors. Abstract Primary somatosensory neurons become hyperexcitable in many chronic pain conditions. Hyperexcitability can include a switch from transient to repetitive spiking during sustained somatic depolarization. This switch results from diverse pathological processes that impact ion channel expression or function. Because multiple pathological processes co‐occur, isolating how much each contributes to switching the spiking pattern is difficult. Our approach to this challenge involves adding a virtual sodium conductance via dynamic clamp. The magnitude of that conductance was titrated to determine the minimum required to enable rheobasic stimulation to evoke repetitive spiking. The minimum required conductance, termed g¯ Na ∗, was re‐measured before and during manipulations designed to model various pathological processes in vitro. The reduction in g¯ Na ∗ caused by each pathomimetic manipulation reflects how much the modelled process contributes to switching the spiking pattern. We found that elevating extracellular potassium or applying inflammatory mediators reduced g¯ Na ∗ whereas direct hyperpolarization had no effect. Inflammatory mediators reduced g¯ Na ∗ more in medium–large (>30 μm diameter) neurons than in small (⩽30 μm diameter) neurons, but had equivalent effects in cutaneous and muscle afferents. The repetitive spiking induced by dynamic clamp was also found to differ between small and medium–large neurons, thus revealing latent differences in adaptation. Our study demonstrates a novel way to determine to what extent individual pathological factors facilitate repetitive spiking. Our results suggest that most factors facilitate but do not cause repetitive spiking on their own, and, therefore, that a switch to repetitive spiking results from the cumulative effect of many co‐occurring factors.


Introduction
Neurons use action potentials, or spikes, to transmit information. Spike generation depends on neuronal excitability. If excitability is misregulated, neurons may produce too many or too few spikes in response to input, thus compromising the encoding of that input. Primary afferent neurons, which relay somatosensory information from the periphery (e.g. skin and muscle) to the central nervous system, can become hyperexcitable in chronic pain conditions (Devor, 2005). In fact, primary afferent hyperexcitability is necessary and sufficient to explain the hypersensitivity and spontaneous pain associated with many chronic pain conditions (Gracely et al. 1992;Gold & Gebhart, 2010;Shankarappa et al. 2012;Vaso et al. 2014). One of the more dramatic manifestations of cellular hyperexcitability is a switch in spiking pattern during sustained somatic depolarization (Xing et al. 2001;Liu et al. 2002;Fan et al. 2011;Ratté et al. 2014). The switch from transient to repetitive spiking reflects a qualitative change in spike initiation dynamics (Rho & Prescott, 2012). This switch not only dramatically amplifies evoked spiking, it also enables spontaneous spiking insofar as spontaneous spiking requires a depolarizing shift in resting membrane potential and the capacity to spike repetitively when depolarized. Understanding the transition from transient to repetitive spiking is thus an important goal.
Because inflammation and nerve injury trigger many molecular changes that influence excitability, ascribing a shift in excitability to a particular molecular change requires that one account for co-occurring molecular changes. An alternative for establishing such links is to experimentally reproduce a molecular change in isolation, for example, by blocking a specific ion channel pharmacologically or enhancing it via dynamic clamp, an electrophysiological technique whereby virtual conductances can be introduced into real neurons (Robinson & Kawai, 1993;Sharp et al. 1993). Using dynamic clamp, one can titrate the virtual conductance to determine how much of it must be added to a neuron to make it spike repetitively (Ratté et al. 2014). This sort of testing not only provides valuable insight into how the virtual conductance affects excitability, it can also be used to investigate the susceptibility of different neurons to switch their spiking pattern and whether that susceptibility is affected by changes in native ion channels (see below). In other words, one can (i) study the effects of the added conductance or (ii) use the effects of the added conductance to study other factors that affect spiking pattern. We focus here on the latter.
Excitability can be measured in many ways. Each metric should ideally provide independent information, but this is not always true in practice. For instance, if inflammation depolarizes a neuron, the current required to evoke spiking -rheobase -will be reduced. For rheobase to provide information independent from voltage measurements, the confounding change in voltage must be controlled when measuring rheobase. With that in mind, we controlled for changes in resting membrane potential and rheobase when measuring the minimum virtual sodium conductance required to cause repetitive spiking, henceforth referred to asḡ * Na . Changes inḡ * Na were observed despite those controls (see Results), consistent with the minimum virtual conductance required to switch the spiking pattern (i.e.ḡ * Na ) being fundamentally different from the current required to evoke spiking (i.e. rheobase).
In the present study, we have monitored (and reported) changes in resting membrane potential, rheobase and other membrane properties, but our goal was to quantify how much specific pathological conditions facilitate the switch to repetitive spiking. We demonstrate here how dynamic clamp can be combined with manipulations designed to model specific pathological conditions in vitro in order to quantify the effect of those conditions on spiking pattern (see Methods). Our approach involves asking how much less virtual conductance must be added to a neuron to switch its spiking pattern when the virtual conductance is added in conjunction with a pathomimetic manipulation; in other words, how much a certain condition (or factor) facilitates repetitive spiking is revealed by how much it reducesḡ * Na . Using this approach, we quantified how much elevated extracellular potassium and inflammatory mediators -two factors associated with chronic pain conditions (Marchand et al. 2005;Devor, 2006;Gold & Gebhart, 2010;Amaya et al. 2013) -reducedḡ * Na and whether the reduction varied between different types of primary somatosensory neurons. Whereas both of those manipulations reducedḡ * Na , direct neuronal hyperpolarization did not affectḡ * Na despite increasing rheobase. Thus,ḡ * Na does not duplicate traditional excitability metrics but, instead, reflects how far from its tipping point a neuron normally operates. Our results suggest that individual pathological factors facilitate but do not cause a switch in spiking pattern (i.e. they push the neuron toward but not across its tipping point), which suggests that a switch to repetitive spiking typically results from the cumulative effect of multiple co-occurring factors rather than because of any single factor.

Ethical approval
All procedures were approved by the Animal Care Committee at The Hospital for Sick Children and were conducted in accordance with guidelines from the Canadian Council on Animal Care. The authors understand the ethical principles under which The Journal of Physiology operates and ensure full compliance with the guidelines for the ethical use of animals, as described by Grundy (2015).

Animals
Adult (150-250 g) male Sprague-Dawley rats (Charles River, Sherbrooke, Canada) were used for all experiments. Rats were housed under standard conditions in a 12 h light/dark cycle and were provided food and water ad libitum.

Retrograde labelling of cutaneous or muscle afferent neurons
Retrograde labelling was used to target in vitro those neurons that innervate a particular tissue in vivo. To identify neurons innervating the glabrous skin of the hind paw, the fluorescent dye di-alkyl indocarbocyanine (DiI; Sigma-Aldrich, Oakville, ON, Canada) was injected into the glabrous skin. Details of DiI labelling have been previously described (Gold & Traub, 2004). Briefly, DiI (3.4 mg) was prepared in a solution of 20 μl dimethyl sulphoxide (DMSO; Amresco, Mississauga, ON, Canada), which was diluted to a 1:10 solution in 0.9% sterile saline. Under isoflurane anaesthesia (4% induction, 2.5% maintenance), 10 μl of DiI solution was injected intradermally into five sites (2 μl per site) on the plantar surface of the hind paw. Alternatively, to label afferents innervating muscle, 10 μl of DiI solution was injected into five sites of the gastrocnemius muscle. To exclude unintended labelling of cutaneous afferents along the needle track, 10 μl of Fast Blue (1% in sterile saline) was injected intradermally around the intramuscular injection site. Animals were monitored for signs of inflammation or behavioural abnormalities for 10-20 days post-injection, but none required analgesia or other interventions. After 10-20 days, DiI-labelled somata were identified in acute dorsal root ganglion (DRG) cultures by epifluorescent imaging of DiI using Zeiss filter set 43. Absence of Fast Blue labelling was confirmed for muscle afferents using Zeiss filter set 02.

Recordings and data acquisition
For patch clamp recordings, coverslips were transferred to a recording chamber perfused at 2 ml min −1 with artificial cerebral spinal fluid (ACSF) consisting of (in mM): 126 NaCl, 2.5 KCl, 2 CaCl 2 , 2 MgCl 2 , 10 D-glucose, 26 NaHCO 3 , and 1.25 NaH 2 PO 4 ; pH = 7.4, osmolality = 300 mosmol kg −1 , and bubbled continuously with carbogen (95% O 2 -5% CO 2 ). To cause a depolarizing shift in equilibrium potential for potassium (E K ) in certain experiments, KCl was increased to 5.5 mM, and NaCl was decreased to 123 mM to maintain solution osmolarity. To reproduce the effects of acute inflammation, the inflammatory mediators histamine, bradykinin and prostaglandin E 2 (PGE 2 ) were added to ACSF to a final concentration of 10 μM each (Ma et al. 2006). All salts were obtained from Caledon Laboratories and inflammatory mediators were obtained from Sigma-Aldrich.
The somatic diameter of DiI-labelled neurons was measured using an ocular graticule under gradient contrast optics using a AxioExaminer microscope (Zeiss, North York, ON, Canada) fitted with a 40× /0.75 NA water immersion objective. DiI-labelled DRG neurons were patched using a 5 M micropipette containing an internal solution composed of (in mM): 125 KMeSO 4 , 5 KCl, 10 HEPES, 2 MgCl 2 , 4 adenosine triphosphate (ATP), 0.4 guanosine triphosphate (GTP), and included 0.1% Lucifer Yellow; pH adjusted to 7.2 with KOH, osmolality = 290 mosmol kg −1 . Whole-cell patch clamp recordings were acquired using an Axopatch 200B amplifier (Molecular Devices, Sunnyvale, CA, USA) with >70% series resistance compensation. Data were low-pass filtered at 2 kHz and digitized at 20 kHz using a CED 1401 computer interface and CED Signal 5 software (Cambridge Electronic Design, Cambridge, UK). All recordings were made at room temperature (22-24°C) unless otherwise noted.
Throughout each protocol, current injection was continuously applied to adjust the membrane potential (V m ) to -65 mV except when measuring the resting V m . Stimulating current (I stim ) was applied as 0.5 s-long steps to measure the membrane time constant (τ m ), input resistance (R in ), and rheobase of each neuron. A small (50 pA) hyperpolarizing current step was used to determine τ m from a single exponential curve fit, and to calculate R in from the change in membrane potential (R in = V m /I stim ). Rheobase was determined as the minimum depolarizing current required to elicit an action potential. The membrane capacitance (C m ) was calculated from τ m and R in (C m = τ m /R in ). All values of voltage were corrected for a -9 mV liquid junction potential.
Two second-long current steps were used to probe spiking pattern. Repetitive spiking was defined as a response of consistently more than one spike across repeated trials at a given I stim intensity; in practice, repetitive spiking was identified as more than three spikes on a single trial because, according to preliminary testing, this always translated into more than one spike during repeated testing with the same I stim intensity (but repeated testing was not feasible when covarying I stim andḡ Na under multiple conditions). Transient spiking typically comprised a single spike at stimulus onset but, when a neuron was near its tipping point, sometimes included an additional one or two inconsistent spikes (see above). Spiking pattern can be determined across a range of stimulus intensities but the transition from transient to repetitive spiking was always determined at rheobase, and subtypes of repetitive spiking (namely phasic or tonic) were also determined at rheobase. Requiring consistently more than one spike to designate the spiking pattern as "repetitive" ensured that we did not underestimateḡ * Na (see below). When testing with I stim steps, transient spiking reflects spike initiation through a quasi-separatrix crossing whereas repetitive spiking reflects spike initiation through a Hopf bifurcation according non-linear dynamical analysis (Prescott et al. 2008;Rho & Prescott, 2012). Notably, a "transient spiking" neuron may spike repetitively during I stim ramps (Ratté et al. 2015), which illustrates the importance of the stimulus protocol. I stim current steps are commonly employed in primary afferent studies and can distinguish between spike initiation mechanisms (see above), and thus satisfy our needs.

Inserting virtual Na V 1.3-like conductance using dynamic clamp
A virtual Na + conductance (g Na ) with activation kinetics based on a Hodgkin-Huxley model was added to patch clamp recordings using a dynamic clamp protocol. Details of the dynamic clamp protocol have been described previously (Ratté et al. 2014). Briefly, g Na was modelled according to: The maximal conductance (ḡ Na ) was adjusted as described below. All other parameters were set as follows: E Na = 50 mV, k α,β = 1.5 m s −1 , V α,β = -15 mV, s α,β = -17 mV. The virtual conductance resembles but was not strictly designed to model Na V 1.3 channels; instead, conductance parameters were identified through an agnostic parameter search in simulations focused on changes in spike initiation mechanism (Rho & Prescott, 2012;Ratté et al. 2014).
To determine the minimumḡ Na required to change the spiking pattern from transient to repetitive spiking, represented asḡ * Na , I stim steps were varied to within 50 pA of rheobase andḡ Na was systematically varied until repetitive spiking was observed in response to I stim . To compareḡ * Na across neurons of different sizes, values of g Na were converted to conductance density by dividing by membrane capacitance (ḡ * Na /C m ). Measurements of g * Na and other membrane properties were conducted in standard ACSF and again during each manipulation (elevated [K + ] o or added inflammatory mediators). To measure how much a pathological factor facilitated repetitive spiking, we comparedḡ * Na in the same neuron before and during each pathomimetic manipulation ( Fig. 1).

Statistical analysis
Data were analysed using SigmaPlot 11.0 software (Systat Software Inc., San Jose, CA, USA). Proportions were compared using a Yate's corrected χ 2 test, a Fisher's exact text for unpaired data or a McNemar's test for paired dichotomous data. Measurements taken from the same cell before and after a manipulation, or at multiple time intervals, were compared using a repeated-measures two-way analysis of variance (ANOVA) with one factor being the manipulation (or time) and the other being classification by somatic diameter. The data from small and medium-large neurons were pooled if no significant interaction was found between cell size and the manipulation, implying that small and medium-large neurons responded equivalently to the manipulation. Post hoc testing was conducted using the Student-Newman-Keuls test. If the underlying distribution was found not to be Gaussian (based on the Lilliefors corrected Kolmogorov-Smirnov test), the Wilcoxon signed-rank test was used to test the effect of each factor. Independent samples were compared using the Student's t test or Mann-Whitney U test. Data are reported as the mean ± SEM for normally distributed data, or as the median and interquartile range for non-normally distributed data. In all studies, statistical significance was defined as P < 0.05.

Results
Unless otherwise stated, we recorded from cutaneous afferents in dissociated DRG cultures identified by retrograde labelling of DiI injected intradermally 10-20 days prior to recording. In one set of experiments, muscle afferents were identified by retrograde labelling of DiI injected intramuscularly and exclusion of Fast Blue injected intradermally. In all cases, soma diameter was used to differentiate small (ࣘ30 μm diameter) and medium-large (>30 μm diameter) neurons, which generally have unmyelinated C fibres and myelinated A fibres, respectively (Harper & Lawson, 1985). Most primary somatosensory neurons respond to sustained somatic current injection (I stim ) with transient spiking but some switch to repetitive spiking under pathological conditions. That switch occurs at a "tipping point" where the non-linear mechanism responsible for spike initiation undergoes a qualitative change. A, the distance to tipping point can be measured by titrating how much virtual Na V 1.3-like conductance (see Methods) is required to switch the spiking pattern. We refer to the liminal change (red arrow) asḡ * Na . Notably, Na V 1.3 channels are one of many different ion channels whose up-or downregulation impacts the spike initiation mechanism; the virtual Na V 1.3-like conductance is used here purely as a tool to help infer the impact of other factors on spiking. B, pathological factors affecting excitability (represented here as black arrows labelled α, β, γ ) may facilitate repetitive spiking without causing repetitive spiking (i.e. shift a neuron toward but not across its tipping point). We reasoned that the degree to which each factor facilitated repetitive spiking could be measured as the difference in g * Na before (x) and during (y) each pathomimetic manipulation. J Physiol 596.11

Baseline spiking characteristics and passive membrane properties
To determine whether small and medium-large neurons differ in their baseline spiking patterns, the spiking evoked by somatic current injection was compared. Pre-stimulus V m was adjusted to −65 mV in all cells. Two patterns were identified ( Fig. 2A): transient and repetitive (see Methods for precise definitions). Figure 2B summarizes the proportion of neurons exhibiting each pattern. Of the 56 small neurons recorded, 35 (63%) displayed transient spiking even to stimulus amplitudes 3-4 times rheobase.
If we assume that excitability (defined here as distance to tipping point) is distributed normally and that the proportion of repetitive spiking neurons represents the part of the distribution located to the right of the tipping point separating the two spiking patterns (Fig. 2C), then the results in Fig. 2B suggest that small neurons, on average, operate closer to their tipping point. This predicts that a smaller perturbation is required to convert small neurons to repetitive spiking than is required to convert medium-large neurons. Only transient spiking neurons were used in subsequent experiments since the goal of our experiments was to convert them to repetitive spiking.
Focusing on transient spiking cutaneous neurons, the passive membrane properties tended to differ between small (n = 35) and medium-large (n = 76) neurons (Table 1). To account for effects of cell size and isolate true differences in membrane excitability, we normalized certain metrics by membrane capacitance, C m . After normalizing by C m , medium-large cells were found to have a significantly higher leak conductance density than small cells (Mann-Whitney U 109 = 568.0, P < 0.001), which partly accounts for a significantly higher rheobase/C m amongst medium-large cells compared with small cells (Mann-Whitney U 109 = 826.0, P < 0.001).

Converting neuronal spiking pattern from transient to repetitive
After determining that a neuron spiked transiently to current injection (I stim ) steps, we used dynamic clamp to insert a virtual sodium conductance (see Methods). The virtual conductance resembles Na v 1.3 channels that are often upregulated after nerve injury (Waxman et al. 1994;Kim et al. 2001;Fukuoka et al. 2008;Huang et al. 2008), but the goal of our dynamic clamp manipulation was not to test the effect of sodium channel upregulation Almost all medium-large neurons (top) fire a single spike at stimulus onset once I stim reaches rheobase (black trace); this pattern is maintained as I stim is increased above rheobase (grey traces). Most small neurons also exhibit transient spiking (middle) but some spike repetitively (bottom) with the spike count increasing as I stim is increased above rheobase (inset graph). In all examples, rheobasic stimulation and the corresponding response are shown in black. B, summary of the number of neurons exhibiting transient or repetitive spiking. Compared with medium-large neurons, a significantly greater proportion of small neurons exhibited repetitive spiking (χ 2 = 17.393, P < 0.001). C, schematic diagram shows how the differential distribution of excitability between small and medium-large neurons could explain the difference in the proportion of spiking patterns reported in B.
Since some small cells exhibit repetitive spiking at baseline, this population is predicted to operate closer to tipping point than medium-large neurons, few of which spike repetitively at baseline. Operating closer to a tipping point predicts that small cells should be easier to convert to repetitive spiking (i.e. require lessḡ Na ) than medium-large cells.
3.9 (2.4-6.1) 5.5 (4.0-11.4) <0.001 Data show median and the interquartile range. Resting V m , resting membrane potential; R in , input resistance; τ m , membrane time constant; C m , membrane capacitance calculated as C m = τ m /R in ; g leak /C m , leak conductance density, where g leak = 1/R in . P values indicate the level of significance of Mann-Whitney U tests.
per se (see Fig. 1 and Discussion). Instead, our strategy was to systematically increaseḡ Na while applying I stim steps near rheobase to determine the value ofḡ Na at which the neuron switched to repetitive spiking (Fig. 3A).
Beyond this critical value, denotedḡ * Na , increasingḡ Na further increased the number of spikes (Fig. 3B). Figure 3C summarizes the differential conversion rate in small and medium-large neurons. Under baseline conditions, all small neurons were converted to repetitive spiking but 29 of 76 medium-large neurons (38%) could not be converted despiteḡ Na being raised as high as possible without destabilizing the recording. The difference in conversion rate between small and medium-large cells was significant (χ 2 = 16.155, P < 0.001) (Fig. 3C), consistent with the prediction in Fig. 2C, namely, that small cells operate closer to their tipping point. In other words, the entire distribution of small cells could be pushed across the tipping point by insertingḡ Na whereas part of the distribution of medium-large cells could not be pushed far enough (Fig. 3D), though we cannot exclude the possibility that some medium-large neurons might never be converted even if larger virtual conductances could be applied.
Values ofḡ * Na correlated significantly with soma diameter (r 2 = 0.455, P < 0.001) (Fig. 4A). The median g * Na of 6.0 (4.0-10.0) nS in small neurons was significantly less than the medianḡ * Na of 20.0 (12.0 -26.5) nS in medium-large neurons (Mann-Whitney U 80 = 276.0, P < 0.001). However, as with certain membrane properties (see Table 1), differences inḡ * Na partly reflect differences in cell size. As expected, C m was significantly correlated with soma diameter (r 2 = 0.464, P < 0.001) (Fig. 4B). control conditions was converted to repetitive spiking when sufficient virtual sodium conductance (ḡ Na ) was added using dynamic clamp. By systematically varyinḡ g Na , the minimum conductance required to convert the spiking pattern was identified and is reported as g * Na . B, increasingḡ Na beyondḡ * Na increased the number of spikes evoked by rheobasic stimulation. The horizontal dotted line shows the threshold for repetitive spiking (see Methods). The vertical dotted line highlights the first data point exceeding threshold, and corresponds toḡ * Na . C, whereas all small neurons could be converted to repetitive spiking by adding enoughḡ Na , a significant fraction of medium-large neurons were not converted (χ 2 = 16.155, P < 0.001). D, schematic diagram shows how the differential rate of spike pattern conversion likely relates to the distance of each cell population from its tipping point, as anticipated in Fig. 2C. J Physiol 596.11 Thus, to correct for the effect of cell size and thereby isolate differences in excitability, we normalizedḡ * Na by C m . The medianḡ * Na /C m of 0.228 (0.134-0.319) nS pF −1 in medium-large neurons was still significantly greater than the medianḡ * Na /C m of 0.142 (0.085-0.178) nS pF −1 in small neurons (Mann-Whitney U 80 = 494.0, P = 0.002) (Fig. 4C). This difference demonstrates that transient-spiking small neurons operate significantly closer to their tipping point than medium-large neurons, consistent with the differential distance to tipping point inferred from spiking pattern proportions in Figs 2C and 3D.

Spiking pattern conversion requirements are stable across time, V m and temperature
A number of control experiments were undertaken to establish the feasibility of subsequent experiments. First, to determine whetherḡ * Na /C m or other cell properties drift over the duration of a typical experiment, we repeated measurements at 15 min intervals in five small cells and five medium-large cells. Data were pooled across cell types based on the lack of interaction between cell size and time onḡ * Na /C m or rheobase (two-way repeated measures ANOVAs, F 3,8 = 1.0, P = 0.41 and F 3,8 = 0.75, P = 0.54, respectively). As illustrated for a typical neuron in Fig. 5A, the innate spiking pattern remained trans-ient over time and was readily switched to repetitive spiking with dynamic clamp. Quantitatively,ḡ * Na /C m did not shift significantly over time (F 3,8 = 0.45, P = 0.72) (Fig. 5B) and rheobase was similarly stable (F 3,8 = 0.24, P = 0.87) (Fig. 5C). Nor was there any significant shift in R in (F 3,8 = 1.18, P = 0.34) or τ m (F 3,8 = 0.71, P = 0.56). However, there was a significant depolarizing shift in resting V m (F 3,8 = 12.33, P < 0.001) (Fig. 5D), with the mean (± SEM) voltage shifting from -70.5 ± 2.2 mV at the first test to -66.0 ± 2.4 mV at the fourth test 45 min later. It is, therefore, notable that we standardized the pre-stimulus V m to -65 mV when making all other measurements (see above).
Next, to rule out that changes inḡ * Na always parallel changes in V m and rheobase (and thus do not provide independent information), we re-measuredḡ * Na with the pre-stimulus V m adjusted to -65 mV or -75 mV since many studies on afferent hyperexcitability report changes in resting V m and rheobase. Though perhaps correlated with a switch in spiking pattern, those changes are neither necessary nor sufficient to explain that switch. Specifically, those metrics do not directly address which non-linear process will be utilized to generate spikes (Prescott et al. 2008) and thus we predicted that a change in V m imposed by current injection would not produce a concomitant change inḡ * Na , though it would affect rheobase. Testing was conducted on five small cells and

. Distance to tipping point differs between small and medium-large neurons
A, small neurons (white) require moreḡ Na to convert their spiking pattern than medium-large neurons (grey). Boxes show the group median and 25th-75th percentiles. The medianḡ * Na of 6.0 (4.0-10.0) nS for small neurons was significantly less than the medianḡ * Na of 20.0 (12.0-26.5) nS for medium-large neurons (Mann-Whitney U 80 = 276.0, n small = 35, n medium-large = 47, P < 0.001), but this is at least partly due to cell size and may not, therefore, represent a true difference in excitability between putative C-and A-type neurons. Linear regression revealed a significant correlation between soma diameter andḡ * Na (r 2 = 0.455, P < 0.001). B, membrane capacitance, C m , was also correlated with soma diameter (r 2 = 0.464; P < 0.001) and, as expected, differed significantly between small and medium-large neurons (Mann-Whitney U 80 = 276.0, P < 0.001). C, to isolate true differences in excitability,ḡ * Na was normalized by C m on a cell-by-cell basis, essentially converting the virtual conductance amplitude into a conductance density (ḡ * Na /C m ). The medianḡ * Na /C m of 0.142 (0.085-0.178) nS pF −1 in small neurons was significantly less than the medianḡ * Na /C m of 0.228 (0.134-0.319) nS pF −1 in medium-large neurons (Mann-Whitney U 80 = 494.0, P = 0.002), thus confirming that medium-large neurons do indeed differ in their distance to tipping point. five medium-large cells, but results were pooled based on the lack of interaction between cell size and V m onḡ * Na /C m and rheobase (two-way repeated measures ANOVAs, F 1,8 = 4.76, P = 0.061 and F 1,8 = 0.43, P = 0.53, respectively). Responses from a typical neuron are illustrated in Fig. 6A. As predicted, hyperpolarization did not significantly affectḡ * Na /C m (F 1,8 = 0.03, P = 0.86) ( Fig. 6B) but did yield the expected increase in rheobase (F 1,8 = 14.48, P = 0.005) (Fig. 6C). Lastly, to test whether the innate spiking pattern or our ability to convert it using dynamic clamp was temperature sensitive, experiments were repeated as bath temperature was increased from 22 to 32°C. In 3 of 3 neurons tested, the innate spiking pattern was transient across Hyperpolarization caused a predictable increase in rheobase but no change inḡ * Na . A change in V m is predicted to impactḡ * Na only if channel states are affected (e.g. channels are inactivated) so that the dynamical interaction during rheobasic stimulation is altered; simply requiring more I stim to initiate the same dynamics will not impact g * Na . Five small cells and 5 medium-large cells were tested but data were pooled across cell types based on the lack of significant interaction between membrane potential and cell type (see text). B, hyperpolarization did not significantly affectḡ * Na /C m (two-way repeated measures ANOVA, F 1,8 = 0.03, P = 0.86). C, hyperpolarization significantly affected rheobase (F 1,8 = 14.48, P = 0.005). J Physiol 596.11 this temperature range (Fig. 7A) and could be converted to repetitive spiking by introducing g Na (Fig. 7B), which demonstrates the feasibility of converting spiking pattern regardless of temperature. We did not compareḡ * Na at different temperatures since the kinetics of the virtual conductance should arguably be changed as temperature changes. Indeed, despite the consistency in spiking pattern, individual spikes became shorter and narrower at higher temperature (inset in Fig. 7A). Speeding up the kinetics of the virtual conductance risks destabilizing dynamic clamp recordings and would, therefore, likely reduce the maximal virtual conductance that could be inserted. We did not test whether the effects of other manipulations (e.g. inflammatory mediators) are temperature sensitive, but this could be studied in future experiments.

Depolarizing shift in E K facilitates repetitive spiking in both cell types
The extracellular concentration of potassium ([K + ] o ) can increase during sustained high-rate spiking of the cell of interest or its neighbours (Yaari et al. 1986) or through leakage of intracellular potassium from damaged cells (Tsantoulas et al. 2012), both of which can occur in the context of nerve injury (Amaya et al. 2013). Due to the logarithmic relationship between [K + ] o and the potassium reversal potential (E K ), small changes in [K + ] o can result in relatively large changes in E K , diminishing the potassium driving force and thereby increasing excitability.
To test how an isolated change in [K + ] o contributes to changes in spiking pattern, we switched the perfusing ACSF from one with 2.5 mM [K + ] to one with 5.5 mM [K + ], which shifts E K from -100 to -80 mV according to the Nernst equation. Figure 8A shows sample responses from a typical neuron converted to repetitive spiking in regular ACSF and again after 10 min in ACSF with high [K + ];ḡ * Na in each condition is denoted x and y, respectively. Increasingḡ Na aboveḡ * Na increased the number of spikes evoked by rheobasic stimulation, and that relationship was shifted leftward by high [K + ] (Fig. 8B). Based on the 14 neurons tested, high [K + ] significantly reduced g * Na /C m from a median value of 0.218 (0.159-0.363) to 0.178 (0.121-0.257) nS pF −1 (Wilcoxon signed-rank test, P = 0.010) (Fig. 8C). The change inḡ * Na /C m did not differ significantly between small and medium-large neurons (t 13 = -1.18; P = 0.26) and data were therefore pooled. Although elevated [K + ] o moved neurons towards their tipping point, this manipulation alone (i.e. without insertion ofḡ Na ) was insufficient to convert the spiking pattern in any neurons tested. This modest effect suggests that a change in [K + ] o is only one of many factors that contribute to causing a switch in spiking pattern in primary somatosensory neurons under pathological conditions.
Effects of high [K + ] o on resting V m and rheobase were controlled for when measuringḡ * Na but, as expected, high [K + ] o shifted the mean resting V m from -71.2 ± 2.3 to -63.2 ± 1.5 mV (paired t 14 = -5.48, P < 0.001) (Fig. 8D). In 12 of 15 neurons, high [K + ] o increased the median rheobase from 350 (200-650) to 450 (300-750) pA (Wilcoxon signed-rank test, P < 0.001) (Fig. 8E). The shift in rheobase is in the opposite direction to that expected, but that is explained by the pre-stimulus V m being held at -65 mV for all rheobase measurements; rheobase would likely have been reduced if the 8 mV shift in resting V m had not been controlled for. Neither τ m nor R in significantly differed between control and high [K + ] o conditions: The median τ m for baseline and high [K + ] o groups was 16.6 (9.2-22.9) and 13.8 (10.1-16.4) ms, respectively (Wilcoxon signed-rank test, P = 0.39) and the median R in was 318 (84-457) and 159 (91-303) M , respectively (Wilcoxon signed-rank test, P = 0.055).

Inflammatory mediators facilitate repetitive spiking, especially in medium-large neurons
Inflammatory mediators have been shown to cause repetitive spiking in some somatosensory neurons

. Physiological temperature does not affect spiking pattern or its conversion
A, sample responses show a consistent spiking pattern as the bath temperature was slowly raised from 22°C to 32°C. Despite no change in rheobase or spiking pattern, the spike amplitude and half-width were reduced at higher temperatures, consistent with faster channel gating kinetics. B, sample traces at 32°C showing the conversion to repetitive spiking by addition ofḡ * Na (bottom trace). With I stim constant, the spike count increased asḡ Na was increased (top trace), consistent with the pattern observed at room temperature (see Fig. 3A and B). The same patterns were observed in 3 of 3 neurons tested.
(see Discussion) but it remains unclear if neurons whose spiking remains transient have nonetheless experienced a subliminal shift toward their tipping point. The implication is that inflammation-induced facilitation of repetitive spiking will make those neurons more prone to switching spiking pattern if other changes (e.g. high [K + ] o ) were also to occur. Observation that neurons injured in vivo are more prone to switch to repetitive spiking than uninjured neurons when subsequently exposed to inflammatory mediators in vitro (Ma et al. 2006) supports the notion that repetitive spiking results from the cumulative effect of multiple pathological factors.
To measure the inflammation-induced shift in the distance to tipping point, we measuredḡ * Na before and after adding inflammatory mediators to the ACSF, as illustrated in Fig. 9A. Inflammation shifted the relationship between spike count andḡ Na (Fig. 9B). The effect of inflammation onḡ * Na /C m was found to depend on cell size as revealed by a significant interaction between these factors (two-way repeated measures ANOVA, F 1,14 = 10.60, P = 0.006), thus data were analysed separately for each cell type. Amongst small cells (n = 9), the reduction in mean g * Na /C m from 0.148 ± 0.017 to 0.100 ± 0.027 nS pF −1 was not significant (Student-Newman-Keuls test, P = 0.11) (Fig. 9C red), whereas amongst medium-large cells (n = 7), the reduction in meanḡ * Na /C m from 0.289 ± 0.051 to 0.099 ± 0.029 nS pF −1 was significant (P < 0.001) (Fig. 9C blue). The reduction ofḡ * Na /C m was significantly greater in medium-large neurons than in small neurons (t 14 = -3.25, P = 0.006). Whereas small and medium-large neurons differed significantly inḡ * Na /C m at baseline (Student-Newman-Keuls test, P = 0.005), they did not differ after exposure to inflammatory mediators (P = 0.99). These data argue that medium-large neurons are more strongly affected by inflammatory mediators than are small neurons, but because the latter operate closer to their tipping point under baseline conditions, both cell populations end up equally close to their tipping point after inflammatory mediators are applied. Consistent with this, one cell of each type was converted to repetitive spiking by application of inflammatory mediators alone (without dynamic clamp).
The resting V m was significantly depolarized by inflammatory mediators (Wilcoxon signed-rank test; P < 0.001) (Fig. 9D), but that shift did not differ significantly between small and medium-large neurons (Mann-Whitney U 14 = 21.0, P = 0.29). Inflammatory mediators did not have a significant effect on rheobase (paired t 15 = 1.54, P = 0.14) (Fig. 9E), bearing in mind that changes in resting V m were controlled for during rheobase measurements. The effect on rheobase did not differ between small and medium-large neurons (t 14 = 0.79, P = 0.44). Inflammatory mediators did not have a significant effect on either τ m (Wilcoxon signed-rank test, P = 0.12) or R in (paired t 14 = 0.56, P = 0.58).

Inflammatory mediators also facilitate repetitive spiking in muscle afferents
Past studies have reported that muscle afferents are more likely than cutaneous afferents to spike spontaneously    or to respond to sustained depolarization with repetitive spiking (Liu et al. 2002;Ratté et al. 2014) after nerve injury. Therefore, to compare with cutaneous afferents, we used the same approach described above to test the effects of inflammatory mediators on muscle afferent excitability. Figure 10A shows responses from a typical neuron. Like in cutaneous afferents, the effect of inflammation onḡ * Na /C m was found to depend on cell size (two-way repeated measures ANOVA, F 1,14 = 10.18, P = 0.007) and data were thus analysed separately for each cell type. Amongst small cells (n = 18), the reduction in meanḡ * Na /C m from 0.162 ± 0.039 to 0.145 ± 0.035 nS pF −1 was not significant (Student-Newman-Keuls test, P = 0.55) (Fig. 10B red), whereas amongst medium-large cells (n = 18), the reduction in meanḡ * Na /C m from 0.294 ± 0.053 to 0.158 ± 0.034 nS pF −1 was significant (Student-Newman-Keuls test, P < 0.001) (Fig. 10B blue). The reduction ofḡ * Na /C m was significantly greater in medium-large neurons than in small neurons (t 14 = -3.19, P = 0.007). Whereas small and medium-large neurons differed significantly inḡ * Na /C m at baseline (Student-Newman-Keuls test, P = 0.036), they did not differ after exposure to inflammatory mediators (P = 10.83).
Resting V m was significantly depolarized by inflammatory mediators (two-way repeated measures ANOVA, F 1,14 = 59.09, P < 0.001) (Fig. 10C). This was true in both small and medium-large neurons (Student-Newman-Keuls test, P < 0.001 for each cell type) and the interaction between cell size and inflammatory mediators was not significant (F 1,14 = 4.05, P = 0.064). With respect − g Na y * − g Na x − g Na Figure 9. Inflammatory mediators reduceḡ * Na more in medium-large cells than in small cells A, sample responses before and after spiking pattern conversion byḡ Na under baseline conditions (top) and again after addition of inflammatory mediators (bottom). Values ofḡ * Na before and after addition of inflammatory mediators are denoted x and y, respectively. The absence of repetitive spiking in response to inflammatory mediators alone (i.e. without dynamic clamp; bottom left trace) was typical. B, increasingḡ Na beyondḡ * Na increased the spike count in response to rheobasic I stim . Inflammatory mediators shifted this relationship leftward. Data from small neurons (n = 9, red) and medium-large neurons (n = 7, blue) were analysed separately based on the significant interaction between cell size and inflammation (see text). C, inflammatory mediators did not have a significant effect on theḡ * Na /C m of small cells (Student-Newman-Keuls test, P = 0.11) but did have a significant effect on medium-large cells (P < 0.001). The inflammation-induced reduction ofḡ * Na /C m was significantly larger in medium-large neurons (t 14 = -3.25, P = 0.006). As illustrated by the schematic diagram on the right, and by the group means (±SEM) on the main graph, small and medium-large neurons differed significantly in their g * Na /C m at baseline (Student-Newman-Keuls test, P = 0.005) but not after inflammatory mediators (P = 0.99). D, inflammation had a significant effect on resting V m (Wilcoxon signed-rank test; P < 0.001), but that effect did not differ significantly between small and medium-large neurons (Mann-Whitney U 14 = 21.0, P = 0.29). E, inflammation did not have a significant effect on rheobase (paired t 15 = 1.54, P = 0.14). to rheobase, there was a significant interaction between cell size and inflammatory mediators (two-way repeated measures ANOVA, F 1,14 = 4.67, P = 0.048) (Fig. 10D) with medium-large cells experiencing a significant decrease (Student-Newman-Keuls test, P = 0.02) whereas small cells experienced no change (P = 0.67). Inflammatory mediators did not have a significant effect on either τ m (paired t 14 = -0.51, P = 0.62) or R in (Wilcoxon signed-rank test, P = 0.40).
The pattern of inflammation-induced changes was similar between cutaneous and muscle afferents. Figure 11A reports the averageḡ * Na /C m before and after inflammatory mediators for each group of cells, collating the group averages shown in Fig. 9C and 10B. To compare the effects of inflammatory mediators, we calculated the inflammation-induced reduction inḡ * Na /C m as x − y. The change inḡ * Na /C m did not differ significantly between cutaneous and muscle afferents (two-way ANOVA, F 1,31 = 2.31, P = 0.14) (Fig. 11B), nor was there any interaction between cell size and the tissue innervated (F 1,31 = 0.14, P = 0.71). The same analysis conducted on the inflammation-induced shift in rheobase likewise revealed no significant difference between cutaneous and muscle afferents (F 1,31 = 0.00; P = 0.98; Fig. 11C) or any interaction between cell size and the tissue innervated (F 1,31 = 1.07; P = 0.31). Lastly, the inflammation-induced shift in resting V m did not differ between cutaneous and muscle afferents (Mann-Whitney U 30 = 128, P = 0.99). Overall, these results argue that cutaneous and muscle afferents respond similarly to the cocktail of inflammatory mediators that we tested, which contrasts the differential effect of inflammation on small vs. medium-large neurons (see Figs 9 and 10). Our results do not contradict past studies reporting differences between cutaneous and muscle afferents but, rather, argue that those differences are due to other inflammatory mediators or to other aspects of nerve injury.

Variation in repetitive spiking pattern revealed by dynamic clamp
The switch to repetitive spiking reflects a switch in the underlying spike initiation mechanism such that rapid depolarization (driven by an external stimulus) becomes unnecessary for positive feedback activation of fast sodium channels to outcompete slower processes such as delayed-rectifier potassium channel activation (Prescott et al. 2008;Ratté et al. 2015). This means that sustained depolarization, whether caused by stimulation or by factors affecting resting V m , is sufficient to drive spiking, which is of course important for spontaneous

in muscle afferents
A, sample responses from muscle afferent using same protocol as in Fig. 9 for cutaneous afferents. Data from small neurons (n = 8, red) and medium-large neurons (n = 8, blue) were analysed separately based on the significant interaction between cell size and inflammation (see text). B, inflammatory mediators did not have a significant effect on theḡ * Na /C m of small cells (Student-Newman-Keuls test, P = 0.55) but did have a significant effect on medium-large cells (P < 0.001). The inflammation-induced reduction ofḡ * Na /C m was significantly larger in medium-large neurons (t 14 = -3.19, P = 0.007). Like in cutaneous afferents, small and medium-large neurons differed significantly in theirḡ * Na /C m at baseline (Student-Newman-Keuls test, P = 0.036) but not after inflammatory mediators (P = 0.83). C, inflammation had a significant effect on resting V m (two-way repeated measures ANOVA, F 1,14 = 59.09, P < 0.001), but the interaction between cell size and inflammation was not quite significant (F 1,14 = 4.05, P = 0.064). D, there was a significant interaction between cell size and inflammation (F 1,14 = 4.67, P = 0.048). Inflammation significantly reduced rheobase in medium-large cells (Student-Newman-Keuls test, P = 0.02) but not in small cells (P = 0.67). J Physiol 596.11 spiking, where there is no external input causing rapid depolarization. Hyperexcitable neurons can fire spontaneously in bursts or in a regular pattern Zhang et al. 1999;Liu et al. 2002;Ma et al. 2003). We have shown previously that adaptive processes that are slow relative to spike kinetics are essential for bursting (Rho & Prescott, 2012). This raises the question of whether neurons have latent differences in their adaptation that only become evident when the neuron becomes capable of repetitive spiking, or whether adaptation is also pathologically altered. The two possibilities are not mutually exclusive, but the former possibility is typically overlooked.
By adding virtual g Na to cause repetitive spiking, we observed latent differences in the pattern of repetitive spiking at the tipping point. Figure 12A shows typical examples of phasic (top) and tonic (bottom) patterns of repetitive spiking. Phasic spiking was defined as repetitive spiking that stopped before the end of the I stim step (consistent with strong adaptation) whereas tonic spiking was defined as repetitive spiking that continued throughout the I stim step (consistent with weak adaptation). Based on the response during dynamic clamp insertion ofḡ * Na , the cumulative probability of spiking during rheobasic I stim revealed two recognizable clusters (Fig. 12B).
Next, we asked whether the pattern of repetitive spiking depended on the manipulation used to cause repetitive spiking (i.e. dynamic clamp alone vs. dynamic clamp plus high [K + ] o or inflammatory mediators). Fig. 12A, where each row represents a different neuron, analysis in Fig. 12C argues that the pattern of repetitive spiking is independent of the manipulation. Specifically, of the 15 cutaneous afferents converted to repetitive spiking before and after application of high [K + ] o , two switched from phasic to tonic spiking in high [K + ] o , and another two switched in the opposite direction, which does not represent a significant change in repetitive spiking pattern (McNemar's test; χ 2 = 0.250; P = 0.617). Of the 16 cutaneous afferents converted to repetitive spiking before and after application of inflammatory mediators, two switched from phasic to tonic spiking in inflammatory mediators, and one switched in the other direction, which is also not significant (χ 2 = 0.000; P = 1.000). Of the 16 muscle afferents converted to repetitive spiking, all of them exhibited the same pattern of repetitive spiking before and after application of inflammatory mediators. These results suggest that the pattern of repetitive spiking does not depend on the manipulations, though we cannot exclude that other manipulations that facilitate repetitive spiking -especially those that do so without any virtual sodium conductance being added -might facilitate a certain pattern of repetitive spiking.

Consistent with examples in
Consistent with the latent pattern of repetitive spiking being an intrinsic neuronal property, the proportion of phasic spiking was significantly more common amongst medium-large neurons than amongst small neurons (χ 2 = 6.221, P = 0.013 for cutaneous afferents; Fisher's exact test, P = 0.026 for muscle afferents) (Fig. 12D). This difference in repetitive spiking pattern is consistent with differences in slow adaptive processes, the implication being that different cell types are predisposed to different patterns of pathological spiking not necessarily because they experience different pathological changes (e.g. slow adaptive processes are compromised in one cell type but not another) but, rather, because the same pathological change (e.g. a switch to repetitive spiking) manifests differently because of pre-existing differences between cell types. . Cutaneous and muscle afferents respond similarly to inflammatory mediators A, group means (±SEM) ofḡ * Na before (x) and after (y) inflammation in cutaneous (grey) and muscle afferents (white) collated from Figs 9 and 10, respectively. B, the inflammation-induced reduction inḡ * Na /C m (measured as x − y) did not differ significantly between cutaneous and muscle afferents (two-way ANOVA, F 1,31 = 2.26, P = 0.14), nor was there any significant interaction between cell size and the tissue innervated (F 1,31 = 0.05, P = 0.82). C, the inflammation-induced reduction in rheobase did not differ significantly between cutaneous and muscle afferents (F 1,31 = 0.01, P = 0.92), nor was there any significant interaction between cell size and the tissue innervated (F 1,31 = 2.56, P = 0.12).

Discussion
In this study, we have demonstrated a novel way in which dynamic clamp can be used to explore pathological changes in spiking pattern. Primary somatosensory neurons normally respond to abrupt somatic depolarization with transient spiking at the onset of stimulation (see Fig. 2), but, under conditions associated with chronic pain, some neurons develop the capacity to spike repetitively during sustained depolarization (Liu et  . Two subtypes of repetitive spiking were observed: phasic (black), in which spiking abruptly ceases before the end of I stim steps due to strong adaptation, and tonic (grey), in which spiking continues throughout I stim steps because adaptation is weaker. Sample traces on the right suggest that the pattern of repetitive spiking is independent of the pathomimetic manipulations. As I stim is increased above rheobase or asḡ Na is increased aboveḡ * Na , phasic spiking may transition to tonic spiking (data not shown). In the subsequent analysis, we focus on the repetitive spiking pattern at the tipping point, namely, with rheobasic I stim andḡ * Na . B, using spike times from the response to 2 s-long rheobasic I stim andḡ * Na , the cumulative probability of spiking plots revealed two profiles that correspond to phasic (black) and tonic (grey). C, proportions of neurons exhibiting tonic and phasic spiking under baseline conditions and during high [K + ] or inflammatory mediators. Amongst cutaneous afferents, the number of neurons switching between patterns (indicated by arrows) was not significant for high [K + ] (McNemar's test, χ 2 = 0.250; P = 0.617) or inflammatory mediators (χ 2 = 0.000; P = 1.000). All muscle afferents exhibited the same pattern before and after inflammatory mediators. These data suggest that the pattern of repetitive spiking is independent of the manipulations used to facilitate repetitive spiking. D, proportion of phasic spiking was significantly greater amongst medium-large neurons than amongst small neurons for cutaneous afferents (χ 2 = 6.221, P = 0.013) and muscle afferents (Fisher's exact test, P = 0.026). These data suggest that the pattern of repetitive spiking is dependent on the cell type. J Physiol 596.11 2000J Physiol 596.11 , 2002Xing et al. 2001;Ma & LaMotte, 2007;Fan et al. 2011;Xie et al. 2011;Song et al. 2012). This switch in spiking pattern, whether assessed by stimulation or inferred from spontaneous spiking, occurs in only a fraction of neurons and is more common in muscle afferents than in cutaneous afferents Liu et al. 2002;Ratté et al. 2014), but grossly altered spiking in even a few neurons may have major sensory consequences. Moreover, our data suggest that most (if not all) "unaffected" neurons experience a subliminal change in excitability that makes them more prone to switch their spiking pattern if additional insults were to be experienced by that neuron.
By inserting a virtual sodium conductance known to facilitate repetitive spiking, and measuring exactly how much of that conductance is required to cause repetitive spiking -the liminal conductance change that we refer to asḡ * Na (see Fig. 1) -we showed that small neurons are more prone to repetitive spiking than are medium-large neurons under control conditions. Small and medium-large neurons typically have unmyelinated or myelinated fibres, respectively. By combining dynamic clamp with other pathomimetic manipulations, namely high [K + ] o and inflammatory mediators, we also showed how the effect of these pathological factors on excitability can be indirectly measured based on how much they reduceḡ * Na . Using this approach, we found that high [K + ] o had similar effects on the excitability of small and medium-large neurons whereas inflammatory mediators had a significantly greater effect in medium-large neurons.

Different ways of using dynamic clamp
Dynamic clamp was developed over two decades ago (Robinson & Kawai, 1993;Sharp et al. 1993) but remains relatively uncommon, especially in studies examining pathophysiological changes associated with pain. Dynamic clamp has recently been applied to primary somatosensory neurons to explore the effects of specific changes in sodium channels (Vasylyev et al. 2014;Han et al. 2015;Estacion & Waxman, 2017), potassium channels (Ritter et al. 2015) and GABA A receptor signalling (Takkala et al. 2016). Beyond testing the effects of known molecular changes, our group has used dynamic clamp to reproduce known changes in cellular excitability in order to explore the underlying molecular changes in a more general way, including how such changes may combine to affect excitability (Ratté et al. 2014). The virtual sodium conductance that we inserted in this study mimics Na v 1.3 channels that can be upregulated after nerve injury (Waxman et al. 1994;Kim et al. 2001;Fukuoka et al. 2008;Huang et al. 2008), but even if that particular molecular change is not induced in a certain cell by a certain injury, the manipulation nonetheless enables one to study how a neuron operates under two well-defined conditions (i.e. with and without the added conductance). In other words, the added conductance serves as an acute and precisely controllable perturbation to explore excitability (Tomaiuolo et al. 2012;Zeberg et al. 2015). By titrating the virtual conductance, we determined how strong the perturbation must be to cause a qualitative change in spiking pattern. We introduced this "distance-to-tipping-point" measurement previously (Ratté et al. 2014) but demonstrate here how it can be adapted to measure modulation of the distance to tipping point.
Before discussing modulation of the distance to tipping point, it is worth comparing distance-to-tipping-point measurements across different types of neurons as those data provide significant insight into the susceptibility of neurons to switch to repetitive spiking. Indeed, an understanding of that susceptibility and how different molecular changes affect excitability are both necessary for a more holistic understanding of how neuronal excitability becomes pathologically altered.

Differential susceptibility to spiking pattern changes
Most of the neurons that we tested spiked transiently under baseline conditions but a significantly higher proportion of small cells than medium-large cells exhibited repetitive spiking (Fig. 2). This observation suggests that small cells, on average, operate closer to their tipping point than do medium-large cells. Other data corroborated that interpretation: a higher proportion of small cells could be converted to repetitive spiking by dynamic clamp (Fig. 3) and significantly less virtual conductance was required for that conversion even after accounting for differences in cell surface area (Fig. 4). As a technical note, most neurons that we tested could be converted from transient to repetitive spiking once sufficient virtual sodium conductance was added; those that were not converted may reflect either a technical limitation on the maximum current we could apply without destabilizing the recording, though we cannot exclude the possibility that some medium-large neurons might never be converted, even if very large virtual conductances could be applied. Compared with cutaneous afferents, muscle afferents appeared to operate at a similar distance from their tipping point (Fig. 11) though neurons innervating other tissues (e.g. joints, or viscera) may differ in this regard.
If different cells operate at different distances from their tipping point, they will require more or less net molecular change -sodium channel upregulation, potassium channel downregulation, or myriad other changes and any combination thereof -to convert their spiking pattern. Under these conditions, the magnitude of the net molecular change is not sufficient to predict whether spiking pattern will be switched as this also depends on the susceptibility of the neuron. Our data suggest that small cells (with unmyelinated fibres) are switched to repetitive spiking by molecular changes that are too subtle to affect the spiking pattern of medium-large cells (with myelinated fibres). Yet the impact of molecular changes also differs between cell types (see below). The similarity between small and medium-large cells suggested by their transient spiking pattern may belie differences in the underlying balance of different ion channels that can manifest as different patterns of repetitive spiking (Fig. 12) and differential susceptibility to perturbation, reminiscent of recent studies in other systems (Rinberg et al. 2013;Sakurai et al. 2014). We are unaware of any comparable studies directly addressing this issue in somatosensory afferents.

Measuring modulation of the distance to tipping point
Beyond measuring the distance to tipping point under a single condition, we have introduced in this study how to measure the contribution of individual pathophysiological changes based on how they modulate the distance to tipping point. Specifically, by measuring (1) how much virtual sodium conductance is required to convert the spiking pattern of a given neuron under baseline conditions, and (2) how much less of that conductance is required when applied in conjunction with another pathomimetic manipulation, the contribution of the second manipulation can be measured indirectly (see Fig. 1). Using this approach, we have shown that high [K + ] o facilitates repetitive spiking to the same degree in small and medium-large neurons (Fig. 8) whereas inflammatory mediators facilitate repetitive spiking more in medium-large neurons (Figs 9 and 10).
As alluded to above, the magnitude of excitability changes must be considered in light of how near or far different cell types operate from their tipping point. Although inflammation shifted medium-large neurons more towards their tipping point than it did for small neurons, the medium-large neurons were not more likely to convert to repetitive spiking than small neurons because the former normally operate further from their tipping point (see above). More generally, both high [K + ] o and inflammation pushed neurons towards their tipping point, but neither, on its own (i.e. without dynamic clamp), caused repetitive spiking except in a very small minority of neurons. This is consistent with small effects from multiple different pathological factors needing to summate to cause gross changes in spiking. It is possible that some pathological changes may also interact non-linearly (i.e. cooperate or interfere with each other) rather than summing linearly. In any case, only a subset of neurons (i.e. those in the tail of the Gaussian distribution describing excitability) are likely to experience a change in spiking pattern unless the net molecular change is especially large. Consistent with this, Ma et al. (2006) showed that chronic compression of the dorsal root ganglion caused spontaneous spiking in ß10% of neurons, but inflammatory mediators applied to injured neurons more than doubled that percentage (with equal effects observed in small, medium and large neurons); the same inflammatory mediators applied to uninjured neurons caused spontaneous spiking in only ß1% of all neurons. Song et al. (2003) reported similar findings but, in contrast, Gold et al. (1996) reported that PGE 2 sensitized 56% of neurons harvested from uninjured animals. In the latter study, sensitization was defined as increased spiking and/or reduced spike threshold, which makes it unclear what fraction of neurons switched spiking pattern, and the reported 300% increase in spike number is based only on "sensitized" neurons. On the one hand, this means that at least 44% of neurons exhibited no increase in spike number, let alone tripling, but, on the other hand, one would be remiss in assuming 44% of neurons were unaffected insofar as they may have been shifted toward their tipping point. Notably, we tested acute application of only a few inflammatory mediators; chronic exposure and/or other mediators may cause repetitive spiking (i.e. have a supraliminal effect) in a larger fraction of neurons.
In summary, this study presents a novel approach to quantify how different pathological factors contribute to qualitative changes in neuronal excitability, and whether different cell types are equally prone to a switch in spiking pattern. Our approach, which involves applying an artificial, yet quantifiable, perturbation to a neuron and assessing how that neuron responds, is conceptually distinct from the more traditional approach of measuring how nerve injury or inflammation affects different ion channels and correlating those molecular changes with changes in neuronal excitability. Necessity-testing experiments in which a particular ion channel is blocked or knocked down/out are invaluable in helping to establish causal links, but quantifying the manipulation tends to be difficult; for example, conducting the required recordings in the same neuron before and after blocking a channel of interest may be technically impossible if certain other channels must be blocked in voltage clamp but not in current clamp. Our dynamic clamp experiments constitute sufficiency-testing and, as demonstrated, can be very quantitative. Beyond adding (or subtracting) specific conductances to test their direct effects on excitability, we have shown here how titrating the added conductance can be used to gauge the susceptibility of a neuron to switch its spiking pattern, and whether pathological factors like inflammation predispose a neuron to switching. This is particularly valuable for deciphering if and how the effects of co-occurring factors combine to cause gross changes in neuronal excitability.