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The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (gNaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear + quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances.

Nonlinear biophysical properties of individual neurons are known to play a major role in the nervous system, especially those active at subthreshold membrane potentials that integrate synaptic inputs during action potential initiation. Previous electrophysiological studies have made use of a piecewise linear characterization of voltage clamped neurons, which consists of a sequence of linear admittances computed at different voltage levels. In this paper, a fundamentally new theory is developed in two stages. First, analytical equations are derived for a multi-sinusoidal voltage clamp of a Hodgkin-Huxley type model to reveal the quadratic response at the ionic channel level. Second, the resulting behavior is generalized to a novel Hermitian neural operator, which uses an algebraic formulation capturing the entire quadratic behavior of a voltage clamped neuron. In addition, this operator can also be used for a nonlinear identification analysis directly applicable to experimental measurements. In this case, a Hermitian matrix of interactions is built with paired frequency probing measurements performed at specific harmonic and interactive output frequencies. More importantly, eigenanalysis of the neural operator provides a concise signature of the voltage dependent conductances determined by their particular distribution on the dendritic and somatic membrane regions of neurons. Finally, the theory is concretely illustrated by an analysis of an experimentally measured vestibular neuron, providing a remarkably compact description of the quadratic responses involved in the nonlinear processing underlying the control of eye position during head rotation, namely the neural integrator.

Head motion-related sensory signals are transformed by second-order vestibular neurons (2°VNs) into appropriate commands for retinal image stabilization during body motion. In frogs, these 2°VNs form two distinct subpopulations that have either tonic or highly phasic intrinsic properties, essentially compatible with low-pass and bandpass filter characteristics, respectively. In the present study, physiological data on cellular properties of 2°VNs of the grass frog (Rana temporaria) have been used to construct conductance-based spiking cellular models that were fine-tuned by fitting to recorded spike-frequency data. The results of this approach suggest that low-threshold, voltage-dependent potassium channels in phasic and spike-dependent potassium channels in tonic 2°VNs are important contributors to the differential, yet complementary response characteristics of the two vestibular subtypes. Extension of the cellular model with conductance-based synapses allowed simulation of afferent excitation and evaluation of the emerging properties of local feedforward inhibitory circuits. This approach revealed the relative contributions of intrinsic and synaptic factors on afferent signal processing in phasic 2°VNs. Additional extension of the single-cell model to a population model allowed testing under more natural conditions including asynchronous afferent labyrinthine input and synaptic noise. This latter approach indicated that the feedforward inhibition from the local inhibitory network acts as a high-pass filter, which reinforces the impact of the intrinsic membrane properties of phasic 2°VNs on peak response amplitude and timing. Thus, the combination of cellular and network properties enables phasic 2°VNs to work as a noise-resistant detector, suitable for central processing of short-duration vestibular signals.

Neural integrators and working memory rely on persistent activity, a widespread neural phenomenon potentially involving persistent sodium conductances. Using a unique combination of voltage-clamp, dynamic-clamp, and frequency-domain techniques, we have investigated the role of voltage-dependent conductances on the dendritic electrotonic structure of neurons of the prepositus hypoglossi nucleus (PHN), which is known to be involved in oculomotor integration. The PHN contains two main neuronal populations: type B neurons with a double afterhyperpolarization and type D neurons, which not only are oscillatory but also have a greater electrotonic length than that of type B neurons. The persistent sodium conductance is present in all PHN neurons, although its effect on the dynamic electrotonic structure is shown to significantly differ in the two major cell types present in the nucleus. The electrotonic differences are such that the persistent sodium conductance can be almost perfectly manipulated in a type B neuron using an on-line dynamic clamp to add or subtract virtual sodium ion channels. The dynamic-clamp results are confirmed by data-fitted models, which suggest that the persistent sodium conductance has two different roles depending on its somatic versus dendritic location: perisomatic conductances could play a major role in maintaining action potential discharge and dendritic conductances would be more involved in other computational properties, such as those involving remote synaptic processing or bistable events.

Central vestibular neurons play an important role in the processing of body motion-related multisensory signals and their transformation into motor commands for gaze and posture control. Over recent years, medial vestibular nucleus (MVN) neurons and to a lesser extent other vestibular neurons have been extensively studied in vivo and in vitro, in a range of species. These studies have begun to reveal how their intrinsic electrophysiological properties may relate to their response patterns, discharge dynamics and computational capabilities. In vitro studies indicate that MVN neurons are of two major subtypes (A and B), which differ in their spike shape and after-hyperpolarizations. This reflects differences in particular K(+) conductances present in the two subtypes, which also affect their response dynamics with type A cells having relatively low-frequency dynamics (resembling "tonic" MVN cells in vivo) and type B cells having relatively high-frequency dynamics (resembling "kinetic" cells in vivo). The presence of more than one functional subtype of vestibular neuron seems to be a ubiquitous feature since vestibular neurons in the chick and frog also subdivide into populations with different, analogous electrophysiological properties. The ratio of type A to type B neurons appears to be plastic, and may be determined by the signal processing requirements of the vestibular system, which are species-variant. The membrane properties and discharge pattern of type A and type B MVN neurons develop largely post-natally, through the expression of the underlying ion channel conductances. The membrane properties of MVN neurons show rapid and long-lasting plastic changes after deafferentation (unilateral labyrinthectomy), which may serve to maintain their level of activity and excitability after the loss of afferent inputs.

Membrane and discharge properties were determined in second-order vestibular neurons (2 degrees VN) in the isolated brain of grass frogs. 2 degrees VN were identified by monosynaptic excitatory postsynaptic potentials after separate electrical stimulation of the utricular nerve, the lagenar nerve, or individual semicircular canal nerves. 2 degrees VN were classified as vestibulo-ocular or -spinal neurons by the presence of antidromic spikes evoked by electrical stimulation of the spinal cord or the oculomotor nuclei. Differences in passive membrane properties, spike shape, and discharge pattern in response to current steps and ramp-like currents allowed a differentiation of frog 2 degrees VN into two separate, nonoverlapping types of vestibular neurons. A larger subgroup of 2 degrees VN (78%) was characterized by brief, high-frequency bursts of up to five spikes and the absence of a subsequent continuous discharge in response to positive current steps. In contrast, the smaller subgroup of 2 degrees VN (22%) exhibited a continuous discharge with moderate adaptation in response to positive current steps. The differences in the evoked spike discharge pattern were paralleled by differences in passive membrane properties and spike shapes. Despite these differences in membrane properties, both types, i.e., phasic and tonic 2 degrees VN, occupied similar anatomical locations and displayed similar afferent and efferent connectivities. Differences in response dynamics of the two types of 2 degrees VN match those of their pre- and postsynaptic neurons. The existence of distinct populations of 2 degrees VN that differ in response dynamics but not in the spatial organization of their afferent inputs and efferent connectivity to motor targets suggests that frog 2 degrees VN form one part of parallel vestibulomotor pathways.

In vitro intracellular recordings of central vestibular neurons have been restricted so far to the medial vestibular nucleus (MVN). We performed intracellular recordings of large Deiters' neurons in the lateral vestibular nucleus (LVN) to determine their static and dynamic membrane properties, and compare them with those of type A and type B neurons identified in the MVN. Unlike MVN neurons (MVNn), the giant-size LVN neurons (LVNn) form a homogeneous population of cells characterized by sharp spikes, a low-amplitude, biphasic after-hyperpolarization like type B MVNn, but also an A-like rectification like type A MVNn. In accordance with their lower membrane resistance, the sensitivity of LVNn to current injection was lower than that of MVNn over a large range of frequencies. The main difference between LVNn and MVNn was that the Bode plots showing the sensitivity of LVNn as a function of stimulation frequency were flatter than those of MVNn, and displayed a weaker resonance. Furthermore, most LVNn did not show a gradual decrease of their firing rate modulation in the frequency range where it was observed in MVNn. LVNn synchronized their firing with the depolarizing phase of high-frequency sinusoidal current injections. In vivo studies have shown that the MVN would be mainly involved in gaze control, whereas the giant LVNn that project to the spinal cord are involved in the control of posture. We suggest that the difference in the membrane properties of LVNn and MVNn may reflect their specific physiological roles.

Unilateral labyrinthectomy results in oculomotor and postural disturbances that regress in a few days during vestibular compensation. The long-term (after 1 mo) consequences of unilateral labyrinthectomy were investigated by characterizing the static and dynamic membrane properties of the ipsilesional vestibular neurons recorded intracellularly in guinea pig brain stem slices. We compared the responses of type A and type B medial vestibular nucleus neurons identified in vitro to current steps and ramps and to sinusoidal currents of various frequencies. All ipsilesional vestibular neurons were depolarized by 6-10 mV at rest compared with the cells recorded from control slices. Both their average membrane potential and firing threshold were more depolarized, which suggests that changes in active conductances compensated for the loss of excitatory afferents. The afterhyperpolarization and discharge regularity of type B but not type A neurons were increased. All ipsilesional vestibular cells became more sensitive to current injections over a large range of frequencies (0.2-30 Hz), but this increase in sensitivity was greater for type B than for type A neurons. This was associated with an increase of the peak frequency of linear response restricted to type B neurons, from 4-6 to 12-14 Hz. Altogether, we show that long-term vestibular compensation involves major changes in the membrane properties of vestibular neurons on the deafferented side. Many of the static and dynamic membrane properties of type B neurons became more similar to those of type A neurons than in control slices, leading to an increase in the overall homogeneity of medial vestibular nucleus neurons.

The modulation of action potential discharge rates is an important aspect of neuronal information processing. In these experiments, we have attempted to determine how effectively spike discharge modulation reflects changes in the membrane potential in central vestibular neurons. We have measured how their spike discharge rate was modulated by various current inputs to obtain neuronal transfer functions. Differences in the modulation of spiking rates were observed between neurons with a single, prominent after hyperpolarization (AHP, type A neurons) and cells with more complex AHPs (type B neurons). The spike discharge modulation amplitudes increased with the frequency of the current stimulus, which was quantitatively described by a neuronal model that showed a resonance peak >10 Hz. Modeling of the resonance peak required two putative potassium conductances whose properties had to be markedly dependent on the level of the membrane potential. At low frequencies (< or =0.4 Hz), the gain or magnitude functions of type A and B discharge rates were similar relative to the current input. However, resting input resistances obtained from the ratio of the membrane potential and current were lower in type B compared with type A cells, presumably due to a higher level of active potassium conductances at rest. The lower input resistance of type B neurons was compensated by a twofold greater sensitivity of their firing rate to changes in membrane potential, which suggests that synaptic inputs on their dendritic processes would be more efficacious. This increased sensitivity is also reflected in a greater ability of type B neurons to synchronize with low-amplitude sinusoidal current inputs, and in addition, their responses to steep slope ramp stimulation are enhanced over the more linear behavior of type A neurons. This behavior suggests that the type B MVNn are moderately tuned active filters that promote high-frequency responses and that type A neurons are like low-pass filters that are well suited for the resting tonic activity of the vestibular system. However, the more sensitive and phasic type B neurons contribute to both low- and high-frequency control as well as signal detection and would amplify the contribution of both irregular and regular primary afferents at high frequencies.

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.

Whole cell voltage- and current-clamp measurements were done on intact Xenopus laevis larval spinal neurons at developmental stages 42-47. Firing patterns and electrotonic properties of putative interneurons from the dorsal and ventral medial regions of the spinal cord at myotome levels 4-6 were measured in isolated spinal cord preparations. Passive electrotonic parameters were determined with internal cesium sulfate solutions as well as in the presence of active potassium conductances. Step-clamp stimuli were combined with white-noise frequency domain measurements to determine both linear and nonlinear responses at different membrane potential levels. Comparison of analytic and compartmental dendritic models provided a way to determine the number of compartments needed to describe the dendritic structure. The electrotonic structure of putative interneurons was correlated with their firing behavior such that highly accommodating neurons (Type B) had relatively larger dendritic areas and lower electrotonic lengths compared with neurons that showed sustained action potential firing in response to a constant current (Type A). Type A neurons had a wide range of dendritic areas and potassium conductances that were activated at membrane potentials more negative than observed in Type B neurons. The differences in the potassium conductances were in part responsible for a much greater rectification in the steady-state current voltage (I-V curve) of the strongly accommodating neurons compared with repetitively firing cells. The average values of the passive electrotonic parameters found for Rall Type A and B neurons were c(soma) = 3.3 and 2.6 pF, g(soma) = 187 and 38 pS, L = 0.36 and 0.21, and A = 3.3 and 6.5 for soma capacitance, soma conductance, electrotonic length, and the ratio of the dendritic to somatic areas, respectively. Thus these experiments suggest that there is a correlation between the electrotonic structure and the excitability properties elicited from the somatic region.

Voltage- and current-clamp measurements of inwardly directed currents were made from the somatic regions of Xenopus laevis spinal neurons. Current-voltage (I-V) curves determined under voltage clamp, but not current clamp, were able to indicate a negative slope conductance in neurons that showed strong accommodating action potential responses to a constant current stimulation. Voltage-clamp I-V curves from repetitive firing neurons did not have a net negative slope conductance and had identical I-V plots under current clamp. Frequency domain responses indicate negative slope conductances with different properties with or without tetrodotoxin, suggesting that both sodium and calcium currents are present in these spinal neurons. The currents obtained from a voltage clamp of the somatic region were analyzed in terms of spatially controlled soma membrane currents and additional currents from dendritic potential responses. Linearized frequency domain analysis in combination with both voltage- and current-clamp responses over a range of membrane potentials was essential for an accurate determination of consistent neuronal model behavior. In essence, the data obtained at resting or hyperpolarized membrane potentials in the frequency domain were used to determine the electrotonic structure, while both the frequency and time domain data at depolarized potentials were required to characterize the voltage-dependent channels. Finally, the dendritic and somatic membrane properties were used to reconstruct the action potential behavior and quantitatively predict the dependence of neuronal firing properties on electrotonic structure. The reconstructed action potentials reproduced the behavior of two broad distributions of interneurons characterized by their degree of accommodation. These studies suggest that in addition to the ionic conductances, electrotonic structure is correlated with the action potential behavior of larval neurons.

An investigation of dendritic membrane properties was performed by whole-cell patch measurements of the biophysical properties of intact chick spinal neurons that are involved in rhythmogenesis. A whole-cell voltage clamp of the somatic membrane was used to block NMDA-induced voltage oscillations from the cell body, thus partially isolating the intrinsic oscillatory properties of dendritic membranes from those of the soma. An experimental approach was developed that takes into account the complexity of the dendritic tree in an environment as normal as possible, without the need for cell isolation or slice preparations. A computational study of the experimentally determined model showed that excitatory amino acid receptors on dendrites can dynamically control the electrotonic length of the dendrites through the activation of negative slope conductances. These experiments demonstrate the presence of NMDA receptors on the dendrites and that they induce intrinsic oscillations when the synaptic input from other cells is significantly reduced.

The patch-clamp technique was used to measure the effect of N-methyl-D-aspartate (NMDA) on Xenopus embryonic neurons in an isolated, but intact spinal cord. Whole cell recordings were done at external calcium concentrations of 1 mM. NMDA alone (50-200 microM) or in association with 10 microM serotonin or glycine induced oscillatory activity in most presumed motoneurons, which were therefore considered part of rhythm generating networks. In the presence of TTX, one-half of these neurons maintained this activity. The oscillations fell into two main categories: voltage-dependent, low-frequency (0.3-0.5 Hz) and voltage-independent, high-frequency (3-8 Hz) oscillations. NMDA alone induced TTX-insensitive oscillations in one-third of the neurons; however, the percentage of neurons showing oscillations was greater in the presence of exogenous 5-hydroxytryptamine (5-HT) or glycine. Because these observations were made at embryonic stages where little or no serotonergic innervation exists, it is likely that NMDA-induced intrinsic oscillatory activity in Xenopus embryonic neurons does not require 5-HT.

Simple neural network models of the Xenopus embryo swimming CPG, based on the one originally developed by Roberts and Tunstall (1990), were used to investigate the role of the voltage-dependent N-methyl-D-aspartate (NMDA) receptor channels, in conjunction with faster non-NMDA components of synaptic excitation, in rhythm generation. The voltage-dependent NMDA current "follows" the membrane potential, leading to a postinhibitory rebound that is more efficient than one without voltage dependency and allows neurons to fire more than one action potential per cycle. Furthermore, the model demonstrated limited rhythmic activity in the absence of synaptic inhibition, supporting the hypothesis that the NMDA channels provide a basic mechanism for rhythmicity. However, the rhythmic properties induced by the NMDA current were observed only when there was moderate activation of the non-NMDA synaptic channels, suggesting a modulatory role for this component. The simulations also show that the voltage dependency of the NMDA conductance, as well as the fast non-NMDA current, stabilizes the alternation pattern versus synchrony. To verify that these effects and their implications on the mechanism of swimming and transition to other types of activity take place in the real preparation, constraints on parameter values have to be specified. A method to estimate synaptic parameters was tested with generated data. It is shown that a global analysis, based on multiple iterations of the optimization process (Foster et al., 1993), gives a better understanding of the parameter subspace describing network activity than a standard fit with a sensitivity analysis for an individual solution.

Parameter optimization methods were used to quantitatively analyze frequency-domain-voltage-clamp data of NMDA-activated lamprey spinal neurons simultaneously over a wide range of membrane potentials. A neuronal cable model was used to explicitly take into account receptors located on the dendritic trees. The driving point membrane admittance was measured from the cell soma in response to a Fourier synthesized point voltage clamp stimulus. The data were fitted to an equivalent cable model consisting of a single lumped soma compartment coupled resistively to a series of equal dendritic compartments. The model contains voltage-dependent NMDA sensitive (INMDA), slow potassium (IK), and leakage (IL) currents. Both the passive cable properties and the voltage dependence of ion channel kinetics were estimated, including the electronic structure of the cell, the steady-state gating characteristics, and the time constants for particular voltage- and time-dependent ionic conductances. An alternate kinetic formulation was developed that consisted of steady-state values for the gating parameters and their time constants at half-activation values as well as slopes of these parameters at half-activation. This procedure allowed independent restrictions on the magnitude and slope of both the steady-state gating variable and its associated time constant. Quantitative estimates of the voltage-dependent membrane ion conductances and their kinetic parameters were used to solve the nonlinear equations describing dynamic responses. The model accurately predicts current clamp responses and is consistent with experimentally measured TTX-resistant NMDA-induced patterned activity. In summary, an analysis method is developed that provides a pragmatic approach to quantitatively describe a nonlinear neuronal system.

Small volumes of N-Methyl-D-Aspartate (NMDA) and non-NMDA excitatory amino acid receptor agonists were applied to localized regions of the dendritic trees of lamprey spinal neurons along their medial-lateral axis to obtain a spatial map of glutamate receptor distribution. Voltage clamp and frequency domain methods were used to obtain quantitative kinetic data of the voltage dependent ionic channels located both on the soma and on highly branched dendritic membranes. Pressure pulses of NMDA applied to the most peripheral regions of the dendritic tree elicited large somatic impedance increases, indicating that the most peripheral dendrites are well supplied with NMDA receptors. Experiments done with kainate did not elicit somatic responses to agonist applications on peripheral dendrites. The data obtained are consistent with the hypothesis that the activation of NMDA receptors by exogenous glutamate is significantly modified by the simultaneous activation of non-NMDA receptors, which shunts the NMDA response. The non-NMDA shunting hypothesis was tested by a combined application of kainate and NMDA to mimic the action of glutamate showing that the shunting effect of non-NMDA receptor activation virtually abolished the marked voltage dependency typical of NMDA receptor activation. These data were interpreted with a compartmental neuronal model having both NMDA and non-NMDA receptors.

1. The integrative behavior of lamprey central neurons was analyzed by white noise frequency domain methods and simulated with a minimal, non-linear neuronal model consisting of two voltage-dependent processes: (i) a depolarizing inwardly directed conductance carrying calcium and monovalent ions and (ii) a repolarizing outwardly directly conductance representing a generalized potassium conductance. In addition to normal properties, the effects of neurotransmitters were interpreted with the model. Specifically, N-methyl-D-aspartate (NMDA)-induced properties were simulated under conditions where the intrinsic voltage dependence of the potassium channels was constrained by properties of lamprey neurons. However, the NMDA channel kinetics were fixed by the single-channel properties of other neurons. The effects of focally applied neurotransmitters on the membrane properties of intact spinal cord neurons were quantitatively described with a reduced neuronal model that was also used to simulate transmitter-induced responses. In addition, transmitters were also released synaptically by KCl depolarization of projecting neurons. 2. Both synaptically released transmitters and focally applied putative excitatory or inhibitory transmitters directly applied to the spinal cord generally resulted in a decrease in the magnitude of the impedance function that was modeled by a decrease in membrane resistance (shunting effect). 3. Local application of the inhibitory neurotransmitters glycine or gamma-aminobutyric acid (GABA) led to small voltage responses when recorded near the resting potential. However, large decreases in the magnitude of the impedance function were observed in both current-clamp or voltage-clamp recording modes. 4. The excitatory amino acids quisqualate, kainate and glutamate evoked depolarizations in current clamp that activated intrinsic voltage-dependent conductances and obscured the direct effects of the transmitters. Under voltage-clamp conditions these transmitters caused a small decrease in the impedance magnitude that could be modeled by a shunt. 5. In contrast to the other excitatory amino acids, NMDA elicited large increases, rather than decreases, in both the magnitude and the phase lag of the impedance function. These changes were modeled by a negative conductance (a voltage-dependent conductance that produces an inward current). 6. The reduced neuron model provides an experimentally based description of the highly oscillatory and non-linear responses observed during NMDA activation of the spinal neurons involved in the pattern generation of locomotion. Simulations of sustained oscillatory behaviors consistent with experimental observations were carried out to illustrate the NMDA-induced integrative properties of central neurons.(ABSTRACT TRUNCATED AT 400 WORDS)

1. Voltage and current-clamp steps were added to a sum of sine waves to measure the tetrodotoxin-insensitive membrane properties of neurons in the intact lamprey spinal cord. A systems analysis in the frequency domain was carried out on two types of cells that have very different morphologies in order to investigate the structural dependence of their electrophysiological properties. The method explicitly takes into account the geometrical shapes of (i) nearly spherical dorsal cells with one or two processes and (ii) motoneurons and interneurons that have branched dendritic structures. Impedance functions were analysed to obtain the cable properties of these in situ neurons. These measurements show that branched neurons are not isopotential and, therefore, a conventional voltage-clamp analysis is not valid. 2. The electrophysiological data from branched neurons were curve-fitted with a lumped soma-equivalent cylinder model consisting of eight equal compartments coupled to an isopotential cell body to obtain membrane parameters for both passive and active properties. The analysis provides a quantitative description of both the passive electrical properties imposed by the geometrical structure of neurons and the voltage-dependent ionic conductances determined by ion channel kinetics. The model fitting of dorsal cells was dominated by a one-compartment resistance and capacitance in parallel (RC) corresponding to the spherical, non-branched shape of these cells. Branched neurons required a model that contained both an RC compartment and a cable that reflected the structure of the cells. At rest, the electrotonic length of the cable was about two. Uniformly distributed voltage-dependent ionic conductance sites were adequate to describe the data at different membrane potentials. 3. The frequency domain admittance method in conjunction with a step voltage clamp was used to control and measure the oscillatory behavior induced by N-methyl-D-aspartate (NMDA) on lamprey spinal cord neurons. Voltage-clamp currents and impedance functions were measured at different membrane potentials. The impedance functions had a voltage-dependent resonance and phase shift characteristic of a negative conductance. These measurements provide a quantitative analysis of the conductances induced by NMDA in central neurons of the lamprey spinal cord and directly establish the basis of the non-linear oscillatory behavior previously observed in the presence of NMDA. NMDA was shown specifically to activate a negative and a positive conductance, both of which were markedly affected by the membrane potential. It is shown that the net current in the presence of NMDA must be considered as the algebraic sum of currents in opposite directions.(ABSTRACT TRUNCATED AT 400 WORDS)

The integrative properties of two kinds of excitable cells, a cultured neuroblastoma cell and the lamprey giant interneuron, are described using a white-noise impedance method. The impedance functions were fitted with a neuron model consisting of an isopotential soma plus a single equivalent dendritic process, which contained up to 16 equal elements. The frequency-domain characteristics of both the passive and active conductances were used to estimate the dendritic-to-soma areas, the electrotonic length of an equivalent dendrite, the membrane time constant, and the relaxation time constants associated with the voltage-dependent conductances. The effect of differing degrees of synaptic input was simulated by localizing the synaptically activated conductances to the soma, a point at the end of the dendrite, or the entire dendritic membrane.

1. Impulse response functions were determined from complex point impedance and transfer functions from cultured NG-108 cells to simulate the propagation of a synaptic potential in response to the release of transmitter. In general, the flow of synaptic current has a much shorter duration than the normal membrane time constant, thereby making the use of impulse response functions useful approximations to synaptic events. 2. The resonance observed during the activation of the potassium conductance was reflected in the impulse response function as a pronounced damped oscillation. A comparison of the impulse response functions calculated from point impedance and transfer functions showed similar results for current injections in the growth cone. 3. In addition to the resonance effects of the voltage-dependent conductances on transfer and impulse response functions due principally to the activation of conductances for outward currents, transfer functions were measured during the activation of a steady-state negative conductance. Under these conditions the phase function approaches 180 degrees, indicating that the voltage response is out of phase with the current. 4. In the steady state, the effect of a negative conductance is to algebraically add to the positive conductances and generally decrease the absolute conductance unless there is a net negative current. The decreased conductance enhances the impulse response and the DC space constant, thus leading to a better propagation of slow potentials. This effect can be seen as a decrease in the electrotonic length, L, with intermediate depolarizations. At large depolarizations the steady-state activation of the K conductance generally dominates and leads to a greatly increased electrotonic length. 5. Both the net conductances and the associated kinetics play a role in shaping the potential changes during a synaptic current. This is especially critical if there is a net negative steady-state conductance. Under these conditions there is a surprising reduction in the impulse response function. 6. Thus, during a subthreshold activation of the voltage-dependent negative conductances, the observable synaptic potentials would be either large potential responses due to an apparent increase in the impedance (algebraic summation of positive and negative conductances with a net positive conductance) or a minimal response because of the phasic cancellation due to a net negative conductance. The latter condition could exist near the synaptic reversal potential due to a large synaptic drive and would appear experimentally as a form of inhibition.(ABSTRACT TRUNCATED AT 400 WORDS)

1. The excitable properties of branched cells were measured using a combination of voltage-clamp and frequency-domain techniques. Point impedance functions from either the soma or growth cone of NG-108 cells were curve fitted with a reduced cable model at different membrane potentials to establish kinetic parameters. 2. Transfer impedance functions between the soma and growth cone were measured and simulated with a morphologically determined model. In these experiments the membrane potential was controlled by a single-electrode voltage clamp thus allowing an estimate of transfer functions for any arbitrary input, such as a single synaptic current for differing degrees of tonic synaptic drive. Furthermore, the integration of different regional inputs was evaluated based on the transfer functions between different locations on an individual cell. 3. The activation of an outward steady-state current leads to resonating impedance functions that were used to evaluate the kinetic properties of ionic channels in different regions of branched excitable cells. For simple branching patterns the point and transfer impedances show lower resonant frequencies for active growth cones compared with active somas. 4. More complex branching patterns showed the unexpected result that the voltage-dependent resonant frequency was higher for the growth cone recording than the soma. The presence of a higher resonant frequency when the growth cone is activated does not require more rapid kinetics of the active potassium conductance, since the time constant of the active conductance can be the same in the growth cone and the soma membrane. 5. In conclusion, the resonant frequencies, as well as all other aspects of the impedance functions, are complicated interactions of the detailed branching patterns and active conductances. In general, these interactions are not predictable from a passive electrotonic analysis, especially when the voltage-dependent conductances are distributed throughout the dendritic tree.

1. A voltage clamp for single myelinated nerve fibres was developed from commercially available operational amplifiers.2. Under voltage clamp conditions steady-state currents were measured. The currents reached a maximum value at about E = + 100 mV. Currents for greater potentials decreased.3. The preceding polarization markedly affected the magnitude of the delayed current at high cathodal potentials; however, the currents continued to reach maximum values.4. As predicted by the constant field theory, currents at high cathodal polarizations were essentially independent of the external potassium concentration. Also, these currents were independent of the external calcium concentration.5. Two pulse voltage clamp experiments showed that instantaneous outward currents did not reach a limiting value. The limiting steady-state current was reached with an exponential time constant of about 1 msec.

A temperature-jump technique for single nodes of Ranvier has been developed using a pulsed laser system. The temperature perturbation was accomplished by firing the laser beam obtained from a neodymium rod through the solution surrounding a single node. The temperature step was achieved within 1 msec using the laser in the normal mode of operation. During the voltage-clamped steady-state current a temperature jump from 4 degrees C increased the current to a new steady-state value within the time course of the T-jump. This finding suggests that the maximum potassium permeability P(K) has a rapid relaxation time and that the steady-state value of n (the value of potassium permeability divided by its maximum value) is relatively independent of temperature. T-jumps applied during the voltage-clamped sodium currents showed that the sodium permeability changed with a relaxation time that was also shorter than the duration of the normal mode laser output. T-jumps observed during a hyperpolarization or at the resting potential showed no detectable conductance change. When a T-jump immediately preceded a voltage clamp pulse the technique was then used to investigate the effect of changes in the steady-state temperature on the ionic conductances. It was found that the magnitude of the change in membrane current due to a T-clamp was directly related to the level of cathodal polarization.