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.

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.

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.

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.

High resolution recording of asymmetry currents from the squid giant axon: technical aspects of voltage clamp design.

The design, realisation and performance of a voltage clamp system dedicated to recording asymmetry currents from the squid giant axon is presented. The design has been optimised with respect to dynamic response, signal-to-noise ratio and linearity. Analytical expressions are given for both the dynamic performance and noise characteristics which simplify the design and setting up of the clamp and provide excellent agreement between design theory and practice. A 0.5 cm2 area of membrane can be voltage clamped in response to a command input voltage step within 10 microseconds with smooth settling and up to 100% of the effective series resistance being compensated. The noise contributions of the recording chamber, voltage sensing electrodes and clamp electronics have been reduced such that recording of gating currents with a more than 10-fold reduction in the number of averages required compared with previous clamp designs is possible. The overall system nonlinearity results in typically less than 1% contribution to the measured asymmetry charge.

Technical aspects of voltage-clamping the cut-open squid giant axon.

The design of a voltage-clamp system dedicated to recording the fluctuation of sodium currents under non-stationary conditions from a leaflet of cut-open squid axon is presented. The membrane leaflet is mechanically sandwiched between the apices of two finely machined plexiglass cones which enable fluid access to each side of the membrane and a known area of membrane to be voltage-clamped. The design requirements necessary to achieve satisfactory signal resolution have been assessed in terms of the overall digitising resolution of the ADC hardware and the intrinsic and extrinsic components of the clamp-system noise. Good agreement between the predicted and measured noise performance was found. The clamp system has enabled simultaneous estimates of the single-channel conductance and channel density to be made over a much wider range of experimental conditions than previously possible.

Single-channel current simulation and recording using a photodiode as current generator.

A device which can generate rectangular currents in the picoampere range is described. The current generator is a photodiode connected to the head stage of a single-channel recording amplifier. The photodiode is activated by a light-emitting diode controlled by a computer or any other current source. The device can transmit signals corresponding to simulated single-channel behaviour. Since the kinetic parameters of the simulation are known, the user can test the data acquisition and analysis system under conditions similar to those prevailing during recording from a biological membrane. This current generator can also be used for the tuning of patch-clamp amplifiers; rectangular currents generated by the photodiode allow the frequency response of the amplifier to be properly adjusted.

Data recording and playback on video tape--a multi-channel analog interface for a digital audio processor system.

The design of an analog interface to a digital audio signal processor (DASP)-video cassette recorder (VCR) system is described. The complete system represents a low-cost alternative to both FM instrumentation tape recorders and multi-channel chart recorders. The interface or DASP input-output unit described in this paper enables the recording and playback of up to 12 analog channels with a maximum of 12 bit resolution and a bandwidth of 2 kHz per channel. Internal control and timing in the recording component of the interface is performed using ROMs which can be reprogrammed to suit different analog-to-digital converter hardware. Improvement in the bandwidth specifications is possible by connecting channels in parallel. A parallel 16 bit data output port is provided for direct transfer of the digitized data to a computer.

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.

A multiple electrode cochlear implant.

The University of Melbourne Departments of Otolaryngology and Electrical Engineering (UMDOLEE) receiving and stimulating component of a multiple-electrode cochlear implant hearing prosthesis produces constant stimulation. It has a stimulating pulse shape that minimizes the production of toxic substances and loss of metal from the electrodes, and this is achieved with a biphasic rectangular waveform where the first phase is negative with respect to ground. The duration of each stimulus phase in 180 msec, which is long enough to allow low levels of current stimulation, and short enough to permit rates of 1000 pulses/second to be achieved. In order to be consistent with our present understanding of the perception of pitch, the device permits the independent stimulation of a number of electrodes. Furthermore, to electrically isolate the stimulus to small areas, there is the capacity to vary the current and set the threshold independently at individual electrodes. The phase and amplitude of the pulses to neighbouring electrodes with also be varied to assist in localizing the current flow. The pattern to stimulation to individual or groups of electrodes can also be altered to enable studies to be carried out to determine ways of conveying frequency and intensity information over a more normal dynamic range.

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.

Theoretical design and implementation of a transcutaneous, multichannel stimulator for neural prosthesis applications.

The development of a transcutaneous, implantable, multichannel neural stimulator is described. This was originally dedicated to the stimulation of the auditory nerve in profoundly deaf persons, but is sufficiently flexible in design and operation to be applicable to other areas of neural prosthetics. Control of both the amplitude and time of stimulation for up to fifteen independent channels is possible with a maximum stimulation rate of 1 kHz. Particular attention is given to the design of the transcutaneous link stage which allows both power and data to be transferred to the implanted device using a compact coupling inductor configuration. All circuit timing is derived from a single clock in the external transmitter unit, resulting in stable operation with predictable stimulus output characteristics. The implantable device, realised using thick film hybrid techniques, employs CMOS logic extensively to reduce power consumption. One such device has been implanted in a profoundly deaf volunteer for a period exceeding two years and has continued to operate reliably in conjunction with the complete prosthesis system.

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.

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.

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.

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.

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.