Quantitative analysis of electrotonic structure and membrane properties of NMDA-activated lamprey spinal neurons

Cellular and network contributions to vestibular signal processing: impact of ion conductances, synaptic inhibition, and noise

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.

Quadratic sinusoidal analysis of voltage clamped neurons

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.

Frequency-Domain Analysis of Intrinsic Neuronal Properties using High-Resistant Electrodes

Intrinsic cellular properties of neurons in culture or slices are usually studied by the whole cell clamp method using low-resistant patch pipettes. These electrodes allow detailed analyses with standard electrophysiological methods such as current- or voltage-clamp. However, in these preparations large parts of the network and dendritic structures may be removed, thus preventing an adequate study of synaptic signal processing. Therefore, intact in vivo preparations or isolated in vitro whole brains have been used in which intracellular recordings are usually made with sharp, high-resistant electrodes to optimize the impalement of neurons. The general non-linear resistance properties of these electrodes, however, severely limit accurate quantitative studies of membrane dynamics especially needed for precise modelling. Therefore, we have developed a frequency-domain analysis of membrane properties that uses a Piece-wise Non-linear Electrode Compensation (PNEC) method. The technique was tested in second-order vestibular neurons and abducens motoneurons of isolated frog whole brain preparations using sharp potassium chloride- or potassium acetate-filled electrodes. All recordings were performed without online electrode compensation. The properties of each electrode were determined separately after the neuronal recordings and were used in the frequency-domain analysis of the combined measurement of electrode and cell. This allowed detailed analysis of membrane properties in the frequency-domain with high-resistant electrodes and provided quantitative data that can be further used to model channel kinetics. Thus, sharp electrodes can be used for the characterization of intrinsic properties and synaptic inputs of neurons in intact brains.

Differential dynamic processing of afferent signals in frog tonic and phasic second-order vestibular neurons

The sensory-motor transformation of the large dynamic spectrum of head-motion-related signals occurs in separate vestibulo-ocular pathways. Synaptic responses of tonic and phasic second-order vestibular neurons were recorded in isolated frog brains after stimulation of individual labyrinthine nerve branches with trains of single electrical pulses. The timing of the single pulses was adapted from spike discharge patterns of frog semicircular canal nerve afferents during sinusoidal head rotation. Because each electrical pulse evoked a single spike in afferent fibers, the resulting sequences with sinusoidally modulated intervals and peak frequencies up to 100 Hz allowed studying the processing of presynaptic afferent inputs with in vivo characteristics in second-order vestibular neurons recorded in vitro in an isolated whole brain. Variation of pulse-train parameters showed that the postsynaptic compound response dynamics differ in the two types of frog vestibular neurons. In tonic neurons, subthreshold compound responses and evoked discharge patterns exhibited relatively linear dynamics and were generally aligned with pulse frequency modulation. In contrast, compound responses of phasic neurons were asymmetric with large leads of subthreshold response peaks and evoked spike discharge relative to stimulus waveform. These nonlinearities were caused by the particular intrinsic properties of phasic vestibular neurons and were facilitated by GABAergic and glycinergic inhibitory inputs from tonic type vestibular interneurons and by cerebellar circuits. Coadapted intrinsic filter and emerging network properties thus form dynamically different neuronal elements that provide the appropriate cellular basis for a parallel processing of linear, tonic, and nonlinear phasic vestibulo-ocular response components in central vestibular neurons.

Control of neuronal persistent activity by voltage-dependent dendritic properties

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.

Oscillatory and Intrinsic Membrane Properties of Guinea Pig Nucleus Prepositus Hypoglossi Neurons In Vitro

Numerous models of the oculomotor neuronal integrator located in the prepositus hypoglossi nucleus (PHN) involve both highly tuned recurrent networks and intrinsic neuronal properties; however, there is little experimental evidence for the relative role of these two mechanisms. The experiments reported here show that all PHN neurons (PHNn) show marked phasic behavior, which is highly oscillatory in ∼25% of the population. The behavior of this subset of PHNn, referred to as type D PHNn, is clearly different from that of the medial vestibular nucleus neurons, which transmit the bulk of head velocity-related sensory vestibular inputs without integrating them. We have investigated the firing and biophysical properties of PHNn and developed data-based realistic neuronal models to quantitatively illustrate that their active conductances can produce the oscillatory behavior. Although some individual type D PHNn are able to show some features of mathematical integration, the lack of robustness of this behavior strongly suggests that additional network interactions, likely involving all types of PHNn, are essential for the neuronal integrator. Furthermore, the relationship between the impulse activity and membrane potential of type D PHNn is highly nonlinear and frequency-dependent, even for relatively small-amplitude responses. These results suggest that some of the synaptic input to type D PHNn is likely to evoke oscillatory responses that will be nonlinearly amplified as the spike discharge rate increases. It would appear that the PHNn have specific intrinsic properties that, in conjunction with network interconnections, enhance the persistent neural activity needed for their function.

Resonance of spike discharge modulation in neurons of the guinea pig medial vestibular nucleus

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.

Contributions of identifiable neurons and neuron classes to lamprey vertebrate neurobiology

Among the advantages offered by the lamprey brainstem and spinal cord for studies of the structure and function of the nervous system is the unique identifiability of several pairs of reticulospinal neurons in the brainstem. These neurons have been exploited in investigations of the patterns of sensory input to these cells and the patterns of their outputs to spinal neurons, but no doubt these cells could be used much more effectively in exploring their roles in descending control of the spinal cord. The variability of cell positions of neurons in the spinal cord has precluded the recognition of unique spinal neurons. However, classes of nerve cells can be readily defined and characterized within the lamprey spinal cord and this has led to progress in understanding the cellular and synaptic mechanisms of locomotor activity. In addition, both the identifiable reticulospinal cells and the various spinal nerve cell classes and their known synaptic interactions have been used to demonstrate the degree and specificity of regeneration within the lamprey nervous system. The lack of uniquely identifiable cells within the lamprey spinal cord has hampered progress in these areas, especially in gaining a full understanding of the locomotor network and how neuromodulation of the network is accomplished.

Parameter estimation methods for single neuron models

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.

Active dendritic membrane properties of Xenopus larval spinal neurons analyzed with a whole cell soma voltage clamp

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.

Firing properties and electrotonic structure of Xenopus larval spinal neurons

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.

NMDA-induced dendritic oscillations during a soma voltage clamp of chick spinal 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.

Commissural interneurons in rhythm generation and intersegmental coupling in the lamprey spinal cord

Commissural interneurons in rhythm generation and intersegmental coupling in the lamprey spinal cord. To test the necessity of spinal commissural interneurons in the generation of the swim rhythm in lamprey, longitudinal midline cuts of the isolated spinal cord preparation were made. Fictive swimming was then induced by bath perfusion with an excitatory amino acid while recording ventral root activity. When the spinal cord preparation was cut completely along the midline into two lateral hemicords, the rhythmic activity of fictive swimming was lost, usually replaced with continuous ventral root spiking. The loss of the fictive swim rhythm was not due to nonspecific damage produced by the cut because rhythmic activity was present in split regions of spinal cord when the split region was still attached to intact cord. The quality of this persistent rhythmic activity, quantified with an autocorrelation method, declined with the distance of the split spinal segment from the remaining intact spinal cord. The deterioration of the rhythm was characterized by a lengthening of burst durations and a shortening of the interburst silent phases. This pattern of deterioration suggests a loss of rhythmic inhibitory inputs. The same pattern of rhythm deterioration was seen in preparations with the rostral end of the spinal cord cut compared with those with the caudal end cut. The results of this study indicate that commissural interneurons are necessary for the generation of the swimming rhythm in the lamprey spinal cord, and the characteristic loss of the silent interburst phases of the swimming rhythm is consistent with a loss of inhibitory commissural interneurons. The results also suggest that both descending and ascending commissural interneurons are important in the generation of the swimming rhythm. The swim rhythm that persists in the split cord while still attached to an intact portion of spinal cord is thus imposed by interneurons projecting from the intact region of cord into the split region. These projections are functionally short because rhythmic activity was lost within approximately five spinal segments from the intact region of spinal cord.

Simulation and parameter estimation study of a simple neuronal model of rhythm generation: role of NMDA and non-NMDA receptors

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.

Spectral analysis of oscillatory neural circuits

Oscillatory dynamics are found at all levels of the nervous system. The goal of our current research on the control of rhythmic motor output by the lamprey spinal cord is to determine the features of neuronal coupling that lead to stable oscillatory activity and precisely-controlled intersegmental phase. Since our experimental manipulations can greatly increase the variability of the ventral root bursting pattern, it is important for us to employ a data analysis method which remains valid independent of this variability. Traditional analysis approaches which rely on identification of burst event times do not generally satisfy this requirement. In this paper, we illustrate the application of a straightforward statistically-based method for determining important parameters of oscillatory motor circuits using Fourier spectral analysis of spike trains. The frequency, phase, and their variabilities can be quantified; and the relative strength of coupling between different parts of the circuit can be tested for statistical significance. The approach we adopt is highly convenient for neuroscientists who study oscillatory systems as it operates directly on trains of action potentials stored as lists of event times (point-processes). Basic concepts and practical issues concerning use of Fourier analysis are discussed.

Inhibition of crossed caudal interneurons by lateral interneurons in lamprey spinal chord during fictive locomotion

Templates of the membrane potential profiles from lateral (LI) interneurons and motoneurons during glutamate- and N-methyl-D-aspartate (NMDA)-induced fictive locomotion showed pronounced plateau phases. In contrast, crossed caudal (CC) interneurons had a less obvious and steeper plateau region that was followed by a clear notch coinciding with the end of the lateral interneuron plateau phase. These results indicate a significant inhibitory input from LI to CC interneurons.