Complex nonlinear dynamics of the Hodgkin-Huxley equations induced by time scale changes

 The Hodgkin–Huxley equations with a slight modification are investigated, in which the inactivation process (h) of sodium channels or the activation process of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau potential, such as in heart muscle cells, to chaotic bursting firings. When h is slowed down – differently from the case of n variable being slow – chaotic bursting oscillations are observed for a wide range of parameter values although both variables cause a decrease in the membrane potential. The underlying nonlinear dynamics of various action potentials are analyzed using bifurcation theory and a so-called slow–fast decomposition analysis. It is shown that a simple topological property of the equilibrium curves of slow and fast subsystems is essential to the production of chaotic oscillations, and this is the cause of the large difference in global firing characteristics between the h-slow and n-slow cases. Received: 9 August 2000 / Accepted in revised form: 10 January 2001     

The potassium A-current,low firing rates and rebound excitation in Hodgkin-Huxley models

It is widely believed, following the work of Connor and Stevens (1971,J. Physiol. Lond. 214, 31–53) that the ability to fire action potentials over a wide frequency range, especially down to very low rates, is due to the transient, potassium A-current (I _A). Using a reduction of the classical Hodgkin-Huxley model, we study the effects ofI _A on steady firing rate, especially in the near-threshold regime for the onset of firing. A minimum firing rate of zero corresponds to a homoclinic bifurcation of periodic solutions at a critical level of stimulating current. It requires that the membrane's steady-state current-voltage relation be N-shaped rather than monotonic. For experimentally based genericI _A parameters, the model does not fire at arbitrarily low rates, although it can for the more atypicalI _A parameters given by Connor and Stevens for the crab axon. When theI _A inactivation rate is slow, we find that the transient potassium current can mediate more complex firing patterns, such as periodic bursting in some parameter regimes. The number of spikes per burst increases asg _A decreases and as inactivation rate decreases. We also study howI _A affects properties of transient voltage responses, such as threshold and firing latency for anodal break excitation. We provide mathematical explanations for several of these dynamic behaviors using bifurcation theory and averaging methods.     

Sodium Metabisulfite Modulation of Potassium Channels in Pain-Sensing Dorsal Root Ganglion Neurons

The effects of sodium metabisulfite (SMB), a general food preservative, on potassium currents in rat dorsal root ganglion (DRG) neurons were investigated using the whole-cell patch-clamp technique. SMB increased the amplitudes of both transient outward potassium currents and delayed rectifier potassium current in concentration- and voltage-dependent manner. The transient outward potassium currents (TOCs) include a fast inactivating (A-current or I _A) current and a slow inactivating (D-current or I _D) current. SMB majorly increased I_A, and I_D was little affected. SMB did not affect the activation process of transient outward currents (TOCs), but the inactivation curve of TOCs was shifted to more positive potentials. The inactivation time constants of TOCs were also increased by SMB. For delayed rectifier potassium current (I _K), SMB shifted the activation curve to hyperpolarizing direction. SMB differently affected TOCs and I _K, its effects major on A-type K⁺ channels, which play a role in adjusting pain sensitivity in response to peripheral redox conditions. SMB did not increase TOCs and I _K when adding DTT in pipette solution. These results suggested that SMB might oxidize potassium channels, which relate to adjusting pain sensitivity in pain-sensing DRG neurons.     

A fully coupled transient excited state model for the sodium channel

Summary The axon membrane is simulated by standard Hodgkin-Huxley leakage and potassium channels plus a coupled transient excited state kinetic scheme for the sodium channel. This scheme for the sodium channel is as proposed previously by the author. Simultations are presented showing the form of the action potential, threshold behavior, accommodation, and repetitive firing. It is seen that the form of the individual action potential, its all-or-none nature, and its refractory period are well simulated by this model, as they are by the standard Hodgkin-Huxley model. However, the model differs markedly from the Hodgkin-Huxley model with respect to repetitive firing and accommodation to stimulating currents of slowly rising intensity, in ways that are anomn to be related to those features of the sodium inactivation which are anomalous to the H-H model. The tendency for repetitive firing is highly dependent on that parameter which primarily determintes the existence of the inactivation shift in voltage clamp experiments, in such a way that the more pronounced the inactivation shift, the less the tendency for repetitive firing,. The tendency for accommodation is highly dependent on that parameter which primarily determines the “τ_c − τ_h” separation, in such a way that the greater the separation the greater the tendency for the membrane to accommodate without firing action potentials to a slowly rising current.     

Voltage-Dependent Behavior of Delayed-Firing Neurons in the Rat <Emphasis Type="Italic">Substantia Gelatinosa</Emphasis>

Upon application of a long-lasting rectangular stimulus, neurons of the substantia gelatinosa (SG) display three main types of intrinsic firing behavior, tonic, adapting, and delayed onset. The electrical landmark of delayed-firing neurons (DFNs), i.e., a significant delay before initiation of action potentials (APs), is believed to result from activation of subthreshold A-type K⁺ current (K_A). We checked out this hypothesis by comparing the voltage dependence of the firing delay with steady-state inactivation of K_A in spinal cord slices of 3- to 5-week-old rats. The delay strongly decreased with membrane depolarization and disappeared at ~ –60 mV; herewith the discharge pattern was transformed to either a tonic or an adapting one. This correlated well with inactivation of K_A recorded in a whole-cell mode in low-Cl^– intracellular solution; inactivation was nearly complete at –60 mV (voltage of half-maximum inactivation, V _1/2 ~ –74.5 mV). Unexpectedly, it was found that filling the cells with high-Cl^– solution, to minimize the liquid junction potential, produced at least a 10 mV-difference between voltage dependences of the firing delay and K_A inactivation; the latter shifted toward negativity (V _1/2 ~ –88.3 mV). The results suggest that the K_A and its inactivation properties determine the appearance and voltage dependence of the firing delay in SG neurons; the apparent influence of intracellular Cl^– on inactivation properties needs further investigation.     

Proton Sensors in the Pore Domain of the Cardiac Voltage-gated Sodium Channel

Protons impart isoform-specific modulation of inactivation in neuronal, skeletal muscle, and cardiac voltage-gated sodium (Na_V) channels. Although the structural basis of proton block in Na_V channels has been well described, the amino acid residues responsible for the changes in Na_V kinetics during extracellular acidosis are as yet unknown. We expressed wild-type (WT) and two pore mutant constructs (H880Q and C373F) of the human cardiac Na_V channel, Na_V1.5, in Xenopus oocytes. C373F and H880Q both attenuated proton block, abolished proton modulation of use-dependent inactivation, and altered pH modulation of the steady-state and kinetic parameters of slow inactivation. Additionally, C373F significantly reduced the maximum probability of use-dependent inactivation and slow inactivation, relative to WT. H880Q also significantly reduced the maximum probability of slow inactivation and shifted the voltage dependence of activation and fast inactivation to more positive potentials, relative to WT. These data suggest that Cys-373 and His-880 in Na_V1.5 are proton sensors for use-dependent and slow inactivation and have implications in isoform-specific modulation of Na_V channels.     

K-Aggravated Myotonia Mutations at Residue G1306 Differentially Alter Deactivation Gating of Human Skeletal Muscle Sodium Channels

Summary Fast inactivation and deactivation gating were compared between wild-type human voltage-gated skeletal muscle sodium channel (hNa_V1.4) and potassium-aggravated myotonia (PAM) mutations G1306A, G1306E, and G1306V. Cell-attached macropatches were used to compare wild-type and PAM-gating properties in normal extracellular K⁺ (4 mM), decreased K⁺ (1 mM), and increased K⁺ (10 mM). G1306E/A increased the apparent valence of the conductance (g(V)) curve. Compared to hNa_V1.4, the steady-state inactivation (h_∞) curve was depolarized for G1306E/A but hyperpolarized by G1306V, and this mutation increased apparent valence. G1306A/E slowed the rate of current rise towards peak activation. G1306V slowed open-state deactivation, inactivated-state deactivation, and recovery from fast inactivation. G1306A/E abbreviated open-state deactivation at negative commands. These mutants slowed open-state deactivation at more positive commands, at voltages for which fast inactivation might influence tail current decay. G1306E abbreviated recovery delay without affecting recovery rate. Low K⁺ increased peak current in hNa_V1.4 and in G1306V. For G1306E, low K⁺ increased the rate of entry into fast inactivation, hyperpolarized the g(V) and h_∞ curves, and increased recovery delay. Biophysical underpinnings of PAM caused by mutations of G1306 thus vary with the specific mutation, and hyperkalemic exacerbation of effects of mutations at this residue are not direct.     

Fast Pseudo-Periodic Oscillation in the Rat Brain Voltage-gated Sodium Channel α Subunit

In the work reported here, we have investigated the changes in the activation and fast inactivation properties of the rat brain voltage-gated sodium channel (rNa_v 1.2a) α subunit, expressed heterologously in the Chinese Hamster Ovary (CHO) cells, by short depolarizing prepulses (10 – 1000 ms). The time constant of recovery from fast inactivation (τ_fast) and steady-state parameters for activation and inactivation varied in a pseudo-oscillatory fashion with the duration and amplitude of a sustained prepulse. A consistent oscillation was observed in most of the steady-state and non-inactivating current parameters with a time period close to 225 ms, although a faster oscillation of time period 125 ms was observed in the τ_fast. The studies on the non-inactivating current and steady-state activation indicate that the phase of oscillation varies from cell to cell. Co-expression of the β1 subunit with the α subunit channel suppressed the oscillation in the charge movement per single channel and free energy of steady-state inactivation, although the oscillation in the half steady-state inactivation potential remained unaltered. Incidentally, the frequencies of oscillation in the sodium channel parameters (4–8 Hz) correspond to the theta component of network oscillation. This fast pseudo-oscillatory mechanism, together with the slow pseudo-oscillatory mechanism found in these channels earlier, may contribute to the oscillations in the firing properties observed in various neuronal subtypes and many pathological conditions.     

The role of a transient potassium current in a bursting neuron model

Presented here is a biophysical cell model which can exhibit low-frequency repetitive activity and bursting behavior. The model is developed from previous models (Av-Ron et al. 1991, 1993) for excitability, oscillations and bursting. A stepwise development of the present model shows the contribution of a transient potassium current (I _A ) to the overall dynamics. By changing a limited set of model parameters one can describe different firing patterns; oscillations with frequencies ranging from 2–200 Hz and a wide range of bursting behaviors in terms of the durations of bursting and quiescence, peak firing frequency and rate of change of the firing frequency.     

Regulation of intrinsic excitability in hippocampal neurons by activity-dependent modulation of the KV2.1 potassium channel

K_V2.1 is the prominent somatodendritic sustained or delayed rectifier voltage-gated potassium (Kv) channel in mammalian central neurons, and is a target for activity-dependent modulation via calcineurin-dependent dephosphorylation. Using hanatoxin-mediated block of K_V2.1 we show that, in cultured rat hippocampal neurons, glutamate stimulation leads to significant hyperpolarizing shifts in the voltage-dependent activation and inactivation gating properties of the K_V2.1-component of delayed rectifier K⁺ (IK) currents. In computer models of hippocampal neurons, these glutamate-stimulated shifts in the gating of the K_V2.1-component of IK lead to a dramatic suppression of action potential firing frequency. Current-clamp experiments in cultured rat hippocampal neurons showed glutamate-stimulation induced a similar suppression of neuronal firing frequency. Membrane depolarization also resulted in similar hyperpolarizing shifts in the voltage-dependent gating properties of neuronal IK currents, and suppression of neuronal firing. The glutamate-induced effects on neuronal firing were eliminated by hanatoxin, but not by dendrotoxin-K, a blocker of K_V1.1-containing channels. These studies together demonstrate a specific contribution of modulation of K_V2.1 channels in the activity-dependent regulation of intrinsic neuronal excitability.     

Central Charged Residues in DIIIS4 Regulate Deactivation Gating in Skeletal Muscle Sodium Channels

Summary 1. Mutations in the S4 segment of domain III in the voltage gated skeletal muscle sodium channel hNa_V1.4 were constructed to test the roles of each charged residue in deactivation gating. Mutations comprised charge reversals at K1-R6, charge neutralization, and substitution at R4 and R5. 2. Charge-reversing mutations at R4 and R5 produced the greatest alteration of activation parameters compared to hNa_V1.4. Effects included depolarization of the conductance/voltage (g/V) curve, decreased valence and slowing of kinetics. 3. Reversal of charge at R2 to R4 hyperpolarized, and reversal at R5 or R6 depolarized the h _∞ curve. Most DIIIS4 mutations slowed inactivation from the open state. R4E slowed closed state fast inactivation and R5E inhibited its completion. 4. Deactivation from the open and/or inactivated state was prolonged in mutations reversing charge at R2 to R4 but accelerated by reversal of charge at R5 or R6. Effects were most pronounced at central charges R4 and R5. 5. Charge and structure each contribute to effects of mutations at R4 and R5 on channel gating. Effects of mutations on activation and deactivation at R4 and, to a lesser extent R5, were primarily owing to charge alteration, whereas effects on fast inactivation were charge independent.     

Unusual Slow Gating of Gap Junction Channels in Oocytes Expressing Connexin32 or Its COOH-Terminus Truncated Mutant

Gap junction channels are gated by a chemical gate and two transjunctional voltage (V _j)-sensitive gates: fast and slow. Slow V _j gate and chemical gate are believed to be the same. The slow gate closes at the negative side of V _j and is mostly inactive without uncouplers or connexin (Cx) mutations. In contrast, our present data indicate otherwise. Oocytes expressing Cx32 were subjected to series of −100 mV V _j pulses (12-s duration, 30-s intervals). Both peak (PK) and steady-state (SS) junctional conductances (G _j), measured at each pulse, decreased exponentially by 50−60% (tau = ∼1.2 min). G _jPK dropped more dramatically, such that G _jSS/G _jPK increased from 0.4 to 0.6, indicating a drop in V _j sensitivity. Less striking effects were obtained with –60 mV pulses. During recovery, G _j, measured by applying 20 mV pulses (2-s duration, 30-s intervals), slowly returned to initial values (tau = ∼7 min). With reversal of V _j polarity, G _jPK briefly increased and G _jSS/G _jPK decreased, suggesting that V _j-dependent hemichannel reopening is faster than hemichannel closing. Similar yet more dramatic results were obtained with COOH-terminus truncated Cx32 (Cx32-D225), a mutant believed to lack fast V _j gating. The data indicate that the slow gate of Cx32 is active in the absence of uncouplers or mutations and displays unusual V _j behavior. Based on previous evidence for direct calmodulin (CaM) involvement in chemical/slow gating, this may also be CaM-mediated.     

Role of Outer-pore Residue Y380 in U-type Inactivation of KV2.1 Channels

The interpretation of slow inactivation in potassium channels has been strongly influenced by work on C-type inactivation in Shaker channels. Slow inactivation in Shaker and some other potassium channels can be dramatically modulated by the state of the pore, including mutations at outer pore residue T449, which altered inactivation kinetics up to 100-fold. K_V2.1, another voltage-dependent potassium channel, exhibits a biophysically distinct inactivation mechanism with a U-shaped voltage-dependence and preferential closed-state inactivation, termed U-type inactivation. However, it remains to be demonstrated whether U-type and C-type inactivation have different molecular mechanisms. This study examines mutations at Y380 (homologous to Shaker T449) to investigate whether C-type and U-type inactivation have distinct molecular mechanisms, and whether C-type inactivation can occur at all in K_V2.1. Y380 mutants do not introduce C-type inactivation into K_V2.1 and have little effect on U-type inactivation of K_V2.1. Interestingly, two of the mutants tested exhibit twofold faster recovery from inactivation compared to wild-type channels. The observation that mutations have little effect suggests K_V2.1 lacks C-type inactivation as it exists in Shaker and that C-type and U-type inactivation have different molecular mechanisms. Kinetic modeling predicts that all mutants inactivate preferentially, but not exclusively, from partially activated closed states. Therefore, K_V2.1 exhibits a single U-type inactivation process including some inactivation from open as well as closed states.     

Reduction of a model for an Onchidium pacemaker neuron

The eight-variable model for the giant neuron localized in the esophageal ganglia of the marine pulmonate mollusk Onchidium verruculatum is reduced to four-and-three-dimensional systems by regrouping variables with similar time scales. These reduced models replicate the complex behavior including beating, periodic bursting and aperiodic bursting displayed by the original full model when the parameter I _ext representing the intensity of the constant DC current stimulation is varied across a wide range. The complex behavior of the full model arises from the interaction of fast and slow dynamics, and depends on the time scale C _s of the slow dynamics. The four-variable reduced model is constructed independently from the parameter C _s so that it reproduces the two-dimensional bifurcation structure of the full model for the two parameters I _ext and C _s . The three-variable reduced model is derived for a specific value of C _s . The parameters of this model are tuned so that its one-parameter bifurcation diagram for I _ext closely matches that of the full model. Correspondence between bifurcation structures ensures that both reduced models reproduce the various discharge patterns of the full model. Similarity between the full and reduced models is also confirmed by comparing mean firing frequencies and membrane potential waveforms in various regimes. The reduction exposes the factors essential for reproducing the dynamics of the full model; indeed, it shows that the eight variables representing the membrane potential and seven gating variables of six ionic currents in the full model account, in fact, for three basic processes responsible for excitability, post-discharge refractoriness and slow membrane modulation. Received: 7 May 1996 / Accepted 4 December 1997     

Ionic currents influencing spontaneous firing and pacemaker frequency in dopamine neurons of the ventrolateral periaqueductal gray and dorsal raphe nucleus (vlPAG/DRN): A voltage-clamp and computational modelling study

Dopamine (DA) neurons of the ventrolateral periaqueductal gray (vlPAG) and dorsal raphe nucleus (DRN) fire spontaneous action potentials (APs) at slow, regular patterns in vitro but a detailed account of their intrinsic membrane properties responsible for spontaneous firing is currently lacking. To resolve this, we performed a voltage-clamp electrophysiological study in brain slices to describe their major ionic currents and then constructed a computer model and used simulations to understand the mechanisms behind autorhythmicity in silico. We found that vlPAG/DRN DA neurons exhibit a number of voltage-dependent currents activating in the subthreshold range including, a hyperpolarization-activated cation current (I_H), a transient, A-type, potassium current (I_A), a background, ‘persistent’ (I_NaP) sodium current and a transient, low voltage activated (LVA) calcium current (I_CaLVA). Brain slice pharmacology, in good agreement with computer simulations, showed that spontaneous firing occurred independently of I_H, I_A or calcium currents. In contrast, when blocking sodium currents, spontaneous firing ceased and a stable, non-oscillating membrane potential below AP threshold was attained. Using the DA neuron model we further show that calcium currents exhibit little activation (compared to sodium) during the interspike interval (ISI) repolarization while, any individual potassium current alone, whose blockade positively modulated AP firing frequency, is not required for spontaneous firing. Instead, blockade of a number of potassium currents simultaneously is necessary to eliminate autorhythmicity. Repolarization during ISI is mediated initially via the deactivation of the delayed rectifier potassium current, while a sodium background ‘persistent’ current is essentially indispensable for autorhythmicity by driving repolarization towards AP threshold.     

Extremely slow inactivation of the ion channels formed by transfected α2 of L-type Ca2+ channelsof L-type Ca2+ channels

Barium currents through ion channels formed by α1-subunit of L-type Ca²⁺ channel (I _α1) were recorded from cultured chinese hamster ovary (CHO) cells. The cells were stably transfected with either a cardiac or a smooth muscle (SM) variant of α1-subunit. TheI _α1 in both cases exhibited similar fast voltage-dependent activation kinetics and slow apparent inactivation kinetics. With 10 mM Ba²⁺ in the bath solution,I _α1 was activated at potentials more positive than −40 mV, peaked between 0 and +10 mV, and reversed at about +50 mV. In addition to slow apparent inactivation of inward current, both subunits provided an extremely slow voltage-dependent inactivation at potentials more positive than −100 mV, with half-maximum inactivation at −43.4 mV for cardiac and −41.4 mV for SM α1-subunits. The onset of inactivation as well as recovery from this process were within a time range of minutes. The voltage dependence of steady-state inactivation could be fitted by the sum of two Boltzmann's equations with slope factors of about 12 mV and 5 mV. A less sloped component has its midpoints at −75.6 and −63.7 mV, and a steeper component has its midpoints at −42.8 and −37.7 mV for cardiac and SM α1-subunits, respectively. Relative contribution of the steeper component was higher in both subunits (0.86 and 0.66 for cardiac and SM subunits, respectively). For comparison, the inactivation curves for 5-sec-long conditioning prepulses could be fitted by single Boltzmann's distribution with a 20 mV more positive midpoint and a slope factor of about 13 mV. In contrast to the steady-state inactivation curves, they showed considerable overlap with the steady-state activation curve. Our results reflect functional consequences of known sequence differences between α1-subunits of the cardiac and SM L-type Ca²⁺ channels and could be used in structural modeling of Ca²⁺ channel gating. In addition, they show that depolarization-induced window current has a transient nature and decays with the development of extremely slow inactivation. This is the first demonstration that slow inactivation of the L-type Ca²⁺ channel is an intrinsic property of its α1-subunits.     

Two components of extracellularly-recorded photoreceptor potentials in the cephalopod retina: Differential effects of Na+, K+ and Ca2+

The ERG of the isolated, superfused half-eye of the cephalopod Sepiola atlantica, evoked by a brief (10 s) light flash, has been studied by recording intraretinal potentials with glass microelectrodes. The intensity-response characteristics of the potentials recorded at an electrode fixed at the surface (V _s ) can be fitted by a simple equation derived from an equivalent circuit model based on a sodium conductance increase mechanism. Raising the external potassium level reduces the maximal response (V _m ), but does not alter the half-saturation intensity value (I ₀). Reducing external sodium does not affect (V _m ), but increases I ₀. Reducing external calcium also does not affect (V _m ), but decreases I ₀. These effects are adequately described by the model if it is also assumed (a) that changing the external sodium does not significantly alter the transmembrane sodium gradient, and (b) that sodium and calcium ions compete for the sensitivity control mechanism.Differential-depth recording between the fixed electrode at the surface and another electrode that could be moved into the retina revealed that the two component appearance of the transretinal ERG arose from the superposition of two vitreal-negative waveforms. An initial fast component was mainly recorded in the photoreceptive distal segments while a slow component was prominent in the more proximal regions of the retina. Perfusion with high K⁺ salines resulted in a decrease in the amplitudes of both fast and slow components of the response whereas reducing external Na⁺ reduced the amplitude of the fast component at all light intensities but reduced the amplitude of the slow component only at low intensities. The amplitudes of both the fast and slow components increased on reducing external calcium, but the rate of rise and fall of the fast component was independent of external calcium. The rate of rise of the slow component was also independent of the external Ca²⁺ level but a minimum in the recovery time (t _F ) was shifted to a lower intensity value at lower calcium concentrations. The shift of the minimum was to a higher intensity value with lowered sodium perfusing solutions. On the basis of the differential sensitivity of the two components to ion changes, as well as stimulus intensity and intraretinal distribution of the components, it is suggested that they reflect two distinct processes in the light-evoked potential of the photoreceptor cells.List of the more important symbols V _s Potential of fixed electrode at the surface of retina relative to grounded electrode - V _p Potential of moveable electrode relative to ground - V _D V _s - V _p - V _m Maximum value of V _s produced by saturating light intensities - I _o Stimulus required to evoke a response of half-maximal amplitude - g _K Membrane potassium conductance - g _Na Membrane sodium conductance - E _K Nernst potential for potassium - E _Na Nernst potential for sodium - G Coefficient connecting light intensity and light-induced change of conductance - t _R Time, measured from the stimulus onset, for the response to reach 50% of peak amplitude - t _F Time, measured from the time to peak, for the response to fall to 50% of its maximal value     

State-Dependent Inhibition of Inactivation-Deficient CaV1.2 and CaV2.3 Channels By Mibefradil

The structural determinants of mibefradil inhibition were analyzed using wild-type and inactivation-modified Ca_V1.2 (α1C) and Ca_V2.3 (α1E) channels. Mibefradil inhibition of peak Ba²⁺ currents was dose- and voltage-dependent. An increase of holding potentials from −80 to −100 mV significantly shifted dose-response curves toward higher mibefradil concentrations, namely from a concentration of 108 ± 21 μm (n= 7) to 288 ± 17 μm (n= 3) for inhibition of half of the Ca_v1.2 currents (IC ₅₀) and from IC ₅₀= 8 ± 2 μm (n= 9) to 33 ± 7 μm (n= 4) for Ca_V2.3 currents. In the presence of mibefradil, Ca_V1.2 and Ca_V2.3 experienced significant use-dependent inhibition (0.1 to 1 Hz) and slower recovery from inactivation suggesting mibefradil could promote transition(s) to an absorbing inactivated state. In order to investigate the relationship between inactivation and drug sensitivity, mibefradil inhibition was studied in inactivation-altered Ca_V1.2 and Ca_V2.3 mutants. Mibefradil significantly delayed the onset of channel recovery from inactivation in CEEE (Repeat I + part of the I–II linker from Ca_V1.2 in the Ca_V2.3 host channel), in EC(AID)EEE (part of the I–II linker from Ca_V1.2 in the Ca_V2.3 host channel) as well as in Ca_V1.2 E462R, and Ca_V2.3 R378E (point mutation in the β-subunit binding motif) channels. Mibefradil inhibited the faster inactivating chimera EC(IS1-6)EEE with an IC ₅₀= 7 ± 1 μm (n= 3), whereas the slower inactivating chimeras EC(AID)EEE and CEEE were, respectively, inhibited with IC ₅₀= 41 ± 5 μm (n= 4) and IC ₅₀= 68 ± 9 μm (n= 5). Dose-response curves were superimposable for the faster EC(IS1-6)EEE and Ca_V2.3, whereas intermediate-inactivating channel kinetics (CEEE, Ca_V1.2 E462R, and Ca_V1.2 E462K) were inhibited by similar concentrations of mibefradil with IC ₅₀≈ 55–75 μm. The slower Ca_V1.2 wild-type and Ca_V1.2 Q473K channels responded to higher doses of mibefradil with IC ₅₀≈ 100–120 μm. Mibefradil was also found to significantly speed up the inactivation kinetics of slower channels (Ca_V1.2, CEEE) with little effect on the inactivation kinetics of faster-inactivating channels (Ca_V2.3). A open-channel block model for mibefradil interaction with high-voltage-activated Ca²⁺ channels is discussed and shown to qualitatively account for our observations. Hence, our data agree reasonably well with a ``receptor guarded mechanism' where fast inactivation kinetics efficiently trap mibefradil into the channel. Received: 14 March 2001/Revised: 25 June 2001     

Pertussis toxin modulation of sodium channels in the central neurons of cyhalothrin-resistant and cyhalothrin-susceptible cotton bollworm, Helicoverpa armigera

Pertussis toxin （FIX） inhibits the activation of the α-subunit of the inhibitory heterotrimeric G-proteins （Cαi/o） and modulates voltage-gated sodium channels, which may be one of the primary targets of pyrethroids. To investigate the potential mechanisms of agricultural pests resistance to pyrethroid insecticides, we examined the modulations by PTX on sodium channels in the central neurons of the 3rd-4th instar larvae of cyhalothrin-resistant （Cy-R） and cyhaiothrin-susceptible （Cy-S） Helicoverpa armigera by the whole-cell patch-clamp technique. The isolated neurons were cultured for 12-16 h in an improved L15 insect culture medium with or without PTX （400 ng/mL）. The results showed that both the Cy-R and Cy-S sodium channels exhibited fast kinetics and tetrodotoxin （TTX） sensitivity. The Cy-R sodium channels exhibited not only altered gating properties, including a 8.88-mV right shift in voltage-dependent activation （V0.5act） and a 6.54-mV right shift in voltage-dependent inactivation （V0.5inact）, but also a reduced peak in sodium channel density （Ⅰdensity） （55.2% of that in Cy-S neurons）. Cy-R sodium channels also showed low excitability, as evidenced by right shift of activation potential （Ⅴacti） by 5-10 mV and peak potential （Ⅴpcak） by 20 mV. FIX exerted significant effects on Cy-S sodium channels, reducing sodium channel density by 70.04%, right shifting V0.5act by 14.41 mV and V0.5inact by 9. 38 mV. It did not cause any significant changes of the parameters mentioned above in the Cy-R sodium channels. The activation time （Tpeak） from latency to peak at peak voltage and the fast inactivation time constant （τinact） in both Cy-S and Cy-R neurons were not affected. The results suggest that cotton bollworm resistant to pyrethroid insecticides involves not only mutations and allosteric alterations of voltage-gated sodium channels, but also might implicate perturbation of PTX-sensitive Gαi/o-COupled signaling Wansduction pathways.     

Control of firing patterns by two transient potassium currents: leading spike,latency, bistability

Transient potassium currents distinctively affect firing properties, particularly in regulating the latency before repetitive firing. Pyramidal cells of the dorsal cochlear nucleus (DCN) have two transient potassium currents, I _Kif and I _Kis, fast and slowly inactivating, respectively, and they exhibit firing patterns with dramatically variable latencies. They show immediate repetitive firing, or only after a long latency with or without a leading spike, the so-called pauser and buildup patterns. We consider a conductance-based, ten-variable, single-compartment model for the DCN pyramidal cells (Kanold and Manis 2001). We develop and analyze a reduced three-variable integrate-and-fire model (KM-LIF) which captures the qualitative firing features. We apply dynamical systems methods to explain the underlying biophysical and mathematical mechanisms for the firing behaviors, including the characteristic firing patterns, the latency phase, the onset of repetitive firing, and some discontinuities in the timing of latency duration (e.i. first spike latency and first inter spike interval). Moreover, we obtain new insights associated with the leading spike by phase plane analysis. We further demonstrate the effects of possible heterogeneity of I _Kis. The latency before repetitive firing can be controlled to cover a large range by tuning of the relative amounts of I _Kif and I _Kis. Finally, we find for the full system robust bistability when enough I _Kis is present.