Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials

Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo. We use a three-compartment model calibrated to reproduce DA neuron responses to several pharmacological manipulations to uncover mechanisms of frequency limitation. The model exhibits a slow oscillatory potential (SOP) dependent on the interplay between the L-type Ca²⁺ current and the small conductance K⁺ (SK) current that is unmasked by fast Na⁺ current block. Contrary to previous theoretical work, the SOP does not pace the steady spiking frequency in our model. The main currents that determine the spontaneous firing frequency are the subthreshold L-type Ca²⁺ and the A-type K⁺ currents. The model identifies the channel densities for the fast Na⁺ and the delayed rectifier K⁺ currents as critical parameters limiting the maximal steady frequency evoked by a depolarizing pulse. We hypothesize that the low maximal steady frequencies result from a low safety factor for action potential generation. In the model, the rate of Ca²⁺ accumulation in the distal dendrites controls the transient initial frequency in response to a depolarizing pulse. Similar results are obtained when the same model parameters are used in a multi-compartmental model with a realistic reconstructed morphology, indicating that the salient contributions of the dendritic architecture have been captured by the simpler model.     

Constitutive inactivation of the hKv1.5 mutant channel, H463G, in K+-free solutions at physiological pH

Extracellular acidification and reduction of extracellular K⁺ are known to decrease the currents of some voltage-gated potassium channels. Although the macroscopic conductance of WT hKv1.5 channels is not very sensitive to [K⁺]_o at pH 7.4, it is very sensitive to [K⁺]_o at pH 6.4, and in the mutant, H463G, the removal of K⁺ _o virtually eliminates the current at pH 7.4. We investigated the mechanism of current regulation by K⁺ _o in the Kv1.5 H463G mutant channel at pH 7.4 and the wild-type channel at pH 6.4 by taking advantage of Na⁺ permeation through inactivated channels. Although the H463G currents were abolished in zero [K⁺]_o, robust Na⁺ tail currents through inactivated channels were observed. The appearnnce of H463G Na⁺ currents with a slow rising phase on repolarization after a very brief depolarization (2 ms) suggests that channels could activate directly from closed-inactivated states. In wild-type channels, when intracellular K⁺ was replaced by NMG⁺ and the inward Na⁺ current was recorded, addition of 1 mM K⁺ prevented inactivation, but changing pH from 7.4 to 6.4 reversed this action. The data support the idea that C-type inactivation mediated at R487 in Kv1.5 channels is influenced by H463 in the outer pore. We conclude that both acidification and reduction of [K⁺]_o inhibit Kv1.5 channels through a common mechananism (i.e., by increasing channel inactivation, which occurs in the resting state or develops very rapidly after activation).     

K+ Channels and the Intracellular Calcium Signal in Human Melanoma Cell Proliferation

K⁺ channels, membrane voltage, and intracellular free Ca²⁺ are involved in regulating proliferation in a human melanoma cell line (SK MEL 28). Using patch-clamp techniques, we found an inwardly rectifying K⁺ channel and a calcium-activated K⁺ channel. The inwardly rectifying K⁺ channel was calcium independent, insensitive to charybdotoxin, and carried the major part of the whole-cell current. The K⁺ channel blockers quinidine, tetraethylammonium chloride and Ba²⁺ and elevated extracellular K⁺ caused a dose-dependent membrane depolarization. This depolarization was correlated to an inhibition of cell proliferation. Charybdotoxin affected neither membrane voltage nor proliferation. Basic fibroblast growth factor and fetal calf serum induced a transient peak in intracellular Ca²⁺ followed by a long-lasting Ca²⁺ influx. Depolarization by voltage clamp decreased and hyperpolarization increased intracellular Ca²⁺, illustrating a transmembrane flux of Ca²⁺ following its electrochemical gradient. We conclude that K⁺ channel blockers inhibit cell-cycle progression by membrane depolarization. This in turn reduces the driving force for the influx of Ca²⁺, a messenger in the mitogenic signal cascade of human melanoma cells. Received: 9 May 1995/Revised: 30 January 1996     

Controls on na influx in corn roots

We have investigated the effects of hyperpolarization and depolarization, and the presence of K⁺ and/or Ca²⁺, on ²²Na⁺ influx into corn (Zea mays L.) root segments. In freshly excised root tissue which is injured, Na⁺ influx is unaffected by hyperpolarization with fusicoccin, or depolarization with uncoupler (protonophore), or by addition of K⁺. However, added Ca²⁺ suppresses Na⁺ influx by 60%. In washed tissue which has recovered, Na⁺ influx is doubled over that of freshly excised tissue, and the influx is increased by fusicoccin and suppressed by uncoupler. This energy-linked component of Na⁺ influx is completely eliminated by low concentrations of K⁺, leaving the same level and kind of Na⁺ influx seen in freshly excised roots. The K⁺-sensitive energy linkage appears to be by the carrier for active K⁺ influx. Calcium is equally inhibitory to Na⁺ influx in washed as in fresh tissue. Other divalent cations are only slightly less effective. Net Na⁺ uptake was about 25% of ²²Na⁺ influx, but proportionately the response to K⁺ and Ca²⁺ was about the same.

The constancy of K⁺-insensitive Na⁺ influx under conditions known to hyperpolarize and depolarize suggests that if Na⁺ transport is by means of a voltage-sensitive channel, the rise or fall of channel resistance must be proportional to the rise or fall in potential difference. The alternative is a passive electroneutral exchange of ²²Na⁺ for endogenous Na⁺. The data suggest that an inwardly directed Na⁺ current is largely offset by an efflux current, giving both a small net uptake and isotopic exchange.

     

Understanding the physiology of the asymptomatic diaphragm of the M1592V hyperkalemic periodic paralysis mouse

The diaphragm muscle of hyperkalemic periodic paralysis (HyperKPP) patients and of the M1592V HyperKPP mouse model rarely suffers from the myotonic and paralytic symptoms that occur in limb muscles. Enigmatically, HyperKPP diaphragm expresses the mutant NaV1.4 channel and, more importantly, has an abnormally high Na⁺ influx similar to that in extensor digitorum longus (EDL) and soleus, two hindlimb muscles suffering from the robust HyperKPP abnormalities. The objective was to uncover the physiological mechanisms that render HyperKPP diaphragm asymptomatic. A first mechanism involves efficient maintenance of resting membrane polarization in HyperKPP diaphragm at various extracellular K⁺ concentrations compared with larger membrane depolarizations in HyperKPP EDL and soleus. The improved resting membrane potential (EM) results from significantly increased Na⁺ K⁺ pump electrogenic activity, and not from an increased protein content. Action potential amplitude was greater in HyperKPP diaphragm than in HyperKPP soleus and EDL, providing a second mechanism for the asymptomatic behavior of the HyperKPP diaphragm. One suggested mechanism for the greater action potential amplitude is lower intracellular Na⁺ concentration because of greater Na⁺ K⁺ pump activity, allowing better Na⁺ current during the action potential depolarization phase. Finally, HyperKPP diaphragm had a greater capacity to generate force at depolarized EM compared with wild-type diaphragm. Action potential amplitude was not different between wild-type and HyperKPP diaphragm. There was also no evidence for an increased activity of the Na⁺–Ca²⁺ exchanger working in the reverse mode in the HyperKPP diaphragm compared with the wild-type diaphragm. So, a third mechanism remains to be elucidated to fully understand how HyperKPP diaphragm generates more force compared with wild type. Although the mechanism for the greater force at depolarized resting EM remains to be determined, this study provides support for the modulation of the Na⁺ K⁺ pump as a component of therapy to alleviate weakness in HyperKPP.     

Genetic Na channelopathies and sinus node dysfunction

Voltage-gated Na⁺ channels are transmembrane proteins that produce the fast inward Na⁺ current responsible for the depolarization phase of the cardiac action potential. They play fundamental roles in the initiation, propagation, and maintenance of normal cardiac rhythm. Inherited mutations in SCN5A, the gene encoding the pore-forming α-subunit of the cardiac-type Na⁺ channel, result in a spectrum of disease entities termed Na⁺ channelopathies. These include multiple arrhythmic syndromes, such as the long QT syndrome type 3 (LQT3), Brugada syndrome (BrS), an inherited cardiac conduction defect (CCD), sudden infant death syndrome (SIDS) and sick sinus syndrome (SSS). To date, mutational analyses have revealed more than 200 distinct mutations in SCN5A, of which at least 20 mutations are associated with sinus node dysfunction including SSS. This review summarizes recent findings bearing upon: (i) the functional role of distinct voltage-gated Na⁺ currents in sino-atrial node pacemaker function; (ii) genetic Na⁺ channelopathy and its relationship to sinus node dysfunction.     

Time-Dependent Molecular Memory in Single Voltage-Gated Sodium Channel

Excitability in neurons is associated with firing of action potentials and requires the opening of voltage-gated sodium channels with membrane depolarization. Sustained membrane depolarization, as seen in pathophysiological conditions like epilepsy, can have profound implications on the biophysical properties of voltage-gated ion channels. Therefore, we sought to characterize the effect of sustained membrane depolarization on single voltage-gated Na⁺ channels. Single-channel activity was recorded in the cell-attached patch-clamp mode from the rNa_v1.2α channels expressed in CHO cells. Classical statistical analysis revealed complex nonlinear changes in channel dwell times and unitary conductance of single Na⁺ channels as a function of conditioning membrane depolarization. Signal processing tools like weighted wavelet Z (WWZ) and discrete Fourier transform analyses attributed a “pseudo-oscillatory” nature to the observed nonlinear variation in the kinetic parameters. Modeling studies using the hidden Markov model (HMM) illustrated significant changes in kinetic states and underlying state transition rate constants upon conditioning depolarization. Our results suggest that sustained membrane depolarization induces novel nonlinear properties in voltage-gated Na⁺ channels. Prolonged membrane depolarization also induced a “molecular memory” phenomenon, characterized by clusters of dwell time events and strong autocorrelation in the dwell time series similar to that reported recently for single enzyme molecules. The persistence of such molecular memory was found to be dependent on the duration of depolarization. Voltage-gated Na⁺ channel with the observed time-dependent nonlinear properties and the molecular memory phenomenon may determine the functional state of the channel and, in turn, the excitability of a neuron.     

Early changes in membrane potential of Saccharomyces cerevisiae induced by varying extracellular K+, Na+ or H+ concentrations

Recently we introduced a fluorescent probe technique that makes possible to convert changes of equilibrium fluorescence spectra of 3,3’-dipropylthiadicarbocyanine, diS-C₃(3), measured in yeast cell suspensions under defined conditions into underlying membrane potential differences, scaled in millivolts (Plasek et al. in J Bioenerg Biomembr 44: 559–569, 2012). The results presented in this paper disclose measurements of real early changes of plasma membrane potential induced by the increase of extracellular K⁺, Na⁺ and H⁺ concentration in S. cerevisiae with and without added glucose as energy source. Whereas the wild type and the ?tok1 mutant cells exhibited similar depolarization curves, mutant cells lacking the two Trk1,2 potassium transporters revealed a significantly decreased membrane depolarization by K⁺, particularly at lower extracellular potassium concentration [K⁺]_out. In the absence of external energy source plasma membrane depolarization by K⁺ was almost linear. In the presence of glucose the depolarization curves exhibited an exponential character with increasing [K⁺]_out. The plasma membrane depolarization by Na⁺ was independent from the presence of Trk1,2 transporters. Contrary to K⁺, Na⁺ depolarized the plasma membrane stronger in the presence of glucose than in its absence. The pH induced depolarization exhibited a fairly linear relationship between the membrane potential and the pH_o of cell suspensions, both in the wild type and the Δtrk1,2 mutant strains, when cells were energized by glucose. In the absence of glucose the depolarization curves showed a biphasic character with enhanced depolarization at lower pH_o values.     

p-CMBS Modifies Extrafacial Sulfhydryl Groups at the Chara Plasma Membrane: Activation of Ca2+ Influx and Inhibition of Two Different K+ Currents

The effect of the membrane impermeant sulfhydryl group (SH) reagent, p-chloromercuribenzenesulfonic acid (p-CMBS), on electrical membrane transport properties of the giant alga, Chara corallina, was determined. In an external medium with a high K⁺ concentration (5 mM) cells typically exhibited stable membrane potentials close to the K⁺equilibrium potential. The steady-state current-voltage (I-V) relation could be dissected into two distinct components: an almost linear ohmic leak current and a voltage-dependent K⁺ current. Adding 0.5 mM p-CMBS to the external medium resulted in an immediate, short depolarization transient (resembling the time course of an action potential) and was associated with a slow down of the cytoplasmic streaming velocity. The depolarization, as well as the streaming inhibition, could be abolished by pretreating cells with the Ca²⁺ channel inhibitor, LaCl₃. This suggests that the depolarization transient reflected a p-CMBS induced Ca²⁺ influx, a scenario known to trigger membrane excitation and slow down of cytoplasmic streaming. From the I-V analysis it appeared that p-CMBS also caused a reversible inhibition of two additional transmembrane currents: (1) a reduction of a leak current and (2) a modification of the deactivation kinetics of the voltage-dependent K⁺ channels. From the I-V difference analysis, the inhibited leak current was identified as a K⁺ current, because the reversal potential was close to the estimated K⁺ equilibrium potential. Control experiments have furthermore shown that the mercapto reagent, dithiothreitol, partly reversed the effect of p-CMBS. This strengthens the view that the action of the mercurial is related to a specific and direct modification of SH groups. The p-CMBS-evoked inhibition of K⁺ currents was not abolished by the LaCl₃ pretreatment, which suggests that the effect of the SH reagent is not induced indirectly by p-CMBS-triggered Ca²⁺ influx. Therefore, it is suggested that the mercurial interacts direcly with the K⁺ transport protein.     

Of cilia,titin, and neurosteroids

Missense mutations at arginine residues in the S4 voltage-sensor domains of Na_V1.4 are an established cause of hypokalemic periodic paralysis, an inherited disorder of skeletal muscle involving recurrent episodes of weakness in conjunction with low serum K⁺. Expression studies in oocytes have revealed anomalous, hyperpolarization-activated gating pore currents in mutant channels. This aberrant gating pore conductance creates a small inward current at the resting potential that is thought to contribute to susceptibility to depolarization in low K⁺ during attacks of weakness. A critical component of this hypothesis is the magnitude of the gating pore conductance relative to other conductances that are active at the resting potential in mammalian muscle: large enough to favor episodes of paradoxical depolarization in low K⁺, yet not so large as to permanently depolarize the fiber. To improve the estimate of the specific conductance for the gating pore in affected muscle, we sequentially measured Na⁺ current through the channel pore, gating pore current, and gating charge displacement in oocytes expressing R669H, R672G, or wild-type Na_V1.4 channels. The relative conductance of the gating pore to that of the pore domain pathway for Na⁺ was 0.03%, which implies a specific conductance in muscle from heterozygous patients of ∼10 µS/cm² or 1% of the total resting conductance.Unexpectedly, our data also revealed a substantial decoupling between gating charge displacement and peak Na⁺ current for both R669H and R672G mutant channels. This decoupling predicts a reduced Na⁺ current density in affected muscle, consistent with the observations that the maximal dV/dt and peak amplitude of the action potential are reduced in fibers from patients with R672G and in a knock-in mouse model of R669H. The defective coupling between gating charge displacement and channel activation identifies a previously unappreciated mechanism that contributes to the reduced excitability of affected fibers seen with these mutations and possibly with other R/X mutations of S4 of Na_V, Ca_V, and K_V channels associated with human disease.     

Patch-clamp recordings of spiking and nonspiking interneurons from rabbit olfactory bulb slices: Membrane properties and ionic currents

Summary Physiological and morphological properties of rabbit, Oryctolagus cuniculus, olfactory bulb interneurons were characterized by using a thin slice preparation in combination with patch-clamp measurements and Lucifer Yellow fills. Two types of interneurons, periglomerular (PG) and juxtaglomerular (JG) cells, were unequivocally distinguished in the glomerular layer. Their properties were compared to those of mitral cells. PG cells closely resembled previously described periglomerular cells in their morphology. During current clamp recording these neurons were characterized by their lack of action potentials upon depolarization. Consistent with these results no Na⁺ currents could be elicited in voltage clamp experiments. Two types of outward K⁺ currents were distinguished: one which inactivated and one which did not. From their morphology JG cells appear to be either short axon cells or external tufted cells. JG cells always responded with a single, TTX-blockable action potential in response to maintained current injection. Two types of membrane currents were identified in JG cells during voltage clamp: a fast, inactivating Na⁺ current that was fully activated at — 80 mV, and a sustained outward current that shared some properties with a delayed rectifier K⁺ current. The particular relationship between the voltage dependence of the Na⁺ and K⁺ currents appeared to preclude repetitive spike activity.Abbreviations JG juxtraglomerular interneuron - LOT lateral olfactory tract - M/T mitral/tufted (cells) - PG periglomerular - SA short axon     

Interactions of K+ ATP channel blockers with Na+/K+-ATPase

Two K⁺ _ATP channel blockers, 5-hydroxydecanoate (5-HD) and glyburide, are often used to study cross-talk between Na⁺/K⁺-ATPase and these channels. The aim of this work was to characterize the effects of these blockers on purified Na⁺/K⁺-ATPase as an aid to appropriate use of these drugs in studies on this cross-talk. In contrast to known dual effects (activating and inhibitory) of other fatty acids on Na⁺/K⁺-ATPase, 5-HD only inhibited the enzyme at concentrations exceeding those that block mitochondrial K⁺ _ATP channels. 5-HD did not affect the ouabain sensitivity of Na⁺/K⁺-ATPase. Glyburide had both activating and inhibitory effects on Na⁺/K⁺-ATPase at concentrations used to block plasma membrane K⁺ _ATP channels. The findings justify the use of 5-HD as specific mitochondrial channel blocker in studies on the relation of this channel to Na⁺/K⁺-ATPase, but question the use of glyburide as a specific blocker of plasma membrane K⁺ _ATP channels, when the relation of this channel to Na⁺/K⁺-ATPase is being studied.     

The influence of electrochemical gradients of Na+ and K+ upon the membrane binding and pore forming activity of the terminal complement proteins

Summary The hemolytic activity of the terminal complement proteins (C5b-9) towards erythrocytes containing high potassium concentration has been reported to be dramatically increased when extracellular Na⁺ is substituted isotonically by K⁺ (Dalmasso, A.P., et al., 1975,J. Immunol. 115:63–68). This phenomenon was now further investigated using resealed human erythrocyte ghosts (ghosts), which can be maintained at a nonlytic osmotic steady state subsequent to C5b-9 binding: (1) The functional state of C5b-9-treated ghosts was studied from their ability to retain trapped [¹⁴C]-sucrose or [³H]-inulin when suspended either in the presence of Na⁺ or K⁺. A dramatic increase in the permeability of the ghost membrane to both nonelectrolytes-in the absence of significant hemoglobin release-was observed for C5b-9 assembly in the presence of external K⁺. (2) The physical binding of the individual¹²⁵I-labeled terminal complement proteins to ghost membranes was directly measured as a function of intra- and extracellular K⁺ and Na⁺. The uptake of¹²⁵I-C7,¹²⁵I-C8, and¹²⁵I-C9 into membrane C5b-9 was unaltered by substitution of Na⁺ by K⁺. (3) The binding of the terminal complement proteins to ghosts subjected to a transient membrane potential generated by the K⁺-ionophore valinomycin (in the presence of K⁺ concentration gradients) was measured. No significant change in membrane binding of any of the C5b-9 proteins was detected under the influence of both depolarizing and hyperpolarizing membrane potentials. It can be concluded that the differential effect of Na⁺ versus K⁺ upon the erythrocyte membrane isnot due to an effect upon the binding of the complement proteins to the membraneper se, but upon the functional properties of the assembled C5b-9 pore site.     

The Ionic Permeability Changes during Acetylcholine-Induced Responses of Aplysia Ganglion Cells

ACh-induced depolarization (D response) in D cells markedly decreases as the external Na⁺ is reduced. However, when Na⁺ is completely replaced with Mg⁺⁺, the D response remains unchanged. When Na⁺ is replaced with Tris(hydroxymethyl)aminomethane, the D response completely disappears, except for a slight decrease in membrane resistance. ACh-induced hyperpolarization (H response) in H cells is markedly depressed as the external Cl^- is reduced. Frequently, the reversal of the H response; i.e., depolarization, is observed during perfusion with Cl^--free media. In cells which show both D and H responses superimposed, it was possible to separate these responses from each other by perfusing the cells with either Na⁺-free or Cl^--free Ringer's solution. High [K⁺]₀ often caused a marked hyperpolarization in either D or H cells. This is due to the primary effect of high [K⁺]₀ on the presynaptic inhibitory fibers. The removal of this inhibitory afferent interference by applying Nembutal readily disclosed the predicted K⁺ depolarization. In perfusates containing normal [Na⁺]₀, the effects of Ca⁺⁺ and Mg⁺⁺ on the activities of postsynaptic membrane were minimal, supporting the current theory that the effects of these ions on the synaptic transmission are mainly presynaptic. The possible mechanism of the hyperpolarization produced by simultaneous perfusion with both high [K⁺]₀ and ACh in certain H cells is explained quantitatively under the assumption that ACh induces exclusively an increase in Cl^- permeability of the H membrane.     

Effect of Neural Stimulation on Acinar Cell Membrane Potentials in Isolated Pancreas and Salivary Gland Segments

The effect of cholinergic neural excitation by field stimulation on the acinar cell membrane potential was investigated in superfused segments of mouse pancreas and salivary glands (sublingual, submaxillary, and parotid glands).

Responses of acinar cells in both exocrine pancreas and salivary glands to the neural excitation obtained by field stimulation were similar to responses previously described in each gland to the externally applied acetylcholine.

In the pancreatic acinar cell, electrical field stimulation induced depolarization with a latency of 0.3 to 1.2 sec. This depolarization was accompanied by a marked decrease in membrane resistance. The equilibrium potential of the depolarization induced by stimulation was between -10 and -20 mV. In the sublingual gland, field stimulation induced depolarization of the acinar cell with a latency of 0.2 to 0.3 sec. The stimulus induced depolarization was blocked by the addition of atropine. In the submaxillary and parotid glands, field stimulation induced depolarization in some acinar cell and hyper-polarization in other cells.

The results support evidence previously presented by Petersen and his colleagues that acetylcholine acts to increase Na⁺ and K⁺ or Na⁺, K⁺, and Cl^- permeabilities in the pancreatic acinar cell and to increase K⁺ and Na⁺ permeabilities in the salivary gland [11,24].     

Gating and Conduction Properties of a Sodium-activated Cation Channel from Lobster Olfactory Receptor Neurons

The gating and conduction properties of a channel activated by intracellular Na⁺ were studied by recording unitary currents in inside-out patches excised from lobster olfactory receptor neurons. Channel openings to a single conductance level of 104 pS occurred in bursts. The open probability of the channel increased with increasing concentrations of Na⁺. At 210 mm Na⁺, membrane depolarization increased the open probability e-fold per 36.6 mV. The distribution of channel open times could be fit by a single exponential with a time constant of 4.09 msec at −60 mV and 90 mm Na⁺. The open time constant was not affected by the concentration of Na⁺, but was increased by membrane depolarization. At 180 mm Na⁺ and −60 mV, the distribution of channel closed times could be fit by the sum of four exponentials with time constants of 0.20, 1.46, 8.92 and 69.9 msec, respectively. The three longer time constants decreased, while the shortest time constant did not vary with the concentration of Na⁺. Membrane depolarization decreased all four closed time constants. Burst duration was unaffected by the concentration of Na⁺, but was increased by membrane depolarization. Permeability for monovalent cations relative to that of Na⁺ (P _X /P _Na ), calculated from the reversal potential, was: Li⁺ (1.11) > Na⁺ (1.0) > K⁺ (0.54) > Rb⁺ (0.36) > Cs⁺ (0.20). Extracellular divalent cations (10 mm) blocked the inward Na⁺ current at −60 mV according to the following sequence: Mn²⁺ > Ca²⁺ > Sr²⁺ > Mg²⁺ > Ba²⁺. Relative permeabilities for divalent cations (P _Y /P _Na ) were Ca²⁺ (39.0) > Mg²⁺ (34.1) > Mn²⁺ (15.5) > Ba²⁺ (13.8) > Na⁺ (1.0). Both the reversal potential and the conductance determined in divalent cation-free mixtures of Na⁺ and Cs⁺ or Li⁺ were monotonic functions of the mole fraction, suggesting that the channel is a single-ion pore that behaves as a multi-ion pore when the current is carried exclusively by divalent cations. The properties of the channel are consistent with the channel playing a role in odor activation of these primary receptor neurons. Received: 17 September 1996/Revised: 15 November 1996     

Characterization of the cardiac Na/K pump by development of a comprehensive and mechanistic model

A large amount of experimental data on the characteristics of the cardiac Na⁺/K⁺ pump have been accumulated, but it remains difficult to predict the quantitative contribution of the pump in an intact cell because most measurements have been made under non-physiological conditions. To extrapolate the experimental findings to intact cells, we have developed a comprehensive Na⁺/K⁺ pump model based on the thermodynamic framework (Smith and Crampin, 2004) of the Post-Albers reaction cycle combined with access channel mechanisms. The new model explains a variety of experimental results for the Na⁺/K⁺ pump current (I_NaK), including the dependency on the concentrations of Na⁺ and K⁺, the membrane potential and the free energy of ATP hydrolysis. The model demonstrates that both the apparent affinity and the slope of the substrate-I_NaK relationship measured experimentally are affected by the composition of ions in the extra- and intracellular solutions, indirectly through alteration in the probability distribution of individual enzyme intermediates. By considering the voltage dependence in the Na⁺- and K⁺-binding steps, the experimental voltage-I_NaK relationship could be reconstructed with application of experimental ionic compositions in the model, and the view of voltage-dependent K⁺ binding was supported. Re-evaluation of charge movements accompanying Na⁺ and K⁺ translocations gave a reasonable number for the site density of the Na⁺/K⁺ pump on the membrane. The new model is relevant for simulation of cellular functions under various interventions, such as depression of energy metabolism.     

Membrane potential, action potential and activation potential of eggs of the sea urchin, Lytechinus variegatus

Unfertilized Lytechinus variegatus eggs in sea water in their normal physiological state have membrane potentials that approximate ?70 to ?80 mV. This conclusion is based on microelectrode measurements and on computation from the Na⁺ and K⁺ fluxes. The ?8 to ?15 mV values for the membrane potential previously reported and which are generally measured are the consequence of depolarization by impalement. The activation potential in inseminated eggs with an initial membrane potential more negative than ?60 mV is a compound event involving sperm-induced as well as voltage dependent conductance changes. The sperm-induced mechanism is a two-phase conductance increase which involves both Na⁺ and Ca²⁺ during the first phase, and Na⁺ alone during the second phase. In addition, the sperm-induced depolarization at the beginning of the first phase activates a voltage dependent Ca²⁺-conductance mechanism resulting in generation of an action potential.     

Roles of subcellular Na+ channel distributions in the mechanism of cardiac conduction

The gap junction and voltage-gated Na⁺ channel play an important role in the action potential propagation. The purpose of this study was to elucidate the roles of subcellular Na⁺ channel distribution in action potential propagation. To achieve this, we constructed the myocardial strand model, which can calculate the current via intercellular cleft (electric-field mechanism) together with gap-junctional current (gap-junctional mechanism). We conducted simulations of action potential propagation in a myofiber model where cardiomyocytes were electrically coupled with gap junctions alone or with both the gap junctions and the electric field mechanism. Then we found that the action potential propagation was greatly affected by the subcellular distribution of Na⁺ channels in the presence of the electric field mechanism. The presence of Na⁺ channels in the lateral membrane was important to ensure the stability of propagation under conditions of reduced gap-junctional coupling. In the poorly coupled tissue with sufficient Na⁺ channels in the lateral membrane, the slowing of action potential propagation resulted from the periodic and intermittent dysfunction of the electric field mechanism. The changes in the subcellular Na⁺ channel distribution might be in part responsible for the homeostatic excitation propagation in the diseased heart.     

Sensitivity of cloned muscle,heart and neuronal voltage-gated sodium channels to block by polyamines: A possible basis for modulation of excitability in vivo

Spermidine and spermine, are endogenous polyamines (PAs) that regulate cell growth and modulate the activity of numerous ion channel proteins. In particular, intracellular PAs are potent blockers of many different cation channels and are responsible for strong suppression of outward K⁺ current, a phenomenon known as inward rectification characteristic of a major class of K_IR K⁺ channels. We previously described block of heterologously expressed voltage-gated Na⁺ channels (Na_V) of rat muscle by intracellular PAs and PAs have recently been found to modulate excitability of brain neocortical neurons by blocking neuronal Na_V channels. In this study, we compared the sensitivity of four different cloned mammalian Na_V isoforms to PAs to investigate whether PA block is a common feature of Na_V channel pharmacology. We find that outward Na⁺ current of muscle (Na_V1.4), heart (Na_V1.5), and neuronal (Na_V1.2, Na_V1.7) Na_V isoforms is blocked by PAs, suggesting that PA metabolism may be linked to modulation of action potential firing in numerous excitable tissues. Interestingly, the cardiac Na_V1.5 channel is more sensitive to PA block than other isoforms. Our results also indicate that rapid binding of PAs to blocking sites in the Na_V1.4 channel is restricted to access from the cytoplasmic side of the channel, but plasma membrane transport pathways for PA uptake may contribute to long-term Na_V channel modulation. PAs may also play a role in drug interactions since spermine attenuates the use-dependent effect of the lidocaine, a typical local anesthetic and anti-arrhythmic drug.