Rate fluctuations and fractional power-law noise recorded from cells in the lower auditory pathway of the cat

Filtered Point Processes Tractably Capture Rhythmic And Broadband Power Spectral Structure in Neural Electrophysiological Recordings

Neural electrophysiological recordings arise from interacting rhythmic (oscillatory) and broadband (aperiodic) biological subprocesses. Both rhythmic and broadband processes contribute to the neural power spectrum, which decomposes the variance of a neural recording across frequencies. Although an extensive body of literature has successfully studied rhythms in various diseases and brain states, researchers only recently have systematically studied the characteristics of broadband effects in the power spectrum. Broadband effects can generally be categorized as 1) shifts in power across all frequencies, which correlate with changes in local firing rates and 2) changes in the overall shape of the power spectrum, such as the spectral slope or power law exponent. Shape changes are evident in various conditions and brain states, influenced by factors such as excitation to inhibition balance, age, and various diseases. It is increasingly recognized that broadband and rhythmic effects can interact on a sub-second timescale. For example, broadband power is time-locked to the phase of <1 Hz rhythms in propofol induced unconsciousness. Modeling tools that explicitly deal with both rhythmic and broadband contributors to the power spectrum and that capture their interactions are essential to help improve the interpretability of power spectral effects. Here, we introduce a tractable stochastic forward modeling framework designed to capture both narrowband and broadband spectral effects when prior knowledge or theory about the primary biophysical processes involved is available. Population-level neural recordings are modeled as the sum of filtered point processes (FPPs), each representing the contribution of a different biophysical process such as action potentials or postsynaptic potentials of different types. Our approach builds on prior neuroscience FPP work by allowing multiple interacting processes and time-varying firing rates and by deriving theoretical power spectra and cross-spectra. We demonstrate several properties of the models, including that they divide the power spectrum into frequency ranges dominated by rhythmic and broadband effects, and that they can capture spectral effects across multiple timescales, including sub-second cross-frequency coupling. The framework can be used to interpret empirically observed power spectra and cross-frequency coupling effects in biophysical terms, which bridges the gap between theoretical models and experimental results.

Resolution of subcomponents of synaptic release from postsynaptic currents in rat hair-cell/auditory-nerve fiber synapses

The synapse between inner hair cells and auditory nerve fiber dendrites shows large excitatory postsynaptic currents (EPSCs), which are either monophasic or multiphasic. Multiquantal or uniquantal (flickering) release of neurotransmitter has been proposed to underlie the unusual multiphasic waveforms. Here the nature of multiphasic waveforms is analyzed using EPSCs recorded in vitro in rat afferent dendrites. Spontaneous EPSCs were deconvolved into a sum of presumed release events having monophasic EPSC waveforms. Results include, first, the charge of EPSCs is about the same for multiphasic versus monophasic EPSCs. Second, EPSC amplitudes decline with the number of release events per EPSC. Third, there is no evidence of a mini-EPSC. Most results can be accounted for by versions of either uniquantal or multiquantal release. However, serial neurotransmitter release in multiphasic EPSCs shows properties that are not fully explained by either model, especially that the amplitudes of individual release events are established at the beginning of a multiphasic EPSC, constraining possible models of vesicle release.NEW & NOTEWORTHY How do monophasic and multiphasic waveshapes arise in auditory-nerve dendrites; mainly are they uniquantal, arising from release of a single vesicle, or multiquantal, requiring several vesicles? The charge injected by excitatory postsynaptic currents (EPSCs) is the same for monophasic or multiphasic EPSCs, supporting uniquantal release. Serial adaptation of responses to sequential EPSCs favors a multiquantal model. Finally, neurotransmitter partitioning into similar sized release boluses occurs at the first bolus in the EPSC, not easily explained with either model.

Supra-Threshold Hearing and Fluctuation Profiles: Implications for Sensorineural and Hidden Hearing Loss

An important topic in contemporary auditory science is supra-threshold hearing. Difficulty hearing at conversational speech levels in background noise has long been recognized as a problem of sensorineural hearing loss, including that associated with aging (presbyacusis). Such difficulty in listeners with normal thresholds has received more attention recently, especially associated with descriptions of synaptopathy, the loss of auditory nerve (AN) fibers as a result of noise exposure or aging. Synaptopathy has been reported to cause a disproportionate loss of low- and medium-spontaneous rate (L/MSR) AN fibers. Several studies of synaptopathy have assumed that the wide dynamic ranges of L/MSR AN fiber rates are critical for coding supra-threshold sounds. First, this review will present data from the literature that argues against a direct role for average discharge rates of L/MSR AN fibers in coding sounds at moderate to high sound levels. Second, the encoding of sounds at supra-threshold levels is examined. A key assumption in many studies is that saturation of AN fiber discharge rates limits neural encoding, even though the majority of AN fibers, high-spontaneous rate (HSR) fibers, have saturated average rates at conversational sound levels. It is argued here that the cross-frequency profile of low-frequency neural fluctuation amplitudes, not average rates, encodes complex sounds. As described below, this fluctuation-profile coding mechanism benefits from both saturation of inner hair cell (IHC) transduction and average rate saturation associated with the IHC-AN synapse. Third, the role of the auditory efferent system, which receives inputs from L/MSR fibers, is revisited in the context of fluctuation-profile coding. The auditory efferent system is hypothesized to maintain and enhance neural fluctuation profiles. Lastly, central mechanisms sensitive to neural fluctuations are reviewed. Low-frequency fluctuations in AN responses are accentuated by cochlear nucleus neurons which, either directly or via other brainstem nuclei, relay fluctuation profiles to the inferior colliculus (IC). IC neurons are sensitive to the frequency and amplitude of low-frequency fluctuations and convert fluctuation profiles from the periphery into a phase-locked rate profile that is robust across a wide range of sound levels and in background noise. The descending projection from the midbrain (IC) to the efferent system completes a functional loop that, combined with inputs from the L/MSR pathway, is hypothesized to maintain "sharp" supra-threshold hearing, reminiscent of visual mechanisms that regulate optical accommodation. Examples from speech coding and detection in noise are reviewed. Implications for the effects of synaptopathy on control mechanisms hypothesized to influence supra-threshold hearing are discussed. This framework for understanding neural coding and control mechanisms for supra-threshold hearing suggests strategies for the design of novel hearing aid signal-processing and electrical stimulation patterns for cochlear implants.

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H∈(1/2,1) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H∈(1/2,1) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

Maturation of Spontaneous Firing Properties after Hearing Onset in Rat Auditory Nerve Fibers: Spontaneous Rates, Refractoriness, and Interfiber Correlations

Auditory nerve fibers (ANFs) exhibit a range of spontaneous firing rates (SRs) that are inversely correlated with threshold for sounds. To probe the underlying mechanisms and time course of SR differentiation during cochlear maturation, loose-patch extracellular recordings were made from ANF dendrites using acutely excised rat cochlear preparations of different ages after hearing onset. Diversification of SRs occurred mostly between the second and the third postnatal week. Statistical properties of ANF spike trains showed developmental changes that approach adult-like features in older preparations. Comparison with intracellularly recorded EPSCs revealed that most properties of ANF spike trains derive from the characteristics of presynaptic transmitter release. Pharmacological tests and waveform analysis showed that endogenous firing produces some fraction of ANF spikes, accounting for their unusual properties; the endogenous firing diminishes gradually during maturation. Paired recordings showed that ANFs contacting the same inner hair cell could have different SRs, with no correlation in their spike timing.

SIGNIFICANCE STATEMENT

The inner hair cell (IHC)/auditory nerve fiber (ANF) synapse is the first synapse of the auditory pathway. Remarkably, each IHC is the sole partner of 10-30 ANFs with a range of spontaneous firing rates (SRs). Low and high SR ANFs respond to sound differently, and both are important for encoding sound information across varying acoustical environments. Here we demonstrate SR diversification after hearing onset by afferent recordings in acutely excised rat cochlear preparations. We describe developmental changes in spike train statistics and endogenous firing in immature ANFs. Dual afferent recordings provide the first direct evidence that fibers with different SRs contact the same IHCs and do not show correlated spike timing at rest. These results lay the groundwork for understanding the differential sensitivity of ANFs to acoustic trauma.

Subdiffusive dynamics of bump attractors: mechanisms and functional roles

Bump attractors are localized activity patterns that can self-sustain after stimulus presentation, and they are regarded as the neural substrate for a host of perceptual and cognitive processes. One of the characteristic features of bump attractors is that they are neutrally stable, so that noisy inputs cause them to drift away from their initial locations, severely impairing the accuracy of bump location-dependent neural coding. Previous modeling studies of such noise-induced drifting activity of bump attractors have focused on normal diffusive dynamics, often with an assumption that noisy inputs are uncorrelated. Here we show that long-range temporal correlations and spatial correlations in neural inputs generated by multiple interacting bumps cause them to drift in an anomalous subdiffusive way. This mechanism for generating subdiffusive dynamics of bump attractors is further analyzed based on a generalized Langevin equation. We demonstrate that subdiffusive dynamics can significantly improve the coding accuracy of bump attractors, since the variance of the bump displacement increases sublinearly over time and is much smaller than that of normal diffusion. Furthermore, we reanalyze existing psychophysical data concerning the spread of recalled cue position in spatial working memory tasks and show that its variance increases sublinearly with time, consistent with subdiffusive dynamics of bump attractors. Based on the probability density function of bump position, we also show that the subdiffusive dynamics result in a long-tailed decay of firing rate, greatly extending the duration of persistent activity.

Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ⁹-tetrahydrocannabinol administration

BACKGROUND

Multifractal analysis quantifies the time-scale-invariant properties in data by describing the structure of variability over time. By applying this analysis to hippocampal interspike interval sequences recorded during performance of a working memory task, a measure of long-range temporal correlations and multifractal dynamics can reveal single neuron correlates of information processing.

NEW METHOD

Wavelet leaders-based multifractal analysis (WLMA) was applied to hippocampal interspike intervals recorded during a working memory task. WLMA can be used to identify neurons likely to exhibit information processing relevant to operation of brain-computer interfaces and nonlinear neuronal models.

RESULTS

Neurons involved in memory processing ("Functional Cell Types" or FCTs) showed a greater degree of multifractal firing properties than neurons without task-relevant firing characteristics. In addition, previously unidentified FCTs were revealed because multifractal analysis suggested further functional classification. The cannabinoid type-1 receptor (CB1R) partial agonist, tetrahydrocannabinol (THC), selectively reduced multifractal dynamics in FCT neurons compared to non-FCT neurons.

COMPARISON WITH EXISTING METHODS

WLMA is an objective tool for quantifying the memory-correlated complexity represented by FCTs that reveals additional information compared to classification of FCTs using traditional z-scores to identify neuronal correlates of behavioral events.

CONCLUSION

z-Score-based FCT classification provides limited information about the dynamical range of neuronal activity characterized by WLMA. Increased complexity, as measured with multifractal analysis, may be a marker of functional involvement in memory processing. The level of multifractal attributes can be used to differentially emphasize neural signals to improve computational models and algorithms underlying brain-computer interfaces.

Synaptic dynamics contribute to long-term single neuron response fluctuations

Firing rate variability at the single neuron level is characterized by long-memory processes and complex statistics over a wide range of time scales (from milliseconds up to several hours). Here, we focus on the contribution of non-stationary efficacy of the ensemble of synapses–activated in response to a given stimulus–on single neuron response variability. We present and validate a method tailored for controlled and specific long-term activation of a single cortical neuron in vitro via synaptic or antidromic stimulation, enabling a clear separation between two determinants of neuronal response variability: membrane excitability dynamics vs. synaptic dynamics. Applying this method we show that, within the range of physiological activation frequencies, the synaptic ensemble of a given neuron is a key contributor to the neuronal response variability, long-memory processes and complex statistics observed over extended time scales. Synaptic transmission dynamics impact on response variability in stimulation rates that are substantially lower compared to stimulation rates that drive excitability resources to fluctuate. Implications to network embedded neurons are discussed.

Fano factor estimation

Fano factor is one of the most widely used measures of variability of spike trains. Its standard estimator is the ratio of sample variance to sample mean of spike counts observed in a time window and the quality of the estimator strongly depends on the length of the window. We investigate this dependence under the assumption that the spike train behaves as an equilibrium renewal process. It is shown what characteristics of the spike train have large effect on the estimator bias. Namely, the effect of refractory period is analytically evaluated. Next, we create an approximate asymptotic formula for the mean square error of the estimator, which can also be used to find minimum of the error in estimation from single spike trains. The accuracy of the Fano factor estimator is compared with the accuracy of the estimator based on the squared coefficient of variation. All the results are illustrated for spike trains with gamma and inverse Gaussian probability distributions of interspike intervals. Finally, we discuss possibilities of how to select a suitable observation window for the Fano factor estimation.

Dynamic systems approaches and levels of analysis in the nervous system

Various analyses are applied to physiological signals. While epistemological diversity is necessary to address effects at different levels, there is often a sense of competition between analyses rather than integration. This is evidenced by the differences in the criteria needed to claim understanding in different approaches. In the nervous system, neuronal analyses that attempt to explain network outputs in cellular and synaptic terms are rightly criticized as being insufficient to explain global effects, emergent or otherwise, while higher-level statistical and mathematical analyses can provide quantitative descriptions of outputs but can only hypothesize on their underlying mechanisms. The major gap in neuroscience is arguably our inability to translate what should be seen as complementary effects between levels. We thus ultimately need approaches that allow us to bridge between different spatial and temporal levels. Analytical approaches derived from critical phenomena in the physical sciences are increasingly being applied to physiological systems, including the nervous system, and claim to provide novel insight into physiological mechanisms and opportunities for their control. Analyses of criticality have suggested several important insights that should be considered in cellular analyses. However, there is a mismatch between lower-level neurophysiological approaches and statistical phenomenological analyses that assume that lower-level effects can be abstracted away, which means that these effects are unknown or inaccessible to experimentalists. As a result experimental designs often generate data that is insufficient for analyses of criticality. This review considers the relevance of insights from analyses of criticality to neuronal network analyses, and highlights that to move the analyses forward and close the gap between the theoretical and neurobiological levels, it is necessary to consider that effects at each level are complementary rather than in competition.

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of responses of auditory nerve fibers to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe spiking activity while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of individual auditory nerve fibers that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semianalytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data of response to high and low pulse rate stimulation. We find that the model, although constructed to fit data from single and paired pulse experiments, can accurately predict responses to unmodulated and modulated pulse train stimuli. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.

Fractals in the nervous system: conceptual implications for theoretical neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.

Adaptation reduces spike-count reliability, but not spike-timing precision, of auditory nerve responses

Sensory systems use adaptive coding mechanisms to filter redundant information from the environment to efficiently represent the external world. One such mechanism found in most sensory neurons is rate adaptation, defined as a reduction in firing rate in response to a constant stimulus. In auditory nerve, this form of adaptation is likely mediated by exhaustion of release-ready synaptic vesicles in the cochlear hair cell. To better understand how specific synaptic mechanisms limit neural coding strategies, we examined the trial-to-trial variability of auditory nerve responses during short-term rate-adaptation by measuring spike-timing precision and spike-count reliability. After adaptation, precision remained unchanged, whereas for all but the lowest-frequency fibers, reliability decreased. Modeling statistical properties of the hair cell-afferent fiber synapse suggested that the ability of one or a few vesicles to elicit an action potential reduces the inherent response variability expected from quantal neurotransmitter release, and thereby confers the observed count reliability at sound onset. However, with adaptation, depletion of the readily releasable pool of vesicles diminishes quantal content and antagonizes the postsynaptic enhancement of reliability. These findings imply that during the course of short-term adaptation, coding strategies that employ a rate code are constrained by increased neural noise because of vesicle depletion, whereas those that employ a temporal code are not.

MEG recording from the human ventro-occipital cortex in response to isoluminant color stimulation

In contrast to PET and fMRI studies, color-selective responses from the ventro-occipital area have rarely been reported in MEG studies. We tried to minimize the stimulation to all areas in the visual system except the color-processing ones by using a color space based on psychophysical and physiological knowledge in order to maximize the signal-to-noise ratio for MEG responses from the ventro-occipital area. MEG obtained from long intermittent reversals (2.0–3.5 s) of isoluminant chromatic gratings showed two major peaks at the latencies of approximately 100 and 150 ms. The estimated location of the equivalent-current dipole for response at 100-ms latency was in the calcarine sulcus and that of the dipole for the response at 150 ms was in the collateral sulcus in the ventro-occipital area. The response around 150 ms was uniquely observed in MEG elicited by chromatic reversals. The average of lags between MEG responses from the calcarine sulcus and ventro-occipital area was 43 ms, which suggests sequential processing of color information across the visual cortices.

The spontaneous-rate histogram of the auditory nerve can be explained by only two or three spontaneous rates and long-range dependence

Estimates of the spontaneous discharge rate (SR) of auditory-nerve (AN) fibers are often based on measurements of the average rate over a long (e.g., 30 s) interval. These measurements are important because SR is apparently correlated with other AN properties, such as threshold to acoustic stimuli, shape of rate-level function, recovery from prior stimulation, and certain anatomical characteristics. Furthermore, histograms of SR estimates from large numbers of fibers suggest that they can be divided into two (i.e., low and high) or three (i.e., low, medium, and high) SR classes. Yet, even "simple" statistical estimates, such as average rate, can behave surprisingly poorly for processes with long-range dependence (LRD), which has been found in the spontaneous activity of AN fibers. In particular, LRD greatly increases the variability of estimates of mean discharge rate. We investigated the implications of this effect of LRD for our understanding of the SRs of AN fibers. The fractional-Gaussian-noise-driven Poisson process (fGnDP) was originally developed to model the LRD action-potential trains of AN fibers. Using rate estimates computed from this model, we were able to reproduce the shape of published histograms of SR using only three fixed SR values. Moreover, by using a Poisson-equivalent integrate-and-fire (IF) model in place of the inhomogeneous Poisson process in the fGnDP model, we were able to reproduce SR histograms using only two fixed SR values. These results suggest that AN fibers may have only two or three possible values for their long-term average spontaneous discharge rates. In other words, all "high-SR" neurons may actually have the same underlying SR. Furthermore, both "low-SR" and "medium-SR" neurons may have a single "true" SR value, or these two classes may have two different "true" SR values. Furthermore, the Poisson-equivalent IF model may prove useful in other applications involving the modeling of trains of action potentials.

Including Long-Range Dependence in Integrate-and-Fire Models of the High Interspike-Interval Variability of Cortical Neurons

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (non-Poissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have longrange dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

Binary spiking in auditory cortex

Neurons are often assumed to operate in a highly unreliable manner: a neuron can signal the same stimulus with a variable number of action potentials. However, much of the experimental evidence supporting this view was obtained in the visual cortex. We have, therefore, assessed trial-to-trial variability in the auditory cortex of the rat. To ensure single-unit isolation, we used cell-attached recording. Tone-evoked responses were usually transient, often consisting of, on average, only a single spike per stimulus. Surprisingly, the majority of responses were not just transient, but were also binary, consisting of 0 or 1 action potentials, but not more, in response to each stimulus; several dramatic examples consisted of exactly one spike on 100% of trials, with no trial-to-trial variability in spike count. The variability of such binary responses differs from comparably transient responses recorded in visual cortical areas such as area MT, and represent the lowest trial-to-trial variability mathematically possible for responses of a given firing rate. Our study thus establishes for the first time that transient responses in auditory cortex can be described as a binary process, rather than as a highly variable Poisson process. These results demonstrate that cortical architecture can support a more precise control of spike number than was previously recognized, and they suggest a re-evaluation of models of cortical processing that assume noisiness to be an inevitable feature of cortical codes.

Afferent response parameters derived from postmasker probe-detection thresholds: 'the decay of sensation' revisited

The classical model of forward masking postulates that the detection threshold for a tone probe that follows a stimulus of similar frequency content is elevated relative to the quiet threshold because the probe must evoke a just-detectable increment in a decaying postmasker sensation. That postmasker decay is charted by probe-detection thresholds if the sensation increment is small and constant. This model was examined for a 2-kHz Gaussian-shaped probe and a 2-kHz forward masker, based on the model's assumption that a just-detectable increment in sensation results from a just-detectable increment in level. Psychometric functions for detection were obtained at 2.5-30 ms postmasker. Their means and standard deviations generally decreased with delay. It was assumed that standard deviation is related to the putative just-detectable level increment by a simple monotonic transformation. Thus, if the standard deviation of the psychometric function for probe detection is neither small nor constant, then the corresponding just-detectable increment in level is neither small nor constant, and the just-detectable increment in sensation is neither small nor constant. The classical model also fails to allow for the variability of internal events. The concept of detection threshold as a sensation increment was preserved in a Signal Detection model, that does allow for internal variability. In this model the postmasker residual is the input to a probe detector. The new model produces an equation for the just-detectable level increment as a function of probe delay. Comparison data were generated by again assuming some relation between the standard deviation of the psychometric function for detection, and the just-detectable increment in level. The fit of equation to data yields robust values for the probe detector's maximum firing rate, dynamic range, and spike-counting time. All that is required to account for the decay of sensation, for a pure tone, is a single neuron operating at some higher center.

Representational accuracy of stochastic neural populations

Fisher information is used to analyze the accuracy with which a neural population encodes D stimulus features. It turns out that the form of response variability has a major impact on the encoding capacity and therefore plays an important role in the selection of an appropriate neural model. In particular, in the presence of baseline firing, the reconstruction error rapidly increases with D in the case of Poissonian noise but not for additive noise. The existence of limited-range correlations of the type found in cortical tissue yields a saturation of the Fisher information content as a function of the population size only for an additive noise model. We also show that random variability in the correlation coefficient within a neural population, as found empirically, considerably improves the average encoding quality. Finally, the representational accuracy of populations with inhomogeneous tuning properties, either with variability in the tuning widths or fragmented into specialized subpopulations, is superior to the case of identical and radially symmetric tuning curves usually considered in the literature.

Nonrenewal statistics of electrosensory afferent spike trains: implications for the detection of weak sensory signals

The ability of an animal to detect weak sensory signals is limited, in part, by statistical fluctuations in the spike activity of sensory afferent nerve fibers. In weakly electric fish, probability coding (P-type) electrosensory afferents encode amplitude modulations of the fish's self-generated electric field and provide information necessary for electrolocation. This study characterizes the statistical properties of baseline spike activity in P-type afferents of the brown ghost knifefish, Apteronotus leptorhynchus. Short-term variability, as measured by the interspike interval (ISI) distribution, is moderately high with a mean ISI coefficient of variation of 44%. Analysis of spike train variability on longer time scales, however, reveals a remarkable degree of regularity. The regularizing effect is maximal for time scales on the order of a few hundred milliseconds, which matches functionally relevant time scales for natural behaviors such as prey detection. Using high-order interval analysis, count analysis, and Markov-order analysis we demonstrate that the observed regularization is associated with memory effects in the ISI sequence which arise from an underlying nonrenewal process. In most cases, a Markov process of at least fourth-order was required to adequately describe the dependencies. Using an ideal observer paradigm, we illustrate how regularization of the spike train can significantly improve detection performance for weak signals. This study emphasizes the importance of characterizing spike train variability on multiple time scales, particularly when considering limits on the detectability of weak sensory signals.

A new method to determine a fractal dimension of non-stationary biological time-serial data

We devised a new analysis using quartile deviation of integrated and subtracted fluctuation, termed QIS-A, to determine a fractal dimension of non-stationary fluctuation. In the algorithm, computations of the quartile deviation, Q(n), of all integrated and subtracted fluctuations are repeated over all scales (n). The fractal scaling exponent is determined as a slope of the line relating log Q(n) to log n. Comparison of the QIS-A and a spectral analysis using 20 computer-simulated fractional Brownian motions demonstrates robustness of the QIS-A to non-stationary fluctuations.

Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex

Although motion-sensitive neurons in macaque middle temporal (MT) area are conventionally characterized using stimuli whose velocity remains constant for 1-3 s, many ecologically relevant stimuli change on a shorter time scale (30-300 ms). We compared neuronal responses to conventional (constant-velocity) and time-varying stimuli in alert primates. The responses to both stimulus ensembles were well described as rate-modulated Poisson processes but with very high precision (approximately 3 ms) modulation functions underlying the time-varying responses. Information-theoretic analysis revealed that the responses encoded only approximately 1 bit/s about constant-velocity stimuli but up to 29 bits/s about the time-varying stimuli. Analysis of local field potentials revealed that part of the residual response variability arose from "noise" sources extrinsic to the neuron. Our results demonstrate that extrastriate neurons in alert primates can encode the fine temporal structure of visual stimuli.

Refractoriness and neural precision

The response of a spiking neuron to a stimulus is often characterized by its time-varying firing rate, estimated from a histogram of spike times. If the cell's firing probability in each small time interval depends only on this firing rate, one predicts a highly variable response to repeated trials, whereas many neurons show much greater fidelity. Furthermore, the neuronal membrane is refractory immediately after a spike, so that the firing probability depends not only on the stimulus but also on the preceding spike train. To connect these observations, we investigated the relationship between the refractory period of a neuron and its firing precision. The light response of retinal ganglion cells was modeled as probabilistic firing combined with a refractory period: the instantaneous firing rate is the product of a "free firing rate, " which depends only on the stimulus, and a "recovery function," which depends only on the time since the last spike. This recovery function vanishes for an absolute refractory period and then gradually increases to unity. In simulations, longer refractory periods were found to make the response more reproducible, eventually matching the precision of measured spike trains. Refractoriness, although often thought to limit the performance of neurons, may in fact benefit neuronal reliability. The underlying free firing rate derived by allowing for the refractory period often exceeded the observed firing rate by an order of magnitude and was found to convey information about the stimulus over a much wider dynamic range. Thus, the free firing rate may be the preferred variable for describing the response of a spiking neuron.

Fractal timing of verbal transforms

The paper deals with the timing pattern of perceptual change elicited by multiple repetitions of a syllable (the verbal-transformation effect). We show that the distribution of the dwell time, the time spent perceiving a given phonemic form before switching to another form, obeys a power law with an exponent valued between 1 and 2. This result is robust, occurring for meaningless syllables and for English words of different initial phonemic salience. Experiment 2 demonstrates that subjects are aware of the temporal dynamics of perceptual change. On the basis of these results, it is argued that within this paradigm the notion of a mean dwell time is ill defined and there is apparently no characteristic time scale for perceptual change.

Quantal neurotransmitter secretion rate exhibits fractal behavior

The rate of exocytic events from both neurons and non-neuronal cells exhibits fluctuations consistent with fractal (self-similar) behavior in time, as evidenced by a number of statistical measures. We explicitly demonstrate this for neurotransmitter secretion at Xenopus neuromuscular junctions and for rat hippocampal synapses in culture; the exocytosis of exogenously supplied neurotransmitter from cultured Xenopus myocytes and from rat fibroblasts behaves similarly. The magnitude of the fluctuations of the rate of exocytic events about the mean decreases slowly as the rate is computed over longer and longer time periods, the periodogram decreases in power-law manner with frequency, and the Allan factor (relative variance of the number of exocytic events) increases as a power-law function of the counting time. These features are hallmarks of self-similar behavior. Their description requires models that exhibit long-range correlation (memory) in event occurrences. We have developed a physiologically plausible model that accords with all of the statistical measures that we have examined. The appearance of fractal behavior at synapses, as well as in systems comprising collections of synapses, indicates that such behavior is ubiquitous in neural signaling.

Fractal character of the neural spike train in the visual system of the cat

We used a variety of statistical measures to identify the point process that describes the maintained discharge of retinal ganglion cells (RGC's) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, the Fano factor, Allan factor, and the periodogram. In addition, we applied these measures to surrogate versions of the data, generated by random shuffling of the order of interevent intervals. The continuing statistics reveal 1/f-type fluctuations in the data (long-duration power-law correlation), which are not present in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indicating that the fractal behavior either is transmitted form one cell to the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, describes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We present a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well.

General relation between variance-time curve and power spectral density for point processes exhibiting 1/f beta-fluctuations, with special reference to heart rate variability

Counting statistics in the form of the variance-time curve provides an alternative to spectral analysis for point processes exhibiting 1/f beta-fluctuations, such as the heart beat. However, this is true only for beta < 1. Here, the case of general beta is considered. To that end, the mathematical relation between the variance-time curve and power spectral density in the presence of 1/f beta-noise is worked out in detail. A modified version of the variance-time curve is presented, which allows us to deal also with the case beta > or = 1. Some applications to the analysis of heart rate variability are given.

Measurement of temporal regularity of spike train responses in auditory nerve fibers of the green treefrog

This paper describes a method which we have developed for quantifying the temporal regularity of neural spike trains in the sensory nervous system. Our method relies on the use of a modified correlation approach for identifying response firing patterns. We apply the concept of an ambiguity function and related coefficients to measure the tonic/phase character and statistical variability of spike patterns. We tested this method in recordings from auditory nerve fibers of the green treefrog (Hyla cinerea) in response to pure tone, multi-tone, and gaussian white noise. Our results indicate that there is a great deal of variability in the trains of spike times generated by any given fiber in response to identically repeated stimulus presentations. Nevertheless, despite this statistical jitter of the pattern to repetitive stimulation, the spike response trains from a single fiber maintain a high degree of individual detectability in signal metric space. The procedures in our method can be implemented in a relatively simple way on a Macintosh computer and the speed is fast enough for real-time spike analysis. This kind of quantification may especially be useful in studying habituation and plasticity in neural spike train data, as well as in judging the selectivity within the neural code of an individual fiber for particular stimulus features.

A nonstationary Poisson point process describes the sequence of action potentials over long time scales in lateral-superior-olive auditory neurons

The behavior of lateral-superior-olive (LSO) auditory neurons over large time scales was investigated. Of particular interest was the determination as to whether LSO neurons exhibit the same type of fractal behavior as that observed in primary VIII-nerve auditory neurons. It has been suggested that this fractal behavior, apparent on long time scales, may play a role in optimally coding natural sounds. We found that a nonfractal model, the nonstationary dead-time-modified Poisson point process (DTMP), describes the LSO firing patterns well for time scales greater than a few tens of milliseconds, a region where the specific details of refractoriness are unimportant. The rate is given by the sum of two decaying exponential functions. The process is completely specified by the initial values and time constants of the two exponentials and by the dead-time relation. Specific measures of the firing patterns investigated were the interspike-interval (ISI) histogram, the Fano-factor time curve (FFC), and the serial count correlation coefficient (SCC) with the number of action potentials in successive counting times serving as the random variable. For all the data sets we examined, the latter portion of the recording was well approximated by a single exponential rate function since the initial exponential portion rapidly decreases to a negligible value. Analytical expressions available for the statistics of a DTMP with a single exponential rate function can therefore be used for this portion of the data. Good agreement was obtained among the analytical results, the computer simulation, and the experimental data on time scales where the details of refractoriness are insignificant.(ABSTRACT TRUNCATED AT 250 WORDS)

Discharge-rate dependence of refractory behavior of cat auditory-nerve fibers

A descriptive model for auditory-nerve (AN) refractory periods is described. The model assumes that interspike intervals consist of a constant-length absolute refractory period (ARP), followed by random-length relative refractory period (RRP) and a random-length waiting time to the next spike. Both the RRP and waiting time are exponentially distributed. This model fits AN hazard functions sufficiently well to provide estimates of the ARP and RRP durations for each fiber. The ARP is found to be constant, independent of discharge rate, with mean value between 0.56 and 0.86 ms in data from 7 experiments. The RRP decreases in duration as discharge rate increases; RRP mean length is less than 2 ms in most cases. There is an additional, slow component of recovery, lasting 20-40 ms, which is not modeled. The variation in RRP with discharge rate is shown to be capable of accounting for the deviation of AN regularity from that predicted for a Poisson process. Finally, properties of peaks seen in hazard functions just at the end of the ARP are described; these peaks are not included in the model, but are shown to be especially prominent in low and medium spontaneous rate fibers.

Sensitization and multiplicative noise in the descending contralateral movement detector (DCMD) of the locust

Spike discharges from the descending contralateral movement detector (DCMD) were recorded extracellularly from the ventral nerve cord of the locust in complete darkness, in response to dim flashes of constant-intensity light, and in response to pairs of identical flashes presented different intervals apart. Three phenomena were discovered: novel long-term sensitization which changes the DCMD's sensitivity to light, a multiplicative cascade process driven by shot events, and the suppression of the spike discharge shortly after a dim flash. The DCMD's spike discharge is stochastic. It can be considered as a two-stage cascade process producing intrinsic multiplicative noise. An effective photon, or thermal isomerization in complete darkness, produces an unseen shot event which in turn initiates a random number of DCMD spikes in a cluster. A short initiates a variable number of spikes when it directs the rate of a Poisson process. The results of statistical analyses are consistent with this model when the amplitudes of shot events are variable. The transmission efficiency is low because at least 2.4-9.6 quantum bumps are required to produce one extra DCMD spike. The DCMD has a constant mean discharge rate of 0.25-1.5 spikes/s in complete darkness. Clustering about particular points in time (shots) leads to a lack of independence between interspike intervals, and the overdispersion of interspike interval and number distributions compared with those from a simple Poisson process. The mean cluster size is 1.3-1.6 spikes in darkness. Similar clustering was found in response to flashes of light. A dim flash changes the DCMD's sensitivity to light, even at threshold when no spike discharge results. Sensitization occurs because the average number of shot events produced by isoquantal flashes depends on the history of visual stimulation. This contributes to the nonlinear response-intensity function. The evolution of sensitization is roughly constant in different DCMD cells, lasting approximately 3 s after a flash. Sensitization was observed in response to light only, presumably because the intensity of dark-light is too low. It is proposed that sensitization is associated with a set of processes or molecular state in the presynaptic region of a chemical synapse.

Further study on 1/f fluctuations observed in central single neurons during REM sleep

Recently, 1/f fluctuations have been discovered in the single-unit activity of mesencephalic reticular formation (MRF) neurons during REM sleep. In a previous paper, such behavior could satisfyingly be interpreted on the basis of the clustering Poisson process. The question of applicability of this model to other MRF neurons remained unanswered. The present paper reports on 1/f fluctuations in 12 MRF neurons all of which can satisfyingly be modeled by the clustering Poisson process.

Toward a Noncomputational Cognitive Neuroscience

The near universally accepted theory that the brain processes information persists in current neural network theory where there is "subsymbolic" computation (Smolensky, 1988) on distributed representations. This theory of brain information processing may suffice for simplifying models simulated in silicon but not for living neural nets where there is ongoing chemical tuning of the input/output transfer function at the nodes, connection weights, network parameters, and connectivity. Here the brain continually changes itself as it intersects with information from the outside. An alternative theory to information processing is developed in which the brain permits and supports "participation" of self and other as constraints on the dynamically evolving, self-organizing whole. The noncomputational process of "differing and deferring" in nonlinear dynamic neural systems is contrasted with Black's (1991) account of molecular information processing. State hyperspace for the noncomputational process of nonlinear dynamical systems, unlike classical systems, has a fractal dimension. The noncomputational model is supported by suggestive evidence for fractal properties of the brain.