Effective Modulation by Lacosamide on Cumulative Inhibition of I_Na during High-Frequency Stimulation and Recovery of I_Na Block during Conditioning Pulse Train

Abstract

The effects of lacosamide (LCS, Vimpat^®), an anti-convulsant and analgesic, on voltage-gated Na⁺ current (I_Na) were investigated. LCS suppressed both the peak (transient, I_Na(T)) and sustained (late, I_Na(L)) components of I_Na with the IC₅₀ values of 78 and 34 μM found in GH₃ cells and of 112 and 26 μM in Neuro-2a cells, respectively. In GH3 cells, the voltage-dependent hysteresis of persistent I_Na (I_Na(P)) during the triangular ramp pulse was strikingly attenuated, and the decaying time constant (τ) of I_Na(T) or I_Na(L) during a train of depolarizing pulses was further shortened by LCS. The recovery time course from the I_Na block elicited by the preceding conditioning train can be fitted by two exponential processes, while the single exponential increase in current recovery without a conditioning train was adequately fitted. The fast and slow τ’s of recovery from the I_Na block by the same conditioning protocol arose in the presence of LCS. In Neuro-2a cells, the strength of the instantaneous window I_Na (I_Na(W)) during the rapid ramp pulse was reduced by LCS. This reduction could be reversed by tefluthrin. Moreover, LCS accelerated the inactivation time course of I_Na activated by pulse train stimulation, and veratridine reversed its decrease in the decaying τ value in current inactivation. The docking results predicted the capability of LCS binding to some amino-acid residues in sodium channels owing to the occurrence of hydrophobic contact. Overall, our findings unveiled that LCS can interact with the sodium channels to alter the magnitude, gating, voltage-dependent hysteresis behavior, and use dependence of I_Na in excitable cells.

1. Introduction

LCS, a functionalized amino acid, is an antiepileptic and analgesic drug available orally and intravenously in clinical practice [1,2,3,4,5,6]. It is commonly administrated in patients with epilepsy and occasionally in patients with trigeminal neuralgia or other neuropathic pain [1,5,7,8,9,10,11,12]. A growing body of evidence demonstrated the effectiveness and tolerability of LCS in patients with epilepsy [13,14,15,16,17,18,19]. Earlier reports have shown that this compound can decrease the frequency of interictal spikes as well as high-frequency oscillations in mesial temporal lobe epilepsy or refractory focal epilepsy [13,20]. The antiepileptic ability of LCS was proposed mainly because it selectively enhances the voltage-dependence of the slow inactivation of Na⁺ current (I_Na) [5,7,21,22,23]. In addition to its antiepileptic effects, additional broad effects of LCS have been observed clinically [3,4]. For instance, a recent report showed that LCS could alter electrocardiographic changes in a status epilepticus animal model [24]. Another report showed that LCS could induce personality changes, which disappeared after its discontinuation [25]. Additional electrophysiological actions of LCS might explain its multiple therapeutic effects and need to be thoroughly established.

The voltage-gated Na⁺ currents form voltage-gated sodium channels (Na_V) are critical for the generation and propagation of action potentials in excitable membranes [26,27]. These channels can briefly shift from the resting to the open state after depolarization, thereby allowing the flow of Na⁺ from the extracellular solution into the cell under the driving forces of the electrical and chemical gradients. After opening briefly in a voltage-dependent manner, the channels are shifted to the inactivated state(s), rendering I_Na intense but brief [27]. In addition to the voltage-dependence of the slow inactivation of I_Na, LCS has also been shown to enhance the frequency-dependent inhibition of I_Na [28]. However, whether the accumulative inhibition of I_Na inactivation during repetitive depolarization and/or recovery from I_Na inactivation during the preceding conditioning pulse train could be perturbed by LCS has not been adequately investigated. In the current study, the following attempts were undertaken to evaluate how LCS could lead to any adjustments to the magnitude, gating kinetics, voltage-dependent hysteresis (Hys_(V)), and use dependence of I_Na residing in two different excitable cells, pituitary tumor (GH₃) cells and neuroblastoma (Neuro-2a) cells. The observations could help to delineate the delicate modulation of functional activities in excitable cells occurring in vivo.

2. Results

2.1. Effects of LCS on Voltage-Gated Na⁺ Current (I_Na)

For the first stage of experiments, whether LCS would exert any perturbations on I_Na was tested. Pituitary tumor (GH3) cells were placed in Ca²⁺-free, Tyrode’s solution, which contained 10 mM tetraethylammonium chloride (TEA) and 0.5 mM CdCl₂ to avoid interference by other types of ionic currents, such as K⁺ and Ca²⁺ currents. Upon membrane depolarization from a holding potential of −100 mV to −10 mV for 30 milliseconds (msec), the transient I_Na (I_Na(T)) was elicited, and it could be attenuated dose-dependently by LCS (Figure 1A). At one minute after adding 30 μM or 100 μM LCS, the I_Na(T) amplitude measured at the beginning of the depolarizing pulse was attenuated to 1012 ± 29 pA (n = 8, p < 0.05) or 783 ± 22 pA (n = 8, p < 0.05) from a control value of 1212 ± 32 pA (n = 8), respectively. When LCS was removed, the current amplitude returned to 1207 ± 31 pA (n = 8).

In addition, late I_Na (I_Na(L)) was measured at the end of the depolarizing test pulse. The extent of LCS-mediated inhibition of I_Na(L) was higher than that at the start of the pulse (i.e., I_Na(T)). For example, 100 μM LCS decreased the I_Na(L) amplitude from 74 ± 9 pA to 29 ± pA (n = 8, p < 0.05). Meanwhile, upon exposure to 100 μM LCS, the slow component in the inactivation time constant (τ) of I_Na(T) decreased from 12.2 ± 2.1 to 8.1 ± 1.3 msec (n = 8, p < 0.05). The relationship between LCS concentration and the inhibition of I_Na(T) and I_Na(L) is constructed in Figure 1B. It demonstrated a differential dose-dependent LCS-mediated inhibition in I_Na(T) and I_Na(L) elicited by the rapid membrane depolarization. Based on a modified Hill equation described in Materials and Methods, the IC₅₀ values required for exerting a suppressive effect on I_Na(T) and I_Na(L) were further estimated as 78 and 34 μM, respectively, reflecting that these two values are distinguishable.

The inhibitory effects of LCS on I_Na were verified in another kind of excitable cell: Neuro-2a cells. LCS (30 or 100 μM) also suppressed both the amplitude of I_Na(T) and I_Na(L) elicited by the rapid membrane depolarization (Figure 2A). Figure 2B shows a differential dose-dependent response of LCS-induced suppression of I_Na(T) and I_Na(L) in Neuro-2a cells. Based on a modified Hill equation, the IC₅₀ values to inhibit the I_Na(T) and I_Na(L) amplitude were 112 and 26 μM, respectively. Thus, LCS can suppress the magnitude of I_Na(T) and I_Na(L) in a time- and concentration-dependent manner both in GH₃ cells and Neuro-2a cells.

2.2. Effects of LCS on Persistent Na⁺ Current (I_Na(P)) Triggered by Isosceles-Triangular Ramp Voltage (V_ramp)

The persistent Na⁺ current (I_Na(P)) is activated in the subthreshold voltage range and is also important in epilepsy by enhancing the repetitive firing capability of neurons. In this experiment, I_Na(P) was elicited in GH₃ cells by an isosceles-triangular ramp voltage (V_ramp), which consisted of an upsloping (ascending) voltage from −100 mV to +50 mV followed by a downsloping (descending) voltage from +50 mV back to −100 mV in 1 s [29,30,31]. Voltage-dependent hysteresis (Hys_(V)) was observed in the instantaneous current–voltage (I–V) relationship of I_Na(P) and presented as two distinct Hys(V) loops of the I_Na amplitude: a high- (a counterclockwise direction) threshold loop and a low- (a clockwise direction) threshold loop (Figure 3A). Figure 3B shows the time course of the inhibitory effect of LCS (30 or 100 μM) on I_Na(P) amplitudes activated by double V_ramp. Compared with the control situation without LCS, LCS reduced the I_Na(P) amplitudes on the loop of Hys_(V) (Figure 3B,C). The 30 and 100 μM LCS attenuated the I_Na(P) amplitudes at the level of −5 mV of the ascending limb to 245 ± 21 pA (n = 8, p < 0.05) and 212 ± 17 pA (n = 8, p < 0.05) from control values of 313 ± 24 pA (n = 8), and the I_Na(P) amplitudes at the level of −60 mV of the descending limb to 151 ± 14 pA (n = 8, p < 0.5) and 101 ± 11 pA (n = 8, p < 0.05) from control values of 198 ± 17 pA (n = 8), respectively. The attenuation of I_Na(P) was reversed by application of tefluthrin (Tef, 10 μM), which is an activator of I_Na [30].

2.3. Effect of LCS on Window I_Na (I_Na(W)) Elicited by a Short Ascending V_ramp

The next question is if the magnitude of I_Na(W) in response to the rapid ascending V_ramp can be modified by LCS. The instantaneous I_Na(W) was evoked by an ascending V_ramp from −80 to +40 mV for 30 msec (i.e., a ramp speed of 4 mV/msec) [32,33]. As shown in Figure 4A, the amplitude of I_Na(W) was markedly reduced within one minute while Neuro-2a cells were exposed to LCS. LCS (100 or 300 μM) decreased the amplitude of I_Na(W) measured at the level of −10 mV from a control value of 602 ± 27 pA (n = 7) to 442 ± 21 pA (n = 7, p < 0.05) or 296 ± 18 pA (n = 7, p < 0.05), respectively. After washout of LCS, the current amplitude at −10 mV was returned to 594 ± 24 pA (n = 7). Figure 4B illustrates a summary graph demonstrating the changes in ∆area of V_ramp-elicited I_Na(W) measured at the voltage between −40 and +40 mV. It showed that LCS effectively diminished the I_Na(W)’s area and Tef (10 μM) could reverse the LCS-mediated decrease in V_ramp-elicited I_Na(W)’s area.

2.4. Effect of LCS on the Cumulative Inhibition of I_Na during a Train of Depolarizing Pulses

I_Na(T) inactivation was previously demonstrated to accumulate before being activated during repetitive short pulses, which consisted of repetitive depolarization from −80 mV to −10 mV for 1 s with 40 msec in each pulse at a rate of 20 Hz [32,34]. To see the effects of LCS on the cumulative inhibition of I_Na, the I_Na(T) or I_Na(L) amplitude with or without treatment of LCS was simultaneously measured at the beginning or the end of each depolarizing pulse. Without LCS, the I_Na(T) or I_Na(L) inactivation evoked by a 1 s repetitive depolarization showed decaying τ values of 86 ± 9 or 234 ± 22 msec (n = 8), respectively (Figure 5). This indicates a pronounced time-dependent decay of I_Na(T) or I_Na(L), which can be fitted with a single-exponential process. Under 30 and 100 μM LCS, the exponential time course of I_Na(T) or I_Na(L) elicited by the same train of depolarizing pulses was shortened to 64 ± 7 msec (n = 8, P < 0.05) and 31 ± 6 msec (n = 8, p < 0.05), or to 143 ± 9 msec (n = 8, p < 0.05) and 104 ± 6 msec (n = 8, p < 0.05), respectively. Thus, that accumulative inactivation of the current can be strikingly enhanced in the cells upon LCS exposure apart from a decrease in I_Na(T) and I_Na(L) amplitude.

The effects of LCS on the cumulative inhibition of I_Na were also verified in Neuro-2a cells. Consistently, LCS (100 μM) diminished the I_Na(T) magnitude and decreased the decaying τ value of I_Na(T) during repetitive depolarizations from a control value of 79 ± 9 msec to 39 ± 5 msec (n = 7, p < 0.05) (Figure 6A,B). In addition, the LCS-mediated reduction in decaying τ value of I_Na(T) could be partially reversed by veratridine (Figure 6C). Veratridine was a sodium channel agonist and was recently reported to modify the gating of the human NaV1.7 channel [35].

2.5. Modification by LCS of the Recovery Process of I_Na(T) Inactivation following Conditioning Train of Depolarizing Stimuli

Earlier investigations have disclosed a unique type of recovery from I_Na(T) inactivation evoked by a train of the preceding conditioning depolarizing stimuli [34,36,37]. The preceding conditioning train was composed of twenty 40 msec pulses separated by 5 msec intervals at −80 mV for 1 s (Figure 7A, top). Following such a conditioning train, the I_Na was produced by a two-step voltage protocol to measure the recovery time course of the current. The two-step voltage protocol included the first step that consisted of a 30 msec pulse from −80 to −10 mV and a second step that consisted of pulses for a variable length of time in a geometric progression (common ratio = 2) from −80 to −10 mV. The relative amplitude of recovery for current inactivation during this protocol was determined by the second step.

In the control situation (i.e., without LCS), the recovery from I_Na(T) inactivation elicited by the preceding conditioning depolarizing stimuli was noticed to emerge in a biphasic manner including a rapid rising recovery phase followed by a late slow phase (Figure 7A). It indicates a train of stimuli enabling the cells to resist the recovery from I_Na(T) inactivation. The recovery time course of this biphasic-manner I_Na(T) inactivation was constructed in Figure 7B. The experimental data points were well fitted with a sum of two exponential functions, i.e., fast (τ_fast) and slow time constant (τ_slow), as elaborated in Materials and Methods. Upon exposure to LCS (30 or 100 μM), both τ_fast and τ_slow in the recovery time course of current inactivation was increased (p < 0.05) compared to the control situation (

Table 1. Summary of data demonstrating the parameter values for the modulatory effect of LCS on the recovery of I_Na block during the preceding train pulse observed in pituitary GH3 cells. These parameters are elaborated in detail in Section 4.

	N	τfast (msec)	τslow (msec)	A	B
Control	8	12.2 ± 0.4	885 ± 16	0.71 ± 0.04	0.28 ± 0.02
LCS (30 μM)	8	13.6 ± 0.6 *	972 ± 17 *	0.78 ± 0.04 *	0.22 ± 0.02 *
LCS (100 μM)	8	14.1 ± 0.6 *	1045 ± 19 *	0.81 ± 0.04 *	0.18 ± 0.02 *

All values are mean ± SEM. * Significantly different from controls (p < 0.05).

).

3. Discussion

The principal finding in this study was that LCS could suppress I_Na in a time-, concentration- and frequency-dependent manner identified in GH₃ and Neuro-2 cells. LCS induced differential inhibitions of I_Na(T) and I_Na(L) activated by a short depolarizing pulse. It also suppressed the high- or low-threshold amplitude of I_Na(P) elicited by the upright isosceles-triangular V_ramp at either the upsloping or downsloping limb leading to a striking reduction in Hys_(V) strength of the current. The accumulative inhibition of I_Na(T) and I_Na(L) during a train of depolarizing pulses was substantially enhanced by LCS, and the values of τ_fast and τ_slow in the recovery time course during the preceding conditioning train of depolarizing pulses were increased. Taken together, LCS could modify the magnitude, gating properties, use-dependence, and Hys_(V) behaviors of I_Na, leading to the inhibition of I_Na(T), I_Na(L), I_Na(P), and I_Na(W).

In the present investigations, the non-equilibrium voltage-dependent hysteresis (Hys_(V)) of I_Na(P) was observed by an upright isosceles-triangular V_ramp with a duration of 1 s (Figure 3). This implies that the I_Na(P) magnitude is contingent on the pre-existing state(s) or conformation(s) of the Na_V channel. There are two types of triangular V_ramp-elicited I_Na(P), that is, low-threshold (i.e., activated at a voltage range near the resting potential) elicited upon the downsloping end of the triangular V_ramp, and high-threshold (i.e., activated at a voltage range near the maximal I_Na(T)) elicited on the upsloping end of such V_ramp [28]. LCS attenuated both types of triangular V_ramp-elicited I_Na(P) of the Hys_(V) behaviors and Tef could effectively reverse this LCS-induced reduction in Hys_(V)’s strength in the current. In the literature, this Hys_(V) behavior of triangular V_ramp-elicited I_Na(P) has been demonstrated to link to the magnitude of background Na⁺ currents closely, and I_Na(L) and I_Na(P) during an extended period of time are likely to share the same Na_V channels [29,31,34,38,39]. This result indicates that LCS could diminish the background Na⁺ currents conductance and reduce the subthreshold potential or depolarization drive in these excitable cells.

In addition, the time-dependent decline in I_Na(T) and I_Na(L) during a 20 Hz train of depolarizing voltage commands (i.e., 40 msec pulses applied from −80 to −10 mV at a rate of 20 Hz for 1 sec) was observed in an exponential fashion, as shown in Figure 5 and Figure 6. This accumulative inhibition is a use-dependent property of I_Na(T) and I_Na(L) during rapid repetitive stimuli or high-frequency firing [32,34,40,41,42,43]. LCS could enhance this accumulative inhibition through reducing not only the amplitude but also the τ value of I_Na(T) and I_Na(L). The LCS-mediated enhancement was only reversed partially by veratridine, a sodium channel agonist. This means that LCS would lead to a “loss-of-function” change of Na⁺ channels and keep the Na⁺ channels in inactivated states during repetitive depolarization to prevent excessive excitability. In addition to LCS, a recent study demonstrated that other sodium blockers, such as lidocaine, also had the use-dependent inhibition of corneal nerve activity [44]. It is consistent with the current investigations.

It is important to emphasize that the LCS increased the τ_fast and τ_slow of recovery from the I_Na(T) block elicited by the preceding conditioning train pulse and enlarged the value of A, as summarized in Table 1. This preceding conditioning train pulse consisted of rapid repetitive pulses, which mimics high-frequency firing on excitable cells and would cause a large fraction of Na_V channels to shift toward the slowly recovering pool. The value of A indicates the fraction of the slow recovering pool of Na_V channels. Taken together, LCS could cause a larger fraction of the Na_V channels in an inactivated state and a longer recovery from inactivation after rapid repetitive stimuli or high-frequency firing. These results are partly relevant to the previous study that showed slow inactivation enhancement by LCS [21].

In this work, we further investigated how the protein of Na_V could be delicately docked with LCS by using PyRx software (https://sourceforge.net/projects/pyrx/; accessed on 17 July 2022). The predicted binding sites with LCS are demonstrated in Figure 8. The LCS could form hydrophobic contacts with several residues, including Gly 76, Trp 77, Phe 80, Gln 122, Leu 125, and Leu 126. Phe 80 can interact with the N’-acetylamino acid N’-benzyl amide unit of LCS, Gly 76 and Trp 77 can dock to the linker that connects the two-aryl group, while Gln 122, Leu 125, and Leu 126 are noted to interact with the terminal aromatic ring. These three functional groups (i.e., N’-acetylamino acid N’-benzyl amide unit, the linker that connects the two aryl groups, and the terminal aromatic ring) in the molecule could be essential for its Na_V-channel blocking activity [7]. However, as the 4′ position of the structural moiety in safinamide (α-aminoamide) does not affect the slow inactivation of Na_V channels, the interaction with Phe 80 appears to be unimportant. The detailed structure of this Na_V channel, which is a particularly good exemplar for hNa_V pharmacology, was shown in an earlier study [45]. These results indicate that LCS can favorably interact with the amino-acid residues of the Na_V channel with an estimated binding affinity of −5.0. Kcal/mol, which is adjacent to the transmembrane region (i.e., position: 123–148) or membrane segment (i.e., position: 79–95) of the channel. Consequently, when LCS reaches the Na_V channels on the membrane, the interactions may raise the structural or steric constraints, thereby resulting in a substantial decrease in Na_V-channel openings.

In summary, LCS could suppress I_Na in a time-, concentration-, and frequency-dependent manner and modify the magnitude, gating properties, use-dependence, and Hys_(V) behaviors of I_Na, leading to inhibiting I_Na(T), I_Na(L), I_Na(P), and I_Na(W). Consequently, LCS could reduce the subthreshold potential, enhance the accumulative inhibition during repetitive depolarization, and prolong the recovery from inactivation after repetitive depolarization in excitable cells.

4. Materials and Methods

4.1. Chemicals, Drugs, and Solutions Used in This Study

Lacosamide (LCS, Vimpat^®, R-enantiomer of 2-acetamido-N-benzyl-3-methoxy- propionamide, 2,3-diaminomaleonitrile, C₁₃H₁₈N₂O₃), tefluthrin (Tef), tetraethylammonium chloride (TEA), tetrodotoxin (TTX), and veratridine were supplied by Sigma-Aldrich (Merck, Taipei, Taiwan). For cell preparations, we obtained culture media, fetal bovine or calf serum, horse serum, L-glutamine, and trypsin/EDTA from HyClone^TM (Thermo Fisher, Kaohsiung, Taiwan). All other chemicals used in this work (e.g., CsOH, CsCl, CdCl_2, and HEPES) were of laboratory grade and taken from standard sources. Double-distilled water deionized through a Milli-Q^® purification system (Merck, Tainan, Taiwan) was used in all experiments.

The ionic composition of normal Tyrode’s solution buffered by HEPES was as follows (in mM): NaCl 136.5, CaCl₂ 1.8, KCl 5.4, MgCl₂ 0.53, glucose 5.5, and HEPES-NaOH buffer (pH 7.4). During the measurements recoding K⁺ currents, a patch electrode was filled with a solution (in mM): K-aspartate 130, KCl 20, MgCl₂ 1, KH₂PO₄ 1, Na₂ATP 0.1, Na₂GTP 0.1, EGTA 0.1, and HEPES-KOH buffer (pH 7.2). To measure different patterns of voltage-gated Na⁺ current, we substituted K⁺ ions in the internal solution for equimolar Cs⁺ ions, and the pH value in the solution was adjusted to 7.2 by adding CsOH. The pipette solution and culture media presently used were filtered with an Acrodisc^® syringe filter that contains a 0.2 mm Supor^® nylon membrane (#4612; Pall Corp.; Genechain, Kaohsiung, Taiwan).

4.2. Cell Preparations

Both the mouse neuroblastoma cell line, Neuro-2a (N2a, BCRC-60026), and the pituitary adenomatous cell line, GH₃ (BCRC-60015), were acquired from the Bioresource Collection and Research Center (Hsinchu, Taiwan). GH₃ cells were in Ham’s F medium supplemented with 2.5% (v/v) fetal calf serum, 15% (v/v) horse serum, and 2 mM L-glutamine, while Neuro-2a cells were in Dulbecco’s modified Eagle’s medium with 10% (v/v) fetal bovine serum. These cells were maintained at 5% CO₂ in a 37 ℃ water-jacketed incubator. Growth medium was replaced twice a week, and cells were split into subcultures once a week. Subcultures were made with trypsinization (0.025% trypsin solution (HyClone^TM) containing 0.01% sodium N, N-diethyldithiocarbamate and EDTA). Electrophysiological measurements were undertaken five or six days after cells were cultured up to 60–80% confluence [30].

4.3. Electrophysiological Measurements

During the few hours before the measurements, we harvested Neuro-2a or GH₃ cells with 1% trypsin-EDTA solution, and a few drops of cell suspension were rapidly placed into a custom-built recording chamber fixed on the stage of an inverted DM-IL microscope (Leica; Major Instruments, Tainan, Taiwan). We then suspended cells at room temperature (20–25 °C) in normal Tyrode’s solution until cells attached to the chamber’s bottom before the recordings were made. The pipettes used were fabricated from Kimax-51 glass tubing with an 1.5–1.8 mm outer diameter (#34500; Kimble, Dogger, New Taipei City, Taiwan) with a vertical two-stage puller (PP-83; Narishige, Taiwan Instrument, Tainan, Taiwan). When filled with different internal solutions, the electrodes presently used for measurements had a tip resistance of 3–5 MΩ. Ionic currents were examined in the whole-cell configuration of a modified patch-clamp technique with the use of either an Axoclamp-2B (Molecular Devices, Sunnyvale, CA, USA) or an RK-400 amplifier (Bio-Logic, Claix, France), as described elsewhere [28]. GΩ-seals were achieved in an all-or-nothing fashion and resulted in a dramatic improvement in the signal-to-noise ratio. The liquid junction potentials, which occur when the compositions in bath solution and those of the pipette internal solution are different, became zeroed shortly before GΩ-seal formation was achieved, and the whole-cell data were then corrected as previously desribed [30].

4.4. Data Recordings

The signals were monitored and digitally captured and stored online at 10 kHz or more in an ASUS ExpertBook laptop computer (Yuan-Dai, Tainan, Taiwan). For efficient analog-to-digital (A/D) and digital-to-analog (D/A) conversion to proceed, a Digidata^®-1440A digitizer connected with a laptop computer via a USB 2.0 port was delicately operated by pClamp 10.6 software run under Microsoft Windows 7 (Redmond, WA, USA). Amplified current signals were low-pass-filtered at 2 kHz with an FL-4 four-pole Bessel filter (Dagan, Minneapolis, MN, USA). The voltage-clamp protocols comprising various rectangular and ramp waveforms were specifically designed and were thereafter imposed on the tested cells through D/A conversion. As pulse-train stimulation was needed, we used a dual output pulse stimulator (Astro-Med Grass S88X; Grass, West Warwick, RI, USA).

4.5. Data Analyses

To assess the dose–response curve of LCS-mediated inhibition on the peak (transient, I_Na(T)) and sustained (late, I_Na(L)) components of depolarization-activated I_Na present in GH₃ or Neuro-2a cells, I_Na’s were evoked by a 30 msec depolarizing pulse to −10 mV from a holding potential of −100 mV (indicated in the top part of Figure 1A and Figure 2A), and current amplitudes obtained with or without the exposure to different LCS concentrations (3 μM–1 mM) were measured at the beginning (I_Na(T)) and end (I_Na(L)) of the depolarizing pulses. The concentration needed to suppress 50% of the current amplitude (i.e., IC₅₀) was appropriately determined according to the three-parameter logistic model (i.e., a modified form of the sigmoidal Hill equation) by use of goodness-of-fit assessments:

$$Relative amplitude= \raisebox{1ex}{${\left[LCS\right]}^{-n_H}\times \left(1-a\right)$}\!\left/ \!\raisebox{-1ex}{$\left({\left[LCS\right]}^{-n_H}+I{C}_{50}^{-n_H}\right)$}\right.+a$$

(1)

In this equation, [LCS] = the LCS concentration; n_H = the Hill coefficient; IC₅₀ = the concentration required for a 50% inhibition. Maximal inhibition (i.e., 1 − a) was also approximated in this formula.

By a two-step voltage protocol with varying interpulse intervals in a geometric progression (common ratio = 2), the recovery time course of I_Na(T) from the block activated in response to the 1 sec conditioning pulse train was constructed, and the results acquired with or without the addition of LCS to GH₃ or Neuro-2a cells were thereafter drawn by plotting the relative I_Na(T) amplitude (normalized with respect to the steady-state amplitude activated at 0.1 Hz). A basic assumption of the analyses is that the recovery time course of the current established under these experimental conditions can be reliably described by an exponential function [34]. Because the recovery time course in GH₃ cells exhibits a rapid rising recovery phase followed by a late slow phase, there should be at least two underlying exponential terms. Accordingly, the data points showing a recovery time course with or without the addition of LCS were fitted to the exponential function with the biexponential process, i.e.,

$$y=A\times \left(1-e^{\raisebox{1ex}{$-t$}\!\left/ \!\raisebox{-1ex}{${\tau }_{fast}$}\right.}\right)+B\times \left(1-e^{\raisebox{1ex}{$-t$}\!\left/ \!\raisebox{-1ex}{${\tau }_{slow}$}\right.}\right)$$

(2)

where y is the relative amplitude of I_Na at time t, A or B is the relative amplitude of each exponential component, and τ_fast or τ_slow is the fast or slow time constant in the recovery of I_Na block, respectively.

4.6. Curve-Fitting Approximations and Statistical Analyses

Linear or nonlinear curve fitting to experimental datasets in this work was made with the interactive least-squares procedure by using various tools, such as Microsoft Excel^®-embedded “Solver” (Microsoft, Redmond, WA, USA) and the OriginPro^® 2021 program (OriginLab^®; Scientific Formosa, Kaohsiung, Taiwan). The averaged results are presented as the mean ± standard error of the mean (SEM) with the sizes of independent samples (n) indicating cell numbers from which data were taken. The Student’s t-test (paired or unpaired) between the two different groups was applied. When differences among more than two groups were encountered, we performed either analysis of variance (ANOVA)-1 or ANOVA-2 with or without repeated measures, followed by the post hoc Fisher’s least significant difference test. Statistical significance (indicated with *, **, or ⁺ in the figures) was determined at a p value of <0.05.