Characterization in Potent Modulation on Voltage-Gated Na+ Current Exerted by Deltamethrin, a Pyrethroid Insecticide

Deltamethrin (DLT) is a type-II pyrethroid ester insecticide used in agricultural and domestic applications as well as in public health. However, transmembrane ionic channels perturbed by this compound remain largely unclear, although the agent is thought to alter the gating characteristics of voltage-gated Na+ (NaV) channel current. In this study, we reappraised whether and how it and other related compounds can make any further modifications on voltage-gated Na+ current (INa) in pituitary tumor (GH3) cells. Cell exposure to DLT produced a differential and dose-dependent stimulation of peak (transient, INa(T)) or sustained (late, INa(L)) INa; consequently, the EC50 value required for DLT-stimulated INa(T) or INa(L) was determined to be 11.2 or 2.5 μM, respectively. However, neither the fast nor slow component in the inactivation time constant of INa(T) activated by short depolarizing pulse was changed with the DLT presence; conversely, tefluthrin (Tef), a type-I pyrethroid insecticide, can accentuate INa with a slowing in inactivation time course of the current. The INa(L) augmented by DLT was attenuated by further application of either dapagliflozin (Dapa) or amiloride, but not by chlorotoxin. During pulse train (PT) stimulation, with the Tef or DLT presence, the cumulative inhibition of INa(T) became slowed; moreover, following PT stimuli, a large tail current with a slowly recovering process was observed. Alternatively, during rapid depolarizing pulse, the amplitude of INa(L) and tail INa (INa(Tail)) for each depolarizing pulse became progressively increased by adding DLT, not by Tef. The recovery time constant following PT stimulation with continued presence of Tef or DLT was shortened by further addition of Dapa. The voltage-dependent hysteresis (Hys(V)) of persistent INa was differentially augmented by Tef or DLT. Taken together, the magnitude, gating, frequency dependence, as well as Hys(V) behavior of INa exerted by the presence of DLT or Tef might exert a synergistic impact on varying functional activities of excitable cells in culture or in vivo.


Modification by Deltamethrin (DLT) or Tefluthrin (Tef) on Voltage-Gated Na + Current (I Na ) Measured from Pituitary GH 3 Cells
In the first stage of whole-cell current recordings, we measured the effects of DLT or Tef on the magnitude and inactivation time course of I Na activated in response to abrupt depolarizing pulse. We placed cells in Ca 2+ -free, Tyrode's solution containing 10 mM tetraethylammonium chloride (TEA), and the pipette used was filled up with a Cs +containing solution. As demonstrated in Figure 1A, two minutes after cells were continually exposed to DLT or Tef at a concentration of 10 µM, the amplitude in the transient (I Na(T) ) or late (I Na(L) ) component of I Na activated by 20-ms depolarizing pulse from −80 to −10 mV was progressive raised. For example, as the rectangular voltage step from −80 to −10 mV with a duration of 20 ms was given (indicated in the uppermost part of Figure 1A) to activate I Na , the addition of 10 µM DLT was found to result in a striking increase in either I Na(T) or I Na(L) amplitude to 512 ± 17 pA (n = 9, p < 0.05) or 128 ± 9 pA (n = 9, p < 0.05) from control values of 401 ± 15 or 22 ± 5 pA (n = 9), respectively. After washout of DLT, I Na(T) or I Na(L) was returned to 409 ± 17 or 28 ± 7 pA (n = 9). Likewise, the presence of 10 µM Tef also measurably increased I Na(T) or I Na(L) amplitude from 409 ± 14 pA (n = 9) or 32 ± 6 pA (n = 9) to 499 ± 16 pA (n = 9, p < 0.05) or 162 ± 11 pA (n = 9, p < 0.05), respectively. However, with cell exposure to 10 µM DLT, neither fast nor slow time constant of I Na(T) inactivation in response to rapid membrane depolarization was evidently changed. Alternatively, with the presence of 10 µM Tef, the slow component in the time constant of I Na(T) inactivation was strikingly raised to 19 ± 2 msec (n = 9, p < 0.05) from a control value of 0.9 ± 0.2 msec (n = 9). The time course of effects of DLT (10 µM) on the amplitude of I Na(Tot), I Na(L) or I Na(T) is illustrated in Figure 1B. Of note, during exposure to 10 mM DLT, the amplitude of I Na(Tot) , I Na(L) , or I Na(T) was increased to 177 ± 21 % (n = 8), 1752 ± 105 % (i.e., around 1.7-fold) (n = 8), or 24 ± 6% (n = 8), respectively.  Effect of deltamethrin (DLT) or tefluthrin (Tef) on voltage-gated Na + current (I Na ) measured from pituitary GH 3 lactotrophs. This set of experiments was made in cells placed in Ca 2+ -free, Tyrode's solution containing 10 mM tetraethylammonium chloride (TEA), and the measuring electrode was filled with an internal solution enriched with Cs + . (A) Exemplar current traces obtained in (a, blue color) the control conditions (i.e., neither DLT nor Tef was present) and during cell exposure to either 10 µM DLT (b, upper, red color) or 10 µM Tef (b, lower, red color). The voltage-clamp protocol is illustrated atop recorded current traces. The graph shown in the right side of (A) denotes the expanded record from the observed current trace (red color) in the presence of 10 µM DLT and the definition of transient Na + current (I Na(T) ), late Na + current (I Na(L) ), total Na + current (I Na(Tot) ), or tail Na + current (I Na(Tail) ) is marked (indicated with blue double arrows). (B) Time course of effects of 10 µM DLT on the amplitude of I Na(Tot) (upper), I Na(L) (middle), and I Na(T) (lower). Each point was taken at a rate of 0.1 Hz. The horizontal bar shown above indicated the application of DLT.
(C) Concentration-dependent relationship of DLT on I Na(T) (purple open circles) or I Na(L) (blue solid circles) activated by short depolarizing step. Each data point in this graph represents mean ± SEM of 9 cells. According to the averaged data, the smooth line represents the best fit to the Hill equation as described in Materials and Methods. Figure 1C demonstrates that the addition of DLT to the bath can concentrationdependently increase the amplitude of I Na(T) or I Na(L) activated by short depolarizing step. According to the Hill equation stated under Materials and Methods, the EC 50 value needed for DLT-stimulated I Na(T) or I Na(L) observed in GH 3 cells was calculated as 11.2 or 2.5 µM, respectively. Consistent with previous studies [6,8], the experimental observations, therefore, enable us to reflect that the DLT presence exerts a stimulatory action on the magnitude of I Na(T) and I Na(L) natively expressed in GH 3 cells, and that this compound tends to be selective for I Na(L) over I Na(T) during rectangular depolarizing pulse. Exposure to pyrethroids (e.g., DLT) has been previously demonstrated to activate Cl − currents [14][15][16]. We further compared the effects of Tef, DLT or their combinations with ChloroTx, Dapa, or amiloride on I Na(L) amplitude. ChloroTx was reported to suppress Cl − current, Dapa was an inhibitor of I Na(L) [32,33], and amiloride can attenuate the pyrethroidsstimulated sodium transport [16]. As summarized in Figure 2, with continued presence of Tef or DLT, the further exposure to ChloroTx (1 µM) failed to modify their stimulation of I Na(L) . Dapa (10 mM) or amiloride (10 mM) alone decrease the I Na(L) amptitude to 31 ± 2 pA (n = 8, p < 0.05) or 28 ± 2 pA (n = 8, p < 0.05) from control value of 50.3 ± 3 pA (n = 8). Moreover, the subsequent presence of either Dapa (10 µM) or amiloride (10 µM) was able to attenuate Tef-or DLT-mediated increase of I Na(L) effectively. The results prompted us to suggest that either Dapa or amiloride could directly cause an inhibitory effect on the amplitude of I Na(L) observed in GH 3 cells [32,33].

Effect of DLT on Mean Current Versus Voltage (I-V) Relationship of INa(T) and INa(L)
We  Tef plus dapagliflozin (Dapa), DLT plus Dapa, and DLT plus amiloride on the amplitude of I Na(L) measured from GH 3 cells. The I Na was elicited by 20 ms depolarizing voltage command from −80 to −10 mV for a duration of 20 ms at a rate of 0.2 Hz. The I Na(L) amplitudes during exposure to different tested compounds were measured at the end of each depolarizing step. Each bar represents the mean ± SEM (n = 8). * Significantly different from control (p < 0.05), ** significantly different from Tef (10 µM) alone group (p < 0.05), and + significant different from DLT (10 µM) alone group (p < 0.05).

Effect of DLT on Mean Current Versus Voltage (I-V) Relationship of I Na(T) and I Na(L)
We next explored any perturbations of this compound on the amplitude of I Na(T) or I Na(L) measured from the different level of membrane potentials. As demonstrated in Figure 3A,B, a steady-state I-V relationship of I Na(T) and I Na(L) acquired with or without the DLT (10 µM) presence was established in these cells. The appearance of 10 µM DLT resulted in a striking increase in the I Na(T) or I Na(L) amplitude elicited by abrupt depolarizing steps.
For example, when the tested cells were rapidly depolarized from −80 to −10 mV, the addition of 10 µM DLT raised either I Na(T) or I Na(L) magnitude from 729 ± 54 to 952 ± 76 pA (n = 8, p < 0.05), or from 26 ± 34 to 265 ± 48 pA (n = 8, p < 0.05), respectively. However, the steady-state I-V relationship of I Na(T) or I Na(L) remained unaffected during exposure to 10 µM DLT, despite a marked increase in I Na(T) or I Na(L) magnitude. The relationship (i.e., G-V relationship) for the conductance of I Na(T) or I Na(L)) with or without the application of 10 µM DLT was also established and depicted in Figure 3C. The V 1/2 value for G-V relationship of I Na(T) or I Na(L) between the absence and presence of 10 mM DLT did not differ significantly {(−19.9 ± 1.

Tef-or DLT-Mediated Slowing in Cumulative Inhibition of INa(T) during Rapid Depolarizing Stimuli
It has been demonstrated that, prior to being activated during repetitive short pulses, the inactivation of INa(T) is able to accumulate [22,23,25,[34][35][36]. For this reason, we next explored if Tef or DLT could modify the extent of INa(T) activated either during or following the PT depolarizing stimuli. In this set of measurement, the stimulus protocol, consisting of repetitive depolarization of −10 mV (20 ms in each pulse with a rate of 40 Hz for 1 s), was applied to the tested cells which were voltage-clamped at −80 mV. In accordance with earlier reports [22][23][24][25]36], as demonstrated in Figures 4 and 5, during the control period (i.e., neither Tef nor DLT was present), the exponential time course of INa(T) inactivation Figure 3. Effect of DLT on the steady-state current versus voltage (I-V) relationship of I Na(T) and I Na(L) identified from GH 3 cells. In this set of experiments, we held each cell at −80 mV, and varying depolarizing command voltages from −80 to +10 mV in 10-mV steps were delivered to evoke I Na(T) and I Na(L) . (A) Exemplar current traces obtained either in the control condition (upper) or with the presence of 10 µM DLT (lower). The uppermost part is the voltage-clamp protocol given. (B) The mean I-V relationship of I Na(T) (black symbols) or I Na(L) (red symbols) in control (upper, solid symbols) and during exposure to 10 µM DLT (lower, open symbols) (mean ± SEM; n = 8 for each point). Either I Na(T) or I Na(L) was measured at the beginning or end of each depolarizing pulse. (C) Conductance versus voltage relationship of I Na(T) (black symbols) or I Na(L) (red symbols) in the control period (left side) and during cell exposure to 10 µM DLT (right side) (mean ± SEM; n = 8 for each point).

Tef-or DLT-Mediated Slowing in Cumulative Inhibition of I Na(T) during Rapid Depolarizing Stimuli
It has been demonstrated that, prior to being activated during repetitive short pulses, the inactivation of I Na(T) is able to accumulate [22,23,25,[34][35][36]. For this reason, we next explored if Tef or DLT could modify the extent of I Na(T) activated either during or following the PT depolarizing stimuli. In this set of measurement, the stimulus protocol, consisting of repetitive depolarization of −10 mV (20 ms in each pulse with a rate of 40 Hz for 1 s), was applied to the tested cells which were voltage-clamped at −80 mV. In accordance with earlier reports [22][23][24][25]36], as demonstrated in Figures 4 and 5, during the control period (i.e., neither Tef nor DLT was present), the exponential time course of I Na(T) inactivation observed in GH 3 cells was observed during a 1-s repetitive depolarization from −80 to −10 mV, and an evolving decaying time constant of 22.1 ± 2.8 ms (n = 8) was then yielded. In other words, there appeared to be a progressive current decay (indicated with the dashed arrows in Figure 4A) with a single-exponential process. It also needs to be noted that with cell exposure to DLT (10 µM), the time constant of I Na(T) decaying activated during the same train of depolarizing pulses was increased to 56.4 ± 3.9 ms (n = 8), apart from a progressive increase in I Na(L) or I Na(Tail) (i.e., appearance of tail current following 1-s PT stimulation) magnitude. Of additional notice, a significant increase in tail I Na (I Na(Tail) ) (blue open triangles in Figure 5) with a rising time constant of 87.4 ± 4.6 ms (n = 8) was found in the presence of 10 µM DLT ( Figure 4B,C and Figure 5); however, cell exposure to 10 µM Tef resulted in a gradual decay in I Na(L) with a decaying time constant of 26.3 ± 2.7 ms (n = 8). Alternatively, with continued exposure to 10 mM DLT, further addition of Dapa (10 mM) or Ami (10 mM) significantly decreased the time constant of I Na(L) during PT stimulation. Table 1        The observed I Na(T) or I Na(L) was measured as indicated in the right side of Figure 1. The continuous smooth lines, over which the experimental data points are overlaid, were optimally fitted by a single exponential (i.e., exponential decrease or increase). Notably, during PT stimulation, cell exposure to DLT can increase the decaying time constant of I Na(T) inactivation; however, it led to a progressive increase (i.e., staircase increase) in the amplitude of I Na(Tail) . Moreover, with the DLT presence, an exponential increase in I Na(L) during PT stimuli occurring over time was also observed ( Figure 4B,C). Following 1-s PT stimulation, as cells were continually exposed to 10 µM DLT, there appeared to be a large inward current (i.e., I Na(Tail) ) accompanied by a gradual recovery (indicated with asterisk in Figure 4B) in the second timescale with a recovery time constant of 1.23 ± 0.19 s (n = 8) ( Figure 4B,C). The appearance of I Na(Tail) could reflect changes in the magnitude of I Na(P) , and the I Na(L) and I Na(P) evoked during an extended period of time were thought to share the same Na V channels [22,26]. Likewise, with the presence of 10 µM Tef, the recovery time constant of I Na(Tail) ) (or I Na(P) ) acquired following PT stimuli was estimated to be 123 ± 25 ms (n = 8), a value which is different from DLT-induced change in the recovery time constant of I Na(Tail) following PT stimuli. In contrast, during the control period (i.e., neither Tef nor DLT was present), the recovery time constant of the current following PT stimulation was rather small (i.e., 25 ± 3 ms [n = 8]) ( Figure 6B). Moreover, with continued presence of DL (10 mM), further addition of either Dapa (10 mM) or Ami (10 mM) significantly attenuated the recovery time constant of I Na(T) evoked following PT stimulation, as summarized in Table 1.
Additionally, with continued exposure to Tef (10 µM) or DLT (10 µM), further addition of dapagliflozin (Dap) at a concentration of 10 µM resulted in an attenuation of the drastic appearance of large inward I Na(Tail) following PT stimuli, as demonstrated by a respective reduction in the recovery time constant of the current to 54 ± 17 ms (n = 8, p < 0.05) or 564 ± 62 ms (n = 8, p < 0.05) estimated during further presence of Dapa (10 µM) ( Figure 6B). Taken together, these results prompted us to reflect that the presence of DLT can act as a striking slowing the deactivating kinetics of I Na(Tail) (or I Na(P) ) following return to the holding potential at −80 mV. Therefore, during 1-s PT stimulation, insufficient period of time was allowed for I Na recovery. As a result, particularly during exposure to DLT, single I Na deactivation during PT stimulation presently given (i.e., at a rate of 40 Hz) could be apparently incomplete, thereby leading to frequency-dependent 'accumulation' of the Na V -channel activated state. Therefore, the response of Tef-and DLT-mediated I Na(L) or I Na(Tail) was overly distinguishable. In other words, one (i.e., the Tef presence) is progressive decay of I Na(L) during a train of depolarizing pulses, while the other (i.e., the DLT presence) exhibits a staircase increase in I Na(L) . Moreover, upon continued exposure to 10 µM DLT, the subsequent addition of Dapa (10 µM) could measurably attenuate DLT-mediated increase I Na(Tail) during PT stimuli as well as shortened the recovery time constant of I Na(P) following repetitive depolarizing stimuli ( Figure 6A,B). optimally fitted by a single exponential (i.e., exponential decrease or increase). Notably, during PT stimulation, cell exposure to DLT can increase the decaying time constant of INa(T) inactivation; however, it led to a progressive increase (i.e., staircase increase) in the amplitude of INa(Tail).

Effect of Tef or DLT on the Strength of Voltage-Dependent Hysteresis (Hys (V) ) of Persistent I Na (I Na(P) ) Elicited by an Upright Isosceles-Triangular Ramp Voltage (V ramp )
The nonlinear Hys (V) behavior residing in I Na(P) has been recently disclosed with a figure-of-eight (i.e., ∞-shaped) configuration as current traces were robustly activated by an upright double V ramp (i.e., ascending and descending limbs of triangular V ramp ) [33]. In this regard, efforts were made to explore if the existence of Tef or DLT could have any different adjustments on the Hys (V) 's behavior elicited in response to such upright V ramp . This separate set of measurements was performed in GH 3 cells which were placed in Ca 2+ -free Tyrode's solution, and we filled up the measuring electrodes with a solution containing Cs + . The tested cells were maintained at −80 mV and an upright double V ramp ranging between −80 and +50 mV for a duration of 1 s (i.e., ramp speed of ±0.26 mV/ms) was afterwards applied to them. As shown in Figure 7A, during cell exposure to Tef (10 µM) or DLT (10 µM), current traces in response to such triangular V ramp are distinguishable, although two types of hysteretic loops (i.e., low-and high-threshold loops) became overly noticeable during the presence of Tef or DLT. In particular, the strength of low-threshold hysteretic loop during such V ramp became considerably larger in the presence of Tef (10 µM), as compared with that during exposure to DLT. For example, as cells were continually exposed to Tef (10 µM), the amplitude of I Na(P) at the descending limb of V ramp (i.e., at the level of −70 mV) resulted in a striking increase by 6.6 folds from 61 ± 9 to 403 ± 24 pA (n = 8, p < 0.05); conversely, upon the presence of DLT (10 µM), I Na(P) amplitude at the same level was increased only by 1.5 folds ( Figure 7C). However, upon cell exposure to Tef (10 µM) or DLT (10 µM), the I Na(P) amplitude at the ascending limb (i.e., at −10 mV) was increased to 3.6 or 3.7 folds, respectively, which did not differ significantly between these two compounds. From these data, it was plausible to assume that the strength of I Na(P) 's Hys (V) in response to long-lasting double V ramp was susceptible to being enhanced during Tef or DLT presence; moreover, the low-threshold loop of Hys (V) appeared to be more sensitive to augmentation by Tef than that by DLT.

Discussion
In the current investigations together with previous studies, we provided the evidence to unveil that the presence of DLT, known to be a type II pyrethroid, was able to exert stimulatory actions on vastly different types of

Discussion
In the current investigations together with previous studies, we provided the evidence to unveil that the presence of DLT, known to be a type II pyrethroid, was able to exert stimulatory actions on vastly different types of I Na , including I Na(T) , I Na(L) , I Na(Tail) , and I Na(P) , seen in pituitary tumor (GH 3 ) cells. It is likely, therefore, that the endocrine disrupting potential caused by the existence of DLT or other structurally similar pyrethroids, as demonstrated recently [2,16,20,27,[37][38][39][40][41], could be highly linked to the excitatory actions on varying types of I Na presented herein, presuming that similar pharmacological or toxicological actions take place in variable types of endocrine or neuroendocrine cells present in vivo [2,3,7,11,13,42], although pyrethroids are thought to be around 2250 times more toxic than mammals [12,13].
Upon cell exposure to DLT, the observed I Na(L) activated in response to short depolarizing step was noticed to be stimulated to a greater extent than the I Na(T) . The EC 50 values required for DLT-stimulated I Na(T) and I Na(L) in GH 3 cells were estimated to be 11.2 and 2.5 µM, these values which was noted to differ significantly by 4.5 folds (Figure 1). However, the further addition of chlorotoxin (ChloroTx), still in continued presence of tefluthrin (Tef) or DLT, failed to modify Tef-or DLT-stimulated I Na(L) , although either dapagliflozin (Dapa) or amiloride could effectively reverse their increase in I Na(L) amplitude. Tef is a Type I pyrethroid insecticide [8,10,26]. The overall steady-state I-V relationship of I Na(T) or I Na(L) during exposure to DLT remained unchanged; furthermore, the inactivation time course of I Na(T) during brief step depolarizing did not differ between the absence and presence of DLT. However, the magnitude of I Na(T) following the PT stimulation (i.e., 40-Hz repetitive depolarizing pulse) tended to be pronouncedly larger as well as its decaying time course became slowed in the presence of Tef or DLT (Figure 4).
It needs to be mentioned that a large appearance of inward current (i.e., I Na(P) ) following such PT stimulation clearly emerged during the presence of Tef or DLT, while a rather small transient current following the same PT stimuli was observed during the control conditions (i.e., neither Tef nor DLT was present). The larger magnitude of inward current immediately following PT stimuli by adding DLT was noted as compared to that by Tef. Furthermore, the exposure to Tef markedly rendered the inactivation time course of I Na(T) during rapid membrane depolarization to become slowed, whereas DLT itself had minimal interference with the inactivation time constant of the current. However, the DLT existence, a progressive elevation of I Na(L) and I Na(Tail) during a train of repetitive depolarizations; moreover, it induced a larger tail I Na following repetitive depolarizations. The experimental results can be interpreted to mean that, upon continued exposure to DLT, the I Na deactivation elicited during PT stimuli could be apparently incomplete, thus leading to rate-dependent 'accumulation' of the Na V channel activated state. The slowed inactivation caused by the exposure to Tef thus reflects that the barrier for going from the open to the inactivated state of the Na V channel tends to be higher during its presence. The α-cyano-3-phenoxybenzyl group present in the DLT molecule tends to be a notable structure required preferentially for open/resting state of the channel.
Earlier reports have demonstrated the effectiveness of DLT either in inducing the raise in Ca 2+ transient or exert anti-neoplastic actions in different types of neoplastic cells, including liver, oral, and prostate cancer cells, and Jurkat-J6 cell cells [43][44][45][46][47][48]. The functional expression of Na V channels has also been reported in different neoplastic cells, including prostate cancer and glioma cells [45,[49][50][51][52]. As such, whether DLT-mediated modifications on I Na presented herein can be responsible for the actions of DLT or other structurally similar pyrethroids on intracellular Ca 2+ or aberrant growth in neoplastic cells [44] is worth pursuing further.
Earlier reports have demonstrated the effectiveness of pyrethroids (e.g., DLT, esfenvalerate, or permethrin) in increasing long-term potentiation recorded in CA1 hippocampal region [53][54][55][56]. Indeed, a brief period of high-frequency electrical activity applied artificially to a neuronal pathway is expected to enhance the strength of synapses for various periods of time, which is called long-term potentiation. However, it needs to be stressed that with cell exposure to either Tef or DLT, following 1-s PT stimulation from −80 to −10 mV, a large inward current (i.e., I Na(P) ) with slowly decaying process was considerably observed ( Figure 4A,B). Under such scenario, the observed induction of long-term potentiation (i.e., facilitation of synaptic transmitter [e.g., glutamate] release) evoked during high-frequency stimulation could have been seriously disturbed or even overestimated by the present findings showing a large recovery time course of I Na emerging following PT stimulation in situations where cells present in tissue preparations were exposed to either Tef or DLT.
Previous studies have demonstrated that pyrethroids could affect transepithelial ion transport in the external layers of the skin and the further addition of amiloride could regulate pyrethroids-mediated change in such transepithelial ion transport [16,57]. In this study, the subsequent addition of amiloride can attenuate DLT-induced increase in I Na(L) measured from GH 3 cells; however, further application of chlorotoxin (ChloroTx) had no effect on DLT-or Tef-stimulated I Na . Moreover, further addition of ChloroTx failed to modify changes in DLT-or Tef-stimulated I Na during PT timulation; however, subsequent application of either Dapa or amiloride could significantly attenuate DLT and Tef-stimulated I Na by the same stimulation protocol. Therefore, the amiloride-mediated effect on the modifications by pyrethroids of ion transport through rabbit skin is likely associated with its direct inhibitory action on I Na(L) .
The ability of pyrethroids (e.g., DLT) to augment Cl − currents has been previously demonstrated [14,16]. In our study, the subsequent addition of ChloroTx, an inhibitor of Cl − currents, failed to modify DLT-stimulated I Na(T) or I Na(L) in GH 3 cells ( Figure 2). However, the further application of dapagliflozin (Dapa) or amiloride can effectively attenuate DLT-activated I Na(L) or I Na(P) . Dapa was recently demonstrated to ameliorate Tef-augmented Hys (V) strength of I Na(P) activated by double V ramp [33]. Therefore, DLTmediated stimulation of I Na(T) , I Na(L) , and I Na(P) demonstrated herein is unlikely to be attributed to its activation of Cl − current.
Work in our laboratory has demonstrated the non-equilibrium Hys (V) behavior of I Na(P) activated by the upright isosceles-triangular V ramp [33]. The results indicated that there was a striking voltage dependence of such V ramp -evoked I Na(P) [29,33]. The experimental data also showed two types of Hys (V) loops (i.e., a high-threshold counterclockwise followed by a low-threshold clockwise loop) with a figure-of-eight (i.e., ∞) configuration, which is reminiscent of the dynamics of the Lorenz-like motion [58]. Alternatively, with GH 3 -cell exposure to Tef or DLT, the Hys (V) motion of I Na(P) activated by the upsloping (ascending) and downsloping (descending) ends of such double V ramp as a function of time was noticed to move in both counterclockwise and clockwise directions ( Figure 7A). In particular, one activated during the ascending limb of double V ramp is called a highthreshold counterclockwise loop with a peak of around −10 mV, while the other evoked by the descending limb of V ramp is a low-threshold clockwise loop with a peak falling at around −70 mV [33]. Moreover, as compared with the effect of DLT on Hys (V) 's strength of I Na(P) , the exposure to Tef could augment Hys (V) 's strength at low-threshold loop to a greater extent than that observed at high-threshold loop. However, with continued presence of either Tef or DLT, the further addition of Dapa could attenuate their stimulation of Hys (V) strength in GH 3 cells. Thus, the presence of Tef could slow the inactivation time course of I Na(T) activated by rapid step depolarization as well as augment magnitude of I Na(P) 's low-threshold loop of Hys (V) responding to double V ramp . Conversely, as cells were exposed to DLT, the I Na(T) inactivation time course during step depolarization was found to remain unchanged, and the increased strength of low-threshold Hys (V) loop during double V ramp was relatively smaller in its presence. It is therefore plausible to assume that the low-threshold loop of I Na(P) 's Hys (V) activated during the downsloping end of double V ramp could be closely linked to the extent of the inactivation time course of I Na(T) .

Conclusions
The modifications by DLT and Tef on the magnitude, gating kinetics, frequency dependence, and Hys (V) strength of I Na in electrically excitable cells are noticeably different.
The variable actions of pyrethroids presented here would be of clinical, pharmacological, and toxicological relevance [3].
The standard extracellular solution (i.e., normal Tyrode's solution) used in this study had the ionic compositions containing (in mM): NaCl 136.5, CaCl 2 1.8, KCl 5.4, MgCl 2 0.53, glucose 5.5, HEPES 5.5, and the solution pH was titrated to 7.4 by adding NaOH. The composition of Ca 2+ -free Tyrode's solution used for the measurement of I Na (e.g., I Na(T) , I Na(L) , I Na(P) , and I Na(Tail) ) was the same as normal Tyrode's solution in which CaCl 2 was removed. For the experiments on recording I Na , the electrode used was filled up with the internal pipette solution containing (in mM): Cs-aspartate 130, CsCl 20, KH 2 PO 4 1. MgCl 2 , Na 2 ATP 3, Na 2 GTP 0.1, and HEPES 5, and the pH was then adjusted to 7.2 with CsOH. The twice-distilled water used for the experiments was deionized with a Milli-Q ion exchange and activated carbon cartridge treatment system (Merck, Tainan, Taiwan).

Electrophysiological Measurements (Patch-Clamp Current Recordings)
In the few hours before the experiments, GH 3 cells were detached from culture dishes with a 1% trypsin/EDTA solution, and a few drops of cell suspension (~10 6 /mL) was rapidly placed in a custom-built chamber mounted on the stage of a DM-IL inverted phasecontrast microscope (Leica; Major Instruments, Kaohsiung, Taiwan). We bathed cells at room temperature (20-25 • C) in the extracellular solution (i.e., normal Tyrode's solution), the ionic compositions of which are described above. Before each experiment, cells were allowed to settle on the chamber's bottom. The recording pipettes were pulled from Kimax ® -51 borosilicate glass tube (#DWK34500-99; Kimble ® , Merck, Tainan, Taiwan) and they were then polished to reach the resistances ranging between 3 and 5 MΩ. During each measurement, the electrode was mounted in an air-tight holder, which had a suction port on the side, and a silver-chloride wire was used to make good contact with the internal pipette solution. We recorded varying types of ionic currents (e.g., I Na ) with the whole-cell mode of a modified patch-clamp technique by using an RK-400 patch amplifier (Bio-Logic, Claix, France), as dealt with in our previous works [26,36,59]. All recordings were conducted inside a noise-proof Faraday cage. The junction potentials that commonly develop when the compositions of the pipette internal solution are different from those in the bath were zeroed shortly before giga-Ω formation was made, and the whole-cell data were corrected. As pulse train (PT) stimulation was applied to the tested cell, we used an Astro-Med Grass S88X dual output pulse stimulator (Grass; KYS Technology, Tainan, Taiwan).

Data Recordings and Processing
Throughout the recording period, the signal output (i.e., potential and current traces) was monitored and digitized online at 10 kH or more in an ASUS ExpertBook laptop computer (Yuan-Dai, Tainan, Taiwan). For analog-to-digital (A/D) and digital-to-analog (D/A) conversion, a Digidata ® 1550B converter equipped with the computer was controlled by pCLAMP TM 10.6 program run under Microsoft Windows 7 (Redmond, WA, USA). Current signals were low-pass filtered at 2 kHz by using a FL-4 four-pole Bessel filter (Dagan, Minneapolis, MN, USA). The voltage-clamp protocols with manifold rectangular or ramp waveforms were designed, and they were then given to the examined cell through D/A conversion.

Data Analyses for Whole-Cell Ionic Currents
To establish concentration-dependent stimulation of DLT on the amplitude of I Na(T) or I Na(L) , we bathed GH 3 cells in Ca 2+ -free Tyrode's solution which contained 10 mM tetraethylammonium chloride (TEA). During the recording period, we voltage-clamped each cell at −80 mV, and a brief step depolarization to −10 mV for a 20 ms at a rate 0.2 Hz was applied to evoke I Na . The I Na(T) magnitude was measured as the peak amplitude of I Na at the beginning of depolarizing pulse was subtracted from the sustained I Na (i.e., I Na(L) ), while the I Na(L) magnitude was measured at the end of 20-ms depolarizing pulse in situations where different DLT concentrations were cumulatively given (as indicated in the right side of Figure 1A). The total amplitude of I Na (I Na(Tot) ) taken from each step depolarization is equal to I Na(T) plus I Na(L) . The amplitude of I Na(L) obtained during the presence of DLT at a concentration of 100 µM was considered as 100% and we then compared current magnitudes (i.e., I Na(T) and I Na(L) ) during cell exposure to varying concentrations of DLT. The concentration-dependent stimulation by DLT of I Na(T) or I Na(L) observed in GH 3 cells was determined by fitting experimental data set to a modified Hill function [10,25], which can be given as follows.
percentage increase (%) = E max × [DLT] n H / EC n H 50 + [DLT] n H In this equation, [DLT] = the deltamethrin (DLT) concentration given; n H = the Hill coefficient (i.e., coefficient for cooperativity); EC 50 = the concentration required for a 50% stimulation of I Na(T) or I Na(L) amplitude activated in response to short depolarizing step from −80 to −10 mV; and E max = maximal stimulation of I Na(T) or I Na(L) produced by the DLT presence.

Curve-Fitting Approximations and Statistical Analyses Used in This Work
To determine the model parameters, linear or nonlinear curve-fitting to the experimental data set presently obtained was optimally fitted with least-squares minimization procedure by using manifold analytical tools, such as the Microsoft "Solver" built in Excel ® 2022 (Microsoft) and OriginPro ® 2022 program (OriginLab ® ; Scientific Formosa, Kaoshiung, Taiwan). The experimental results are presented as the mean ± standard error of the mean (SEM). The size of independent observations (n) is indicated in cell numbers collected during the measurements. The data distribution obtained presently was found to satisfy the tests for normality. Paired or unpaired t-tests were used for comparison between the two different groups; however, for comparison among more than two groups, we carried out analysis of variance (for one-or two-way ANOVA) with or without repeated measure followed by a post hoc Fisher's least-significance difference test for multiple-range comparisons. A statistical significance (indicated with *, **, + , or ++ in the figures) was considered when p < 0.01 or < 0.05.

Data Availability Statement:
The original data is available upon reasonable request to the corresponding author.