Dynamic-Clamp Analysis of Wild-Type Human NaV1.7 and Erythromelalgia Mutant Channel L858H*

The Na_V voltage-gated sodium channel is preferentially expressed in primary nociceptors (Persson et al. 2010; Rush et al. 2007; Toledo-Aral et al. 1997) and activates at subthreshold membrane voltages so as to boost membrane responses to small depolarizing stimuli both in neuronal somata (Ahn et al. 2013; Cummins et al. 1998; Herzog et al. 2003; Rush et al. 2007) and at axon endings of small dorsal root ganglia (DRG) neurons (Vasylyev and Waxman 2012). Inherited erythromelalgia (IEM), the first human pain disorder linked to a sodium channel, is widely regarded as a genetic model of neuropathic pain. When studied in a mammalian heterologous expression system, the L858H mutation, one of the first Na_V1.7 mutations linked to IEM (Cummins et al. 2004; Rush et al. 2006; Yang et al. 2004), produces a hyperpolarizing shift in channel activation and increases the amplitude of the response of the channel to slow, small depolarizations. When small DRG neurons transfected with L858H and wild-type (WT) Na_V1.7 channels were studied by current-clamp, L858H was found to render DRG neurons hyperexcitable in a manner consistent with the severe pain characteristic of the erythromelalgia phenotype (Rush et al. 2006).

However, a mechanistic link between altered biophysical properties of mutant Na_V1.7 channels and hyperexcitability of primary nociceptor neurons carrying these mutant channels has not yet been established. In the present study, we used dynamic-clamp (Kemenes et al. 2011; Samu et al. 2012; Sharp et al. 1993) recordings to titrate levels of Na_V1.7 WT and L858H conductances so that we could study the effect of precisely calibrated, physiologically relevant levels of conductance on small DRG neuron excitability. This approach permitted us to vary the ratio of expression levels of WT and L858H within the physiological range within single neurons. This is important because, although the exact ratio of WT and L858H channels is not known, it is reasonable to suggest a 1:1 ratio of functional expressions of WT and L858H mutant allele in the affected individual (Yang et al. 2004). Using dynamic-clamp, we show that action potential (AP) current threshold of DRG neurons is regulated by Na_V1.7 conductance in a remarkably linear manner. We also show, in small DRG neurons in which we inserted the L858H mutant by dynamic-clamp, that the mutation substantially increases channel activity at membrane potentials below the AP threshold, producing a large persistent current that depolarizes the membrane potential. We also show that sodium influx via L858H mutant channels is increased not only during subthreshold membrane depolarizations, but also during interspike intervals. These observations on small DRG neurons within a physiologically relevant range of levels of conductance provide a quantitative mechanistic basis for understanding the role of WT Na_V1.7 in healthy DRG neurons and the enhanced excitability of primary nociceptors expressing L858H channels that underlies the pain phenotype in humans carrying this mutation.

Materials and Methods

Voltage-Clamp Recordings of Na_V1.7

Human Na_V1.7 channels were stably expressed in HEK-293 cell line (Cummins et al. 1998). Pipettes were pulled from glass capillaries (cat. no. PG10165-4; World Precision Instruments, Sarasota, FL) and had resistance 1.5–2 MD when filled with the intracellular solution in mM: 140 CsCl, 10 NaCl, 0.5 EGTA, 10 HEPES, 3 MgATP, 10 glucose, pH 7.3 with CsOH. The extracellular solution was HBSS (cat. no. 14025; Invitrogen) in mM: 1.3 CaCl₂, 0.5 MgCl₂, 0.4 MgSO₄, 5.3 KCl, 0.4 KH₂PO₄, 4.2 NaHCO₃, 138 NaCl, 0.3 Na₂HPO₄, 5.6 glucose, supplemented with 15 mM NaCl (320 mosM). The liquid junction potential (+3.7 mV) between pipette and bath solutions was measured according to Neher (1992) and was not compensated. Whole cell voltage-clamp recordings were made using Axopatch 200B amplifier. Currents were low-pass filtered at 10 kHz and digitized/stored at 100 kHz by Digidata 1440A DAC using pCLAMP 10 software (Molecular Devices, Sunnyvale, CA). The series resistance was compensated by 80–85%. -P/4 protocol was used for current-voltage (I–V) and deactivation protocols to subtract uncompensated leak and capacitive currents. Recordings were made at room temperature (23–24°C). All data are presented as means ± SE. Data were analyzed using pCLAMP 10 and Origin 8.5 (OriginLab, Northampton, MA) software.

Assessment of Na_V1.7 Contribution to TTX-S Current in Small DRG Neurons

For assessment of the contribution of Na_V1.7 to the TTX-sensitive (TTX-S) current, DRG neurons were isolated from WT or Na_V1.7-knockout (KO) mice (11–16 wk old) and cultured as previously described (Dib-Hajj et al. 2009). Whole cell voltage-clamp recordings of small (20–25 µm) DRG neurons were obtained at room temperature (20–22°C) within 2–8 h in culture using an EPC 10 amplifier (HEKA Electronics) and fire-polished electrodes (1–2 MD) fabricated from 1.6-mm-outer-diameter borosilicate glass micropipettes (World Precision Instruments). The pipette potential was adjusted to zero before seal formation, and liquid junction potential was not corrected. Voltage errors were minimized with 80–90% series resistance compensation, and linear leak currents and capacitance artifacts were subtracted out using the P/6 method. Currents were acquired with PULSE software (HEKA Electronics) 5 min after establishing whole cell configuration, sampled at a rate of 50 kHz, and filtered at 2.9 kHz. The pipette solution contained in mM: 140 CsF, 10 NaCl, 1 EGTA, and 10 HEPES, pH 7.3 with CsOH (adjusted to 315 mosM with dextrose). The extracellular bath solution contained in mM: 70 NaCl, 70 choline chloride, 3 KCl, 1 MgCl₂, 1 CaCl₂, 20 TEACl, 5 CsCl, 1 4-AP, 0.1 CdCl₂, and 10 HEPES, pH 7.31 with NaOH (326 mosM). The amplitude of TTX-S sodium current was estimated by two protocols as previously described (Rush et al. 2005). Cells were first CsCl, 1 4-AP, 0.1 CdCl held at –80 mV, and a 500-ms depolarizing prepulse to –50 mV was applied to inactivate the TTX-S sodium channels while leaving Na_V1.8 current intact, followed by a series of step depolarizations from –70 to +20 mV (in 5-mV increments). Cells exhibiting Na_V1.9 currents were excluded from data analysis. For the second protocol, cells were held at –80 mV, a 500-ms hyperpolarizing prepulse to –120 mV was applied to rescue the TTX-S sodium channels from inactivation, and total sodium currents were evoked by a series of depolarizing steps from –70 to +20 mV (in 5-mV increments). The TTX-S sodium current was obtained by subtraction of the currents obtained from the two protocols.

Dynamic-Clamp Recording

DRG neurons (soma diameter 21–26 µm; 24.4 ± 0.3, n = 25) obtained from postnatal day 0–5 Sprague-Dawley rats were grown in primary culture for 2–3 days (Ahn et al. 2013; Dib-Hajj et al. 2009). Small DRG neurons were dynamically clamped (Kemenes et al. 2011; Samu et al. 2012; Sharp et al. 1993) in whole cell configuration using patch pipettes pulled from glass capillaries (cat. no. PG10165-4; World Precision Instruments). Pipette resistance was 1.5–2 MD when filled with the intracellular solution in mM: 140 KCl, 3 MgATP, 0.5 EGTA, 5 HEPES, 10 glucose, pH 7.3 with KOH (adjusted to 325 mosM with sucrose). The extracellular solution was HBSS (cat. no. 14025; Invitrogen) in mM: 1.3 CaCl₂, 0.5 MgCl₂, 0.4 MgSO₄, 5.3 KCl, 0.4 KH₂PO₄, 4.2 NaHCO₃, 138 NaCl, 0.3 Na₂HPO₄, 5.6 glucose (adjusted to 325 mosM with sucrose). Liquid junction potential (+3.8 mV) between pipette and bath solutions was not compensated. Membrane voltages and currents were recorded in dynamic-clamp using MultiClamp 700B amplifier (Molecular Devices) interfaced with CED Power1401 mk II DAI and Signal software (Cambridge Electronic Design, Cambridge, United Kingdom), digitized by Digidata 1440A DAC, and stored on the hard disk using pCLAMP 10 software. Capacitance neutralization and bridge balance were rigorously employed to minimize the effect of electrode capacitance and series resistance on the dynamic-clamp recordings. I–V traces were filtered at 10 kHz and digitized at 50 kHz. Series resistance was compensated by 80–85%. Endogenous sodium current recorded in whole cell voltage-clamp was evoked from a holding potential of –50 mV by a test pulse to –10 mV with or without preceding 0.5-s prepulse to –100 mV to remove steady-state inactivation of TTX-S channels. TTX-S channels are mainly inactivated at –50 mV, whereas Na_V1.8 channels are still available for activation at this potential because steady-state inactivation of Na_V1.8 is shifted in a depolarized direction (Catterall et al. 2005). Thus, as described by Cummins and Waxman (1997) and Rush et al. (2005), as a measure of total TTX-S current, we used a conditioning/subtraction protocol and assessed the peak current on the trace obtained by digital subtraction of the current trace evoked by the test voltage without preceding prepulse from that with the prepulse, respectively.

We estimated the contribution of Na_V1.7 to the total TTX-S current in our assay based on measurements of the total TTX-S current amplitude in WT and Na_V1.7-KO DRG neurons (see above). To evaluate the effect of defined levels of L858H functional expression on excitability of small DRG neuron using dynamic-clamp recording, we first estimated the endogenous Na_V1.7 conductance and then substituted graded amounts of endogenous conductance by equal amounts of L858H channel conductance, thus achieving a specified substitution ratio (SR) via a dynamic-clamp operation, SR × g_max(L858H – WT), where g_max is maximal Na_V1.7 endogenous conductance.

Recordings were made at room temperature (23–24°C). All data are presented as means ± SE. Data were analyzed using pCLAMP 10 and Origin 8.5 software. Unless specified otherwise, the hypothesis that population means are significantly different was checked using Mann-Whitney nonparametric test (P < 0.05, P < 0.01, and P < 0.001).

Kinetic Model of Na_V1.7 Channel

We developed our model of Na_V1.7 channel using Hodgkin–Huxley equations dm/dt = α_m(1 − m) − ß_mm; dh/dt = α_h(1 − h) − ß_hh, where m and h are channel activation and inactivation variable and α (ß) are forward (backward) rate constants, respectively. Channel states were independent with a first-order reaction between states. Thus channel activation and deactivation were considered as transitions between closed and open states, whereas channel inactivation and repriming were assumed to be transitions between primed and inactivated states, respectively. Na_V1.7 channel steady-state parameters and kinetics obtained based on electrophysiological recordings were converted into appropriate rate constants at respective voltages using the equations α = m_∞/τ, ß = (1 − m_∞)/τ. These reaction rate constants were fitted with Boltzmann equations of the form y = A2 + (A1 − A2)/{1 + exp[(V − V_1/2)/k]}, where V is membrane voltage, V_1/2 is voltage when reaction rate is half-maximal, and k is slope coefficient. Fits were converted into steady-state inactivation (activation) variables and inactivation (activation) time constants according to m_∞ = α/( α + ß) and τ = 1/(α + ß). The latter curves were overplayed on the experimental data to provide feedback to the rate constants fitting step. This cycle was manually repeated until the best possible fit of the experimental data was achieved. We obtained the following rate constants for the WT Na_V1.7 channel model:

α_m = 10.22 − 10.22/{1 + exp[(V + 7.19)/15.43]}, ß_m = 23.76/{1 + exp[(V + 70.37)/14.53]};

α_h = 0.0744/{1 + exp[(V + 99.76)/11.07]}, ß_h = 2.54 − 2.54/{1 + exp[(V + 7.8)/10.68]}.

We modeled the L858H IEM mutation because it has been well-studied at the voltage-clamp (Cummins et al. 2004) and current-clamp (Rush et al. 2006) levels. We focused on altered activation of the mutant channels because a hyperpolarizing shift in activation is common to all IEM mutant channels (Dib-Hajj et al. 2010). We did not model slow inactivation in the mutant channel because we limited stimulation to 1-s trains at 10 Hz where the development of slow inactivation is not appreciable. The L858H Na_V1.7 channel model was described by the following equations:

α_m = 9.1 − 9.1/{1 + exp[(V + 11.52)/22.49]}, ß_m = 23.76/{1 + exp[(V + 87.6)/14.53]};

α_h = 0.0744/{1 + exp[(V + 99.76)/11.07]}, ß_h = 2.54 − 2.54/{1 + exp[(V + 7.8)/10.68]}.

Sodium current was described by I_Na = g_max × m × h × (V_m − E_Na), where V_m is membrane voltage potential and E_Na = 65 mV is sodium reversal potential. Currents evoked by different voltage protocols were calculated in 10-µs precision using a custom program written in Origin 8.5 LabTalk.

Na_V1.7 current kinetics in response to square test pulses and the resulting I–V curve were identical either when calculated in LabTalk or obtained from dynamic-clamp recordings on a vendors-supplied physical cell model. All data are presented as means ± SE. Data were analyzed using pCLAMP 10 and Origin 8.5 software.

Results

Kinetic Model of WT Na_V1.7 Based on Hodgkin–Huxley Equations

Channel kinetics were described based on a Hodgkin–Huxley model of sodium channel with several independent states and a first-order reaction between the states. Channel activation and deactivation were considered as transitions between closed and open states, whereas channel inactivation and repriming were assumed to be transitions between primed (open or closed) and inactivated states (Hille 1978; Hodgkin and Huxley 1952).

Na_V1.7 currents were recorded in whole cell voltage-clamp to obtain channel steady-state and kinetics parameters. Steady-state inactivation (h_∞) was calculated as the ratio of peak current amplitude to the maximal peak current amplitude elicited by a 0-mV test voltage following a 1-s prepulse at different voltages ranging from –100 to –40 mV in 5-mV increments from a holding potential of –100 mV (figure 1A). Steady-state activation (m_∞) was defined as the ratio of Na_V1.7 g = I_peak/(V_m − E_Na) determined at the respective membrane potentials to the Na_V1.7 g_max (figure 1A). Steady-state relationships of recombinant Na_V1.7 (n = 8 cells) were best fit using a Boltzmann equation with the following parameters: V_1/2 = –73.9 mV, k = 6.2 mV and V_1/2 = –20.4 mV, k = 7.2 mV for channel steady-state inactivation (n = 8) and steady-state activation (n = 17), respectively. Our model accurately described Na_V1.7 channel steady-state properties as can be seen from the respective Boltzmann fits of the modeled steady-state curves, V_1/2 = –72.6 mV, k = 5.7 mV and V_1/2 = –20.4 mV, k = 7.1 mV (figure 1A).

Figure 1 Kinetic model of Na_V1.7 voltage-gated sodium channel based on Hodgkin–Huxley equations. (A) Voltage dependence of conductance/maximal conductance (G/Gmax) at steady-state for inactivation (squares; n = 8) and activation (circles; n = 17) of Na_V1.7 channel. Solid lines are derived from the following equations: h_∞ = *α_h*/(*α_h* + *ß_h*); (m_∞)³ = [*α_m*/(*α_m* + *ß_m*)]³, where m and h are channel activation and inactivation variables and α and ß are forward and backward rate constants (see Materials and Methods). (B) Voltage dependencies of activation (solid circles; n = 8) and deactivation (open circles; n = 14) time constants. Deactivation of the Na_V1.7 current was fitted with a single exponential, whereas channel activation was fitted with a single exponential raised to the 3rd power. (C) Inactivation (solid squares; n = 13) and removal of inactivation (open squares; n = 7) time constant obtained from a single-exponential fit of the respective data. *Inset* shows data replotted with time constants on a log scale. (D) Time sequences of m³ and h variables along with the resulting open probability (m³h) obtained in the model response to a series of voltage steps ranged from –60 to 40 mV in 5-mV increments from a holding potential of –110 mV. (E) Rising phase of the Na_V1.7 current (bottom) in response to a –30-mV test voltage (top) was fitted with a single exponential function of different powers. The best fit was obtained using 3rd-power exponential as determined based on the residual (middle); the residual of the 3rd-power exponential fit was not substantially different from the background noise, thus 4th-power exponential had not further improved the fit. (F and G) Na_V1.7 current evoked by test pulses ranged from –50 to –25 mV in 5-mV increments (black) and overlaid on the m³h model (blue) at the respective voltages. Vertical dashed line denotes stimulus onset time. (H) Current traces (top) and the current-voltage (I–V) curve (bottom) of Na_V1.7 current (black) and the m³h model (blue) at the respective test voltages.

Na_V1.7 current activated in a sigmoidal manner with an apparent delay (figure 1, E and F), which suggests that the channel undergoes multiple closed-state transitions before activation. Channel activation kinetics were best described by a single exponential raised to the third power (figure 1E). Channel activation (figure 1B; n = 8) was determined from current traces elicited by test voltages ranging from –55 to 60 mV in 5- to 10-mV increments applied from –100-mV holding potential. Deactivation time constant (figure 1B; n = 14) was determined from a single-exponential fit of the respective portions of current traces (“tail currents”) measured at different test voltages ranging from –100 to –20 mV following a 0.5-ms voltage step to –10 mV from a holding potential of –100 mV. The falling phase of the current (90 to 10% amplitude) was fitted with a single exponential to obtain the inactivation time constant (figure 1C; n = 7). The following protocol was used to evaluate channel repriming kinetics [for details, see Cummins et al. (1998)]. First, a 20-ms test voltage step to 0 mV was applied from a holding potential of –100 mV to inactivate the channel, and then repriming voltage steps of different durations (from 2 to 1,000 ms) were applied at a given voltage followed by the second 20-ms test voltage to 0 mV. The ratios of peak current amplitudes measured at the first and second test voltages were plotted as a function of the repriming step duration; this function was fitted with a single exponential to obtain a time constant of channel removal from inactivation (figure 1C; n = 14).

Our model effectively described channel kinetics as can be seen from the close match between the modeled and experimentally determined activation-deactivation (figure 1B) and inactivation-repriming (figure 1C) time constants at a wide range of physiological membrane voltages. The obtained Hodgkin–Huxley variables m³ and h were both highly voltage-dependent with submillisecond activation kinetics resulting in a transient channel open probability in response to a series of voltage steps (figure 1D). Our model accurately followed the kinetics of Na_V1.7 current evoked by a series of depolarization steps (figure 1, F and G). The resulting I–V relationships also provided a match between modeled and experimentally determined data at a wide range of physiological membrane voltages (figure 1H). Thereafter, we utilized this model (WT) and its modification for the L858H mutant channel to study mechanisms of functional contribution of Na_V1.7 channel to neuronal excitability in normal and pathological conditions.

Na_V1.7 Conductance Regulates Current Threshold for AP Generation in a Linear Manner

We performed a quantitative analysis of the effect of graded additions or subtractions of sodium conductance resulting from Na_V1.7 channel function on small DRG neuron excitability using dynamic-clamp. Although we had the capability to transfect DRG neurons with Na_V1.7 channels to study the effect of the channel on neuronal excitability (Dib-Hajj et al. 2009; Rush et al. 2006), transfection does not permit accurate calibration of the level of Na_V1.7 channel that is being expressed. Thus we carried out dynamic-clamp recording in DRG neurons based on experimentally determined Na_V1.7 gating properties and an assumption that Na_V1.7 contributes on average 70% of the TTX-S current in small DRG neurons. We based our estimate of the Na_V1.7 contribution of 70% of the TTX-S current in small DRG neurons on our measurements of total TTX-S currents in mice that are deficient in Na_V1.7 (figure 2). Figure 2A shows representative family traces of TTX-S sodium currents recorded in DRG neurons from WT and Na_V1.7-KO mice, respectively. Peak current densities were 143 ± 17 pA/pF (n = 16) for TTX-S sodium channels recorded from WT DRG neurons. However, DRG neurons from Na_V1.7-KO mice produced significantly smaller TTX-S sodium currents with current densities ~32% (46 ± 9 pA/pF, n = 16) of that in WT DRG neurons (figure 2B).

Figure 2 Measurement of Na_V1.7 contribution to TTX-sensitive (TTX-S) current in small dorsal root ganglia (DRG) neurons. (A) Representative I–V curve family traces of TTX-S sodium currents recorded from wild-type (WT) and Na_V1.7-knockout (KO) DRG neurons, respectively. (B) TTX-S currents in Na_V1.7-KO DRG neurons are significantly smaller than in WT DRG neurons. ***P < 0.001.

Using dynamic-clamp with the Na_V1.7 channel model, we studied how increases in the level of Na_V1.7 conductance affect small DRG neuron excitability. Dynamic-clamp allowed us to add graded increments of Na_V1.7 current to the cell, matching the injected conductances to the predicted contribution of Na_V1.7 channels to the TTX-S current (70% of total TTX-S current in each cell is assumed to be produced by Na_V1.7; see above). We found that the current threshold (defined when the 2nd differential of AP changes its sign) inversely correlated in a linear fashion (r² = 0.97, current threshold; r² = 0.98, incremental threshold change) with the addition of Na_V1.7 conductance (figure 3, A and B). Current threshold decreased from its original value (426 ± 82 pA, n = 9) to a value of 310 ± 65 pA (n = 9) when Na_V1.7 was doubled by dynamic-clamp. Since current threshold variability was large (current threshold in 9 control cells was 350, 230, 470, 525, 340, 240, 90, 840, and 750 pA) in small DRG neurons, we normalized the effect of the Na_V1.7 channel addition on current threshold and expressed it in the form 100% × ΔCT/CT₀, where ΔCT is current threshold change at the respective level of Na_V1.7 addition and CT₀ is native current threshold. The normalized current threshold change significantly decreased (Mann-Whitney, P < 0.001) from –5.6 ± 0.8% (addition of 12.5% Na_V1.7) to –28.1 ± 3.5% (addition of 100% Na_V1.7). Importantly, stimulation with a current equivalent to the current threshold when Na_V1.7 conductance was doubled did not elicit an AP in a DRG neuron with native levels of Na_V1.7 (figure 3, A and B). Electronic addition of Na_V1.7 conductance also resulted in an enhancement of AP firing probability (figure 3C). A 10-Hz train of 10 current pulses 10-ms duration each applied at the threshold level evoked 1.7 ± 0.3 APs in control cells vs. 4.3 ± 0.5 (n = 8; P < 0.01), 6.1 ± 0.7 (n = 8; P < 0.01), 8.4 ± 0.7 (n = 8; P < 0.001), and 9.4 ± 0.5 (n = 8; P < 0.001) after electronic addition of 12.5, 25, 50, and 100% Na_V1.7 conductance, respectively (figure 3D).

Figure 3 Additional Na_V1.7 conductance lowers current threshold for action potential (AP) generation and increases AP firing probability. (A) 10-ms-long test pulses (top) applied at the original threshold without additional conductance (left) and at the threshold after electronic addition of 50% Na_V1.7 conductance (right) elicited APs (bottom). Control stimulus and AP traces are shown in black, and those after addition of 50% Na_V1.7 conductance are shown in blue. (B) Averages of current threshold (top) and current threshold change (bottom) plotted as a function of additional Na_V1.7 conductance (n = 9). The solid line is a linear regression fit (r² = 0.97, top; r² = 0.97, bottom) of the data. Statistical analysis on the bottom was performed between threshold increments obtained at 12.5% and at the respective percentage of conductance increment. *P < 0.05, **P < 0.01, and ***P < 0.001. (C) APs evoked by a 1-s-long, 10-Hz train of current pulses (10-ms pulse width) applied at the original threshold level (100% native Na_V1.7 conductance). Electronic addition of Na_V1.7 conductance (expressed as the incremental increase over the endogenous Na_V1.7 conductance) is noted on the y-axis. Scale bar, 200 ms. (D) Averages of the number of APs evoked by the protocol described in C plotted as a function of dynamically introduced Na_V1.7 conductance (n = 8).

It is reasonable to suggest that electronic subtraction of Na_V1.7 conductance will reduce neuronal excitability. Indeed, incremental addition of graded levels of negative Na_V1.7 conductance resulted in an increase of current threshold in a linear fashion (r² = 0.99) and in incremental (r² = 0.98) reduction of AP firing probability (figure 4, A and B). A 10-Hz train of 10 current pulses applied at 1.5× threshold level evoked 9.9 ± 0.1 APs (n = 15) in control cells vs. 9.4 ± 0.4 (n = 15), 7.8 ± 0.6 (n = 15; P < 0.001), 5.3 ± 1.7 (n = 15; P < 0.001), and 2.0 ± 1.0 (n = 15; P < 0.001) after dynamic-clamp subtraction of 12.5, 25, 50, and 100% Na_V1.7 conductance, respectively (figure 4, A and B). In the same cells, current threshold increment significantly increased from 3.9 ± 0.7 to 9.4 ± 1.6% (n = 13; P < 0.01), 17.1 ± 2.3% (n = 13; P < 0.001), and 32.8 ± 3.4% (n = 13; P < 0.001) in response to 12.5, 25, 50, and 100% reduction of Na_V1.7 conductance. Since the Na_V1.7 channel begins to activate at –55 to –50 mV (figure 1A), it is possible that subtraction of Na_V1.7 conductance results in a reduced sodium current at subthreshold voltages, lowering the net current influx so that, to achieve AP threshold, the stimulus intensity would need to be increased to compensate for the lower sodium charge. Our measurements of Na_V1.7 channel activity in a dynamic-clamped DRG neuron support this hypothesis. Na_V1.7 began to activate at about –53 mV, reached 62% of its peak value at–32-mV threshold voltage, and reached peak amplitude at –19 mV (figure 4C). In the example shown, Na_V1.7 sodium influx at subthreshold voltages comprises ~21% of the total sodium charge due to Na_V1.7 channel activity occurring in the time interval between stimulus onset and AP undershoot (figure 4C). Subsequently, the channel inactivates quickly, and the resulting current is not present during the interspike interval provided membrane potential is not ramping back to the threshold level (figure 4D, but see figure 5C). The relatively slow channel repriming kinetics at membrane voltages close to resting membrane potential (RMP; figure 1C) still allow the channel to recover from inactivation during 10-Hz stimulation cycle without significant accumulation of inactivation (figure 4D, bottom). These data suggest that Na_V1.7 channel activity at subthreshold membrane voltages drives the set point of current threshold for AP generation, thus regulating AP firing probability.

Figure 4 Removal of Na_V1.7 conductance raises current threshold for AP generation and reduces AP firing probability. (A) APs were evoked by 10-ms-long current pulses applied at 1.5× threshold amplitude in control (Ctrl; black) and after electronic subtraction of the incremental values of Na_V1.7 conductance. Dynamic-clamp subtraction of Na_V1.7 conductance (expressed as the incremental decrease over the endogenous Na_V1.7 conductance) is noted on the y-axis. Scale bar: 200 ms. (B, top) Averages (n = 13) of current threshold change in response to the subtraction of respective proportion of endogenous Na_V1.7 conductance. The solid line is a linear regression fit (r² = 0.99) of the data. Statistical analysis on the top was performed between threshold increments obtained at 12.5% and at the respective percentage of conductance increment. (B, bottom) Averages (n = 15) of the number of APs evoked by the protocol described in A and plotted as a function of dynamically subtracted Na_V1.7 conductance; the solid line is a linear regression fit (r² = 0.98) of the data. **P < 0.01 and ***P < 0.001. (C) AP (top) evoked by a 10-ms-long current stimulus of 1.5× threshold intensity in control (black) and after dynamic-clamp subtraction of 12.5% of Na_V1.7 conductance (blue) and the respective Na_V1.7 model current (bottom). (D) APs (top) evoked by the protocol described above in control (black) and after dynamic-clamp subtraction (middle) of 12.5% of endogenous Na_V1.7 conductance. The I–V phase plot of the model Na_V1.7 conductance dynamically subtracted during neuronal repetitive firing is shown on the bottom. Note that the positive-going (outward) dynamic-clamp current shown in C and D is flipped over 0 line to facilitate comparison of Na_V1.7 current across the manuscript.

Figure 5 Kinetic model of L858H Na_V1.7 channel predicts a substantial enhancement of the persistent sodium current (I_Na) during repetitive firing of DRG neuron. (A) Normalized I–V relationships obtained from WT (blue) and L858H (LH; red) Na_V1.7 channel models. Respective traces of the I_Na = g_maxm³h(V_m – E_Na) model, where V_m is membrane voltage potential and E_Na = 65 mV is sodium reversal potential, used to obtain the I–V plot are presented on top. (B) Comparison of steady-state inactivation and steady-state activation (left), steady-state channel open probability (Po; middle), and activation time constant (τ; right) of the kinetic model of WT (blue) and L858H (red) Na_V1.7 channel. (C, top) The trace shows repetitive firing of a spontaneously active small DRG neuron. The neuron spontaneously fired APs under i=o current-clamp conditions, i.e., with no additional injected current. A small –50-pA constant current was injected to stop AP firing. The trace presented in C, top, was recorded in response to the removal of the stabilizing –50-pA current. (C, bottom) Modeled WT (blue) and L858H (red) Na_V1.7 currents obtained in response to the voltage command shaped in the form of the AP shown in C, top. Current-clamp recordings shown in C, *top*, were obtained from small DRG neuron in primary culture transfected by electroporation with WT Na_V1.7 (Dib-Hajj et al. 2009). D: I–V phase plots of WT (blue) and L858H (red) Na_V1.7 currents presented in C, bottom. Both models were calculated in a 28-pF equipotential sphere of 1 µF/cm² capacitance; conductance density was set to 0.029 S/cm².

Model of Na_V1.7 L858H Mutant Predicts an Enhanced Level of Channel Activity during Repetitive Firing of DRG Neuron

The L858H mutation in human Na_V1.7 has been shown to be associated with a neuropathic pain syndrome, IEM (Yang et al. 2004). The mutation produces a hyperpolarizing shift in channel activation, slows channel deactivation, and causes an increase in amplitude of the Na_V1.7 current in response to slow, small depolarizations (Cummins et al. 2004). When expressed in the native cell environment, transfection with mutant channels renders small DRG neurons hyperexcitable and is associated with depolarized RMP and reduced current threshold (Rush et al. 2006). To study the mechanism of Na_V1.7 L858H-induced neuronal hyperexcitability in more detail, we performed quantitative evaluations of the effect of graded dynamic-clamp substitutions of L858H mutant conductance for WT Na_V1.7 conductance on the electrical excitability of small DRG neurons. In the absence of empirical data, we assumed that the level of functional WT and L858H channels in the DRG neuron plasma membrane was the same.

First, we constructed a Hodgkin–Huxley (Hodgkin and Huxley 1952) model of the L858H channel based on the previously reported data (Cummins et al. 2004) by appropriately modifying our kinetic model of WT Na_V1.7 channel. We adjusted activation rate constants to account for the –14-mV shift of L858H channel steady-state activation and for the altered mutant deactivation (figure 5B). The resulting kinetic model of L858H channel had a significantly enhanced window current (window current is defined as m³ × h at steady-state; figure 5B) and an apparent leftward shift of I–V curve in a manner consistent with data reported by Cummins et al. (2004) (figure 5, A and B). Maximal steady-state channel open probability increased 17-fold from 9.5 × 10^–5 at –32.3 mV to 1.6 × 10^–3 at –51.5 mV (figure 5B); when measured at –63-mV RMP, it increased 255-fold from 3.8 × 10^–6 to 9.7 × 10^–3 (figure 5B). Here and thereafter, both WT and L858H models were calculated in a 28-pF equipotential sphere of 1 µF/cm² capacitance; conductance density was set to 0.029 S/cm². We further studied differences of WT and L858H channel behavior in response to a voltage command shaped in the form of membrane potential previously recorded from spontaneously active small DRG neuron (figure 5C, top). Both WT and L858H channels were active at subthreshold levels during ramplike membrane depolarizations between APs (figure 5C, left) as well as during APs (figure 5C, right). L858H model channel was already activated at a –62-mV initiation point producing –115-pA inward current, whereas WT channel produced only –0.5-pA current at this voltage. During the second cycle of AP firing, L858H channel began to activate at –70-mV undershoot (–2 pA) and reached –209 pA at –54 mV, whereas WT channel just began to activate (–2 pA) at –54 mV. At the –33.5-mV AP voltage threshold, WT current was –115 pA, whereas L858H current was –657 pA. L858H current peaked (–659 pA) at –32.7 mV, and WT current peaked (–320 pA) at –2.9 mV. Within the postpeak 0.5 ms (WT) and 1 ms (L858H), current declined sharply to about –20 pA at the 56.8-mV AP overshoot. This pattern of L858H channel activity resulted in a substantial enhancement of the sodium influx at subthreshold membrane voltages (WT, 4.1 × 10^–13 C and L858H, 1.1 × 10^–11 C) as well as during AP (WT, 2.8 × 10^–13 C and L858H, 7.7 × 10^–13 C). The differences in the pattern of WT and L858H channel activity remain unchanged throughout the repetitive cycle of AP firing (figure 5, C and D). Steady-state inactivation and inactivation kinetics were not affected by L858H mutation. Hence, both WT and L858H channels showed a similar level of use-dependent inactivation (figure 5, C and D).

The model predicts a substantial enhancement of Na_V1.7 L858H mutant activity over a wide range of physiological membrane voltages during interspike intervals, at subthreshold levels of depolarization, and in the course of AP, thus increasing the sodium charge inflow.

Our kinetic model of the L858H mutant channel, consistent with the data published previously (Rush et al. 2006), predicted that expression of L858H mutant should enhance neuronal excitability. To test this hypothesis, we evaluated the effect of defined levels of L858H functional expression on electrical excitability of small DRG neurons using dynamic-clamp recording. A single-allele mutation of SCN9A, assuming equal efficiency of expression of WT and mutant channels, most probably results in 1:1 ratio of WT and L858H expressions in sensory neurons of the affected individual; however, the exact stoichiometry of WT-to-L858H expression is not known. We therefore used dynamic-clamp to assess the effect of substitutions of graded amounts of L858H current for WT current. In designing our experiments on rat DRG neurons, we first estimated the endogenous Na_V1.7 conductance (see above for details) and then dynamically substituted graded amounts of endogenous conductance by equal amounts of L858H channel conductance. Essentially, we performed dynamic-clamp operation SR × g_max(L858H – WT).

We first tested the effect of WT-to-L858H substitution on current threshold. An AP was first evoked in a control DRG neuron without any current substitution by a 10-ms current pulse of threshold intensity (figure 6A). WT-to-L858H substitution was then implemented and resulted in a substantial inward current that developed at subthreshold voltages during stimulation and an apparent shortening of the delay for AP generation. The amplitude of the AP was not affected and was (from overshoot to undershoot) 113.9 mV in control vs. 114.8 (112.6) mV at a 25% (50%) SR [i.e., at 25% (50%) L858H]. At the same time, the maximal rate of AP rise became progressively smaller, being 114.2, 109.5, and 96.1 mV/ms in control and 25 and 50% SR, respectively (figure 6, A and B). We suggest that this deceleration of AP rate of rise could be the result of the additional inactivation of endogenous channels due to the depolarization of RMP described below; however, we cannot exclude the possibility that the reduction of net (L858H – WT) current seen at the respective voltage of AP maximal rise rate (20 mV; 527 pA at 25% SR and 385 pA at 50% SR) is a causative factor (figure 6B, right). Substitution of WT-to-L858H conductance in incremental amounts resulted in the reduction of AP current threshold in a linear manner (r² = 0.96, figure 6C, top; r² = 0.97, figure 6C, bottom). Current threshold was 668 ± 142 pA (control, n = 5) and was reduced to 598 ± 188, 457 ± 92, 328 ± 53, and 133 ± 20 pA (n = 5; P < 0.05) after 12.5, 25, 50, and 100% WT-to-L858H substitution, respectively (figure 6C). The reduction of current threshold was accompanied by enhancement of AP firing probability (figure 6D). A 10-Hz train of 10 current pulses applied at the threshold level evoked on average 1.3 ± 0.2 APs in control and 8.9 ± 0.5, 9.3 ± 0.6, 8.9 ± 1.0, and 8.4 ± 1.0 APs (n = 5; P < 0.01) after 12.5, 25, 50, and 100% WT-to-L858H substitution, respectively (figure 6E).

Figure 6 L858H mutant lowers current threshold and enhances AP firing probability of DRG neuron. (A) AP (bottom, left) evoked by 10-ms-long stimulus (on top) of threshold intensity in control (black) and after implementation of 25% (green) and 50% (red) WT-to-L858H substitution ratio (SR); traces of the respective AP rate of change are shown in bottom, right. (B) Trajectory plots of AP rate of change (left) and the respective trajectory of stimulus (right) recorded at incremental levels of WT-to-L858H substitution; data are obtained from APs shown in A. (C) Current threshold (top) and current threshold change (bottom) obtained at different levels of WT-to-L858H conductance substitution in dynamically clamped DRG neuron. Solid line represents linear regression fit of the data (n = 5; top, r² = 0.96; bottom, r² = 0.97). Statistical analysis on the bottom was performed between threshold increments obtained at 12.5% and at the respective percentage of conductance increment. *P < 0.05. (D) APs evoked by a 10-Hz train of 10-ms-long current pulses of threshold intensity in control (black) and after incremental levels (the value is depicted on the left to the y-axis) of WT-to-L858H conductance substitution. Scale bar, 200 ms. (E) Averages (n = 5) of the number of APs evoked by the protocol presented in D at different levels of WT-to-L858H conductance substitution. **P < 0.01.

The present findings confirm earlier results (Rush et al. 2006) showing that the reduction of current threshold and the enhancement of AP firing probability are accompanied by RMP depolarization (figure 7C). At a mechanistic level, the present results add to the previous findings by showing that RMP depolarization is driven by the persistent window activity of L858H channel at membrane voltages close to RMP (figure 5B, middle). The effect of WT conductance subtraction in (L858H – WT) model on DRG neuron RMP was negligible since addition or subtraction of up to 100% of WT Na_V1.7 conductance, performed in a set of additional experiments, did not significantly affect RMP of DRG neurons in the –65- to –62-mV range of recorded RMP (figure 7, A and B). The average RMP of DRG neurons was (mean ± SE, n = 6; P > 0.05): –64 ± 0.6 mV in control and –63.5 ± 0.8, –63.8 ± 0.7, –64.0 ± 0.5, –63.6 ± 0.6, –63.6 ± 0.6, –63.7 ± 0.7, –63.9 ± 0.8, and –64.0 ± 1.0 mV after addition of –100, –50, –25, –12.5, +12.5, +25, +50, and +100% WT conductance, respectively (figure 7, A and B). In contrast, WT-to-L858H substitution significantly depolarized RMP from –63.4 ± 0.6 mV in control to –62.3 ± 0.5 mV (n = 6; P > 0.05), –60.7 ± 0.8 mV (n = 6; P < 0.05), –58.4 ± 0.9 mV (n = 6; P < 0.01), and –56.6 ± 1.3 mV (n = 6; P < 0.01) after 12.5, 25, 50, and 100% WT-to-L858H conductance exchange, respectively (figure 7D).

Figure 7 L858H mutant drives depolarization of resting membrane potential (RMP) of DRG neuron. (A) Dynamic-clamp recordings of RMP (bottom) and WT current (top) of DRG neuron in control and after addition of 100% WT Na_V1.7 conductance. (B) Averages (n = 6) of the RMP (top) and the RMP changes (bottom) as a function of addition or subtraction of the incremental values of WT Na_V1.7 conductance. (C and D) Data description is similar to A and B, but the RMP data were obtained as a response of WT-to-L858H substitution (WT conductance was dynamically subtracted while the equivalent amount of L858H conductance was added) at incremental levels ranging from 12.5 to 100% (n = 6). Statistical analysis on the bottom was performed between RMP changes obtained at 12.5% SR and at the respective percentage of conductance SRs. *P < 0.05 and **P < 0.01.

L858H Mutant Enhances DRG Neuron Excitability by Increasing Sodium Influx during Subthreshold Membrane Depolarizations and Interspike Intervals

Our model of the L858H mutant predicts an enhanced level of channel activity at subthreshold and suprathreshold voltages during repetitive firing of DRG neuron (see figure 5 and text above). The additional sodium charge inflow predicted by our results would be expected to be proexcitatory and should lead to enhanced neuronal excitability. We tested this hypothesis in dynamically clamped DRG neurons by assessing the response to a 10-Hz train of 10-ms depolarizing stimuli of two models: WT and (L858H – WT). We wanted to compare numerically the effect of these two models of channel activity on neuronal excitability side by side and first present data at 12.5% WT channel conductance addition and the respective 12.5% WT-to-L858H conductance exchange, since 12.5% SR is the minimal substitution studied for which AP firing is affected.

We found that L858H channels were already active at –63.4-mV RMP, producing current responsible for ~1-mV depolarizing shift of the RMP (–63.4 ± 0.6 mV in control and –62.3 ± 0.5 mV after 12.5% SR, n = 6, P > 0.05, but with a clear depolarizing trend of RMP), whereas WT current was not detectable above the noise, thus having no effect on RMP (–64 ± 0.6 mV in control and –63.6 ± 0.6 mV after addition of 12.5% WT conductance; figure 8, A–D). WT current began to activate (–3 pA) at –50.9 mV and reached its –216-pA maximum amplitude at 12.4 mV, a value of membrane voltages well above –40-mV AP threshold. In contrast, (L858H – WT) net current was already active (–21 pA) at –63-mV RMP and reached its maximum (–452 pA) at –30.6 mV. During interspike intervals, the net current resulting from (L858H – WT) substitution gradually increased from –1 pA at –69.5 mV to –20 pA at –64 mV, contributing to the development of slow, ramplike depolarization of the membrane potential (figure 8, D and E), whereas current produced by WT model was not detectable above the noise (figure 8, B and E). Significantly more net charge was carried by the (L858H – WT) compared with WT (in pA*ms/nA, we normalized current charge to the amplitude of native Na_V1.7 current to account for cell-to-cell variability in the level of endogenous Na_V1.7 current): 6.6 ± 1.2 (WT, n = 8) vs. 48 ± 10 (L858H, n = 5; P < 0.01) during subthreshold depolarization; and –0.2 ± 0.32 (WT, n = 8) compared with 58.2 ± 10.4 (L858H, n = 5; P < 0.01) during interspike intervals; whereas the charge during AP actually was smaller for mutant cells, 12.6 ± 6.3 (L858H, n = 5), compared with WT, 22 ± 3.5 (n = 8). These data indicate that the substantial increase of L858H channel activity at subthreshold membrane voltages results in a significant amplification of net sodium influx, subsequent depolarization of the membrane potential, reduction of current threshold, and ensuing enhancement of AP firing probability. These observations reveal enhancement of small DRG neuron excitability by substitution of as little as 12.5% of the Na_V1.7 channels of the cell with L858H channel (i.e., with expression of the mutant channel at a density much lower than expected for a cell with 1 mutant allele) and demonstrate the powerful effect of the mutant channels on nociceptor excitability.

Figure 8 L858H mutant augments DRG neuron excitability by enhancing sodium influx at subthreshold (subthresh) membrane voltages. (A) AP evoked by a 10-ms-long current pulse of threshold intensity in control (black) and after dynamically introduced +12.5% WT conductance (blue). APs are shown on the top (stimulation protocol is shown on top of APs), and the respective Na_V1.7 current is presented in the bottom. (B) AP repetitive firing (top) evoked by a 10-Hz train of 10-ms-long current pulses at threshold intensity in control (black) and after 12.5% WT addition (blue); dynamic-clamp recording of the 12.5% WT current addition is shown on the bottom. (C and D) Same protocols as shown in A and B, but the comparison is made between data obtained in control (black) and after dynamic-clamp substitution of 12.5% WT to 12.5% L858H conductance. (E) I–V phase plots of dynamic-clamp recordings of repetitive AP firing in DRG neuron presented in B and D at +12.5% WT (blue) and at 12.5% WT to 12.5% L858H substitution (red). (F) Modeled sodium currents were recorded in dynamic-clamp mode and subsequently integrated over 3 different time intervals: (1) from stimulus onset to AP threshold (threshold is defined when 2nd differential of AP changes its sign); this interval extends from arrow 1 to 2 in A and C; (2) from threshold to undershoot; this interval extends between arrows 2 and 3 in A and C; and (3) from undershoot to the next stimulus onset. Sodium charge (pA*ms) was normalized to the peak value of the native Na_V1.7 sodium current measured in each DRG neuron in voltage-clamp (see Materials and Methods). The data represent the model channel activity at +12.5% WT addition (n = 8, blue) and 12.5% WT-to-L858H substitution (n = 5, red). **P < 0.01.

Finally, as a model of nociceptors in patients carrying the L858H mutation, where single-allele mutation of SCN9A probably results in a ratio close to 1:1 of WT and L858H, we assessed the effect of a 50% SR of L858H channels. The model produced –37 ± 2 pA (n = 6) persistent current at rest (figure 9, A and B), which depolarized RMP on average by 5 mV from –63.4 ± 0.6 mV in control to –58.4 ± 0.9 mV (n = 6; P < 0.01) after 50% WT-to-L858H conductance exchange (figure 7D and figure 9, A and B). This current activated further at subthreshold membrane potentials in response to depolarizing current injection, reached –432 ± 112 (n = 6) peak at 2.7 ± 0.4 ms poststimulus before AP threshold, and then promptly declined to essentially zero level within the next 3.6 ± 0.7 ms (figure 9A). The net charge inflow due to the (L858H – WT) model activity during subthreshold depolarization and during AP was 0.8 ± 0.3 pC and 0.3 ± 0.2 pC (n = 6), respectively (figure 9C). During first interspike intervals, the net current resulting from 50% (L858H – WT) SR produced 2.9 ± 0.5 pC charge inflow, contributing to the development of slow, ramp-like depolarization of the membrane potential (figure 9, B and C). These observations of increased sodium influx underlying enhancement of small DRG neuron excitability following L858H substitution provide a mechanistic link between altered function of mutant channels and nociceptor hyperexcitability underlying the pain phenotype in patients carrying the Na_V1.7 L858H mutation.

Figure 9 A single-allele *SCN9A* mutation: L858H functional evaluation in small DRG neuron. (A) AP evoked by a current pulse of threshold intensity in control (black) and after dynamic-clamp 50% exchange of WT-to-L858H conductance (red). APs are shown on the top (stimulation protocol is shown on top of APs), and the respective Na_V1.7 current differential is presented in the bottom. (B) AP repetitive firing (top) evoked by a 10-Hz train of current pulses (same as in A) at threshold intensity in control (black) and after 50% WT-to-L858H SR (blue); dynamic-clamp recording of the 50% (L858H – WT) current is shown on the bottom. (C) Dynamic-clamp (L858H – WT) model currents at 50% SR of endogenous Na_V1.7 conductance were integrated over 3 different time intervals: (1) from stimulus onset to AP threshold (arrow 1 to 2 in A); (2) from threshold to undershoot (arrows 2 and 3 in A); and (3) from undershoot to the next stimulus onset. Sodium charge (pA*ms) was normalized to the peak value of the native Na_V1.7 sodium current (n = 6). Kruskal-Wallis ANOVA nonparametric test for 3 populations was used to determine whether the samples come from different populations (P < 0.01).

Discussion

Our dynamic-clamp recording in native rat DRG neurons shows that increasing the Na_V1.7 conductance density lowers threshold for a single AP and increases the number of APs fired in response to a train of depolarizing stimuli. Our data show a linear inverse relationship between functional Na_V1.7 conductance and current threshold (the minimal stimulus capable of eliciting an AP). Consistent with the latter, we found a direct correlation between Na_V1.7 conductance and AP firing probability. The relationship between Na_V1.7 conductance and AP firing probability was also linear in the 0–25% range of additional Na_V1.7 conductances. Saturation at 50–100% level was at least in part due to reaching maximal possible number of APs that could be evoked by our stimulation protocol.

It is generally accepted that TTX-S channels, including Na_V1.7 channel, can function as a subthreshold sodium channel that amplifies membrane response to small depolarizing stimuli at subthreshold membrane voltages both in DRG neuron soma (Blair and Bean 2002; Choi and Waxman 2011; Kovalsky et al. 2009; Rush et al. 2007) and at the axon endings of primary sensory neurons (De Col et al. 2008; Pinto et al. 2008; Vasylyev and Waxman 2012). The functional impact of Na_V1.7 channel activity on neuronal excitability and pain signal processing has been generally studied using an “all-or-none” paradigm using genetic knockout (Nassar et al. 2004) of Na_V1.7 channel function. Functional contributions of Na_V1.7 to DRG neuron excitability, including current and voltage thresholds for AP generation and AP repetitive firing, have also been studied using computer simulations of DRG neurons (Choi and Waxman 2011; Herzog et al. 2001; Kouranova et al. 2008; Kovalsky et al. 2009; Sheets et al. 2007). However, dynamic-clamp recording is superior to computer simulation for quantitative study of Na_V1.7 channel function because it records the response of native neurons without making assumptions regarding which conductances to include in the computer model (Kemenes et al. 2011; Samu et al. 2012; Sharp et al. 1993). Our immediate and quite unexpected observation was that Na_V1.7, when studied in the native DRG neuron environment, regulated the set point for AP current threshold in a remarkably linear manner: increasing or reducing Na_V1.7 conductance by as little as 12.5% or as much as 100% produced a graded effect with a high degree of linearity over a 200% range of Na_V1.7 conductances. We found that substitution of as little as 12.5% of channels with L858H produces hyperexcitability in DRG neurons. This observation predicts that expression of L858H produces hyperexcitability of DRG neurons even if the 50% reduction of current density seen after expression of L858H in HEK-293 cells (Cummins et al. 2004) applies to nociceptors.

Within the domain permitted by our stimulation protocol, Na_V1.7 also regulated AP firing probability in a linear manner. This observation may be relevant to the pathophysiology of acquired pain since abnormal accumulations of Na_V1.7 have been demonstrated at nerve endings within painful neuromas in rats (Persson et al. 2011) and humans (Black et al. 2008), and Na_V1.7 levels and TTX-S current density have been shown to increase in DRG neurons in response to inflammation (Black et al. 2004) and in diabetic rats (Chattopadhyay et al. 2008, 2011). We would note, however, that although our previous patch-clamp analysis of small-diameter DRG neuron axons in vitro demonstrated a resting potential similar to that in DRG neuron somata, and sequential activation during AP clamp of TTX-S and TTX-resistant currents with characteristics attributed to Na_V1.7 and Na_V1.8 (Vasylyev and Waxman 2012) similar to that seen in DRG neuron somata (Blair and Bean 2002), we cannot exclude the possibility that the properties and functional role of Na_V1.7 are not identical in DRG neuron somata vs. sensory axons and their terminals.

Dynamic-clamp requires an input of a kinetic model of the channel under study. Several kinetic models of TTX-S sodium channels, including Na_V1.7 channel, have been recently proposed (Gurkiewicz et al. 2011; Herzog et al. 2001; Kovalsky et al. 2009; Sheets et al. 2007). These models rely on experimental data for TTX-S channels steady-state and kinetic properties with some degree of variability since these were obtained in different studies. This variability may be attributed, at least in part, to differences in recording solutions and in voltage protocols. TTX-S channel recordings were often performed using fluoride-based intracellular solution, which shifts the voltage dependence of Na_V1.7 channel steady-state and kinetic parameters (Coste et al. 2004; Meadows et al. 2002; Saab et al. 2003; Sheets et al. 2007). At the same time, current-clamp recordings of AP firing in DRG neurons are commonly performed in a physiologically relevant chloride-based intracellular solution (Dib-Hajj et al. 2009; Estacion et al. 2011; Rush et al. 2006). It is reasonable to develop the kinetic model of Na_V1.7 channel based on voltage-clamp data obtained under conditions similar to those where this model is utilized. Thus we developed a kinetic model of recombinant Na_V1.7 channel based on voltage-clamp recordings obtained using intracellular solution essentially similar to that used for dynamic-clamp; the single difference between voltage-clamp and dynamic-clamp pipette solutions was that potassium chloride was replaced by cesium chloride on 1:1 basis (see Materials and Methods). We also used the same HBSS bath solution for voltage-clamp and dynamic-clamp recordings. Additionally, we performed a detailed analysis of Na_V1.7 channel activation kinetics. Although an m³ model is generally accepted for sodium channel gating in squid giant axon (Hodgkin and Huxley 1952), mammalian skeletal muscles (Chanda and Bezanilla 2002), and mammalian sensory neurons (Herzog et al. 2001; Kostyuk et al. 1981; Ogata and Tatebayashi 1993; Sheets et al. 2007), an m² model of TTX-S sodium channel activation has been suggested in mammalian central neurons (Baranauskas and Martina 2006). Consistent with previous studies of TTX-S sodium current (Herzog et al. 2001; Kostyuk et al. 1981; McCormick et al. 2007; Ogata and Tatebayashi 1993; Sheets et al. 2007), we found that recombinant Na_V1.7 channel activated with an apparent delay, suggesting multiple transitions between closed states, in a sigmoidal manner with activation kinetics best described by m³ model.

The Na_V1.7 L858H mutation was identified in a patient with hereditary primary erythromelalgia (Yang et al. 2004). Subsequent studies showed that the L858H mutation produces a –13.5-mV hyperpolarizing shift of Na_V1.7 channel activation, slows channel deactivation, and enhances Na_V1.7 current amplitude in response to slow, small depolarizations in a manner consistent with its erythromelalgia phenotype (Cummins et al. 2004). We modeled kinetics of the L858H mutant by appropriately adjusting WT channel activation rate constants to obtain the respective alterations in kinetics and in I–V relationships similar to those reported for recombinant WT and L858H channels (Cummins et al. 2004). Our L858H model predicted enhancement of Na_V1.7 channel activity at subthreshold membrane voltages. In response to a voltage command shaped in the form of membrane voltage of spontaneously firing DRG neuron, substitution of only 12.5% of the channels of the cell with the L858H model, compared with WT, resulted in a 27-fold increase of sodium influx at subthreshold membrane voltages and in a 3-fold sodium influx increase during the AP. When we evoked APs in dynamic-clamp using a 10-ms depolarizing stimulus, persistent L858H channel activity at subthreshold voltages produced >600% additional sodium influx during small depolarizations and resulted in the appearance of a significant sodium influx during interspike intervals (–0.2 ± 0.32, WT; compared with 58.2 ± 10.4, L858H). Such a substantial increase of the sodium influx is proexcitatory, and we were not surprised to observe a hyperexcitable neuronal phenotype due to L858H introduced by dynamic-clamp. Substitution of 50% WT-to-L858H conductance in our dynamic-clamp experiments produced persistent current that depolarized RMP on average by 5 mV and resulted in a reduction of current threshold on average by 51% without changing AP overshoot. This persistent current activated further at subthreshold membrane potentials in response to depolarizing current injection, reached its peak before AP threshold, and then promptly declined to essentially zero level within the next few milliseconds. The net charge inflow due to (L858H – WT) model was larger during subthreshold depolarization than during the AP and produced a significant charge inflow during interspike intervals driving a slow, ramplike depolarization of the membrane potential. On the basis of the present results, we attribute the L858H-induced RMP depolarization described by Rush et al. (2006) and seen in this study to the persistent current due to window channel activity. Steady-state open channel probability at –63-mV RMP increased 255-fold from 3.8 × 10^–6 (WT) to 9.7 × 10^–3 (L858H). Maximal conductance of endogenous Na_V1.7 current (see Materials and Methods and Results) was 317 ± 68 nS (n = 6, WT experiments) and 354 ± 64 nS (n = 6, L858H experiments). Addition of 50% of the respective conductance resulted, assuming the calculated steady-state open probability, in 0.08-pA (WT) and 22-pA (L858H) persistent current at –63-mV RMP for dynamic-clamped neuron.

Our results obtained via dynamic-clamp at physiological levels of WT and mutant Na_V1.7 conductance show, for the first time, that current threshold of small DRG neurons is regulated by Na_V1.7 in a linear manner. Our observations also demonstrate that persistent activity of the L858H mutant channel in small DRG neurons amplifies sodium influx at subthreshold membrane voltages, so as to depolarize RMP and reduce current threshold for AP generation, thus producing hyperexcitability in nociceptive DRG neurons. Taken together, these findings establish a quantitative mechanistic link between the altered biophysical properties of a mutant Na_V1.7 channel and nociceptor hyperexcitability underlying the pain phenotype in IEM.

Dynamic-Clamp Analysis of Wild-Type Human Na_V1.7 and Erythromelalgia Mutant Channel L858H *

Materials and Methods

Voltage-Clamp Recordings of Na_V1.7

Assessment of Na_V1.7 Contribution to TTX-S Current in Small DRG Neurons

Dynamic-Clamp Recording

Kinetic Model of Na_V1.7 Channel

Results

Kinetic Model of WT Na_V1.7 Based on Hodgkin–Huxley Equations

Na_V1.7 Conductance Regulates Current Threshold for AP Generation in a Linear Manner

Model of Na_V1.7 L858H Mutant Predicts an Enhanced Level of Channel Activity during Repetitive Firing of DRG Neuron

L858H Mutant Enhances DRG Neuron Excitability by Increasing Sodium Influx during Subthreshold Membrane Depolarizations and Interspike Intervals

Discussion

Grants

About the Authors

Disclosures

Author Contributions

References