Successive Spikes Research Articles

Rate synchronization as a deterministic signal in neural spike trains

We introduce a simple method to analyze recorded spike trains in sensory neurons that allows to reveal deterministic aspects of spiking dynamics. In particular, events with an associated firing rate f r , are defined whenever two successive spikes on a given cell α occur at times t i α and t i −1 α such that ( f r +Δ f r ) −1 <| t i α − t i −1 α |<( f r −Δ f r ) −1 , for a given Δ f r . We then look for synchronization of those events on different cells. Our results show that synchronized events are sharply correlated with stimuli. The method is used to analyze experimental time series obtained on retinal ganglion cells and synthetic time series.

Rate synchronization as a deterministic signal in neural spike trains

We introduce a simple method to analyze recorded spike trains in sensory neurons that allows to reveal deterministic aspects of spiking dynamics. In particular, events with an associated firing rate f r , are defined whenever two successive spikes on a given cell α occur at times t i α and t i−1 α such that ( f r +Δ f r ) −1<| t i α − t i−1 α |<( f r −Δ f r ) −1, for a given Δ f r . We then look for synchronization of those events on different cells. Our results show that synchronized events are sharply correlated with stimuli. The method is used to analyze experimental time series obtained on retinal ganglion cells and synthetic time series.

Characteristics of GABAergic neurons in the superficial superior colliculus in mice

We investigated characteristics of identified GABAergic neurons in slices of the superficial superior colliculus (sSC) using transgenic mice in which green fluorescent protein (GFP) is specifically expressed in GABAergic neurons. Whole-cell patch clamp recordings and intracellular staining with biocytin revealed electrophysiological and morphological properties of GFP-positive neurons. GFP-positive neurons had a tangentially elongated wide dendritic field. In response to depolarizing current pulses, most of the GFP-positive neurons showed either of two firing properties; 55% ( n=36/65) generated successive spikes with a constant firing frequency and 22% ( n=14/65) showed transient burst firing at a threshold level for spike generation. These results elucidate a functional heterogeneity of GABAergic neurons, and provide fundamental information to understand the function of the GABAergic system in the sSC.

Noise-tolerant stimulus discrimination by synchronization with depressing synapses.

Some synapses between cortical pyramidal neurons exhibit a rapid depression of excitatory postsynaptic potentials for successive presynaptic spikes. Since depressing synapses do not transmit information on sustained presynaptic firing rates, it has been speculated that they are favorable for temporal coding. In this paper. we study the dynamical effects of depressing synapses on stimulus-induced transient synchronization in a simple network of inhibitory interneurons and excitatory neurons, assuming that the recurrent excitation is mediated by depressing synapses. This synchronization occurs in a temporal pattern which depends on a given stimulus. Since the presence of noise is always a potential hazard in temporal coding, we investigate the extent to which noise in stimuli influences the synchronization phenomena. It is demonstrated that depressing synapses greatly contribute to suppressing the influences of noise on the stimulus-specific temporal patterns of synchronous firing. The timing-based Hebbian learning revealed by physiological experiments is shown to stabilize the temporal patterns in cooperation with synaptic depression. Thus, the times at which synchronous firing occurs provides a reliable information representation in the presence of synaptic depression.

Characterization of M proteins as a series of peaks by capillary zone electrophoresis with a linear polyacrylamide-coated capillary.

Human serum proteins including myeloma (M) proteins were analyzed by capillary zone electrophoresis (CZE) using a linear polyacrylamide-coated capillary at pH 7.4. Each of the M proteins, IgG-κ, IgA-κ, and IgA-λ, which were located on the β zone on the cellulose acetate electrophoresis (CAE), was resolved into a group of peaks with a unique profile in a wide area following the transferrin (TF) peak. While the IgG-κ showed a series of narrow peaks, IgA-κ and IgA-λ showed a wide peak with many successive spikes. On the other hand, the increased polyclonal IgA-κ and IgG-κ, which were located on the β zone on the CAE, showed only a broad peak around the TF peak. Another IgG-κ M protein, which was located on the γ zone on the CAE, did not appear on the CZE at pH 7.4, but did appear with several peaks by increasing the pH to 9.0. No peaks were observed in the area following the TF peak when healthy serum proteins including immunoglobulins (Igs) were analyzed at both pHs. The coexistence of albumin did not affect the detection of monoclonal and polyclonal Igs. These results demonstrate that the CZE system is capable of distinguishing IgG M proteins from IgA M proteins, and monoclonal Igs from polyclonal ones. Furthermore, it was found that the CZE is useful for discriminating between isoforms of IgG M proteins.

Regeneration of cerebral-buccal interneurons and recovery of ingestion buccal motor programs in Aplysia after CNS lesions.

In the sea slug Aplysia, rhythmic biting is eliminated after bilateral cerebral-buccal connective (CBC) crushes and recovers within 14 days postlesion (dpl). The ability of cerebral-buccal interneuron-2 (CBI-2) to elicit ingestion buccal motor programs (iBMPs; i.e., fictive rhythmic ingestion) and to regenerate synaptic connections with target buccal neurons was assessed with intracellular recordings and dye injections. Isolated central ganglia were obtained from control animals and from lesioned animals at selected times after bilateral CBC crushes. Within 3 wk postlesion, transected CBI-2 axons sprouted at least 10 fine neurites confined to the core of the CBC that projected across the crush site toward the buccal ganglia. When fired with depolarizing current steps, CBI-2 was not observed to elicit iBMPs in preparations until 14 dpl. Thereafter a progressive enhancement in CBI-2's ability to elicit iBMPs was observed with time postlesion. By 40 dpl, CBI-2-elicited iBMPs were indistinguishable from those of controls. CBI-2 regenerated monosynaptic connections with appropriate buccal premotor- and motorneurons by 14 dpl, and the strength of these connections increased with time postlesion. Dramatic frequency facilitation was exhibited by the regenerating CBI-2 buccal synapses; for instance, at early postlesion times, no observable excitatory postsynaptic potentials (EPSPs) were obtained with 1- Hz stimulation of CBI-2, while at 7 Hz, a dramatic increase in EPSP amplitude was obtained with successive spikes. The present study shows that the time course of axonal and synaptic regeneration by command-like interneuron CBI-2 is correlated with the recovery of ingestion buccal motor programs elicited by CBI-2. These results parallel our previous findings of functional neural regeneration in the feeding system and suggest that functional neural regeneration is at least in part mediated by regeneration of specific synaptic pathways.

Efficient event-driven simulation of large networks of spiking neurons and dynamical synapses.

A simulation procedure is described for making feasible large-scale simulations of recurrent neural networks of spiking neurons and plastic synapses. The procedure is applicable if the dynamic variables of both neurons and synapses evolve deterministically between any two successive spikes. Spikes introduce jumps in these variables, and since spike trains are typically noisy, spikes introduce stochasticity into both dynamics. Since all events in the simulation are guided by the arrival of spikes, at neurons or synapses, we name this procedure event-driven. The procedure is described in detail, and its logic and performance are compared with conventional (synchronous) simulations. The main impact of the new approach is a drastic reduction of the computational load incurred upon introduction of dynamic synaptic efficacies, which vary organically as a function of the activities of the pre- and postsynaptic neurons. In fact, the computational load per neuron in the presence of the synaptic dynamics grows linearly with the number of neurons and is only about 6% more than the load with fixed synapses. Even the latter is handled quite efficiently by the algorithm. We illustrate the operation of the algorithm in a specific case with integrate-and-fire neurons and specific spike-driven synaptic dynamics. Both dynamical elements have been found to be naturally implementable in VLSI. This network is simulated to show the effects on the synaptic structure of the presentation of stimuli, as well as the stability of the generated matrix to the neural activity it induces.

Functional divergence of human genioglossus motor units with respiratory-related activity.

The genioglossus muscle has at least two types of motor unit with respiratory-related activity. Inspiratory motor units show phasic activity during inspiration, whereas inspiratory/expiratory motor units show phasic inspiratory activity superimposed on tonic activity. The purpose of this study was to investigate the physiological roles of these different genioglossus motor units. The unitary activities of 12 inspiratory and 12 inspiratory/expiratory motor units were recorded using fine-wire electrodes during quiet nasal breathing in eight normal adult males. The mean interspike interval and the SD of successive spikes were calculated for inspiratory and inspiratory/expiratory motor units, respectively. Scattergrams of the mean interspike interval versus SD were constructed for the two groups of motor units. The effects of changes in head position on the firing activity and the patterns of distribution of the mean interspike interval versus its SD were significantly different for inspiratory and inspiratory/expiratory motor units. These results suggest that the inspiratory and inspiratory/expiratory motor units have different functional roles in respiration; inspiratory motor units may be phasically active to counteract intraluminal negative pressure during inspiration, whereas inspiratory/expiratory motor units may be tonically active to maintain tongue posture.

Asymptotic analysis of subcritical Hopf–homoclinic bifurcation

This paper discusses the mathematical analysis of a codimension two bifurcation determined by the coincidence of a subcritical Hopf bifurcation with a homoclinic orbit of the Hopf equilibrium. Our work is motivated by our previous analysis of a Hodgkin–Huxley neuron model which possesses a subcritical Hopf bifurcation (J. Guckenheimer, R. Harris-Warrick, J. Peck, A. Willms, J. Comput. Neurosci. 4 (1997) 257–277). In this model, the Hopf bifurcation has the additional feature that trajectories beginning near the unstable manifold of the equilibrium point return to pass through a small neighborhood of the equilibrium, that is, the Hopf bifurcation appears to be close to a homoclinic bifurcation as well. This model of the lateral pyloric (LP) cell of the lobster stomatogastric ganglion was analyzed for its ability to explain the phenomenon of spike-frequency adaptation, in which the time intervals between successive spikes grow longer until the cell eventually becomes quiescent. The presence of a subcritical Hopf bifurcation in this model was the one identified mechanism for oscillatory trajectories to increase their period and finally collapse to a non-oscillatory solution. The analysis presented here explains the apparent proximity of homoclinic and Hopf bifurcations. We also develop an asymptotic theory for the scaling properties of the interspike intervals in a singularly perturbed system undergoing subcritical Hopf bifurcation that may be close to a codimension two subcritical Hopf–homoclinic bifurcation.

Interactions between brainstem and trigeminal neurons detected by cross-spectral analysis

Cells in the nucleus raphe magnus that are inhibited by noxious skin stimuli (off-cells) have been postulated to suppress pain by continuously inhibiting spinal and trigeminal nociceptive neurons. To test this hypothesis, spontaneous activity was simultaneously recorded from off-cells ( n=15) and wide-dynamic range cells ( n=27) of the trigeminal complex (subnucleus interpolaris), in rats anesthetized with pentobarbital. Most off-cells ( n=14) had rhythmic interspike intervals, their modes averaging 106 ms. No trigeminal cell fired rhythmically. Rhythmic firing was defined quantitatively: the autospectrum's peak power had to exceed 1.75 times its asymptote. This formula was obtained by generalizing from a natural cut-off in the theoretical autospectrum for serially uncorrelated, gamma-distributed intervals, whose firing can be varied from Poissonian to highly regular by adjusting one parameter. It encompasses the qualitative judgement of autocorrelograms commonly made in neurophysiology. Cross-correlograms ( n=29) appeared noisy and otherwise featureless. However, their power spectra (cross-periodograms) sometimes showed significant peaks, compared with simulated non-interactive distributions. The latter were generated by interchanging the raphe interval sequences at one random point (as in cutting a deck of cards), thus retaining most of their serial correlation. Of 29 cross-periodograms, 21 were significant at 1 to 13 frequencies (100 points, 0.4 to 39 Hz). These frequencies were often near the peak raphe power, and sometimes near its harmonics too. Furthermore, cross-spectral phase angles at peak power were non-uniform, most falling between 0 and 180 degrees (unit vector sum 60°, n=20). To understand why the frequency domain gave better detection, cross-spectra and cross-correlations were modeled theoretically by convolving idealized input autocorrelations and synaptic response functions. This demonstrated that rhythmic firing is insufficient for better frequency-domain detection, and that serially correlated input intervals or non-additive synaptic responses are necessary. The conclusion was confirmed by stochastic simulation of a simple non-additive synapse, that required successful input spikes to fall within a specified interval of the preceding spike. Experimentally, serial correlation was found in 12 of the 15 raphe cells, and in 20 of the 27 trigeminal cells. It is proposed that the weak experimental cross-correlograms arise because many asynchronous raphe inputs converge on each trigeminal cell, possibly to optimize the resting suppression of pain. The distribution of cross-spectral phase angles at peak raphe power suggested that raphe spikes arriving at the synapses' preferred interval cause a fall in trigeminal activity. In general, cross-spectral analysis can sometimes uncover influences hidden in cross-correlograms, but the firing of one neuron must be rhythmic and non-renewal, or else certain input intervals must be favored in synaptic transmission.

Effects of Two Instructional Models—Skill Teaching and Mastery Learning—On Skill Development, Knowledge, Self-Efficacy, and Game Play in Volleyball

This study examined volleyball achievement and task-specific self-efficacy for 182 students in 6 beginning college volleyball classes taught using either the Mastery Learning or Skill Teaching models. Three instructors each taught one Mastery Learning and one Skill Teaching class. Assessments included the AAHPERD pass, set. and serve tests, the Stanley spike test, successful and unsuccessful game trials. Bandura-type self-efficacy scales, and a knowledge test. A random coefficients growth curve model analyzed the intercepts and slopes of the learning curves and revealed significant pre- to posttest improvement on skills tests, self-efficacy, and the percentage of correct passes and serves in game play for all students. No significant difference existed between the two models on average number of trials per day; rate of improvement for the pass, serve, or spike skills tests; self-efficacy; percentage of correct passes, sets, or serves in game play; contacts per serve in game play; or knowledge scores. The Mastery students’ rate of learning was significantly better on the set skills test (1.3 points higher) and the percentage of successful spikes in game play, in which they started significantly lower. The low-skilled students improved at a faster rate on the serve and on self-efficacy for the pass, set, and serve. Males had higher self-efficacy than females, while females increased more rapidly in self-efficacy for the pass, set, and serve. All results were analyzed at the .05 level of significance. Students learned to play volleyball and improved significantly in skill performances with either model.

Exposure of cultured murine peritoneal macrophages to low concentrations of beryllium induces increases in intracellular calcium concentrations and stimulates DNA synthesis

Exposure of humans to beryllium dusts can induce a specific form of chronic pneumonitis that consists mainly of noncaseating granulomas in the lungs. Multiple studies have documented both genetic and immune components of chronic berylliosis. Much work has focused on T cells and their reactivity in berylliosis, but less work has focused on the end effector cells in granulomatous inflammation, macrophages. Because macrophages must become activated to form granulomas, and they become activated by responding to numerous immunomodulatory signals, we investigated the effects of beryllium (BeCl2) on a central signal transduction pathway in macrophages, increases in intracellular calcium ([Ca2+]i). Exposure of cultured murine peritoneal macrophages to low, nontoxic concentrations induced successive spikes or oscillations in [Ca2+]i. Concentrations as low as 5 nM induced significant increases in [Ca2+]i. The source of the increased [Ca2+]i was exclusively extracellular in that increases in [Ca2+]i could be completely blocked by chelating extracellular Ca2+, were inhibited by the Ca2+ channel blocker verapamil, and exposure of macrophages to BeCl2 had no effect on IP3 concentrations. DNA synthesis, a Ca2+-sensitive function, was enhanced in dividing 1LN cells and induced de novo in quiescent macrophages. Furthermore, BeCl2 enhanced DNA synthesis in the absence of coexposure to the protein kinase C activator phorbol myristate acetate. These data support the hypothesis that beryllium toxicity is in part the result of altered Ca2+ metabolism in mononuclear phagocytes consequent to reversible opening of plasma membrane channels.

Cellular mechanisms underlying intrathalamic augmenting responses of reticular and relay neurons.

Augmenting (or incremental) responses are progressively growing potentials elicited by 5- to 15-Hz stimulation within the thalamus, cerebral cortex, or by setting into action reciprocal thalamocortical neuronal loops. These responses are associated with short-term plasticity processes in thalamic and cortical neurons. In the present study, in vivo intracellular recordings of thalamic reticular (RE) and thalamocortical (TC), as well as dual intracellular recordings, were used to explore the mechanisms of two types of intrathalamic augmenting responses elicited by thalamic stimuli at 10 Hz in decorticated cats. As recently described, after decortication, TC cells display incremental burst responses to thalamic stimuli that occur through either progressive depolarization (high threshold, HT) or progressive hyperpolarization leading to deinactivation of low-threshold (LT) spike bursts. Here, low-intensity stimuli (10 Hz) to dorsal thalamic nuclei elicited decremental responses in GABAergic RE cells, consisting of a progressive diminution in the number of action potentials in successive spike bursts, whereas higher stimulation (>50% of maximal strength) induced augmentation characterized by an increased number of spikes in repetitive responses. These opposing discharge patterns occurred in the absence of changes in the membrane potential of RE cells. In TC cells, augmentation depended on the thalamic site where testing volleys were applied. With stimuli applied closer to the site of impalement, augmenting resulted from a transformation from LT spike bursts into HT responses. Augmenting responses were followed by self-sustained oscillatory activity, within the frequency of spindles (7-14 Hz) or clock-like delta oscillation (1-4 Hz). As LT augmentation in TC cells results from their progressive hyperpolarization, we tested the effects exerted by the activating depolarizing system arising in the mesopontine cholinergic nuclei and found that such conditioning pulse-trains prevented the hyperpolarizing-rebound sequences as well as the LT augmenting in TC cells. We propose that the depolarization-dependent (HT) augmenting responses in TC cells result from decremental responses in RE neurons that are due to intra-RE inhibitory processes leading to disinhibition in target TC neurons, whereas LT-type augmenting in TC cells is produced mainly by incremental responses in GABAergic RE neurons.

Unstable periodic orbits in human epileptic activity

We examine in detail subdural recordings from a patient with an epileptic focal seizure, highly unusual in the ongoing nature of the discharges and in the lack of cognitive impairment. We applied a recent method for detecting unstable periodic orbits to the series of time intervals between successive spike discharges, and report that a few unstable fixed points exist within their apparent random fluctuations. The statistical significance of this underlying deterministic dynamics is assessed using surrogate data. In particular, the approaches of trajectories toward the unstable periodic patterns are observed in the sequences immediately following the perceptual tasks. This suggests that the act of perception contributes in a highly specific manner to pulling the epileptic activities towards particular unstable periodic orbits, which closely resemble the technique called chaos control for stabilization of unstable periodic orbits.

Does the Gamma Distribution Refer to an Underlying Mechanism in Binocular Rivalry?

Thirty years ago, Levelt (1967 British Journal of Psychology58 143 – 145) fitted the distribution of dominance times in binocular rivalry with the gamma distribution (the distribution function of waiting times for N random events with process speed lambda). Ever since, the gamma distribution has been used to describe the rivalry phase durations, without an explanatory underlying mechanism being given. Although Levelt suggested lambda to be proportional to the stimulus strength (eg contrast, luminance, blur, amount of contour) and N to be ‘successive neural spikes’, this suggestion has never been tested. The purpose of this study was to test whether or not N and lambda represent characteristics of the observer and the stimulus, respectively. To collect the data as accurately as possible, we performed a large number of measurements involving different designs and stimuli. In contrast to previous experiments, collected data were not pooled but were compared within each subject. We tested the hypothesis by collecting time intervals from subjects responding to numerous conditions in which disk - ring stimuli were varied in contrast, blur, or amount of contour in one eye.

Temporal patterns in human epileptic activity are modulated by perceptual discriminations

We studied subdural recordings from a patient with an unusually focal and stable occipito-temporal epileptic discharge under four experimental conditions. The series of time intervals between successive spike discharges displayed a few (3-5) clusters of periodic values representing statistically significant short-term periodicities when tested against surrogate data. This short-term predictability was modulated during the different experimental conditions by periodicity shifts of the order of 15-30 ms. Correspondingly, there was an increased gamma-band (30-70 Hz) coherence between the epileptic focus and surrounding recording sites. We conclude that the focal epileptic activity is part of an extended network of neural activities which exert a fast modulation reflected in changes of transiently periodic activities.

Oscillatory and burst discharge across electrosensory topographic maps.

1. Three parallel maps of the distribution of tuberous electroreceptor inputs are found in the medullary electrosensory lateral line lobe (ELL) of weakly electric fish. Pyramidal cells in each map are known to respond differentially to the frequency of amplitude modulations (AMs) of external electric fields in vivo. We used an in vitro ELL slice preparation of Apteronotus leptorhynchus to compare the characteristics of spontaneously active single units across the three tuberous maps. It was our objective to determine whether spontaneous bursting activity of pyramidal cells in each map correlates with the known AM frequency selectivities of pyramidal cells in vivo. 2. Single-unit discharges were recorded from the pyramidal cell layer of the centromedial segment (CMS), centrolateral segment (CLS), and lateral segment (LS) of the ELL. Stochastic analysis of interspike intervals (ISIs) was used to identify bursting and nonbursting unit activity, and to separately analyze intra- and interburst ISIs. Four ISI patterns were identified as 1) bursting, 2) regular spiking, 3) irregular spiking, and 4) highly irregular spiking. This work focuses primarily on the characteristics of bursting units across the ELL segments. 3. Spontaneous bursting discharge was identified in all three maps (68 of 97 units), with several characteristics changing in a gradual manner across the maps. The coefficient of variation (CV) of ISIs and intraburst ISIs decreased significantly from the CMS to the LS, whereas the CV of burst periods increased significantly from the CMS to the LS. Autocorrelations and power spectral density analysis identified units discharging in an oscillatory manner with the following ratio: CMS, 75%; CLS, 4%; LS, 8%. 4. The mean period of spike bursts decreased significantly across the segments (CMS, 2.7 s; CLS, 1.2 s; LS, 1.1 s) primarily because of a shortening of mean burst duration (CMS, 1.0 s; CLS, 0.1 s; LS, 0.05 s). The average number of spikes per burst decreased significantly across the maps (CMS, 61; CLS, 8; LS, 8), whereas the average frequency of spikes per burst increased (CMS, 90 Hz; CLS, 130 Hz; LS, 178 Hz), mainly through an increase in the maximal frequencies attained by units within each map. 5. Bursts in the CMS were unstructured in that the intraburst ISIs were serially independent, whereas for many units in the CLS and especially the LS there were serial dependencies of successive spikes, with alternating short and long ISIs during the burst. 6. These data reveal that the characteristics of bursting unit activity differ between the CMS, CLS, and LS maps in vitro, implying a modulation of the factors underlying burst discharge across multiple sensory maps. Because the pattern of change in burst activity between these maps parallels that of pyramidal cell AM frequency selectivity in vivo, oscillatory and burst discharge may represent the cellular mechanism used to tune these cells to specific frequencies of afferent input during electrolocation and electrocommunication.

Pattern and inhibition-dependent invasion of pyramidal cell dendrites by fast spikes in the hippocampus in vivo.

The invasion of sodium spikes from the soma into dendrites was studied in hippocampal pyramidal cells by simultaneous extracellular and intracellular recordings in anesthetized rats and by simultaneous extracellular recordings of the somatic and dendritic potentials in freely behaving animals. During complex-spike patterns, recorded in the immobile or sleeping animal, dendritic invasion of successive spikes was substantially attenuated. Complex-spike bursts occurred in association with population discharge of CA3-CA1 pyramidal cells (sharp wave field events). Synaptic inhibition reduced the amplitude of sodium spikes in the dendrites and prevented the occurrence of calcium spikes. These findings indicate that (i) the voltage-dependent calcium influx into the dendrites is under the control of inhibitory neurons and (ii) the temporal coincidence of synaptic depolarization and activation of voltage-dependent calcium conductances by the backpropagating spikes during sharp wave bursts may be critical for synaptic plasticity in the intact hippocampus.

Neural correlates of the pitch of complex tones. I. Pitch and pitch salience.

1. The temporal discharge patterns of auditory nerve fibers in Dial-anesthetized cats were studied in response to periodic complex acoustic waveforms that evoke pitches at their fundamental frequencies. Single-formant vowels, amplitude-modulated (AM) and quasi-frequency-modulated tones. AM noise, click trains, and other complex tones were utilized. Distributions of intervals between successive spikes ("1st-order intervals") and between both successive and nonsuccessive spikes ("all-order intervals") were computed from spike trains. Intervals from many fibers were pooled to estimate interspike interval distributions for the entire auditory nerve. Properties of these "pooled interspike interval distributions," such as the positions of interval peaks and their relative heights, were examined for correspondence to the psychophysical data on pitch frequency and pitch salience. 2. For a diverse set of complex stimuli and levels, the most frequent all-order interspike interval present in the pooled distribution corresponded to the pitch heard in psychophysical experiments. Pitch estimates based on pooled interval distributions (30-85 fibers, 100 stimulus presentations per fiber) were highly accurate (within 1%) for harmonic stimuli that produce strong pitches at 60 dB SPL. 3. Although the most frequent intervals in pooled all-order interval distributions were very stable with respect to sound intensity level (40, 60, and 80 dB total SPL), this was not necessarily the case for first-order interval distributions. Because the low pitches of complex tones are largely invariant with respect to level, pitches estimated from all-order interval distributions correspond better to perception. 4. Spectrally diverse stimuli that evoke similar low pitches produce pooled interval distributions with similar most-frequent intervals. This suggests that the pitch equivalence of these different stimuli could result from central auditory processing mechanisms that analyze interspike interval patterns. 5. Complex stimuli that evoke strong or "salient" pitches produce pooled interval distributions with high peak-to-mean ratios. Those stimuli that evoke weak pitches produce pooled interval distributions with low peak-to-mean ratios. 6. Pooled interspike interval distributions for stimuli consisting of low-frequency components generally resembled the short-time auto-correlation function of stimulus waveforms. Pooled interval distributions for stimuli consisting of high-frequency components resembled the short-time autocorrelation function of the waveform envelope. 7. Interval distributions in populations of neurons constitute a general, distributed means of encoding, transmitting, and representing information. Existence of a central processor capable of analyzing these interval patterns could provide a unified explanation for many different aspects of pitch perception.

Analysis of neural bursting: nonrhythmic and rhythmic activity in isolated spinal cord

Neuronal firing recorded from primary afferents and central spinal neurons in isolated mammalian spinal cord in vitro was analyzed using interspike interval histograms and Poincaré maps (Return maps). Interspike interval histograms described the time between two successive spikes. However, Poincaré maps represented the interspike interval preceding a spike against the interspike interval following the spike. The variability in firing of neurons occurring naturally in different preparations was explored. In a presumptive single central spinal neuron, the firing pattern provided a single cluster. During bursting in a presumptive single primary afferent, the Poincaré maps provided information on interburst intervals. Moreover, lengthening and or shortening of interspike intervals within bursts can be detected in the maps. The firing of a population of neurons was modulated using a pharmacological intervention with 4-aminopyridine and resulted in a complex Poincaré map.