Estimating neuronal conductance model parameters using dynamic action potential clamp.

BACKGROUND: Parameterization of neuronal membrane conductance models relies on data acquired from current clamp (CC) or voltage clamp (VC) recordings. Although the CC approach provides key information on a neuron's firing properties, it is often difficult to disentangle the influence of multiple conductances that contribute to the excitation properties of a real neuron. Isolation of a single conductance using pharmacological agents or heterologous expression simplifies analysis but requires extensive VC evaluation to explore the complete state behavior of the channel of interest. NEW METHOD: We present an improved parameterization approach that uses data derived from dynamic action potential clamp (DAPC) recordings to extract conductance equation parameters. We demonstrate the utility of the approach by applying it to the standard Hodgkin-Huxley conductance model although other conductance models could be easily incorporated as well. RESULTS: Using a fully simulated setup we show that, with as few as five action potentials previously recorded in DAPC mode, sodium conductance equation parameters can be determined with average parameter errors of less than 4% while action potential firing accuracy approaches 100%. In real DAPC experiments, we show that by "training" our model with five or fewer action potentials, subsequent firing lasting for several seconds could be predicted with ˜96% mean firing rate accuracy and 94% temporal overlap accuracy. COMPARISON WITH EXISTING METHODS: Our DAPC-based approach surpasses the accuracy of VC-based approaches for extracting conductance equation parameters with a significantly reduced temporal overhead. CONCLUSION: DAPC-based approach will facilitate the rapid and systematic characterization of neuronal channelopathies.

Proximal tubular handling of phosphate: A molecular perspective.

Members of the SLC34 gene family of solute carriers encode for three Na+-dependent phosphate (P i) cotransporter proteins, two of which (NaPi-IIa/SLC34A1 and NaPi-IIc/SLC34A3) control renal reabsorption of P i in the proximal tubule of mammals, whereas NaPi-IIb/SCLC34A2 mediates P i transport in organs other than the kidney. The P i transport mechanism has been extensively studied in heterologous expression systems and structure-function studies have begun to reveal the intricacies of the transport cycle at the molecular level using techniques such as cysteine scanning mutagenesis, and voltage clamp fluorometry. Moreover, sequence differences between the three types of cotransporters have been exploited to obtain information about the molecular determinants of hormonal sensitivity and electrogenicity. Renal handling of P i is regulated by hormonal and non-hormonal factors. Changes in urinary excretion of P i are almost invariably mirrored by changes in the apical expression of NaPi-IIa and NaPi-IIc in proximal tubules. Therefore, understanding the mechanisms that control the apical expression of NaPi-IIa and NaPi-IIc as well as their functional properties is critical to understanding how an organism achieves P i homeostasis.

Functionally important residues in the predicted 3(rd) transmembrane domain of the type IIa sodium-phosphate co-transporter (NaPi-IIa).

The type IIa Na(+)/P(i), cotransporter (NaPi-IIa) mediates electrogenic transport of three Na(+) and one divalent P(i) ion (and one net positive charge) across the cell membrane. Sequence comparison of electrogenic NaPi-IIa and IIb isoforms with the electroneutral NaPi-IIc isoform pointed to the third transmembrane domain (TMD-3) as a possibly significant determinant of substrate binding. To elucidate the role of TMD-3 in the topology and mechanism underlying NaPi-IIa function we subjected it to cysteine scanning mutagenesis. The constructs were expressed in Xenopus oocytes and P(i) transport kinetics were assayed by electrophysiology and radiotracer uptake. Cys substitution resulted in only marginally altered kinetics of P(i) transport in those mutants providing sufficient current for analysis. Only one site, at the extracellular end of TMD-3, appeared to be accessible to methanethiosulfonate reagents. However, additional mutations carried out at D224 (replaced by E, G or N) and N227 (replaced by D or Q) resulted in markedly altered voltage and substrate dependencies of the P(i)-dependent currents. Replacing Asp-224 (highly conserved in electrogenic a and b isoforms) with Gly (the residue found in the electroneutral c isoform) resulted in a mutant that mediated electroneutral Na(+)-dependent P(i) transport. Since electrogenic NaPi-II transports 3 Na(+)/transport cycle, whereas electroneutral NaPi-IIc only transports 2, we speculate that this loss of electrogenicity might result from the loss of one of the three Na(+) binding sites in NaPi-IIa.

Functional studies on a split type II Na/P(i)-cotransporter.

Analysis of rat and mouse proximal tubular brush-border membrane expression of the type IIa Na/P(i)-cotransporter provides evidence for its cleavage in the large extracellular loop (ECL-2). To study functional properties and membrane distribution of this split NaP(i)-IIa transporter we followed two strategies. In one strategy we expressed the transporter as two complementary parts (p40 and p45) in Xenopus laevis oocytes and as another strategy we cleaved the WT protein with trypsin. Both strategies resulted in a split NaP(i)-IIa protein located in the plasma membrane. The two domains were tied together by a disulfide bridge, most likely involving the cysteines 306 and 334. Surface expression of the NaP(i)-IIa fragments was dependent on the presence of both domains. If both domains were coexpressed, the transporter was functional and transport characteristics were identical to those of the WT-NaP(i)-IIa protein. Corresponding to this, the transporter cleaved by trypsin also retains its transport capacity. These data indicate that cleavage of the type IIa Na/P(i)-cotransporter at ECL-2 is compatible with its cotransport function.

Modulation of renal type IIa Na+/Pi cotransporter kinetics by the arginine modifier phenylglyoxal.

The effects of the arginine-modifying reagent phenylglyoxal on the kinetics of the type IIa Na + /Pi cotransporter expressed in Xenopus, oocytes were studied by means of 32Pi uptake and electrophysiology. Phenylglyoxal incubation induced up to 60% loss of cotransport function but only marginally altered the Na+-leak. Substrate activation and pH dependency remained essentially unaltered, whereas the voltage dependency of Pi-induced change in electrogenic response was significantly reduced. Presteady-state charge movements were suppressed and the equilibrium charge distribution was shifted slightly towards hyperpolarizing potentials. Charge movements in the absence of external Na+ were also suppressed, which indicated that the empty-carrier kinetics were modified. These effects were incorporated into an ordered alternating access model for NaPi-IIa, whereby the arginine modification by phenylglyoxal was modeled as altered apparent electrical distances moved by mobile charges, together with a slower rate of translocation of the electroneutral, fully loaded carrier.

Functional pharmacology of GABA(A) receptors containing the chicken brain gamma 4 subunit.

The functional pharmacology of receptors composed of the chicken brain GABA(A) receptor gamma 4 subunit and the mammalian GABA(A) receptor alpha 3 and beta2 subunits was studied by heterologous expression in Xenopus laevis oocytes using the two electrode voltage-clamp technique. GABA-evoked currents had an EC(50) of 180+/-30 microM. Responses were blocked by the competitive and non-competitive GABA(A) receptor antagonists, bicuculline methochloride and picrotoxin. Sodium pentobarbital reversibly potentiated the current several-fold, and Zn(2+) ions blocked the current with high potency (IC50=20 microM). GABA-evoked currents were potentiated by the benzodiazepine site full agonists flunitrazepam and triazolam and less by the partial agonists abecarnil and bretazenil. The inverse agonists methyl-beta-carboline-3-carboxylate (beta-CCM) and methyl 6,7-dimethoxy-4-ethyl-beta-carboline-3-carboxylate (DMCM) reduced the current. However, the imidazobenzodiazepine Ro 15-4513, which acts as an inverse agonist at mammalian alphaxbetaygamma2 GABA(A) receptors (where x=1, 2, 3 or 5, and y=1, 2 or 3), acted as a positive agonist at the gamma 4 subunit-containing receptors.

Cysteine mutagenesis reveals novel structure-function features within the predicted third extracellular loop of the type IIa Na(+)/P(i) cotransporter.

The transport function of the rat type IIa Na(+)/P(i) cotransporter is inhibited after binding the cysteine modifying reagent 2-aminoethyl methanethiosulfonate hydrobromide (MTSEA) to a cysteine residue substituted for a serine at position 460 (S460C) in the predicted third extracellular loop. This suggests that Ser-460 lies in a functionally important region of the protein. To establish a "structure-function" profile for the regions that flank Ser-460, the substituted cysteine accessibility method was employed. 18 mutants were constructed in which selected amino acids from Arg-437 through Leu-465 were substituted one by one for a cysteine. Mutants were expressed in Xenopus oocytes and transport function (cotransport and slippage) and kinetics were assayed by electrophysiology with or without prior treatment with cysteine modifying (methanethiosulfonate, MTS) reagents. Except for mutant I447C, mutants with cysteines at sites from Arg-437 through Thr-449, as well as Pro-461, were inactive. Cotransport function of mutants with Cys substitutions at sites Arg-462 through Leu-465 showed low sensitivity to MTS reagents. The preceding mutants (Cys substitution at Thr-451 to Ser-460) showed a periodic accessibility pattern that would be expected for an alpha-helix motif. Apart from loss of transport function, exposure of mutants A453C and A455C to MTSEA or 2-(triethylammonium)ethyl MTS bromide (MTSET) increased the uncoupled slippage current, which implicated the mutated sites in the leak pathway. Mutants from Ala-453 through Ala-459 showed less pH dependency, but generally stronger voltage dependency compared with the wild type, whereas those flanking this group were more sensitive to pH and showed weaker voltage dependence of cotransport mode kinetics. Our data indicate that parts of the third extracellular loop are involved in the translocation of the fully loaded carrier and show a membrane-associated alpha-helical structure.

Molecular characteristics of phosphate transporters and their regulation.

A key process in overall P(i)-homeostasis is renal proximal tubular reabsorption of inorganic phosphate (P(i)), which involves secondary active sodium/phosphate (Na(+)/P(i)) cotransport reabsorption at the brush border membrane. Among the two different molecularly identified Na(+)/P(i) cotransporters, the type-IIa Na(+)/P(i) cotransporter (NaPi-IIa) accounts for up to 70% of brush border membrane transport. Regulation of renal P(i) reabsorption centers around brush border membrane insertion and retrieval of transporter protein under the influence of hormonal and nonhormonal factors. Immunohistochemical and fluorescence techniques have provided new insights into the tissue distribution and the regulation processes. The intrinsic electrogenicity of NaPi-IIa, has allowed detailed studies of the transport kinetics of NaPi-IIa and, combined with mutagenesis methods, structure-function information at the protein level is emerging.

Cysteine residues and the structure of the rat renal proximal tubular type II sodium phosphate cotransporter (rat NaPi IIa).

The rat renal Na/P(i) cotransporter type IIa (rat NaP(i) IIa) is a 637 amino acid protein containing 12 cysteine residues. We examined the effect of different cysteine modifying methanethiosulfonate (MTS)-reagents and the disulfide bond reducing agent tris(2-carboxyethyl)phosphine (TCEP) on the transport activity of wild-type and 12 single cysteine substitution mutants of rat NaPi IIa expressed in Xenopus laevis oocytes. The transport activity of the wild-type protein was resistant to three membrane impermeant MTS-reagents (MTSEA, MTSET and MTSES). In contrast, membrane permeant methyl methanethiosulfonate (MMTS) and TCEP inhibited the transport activity of both the wild-type, as well as all the single mutant proteins. This indicated the existence of more than one functionally important cysteine residue, not accessible extracellularly, and at least 2 disulfide bridges. To identify the disulfide bridges, three double mutants lacking 2 of the 3 cysteine residues predicted to be extracellular in different combinations were examined. This led to the identification of one disulfide bridge between C306 and C334; reconsideration of the topological model predictions suggested a second disulfide bridge between C225 and C520. Evaluation of a fourth double mutant indicated that at least one of two disulfide bridges (C306 and C334; C225 and C520) has to be formed to allow the surface expression of a functional cotransporter. A revised secondary structure is proposed which includes two partially repeated motifs that are connected by disulfide bridges formed between cysteine pairs C306-C334 and C225-C520.

Proton-sensitive transitions of renal type II Na(+)-coupled phosphate cotransporter kinetics.

In the kidney proximal tubule, acidification of the glomerular filtrate leads to an inhibition of inorganic phosphate (P(i)) reabsorption by type II Na(+)-coupled cotransporters (NaPi-II). As external pH also alters the divalent/monovalent P(i) ratio, it has been difficult to separate putative proton interactions with the cotransporter from direct titration of divalent P(i), the preferred species transported. To distinguish between these possibilities and identify pH-sensitive transitions in the cotransport cycle, the pH-dependent kinetics of two NaPi-II isoforms, expressed in Xenopus laevis oocytes, were investigated electrophysiologically. At -50 mV, both isoforms showed >70% suppression of electrogenic response for an external pH change from 8.0 to 6.2, not attributable to titration of divalent P(i). This was accompanied by a progressive removal of steady-state voltage dependence. The NaPi-II-related uncoupled slippage current was unaffected by a pH change from 7.4 to 6.2, with no shift in the reversal potential, which suggested that protons do not function as substrate. The voltage-dependence of pre-steady-state relaxations was shifted to depolarizing potentials in 100 mM and 0 mM Na(ext)(+) and two kinetic components were resolved, the slower of which was pH-dependent. The changes in kinetics are predicted by a model in which protons interact with the empty carrier and final Na(+) binding step.

The functional unit of the renal type IIa Na+/Pi cotransporter is a monomer.

The composition of the functional unit of the rat renal type IIa Na(+)/P(i) cotransporter (NaPi-IIa) was investigated by using two approaches based on the differential sensitivities of the wild type (WT) and mutant S460C proteins to 2-aminoethylmethanethiosulfonate hydrobromide (MTSEA), a charged cysteine modifier. Transport activity of S460C is completely blocked after incubation in MTSEA, whereas that of the WT remains unaffected. First, Xenopus laevis oocytes were coinjected with cRNAs coding for the WT and S460C in different proportions, and the transport inhibition after MTSEA incubation was assayed by electrophysiology. The relationship between MTSEA inhibition and proportion of cRNA was consistent with that for a functional monomer. Second, concatameric proteins were constructed that either comprised two WT proteins (WT-WT), two S460C mutants (S460C-S460C), or one of each (WT-S460C). Western blots of oocytes injected with fusion protein cRNA showed bands at approximately 200 kDa, whereas a main band at approximately 90 kDa was obtained for the WT cRNA alone. The kinetic properties of concatamers were the same as for the single proteins. Transport activity of the WT-WT concatamer was unaffected by MTSEA incubation, fully inhibited for S460C-S460C, but 50% inhibited for WT-S460C. This behavior was also consistent with NaPi-IIa being a functional monomer.

Properties of the mutant Ser-460-Cys implicate this site in a functionally important region of the type IIa Na(+)/P(i) cotransporter protein.

The substituted cysteine accessibility approach, combined with chemical modification using membrane-impermeant alkylating reagents, was used to identify functionally important structural elements of the rat type IIa Na(+)/P(i) cotransporter protein. Single point mutants with different amino acids replaced by cysteines were made and the constructs expressed in Xenopus oocytes were tested for function by electrophysiology. Of the 15 mutants with substituted cysteines located at or near predicted membrane-spanning domains and associated linker regions, 6 displayed measurable transport function comparable to wild-type (WT) protein. Transport function of oocytes expressing WT protein was unchanged after exposure to the alkylating reagent 2-aminoethyl methanethiosulfonate hydrobromide (MTSEA, 100 microM), which indicated that native cysteines were inaccessible. However, for one of the mutants (S460C) that showed kinetic properties comparable with the WT, alkylation led to a complete suppression of P(i) transport. Alkylation in 100 mM Na(+) by either cationic ([2-(trimethylammonium)ethyl] methanethiosulfonate bromide (MTSET), MTSEA) or anionic [sodium(2-sulfonatoethyl)methanethiosulfonate (MTSES)] reagents suppressed the P(i) response equally well, whereas exposure to methanethiosulfonate (MTS) reagents in 0 mM Na(+) resulted in protection from the MTS effect at depolarized potentials. This indicated that accessibility to site 460 was dependent on the conformational state of the empty carrier. The slippage current remained after alkylation. Moreover, after alkylation, phosphonoformic acid and saturating P(i) suppressed the slippage current equally, which indicated that P(i) binding could occur without cotransport. Pre-steady state relaxations were partially suppressed and their kinetics were significantly faster after alkylation; nevertheless, the remaining charge movement was Na(+) dependent, consistent with an intact slippage pathway. Based on an alternating access model for type IIa Na(+)/P(i) cotransport, these results suggest that site 460 is located in a region involved in conformational changes of the empty carrier.

Protein kinase C activators induce membrane retrieval of type II Na+-phosphate cotransporters expressed in Xenopus oocytes.

1. The rate of inorganic phosphate (Pi) reabsorption in the mammalian kidney is determined by the amount of type II sodium-coupled inorganic phosphate (Na+-Pi) cotransport protein present in the brush border membrane. Under physiological conditions, parathyroid hormone (PTH) leads to an inhibition of Na+-Pi cotransport activity, most probably mediated by the protein kinase A (PKA) and/or C (PKC) pathways. 2. In this study, PKC-induced inhibition of type II Na+-Pi cotransport activity was characterized in Xenopus laevis oocytes using electrophysiological and immunodetection techniques. Transport function was quantified in terms of Pi-activated current. 3. Oocytes expressing the type IIa rat renal, type IIb flounder renal or type IIb mouse intestinal Na+-Pi cotransporters lost > 50 % of Pi-activated transport function when exposed to the PKC activators DOG (1,2-dioctanoyl-sn-glycerol) or PMA (phorbol 12-myristate 13-acetate). DOG-induced inhibition was partially reduced with the PKC inhibitors staurosporine and bisindolylmaleimide I. Oocytes exposed to the inactive phorbol ester 4alpha-PDD (4alpha-phorbol 12,13-didecanoate) showed no significant loss of cotransporter function. 4. Oocytes expressing the rat renal Na+-SO42- cotransporter alone, or coexpressing this with the type IIa rat renal Na+-Pi cotransporter, showed no downregulation of SO42--activated cotransport activity by DOG. 5. Steady-state and presteady-state voltage-dependent kinetics of type II Na+-Pi cotransporter function were unaffected by DOG. 6. DOG induced a decrease in membrane capacitance which indicated a reduction in membrane area, thereby providing evidence for PKC-mediated endocytosis. 7. Immunocytochemical studies showed a redistribution of type II Na+-Pi cotransporters from the oolemma to the submembrane region after DOG treatment. Surface biotinylation confirmed a DOG-induced internalization of the transport protein. 8. These findings document a specific retrieval of exogenous type II Na+-Pi cotransporters induced by activation of a PKC pathway in the Xenopus oocyte.

Stoichiometry and Na+ binding cooperativity of rat and flounder renal type II Na+-Pi cotransporters.

The stoichiometry of the rat and flounder isoforms of the renal type II sodium-phosphate (Na+-Pi) cotransporter was determined directly by simultaneous measurements of phosphate (Pi)-induced inward current and uptake of radiolabeled Pi and Na+ in Xenopus laevis oocytes expressing the cotransporters. There was a direct correlation between the Pi-induced inward charge and Pi uptake into the oocytes; the slope indicated that one net inward charge was transported per Pi. There was also a direct correlation between the Pi-induced inward charge and Na+ influx; the slope indicated that the influx of three Na+ ions resulted in one net inward charge. This behavior was similar for both isoforms. We conclude that for both Na+-Pi cotransporter isoforms the Na+:Pi stoichiometry is 3:1 and that divalent Pi is the transported substrate. Steady-state activation of the currents showed that the Hill coefficients for Pi were unity for both isoforms, whereas for Na+, they were 1.8 (flounder) and 2.5 (rat). Therefore, despite significant differences in the apparent Na+ binding cooperativity, the estimated Na+:Pi stoichiometry was the same for both isoforms.

Electrophysiological characterization of the flounder type II Na+/Pi cotransporter (NaPi-5) expressed in Xenopus laevis oocytes.

The two electrode voltage clamp technique was used to investigate the steady-state and presteady-state kinetic properties of the type II Na+/Pi cotransporter NaPi-5, cloned from the kidney of winter flounder (Pseudopleuronectes americanus) and expressed in Xenopus laevis oocytes. Steady-state Pi-induced currents had a voltage-independent apparent K(m) for Pi of 0.03 mM and a Hill coefficient of 1.0 at neutral pH, when superfusing with 96 mM Na+. The apparent K(m) for Na+ at 1 mM Pi was strongly voltage dependent (increasing from 32 mM at -70 mV to 77 mM at -30 mV) and the Hill coefficient was between 1 and 2, indicating cooperative binding of more than one Na+ ion. The maximum steady-state current was pH dependent, diminishing by 50% or more for a change from pH 7.8 to pH 6.3. Voltage jumps elicited presteady-state relaxations in the presence of 96 mM Na+ which were suppressed at saturating Pi (1 mM). Relaxations were absent in non-injected oocytes. Charge was balanced for equal positive and negative steps, saturated at extremes of potential and reversed at the holding potential. Fitting the charge transfer to a Boltzmann relationship typically gave a midpoint voltage (V0.5) close to zero and an apparent valency of approximately 0.6. The maximum steady-state transport rate correlated linearly with the maximum Pi-suppressed charge movement, indicating that the relaxations were NaPi-5-specific. The apparent transporter turnover was estimated as 35 sec-1. The voltage dependence of the relaxations was Pi-independent, whereas changes in Na+ shifted V0.5 to -60 mV at 25 mM Na+. Protons suppressed relaxations but contributed to no detectable charge movement in zero external Na+. The voltage dependent presteady-state behavior of NaPi-5 could be described by a 3 state model in which the partial reactions involving reorientation of the unloaded carrier and binding of Na+ contribute to transmembrane charge movement.

Activation, inactivation and recovery in the sodium channels of the squid giant axon dialysed with different solutions.

Comparisons were made between families of ion currents recorded in voltage-clamped squid axons dialysed with 20 mM NaF and 330 mM CsF or TMAF, and bathed in a solution in which four fifths of the Na was replaced by Tris. The permeability coefficient PNa,fast for the fast-inactivating current in the initial open state was calculated as a function of test potential from the size of the initial peak of INa. The permeability coefficient PNa,non for the non-inactivating open state was calculated from the steady-state INa that persisted until the end of the test pulse. Dialysis with TMA had no direct effect on the QV curve for gating charge. The reversal potential for INa,non was always lower than that for INa,fast, the mean difference being about -9 mV when dialysing with Cs, but only about -1 mV with TMA. Except close to threshold, PNa,fast was roughly halved by dialysis with TMA as compared with Cs, but PNa,non was substantially increased. The time constant tau h inactivation of the sodium system was slightly increased during dialysis with TMA in place of Cs, and there were small shifts in the steady-state inactivation curve, but the rate of recovery from inactivation was not measurably altered. The flattening off of the tau h curve at increasingly positive test potentials corresponded to a steady reduction of the apparent inactivation charge until a value of about 0.2e was reached for pulses to 100 mV. The instantaneous I-V relationship in the steady state was also investigated. The results have a useful bearing on the effects of dialysis with TMA, on the differences between the initial and steady open states of the sodium channel, and on the relative voltage-dependences of the transitions in each direction between the resting and inactivated states.

The early phase of sodium channel gating current in the squid giant axon. Characteristics of a fast component of displacement charge movement.

A fast component of displacement current which accompanies the sodium channel gating current has been recorded from the membrane of the giant axon of the squid Loligo forbesii. This component is characterized by relaxation time constants typically shorter than 25 microseconds. The charge displaced accounts for about 10% (or 2 nC/cm2) of the total displacement charge attributed to voltage-dependent sodium channels. Using a low noise, wide-band voltage clamp system and specially designed voltage step protocols we could demonstrate that this component: (i) is not a recording artifact; (ii) is kinetically independent from the sodium channel activation and inactivation processes; (iii) can account for a significant fraction of the initial amplitude of recorded displacement current and (iv) has a steady state charge transfer which saturates for membrane potentials above +20 mV and below -100 mV. This component can be modelled as a single step transition using the Eyring-Boltzmann formalism with a quantal charge of 1 e- and an asymmetrical energy barrier. Furthermore, if it were associated with the squid sodium channel, our data would suggest one fast transition per channel. A possible role as a sodium channel activation trigger, which would still be consistent with kinetic independence, is discussed. Despite uncertainties about its origin, the property of kinetic independence allows subtraction of this component from the total displacement current to reveal a rising phase in the early time course of the remaining current. This will have to be taken into account when modelling the voltage-dependent sodium channel.

The effect of tetrodotoxin on the sodium gating current in the squid giant axon.

The effect of tetrodotoxin (TTX) on the sodium gating current in the squid giant axon was examined by recording the current that flowed at the pulse potential at which the ionic current fell to zero, first in the absence and then in the presence of TTX. The addition of 1 microM TTX to the bathing solution had no consistent effect on the size of the initial peak of the gating current, but resulted in small changes in the timecourse of its subsequent relaxation which were mainly caused by a reduction of about one quarter in the component that has a delayed onset and may possibly arise from changes in the state of ionization of groups in the channel wall when the lumen fills with water. Our findings suggest that the binding of TTX at the outer face of the sodium channel does not interfere with the mechanisms of activation and inactivation by the voltage sensors, but has an allosteric effect on the access of internal cations to the inside of the channel.

The quantal gating charge of sodium channel inactivation.

Using a very low noise voltage clamp technique it has been possible to record from the squid giant axon a slow component of gating current (Ig) during the inactivation phase of the macroscopic sodium current (INa) which was hitherto buried in the baseline noise. In order to examine whether this slow Ig contains gating charge that originates from transitions between the open (O) and the inactivated (I) states, which would indicate a true voltage dependence of inactivation, or whether other transitions contribute charge to slow Ig, a new model independent analysis termed isochronic plot analysis has been developed. From a direct correlation of Ig and the time derivative of the sodium conductance dgNa/dt the condition when only O-I transitions occur is detected. Then the ratio of the two signals is constant and a straight line appears in an isochronic plot of Ig vs. dgNa/dt. Its slope does not depend on voltage or time and corresponds to the quantal gating charge of the O-I transition (qh) divided by the single channel ionic conductance (gamma). This condition was found at voltages above -10 mV up to +40 mV and a figure of 1.21 e- was obtained for qh at temperatures of 5 and 15 degrees C. At lower voltages additional charge from other transitions, e.g. closed to open, is displaced during macroscopic inactivation. This means that conventional Eyring rate analysis of the inactivation time constant tau h is only valid above -10 mV and here the figure for qh was confirmed also from this analysis. It is further shown that most of the present controversies surrounding the voltage dependence of inactivation can be clarified. The validity of the isochronic plot analysis has been confirmed using simulated gating and ionic currents.