A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

Cerebellar Nuclear Neurons Use Time and Rate Coding to Transmit Purkinje Neuron Pauses

Neurons of the cerebellar nuclei convey the final output of the cerebellum to their targets in various parts of the brain. Within the cerebellum their direct upstream connections originate from inhibitory Purkinje neurons. Purkinje neurons have a complex firing pattern of regular spikes interrupted by intermittent pauses of variable length. How can the cerebellar nucleus process this complex input pattern? In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. Pause beginning synchronization produced a unique effect on nuclei neuron firing, while the effect of pause ending and pause overlapping synchronization could not be distinguished from each other. Pause beginning synchronization produced better time-locking of nuclear neurons for short length pauses. We also characterize the effect of pause length and spike jitter on the nuclear neuron firing. Additionally, we find that the rate of rebound responses in nuclear neurons after a synchronous pause is controlled by the firing rate of Purkinje neurons preceding it.     

The chronotron: a neuron that learns to fire temporally precise spike patterns

In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that provides high memory capacity (E-learning), and one that has a higher biological plausibility (I-learning). With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.     

Role of microstructure of nerve impulse train in relation to transmission of neuronal activity and coding mechanism of neural information

Input-output relation were of giant neurons of a marine mollusc, Onchidium verruculatum, and a computer-simulated neuron investigated in terms of microstructure of nerve impulse train. The microstructure of input impulse train, the size of a unitary EPSP, and the extent of spontaneous firing activity of a single neuron had an important influence upon the effective summation of arriving synaptic inputs, the elicitation of output spikes, and intervals between succeeding output spikes. The neuron responded differently to respective input trains with different time structures, i.e. it discriminated input time pattern to various degrees. The manner in discrimination of input time pattern was dependent on the size of the unitary EPSP and the extent of the spontaneous firing activity, if it had. Some discussions were made with regard to possible coding systems of neural signal, assuming a frequency code and/or a pattern code.     

Search for cerebral G cluster neurons responding to taste stimulation with seaweed in Aplysia kurodai by the use of calcium imaging

The calcium imaging method can detect the spike activities of many neurons simultaneously. In the present experiments, this method was used to search for unique neurons contributing to feeding behavior in the cerebral ganglia of Aplysia kurodai. We mainly explored the neurons whose cell bodies were located in the G cluster and the neuropile region posterior to this cluster on the ventral surface of the cerebral ganglia. When the extract of the food seaweed Ulva was applied to the tentacle-lip region, many neurons stained with a calcium-sensitive dye, Calcium Green-1, showed changes in fluorescence. Some neurons showed rhythmic responses and others showed transient responses, suggesting that these neurons may be partly involved in the feeding circuits. We also identified three motor neurons among these neurons that showed rhythmic fluorescence responses to the taste stimulation. One of them was a motor neuron shortening the anterior tentacle (ATS), and the other two were motor neurons producing lip opening-like (LO(G)) and closing-like (LC(G)) movements, respectively. Application of the Ulva extract to the tentacle-lip region induced phase-locked rhythmic firing activity in these motor neurons, suggesting that these neurons may contribute to the rhythmic patterned movements of the anterior tentacles and lips during the ingestion of seaweed.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Phase-of-firing coding of natural visual stimuli in primary visual cortex

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.     

Intracellular responses of antennal chordotonal sensilla of the American cockroach

The responses of mechanoreceptor neurons in the antennal chordotonal organ have been examined in cockroaches by intracellular recording methods. The chordotonal organ was mechanically stimulated by sinusoidal movement of the flagellum. Stimulus frequencies were varied between 0.5 and 150 Hz. Receptor neurons responded with spike discharges to mechanical stimulation, and were classed into two groups from plots of their average spike frequencies against stimulus frequency. Neurons in one group responded to stimulation over a wide frequency range (from 0.5 to 150 Hz), whereas those in a second group were tuned to higher frequency stimuli. The peak stimulus frequency at which receptor neurons showed maximum responses differed from cell to cell. Some had a peak response at a stimulus frequency given in the present study (from 0.5 to 150 Hz), whereas others were assumed to have peak responses beyond the highest stimulus frequency examined. The timing for the initiation of spikes or of a burst of spikes plotted against each stimulus cycle revealed that spike generation was phase-locked in most cells. Some cells showed phase-independent discharges to stimulation at lower frequency, but increasing stimulus frequencies spike initiation began to assemble at a given phase of the stimulus cycle. The response patterns observed are discussed in relation to the primary process of mechanoreception of the chordotonal organ.     

Mechanisms of firing patterns in fast-spiking cortical interneurons

Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na(+), delayed-rectifier K(+), and slowly inactivating d-type K(+) conductances. The model is analyzed using nonlinear dynamical system theory. For small Na(+) window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, gd, and it is delayed for larger gd. As gd further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na(+) window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na(+) window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction.     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

The Limited Utility of Multiunit Data in Differentiating Neuronal Population Activity

To date, single neuron recordings remain the gold standard for monitoring the activity of neuronal populations. Since obtaining single neuron recordings is not always possible, high frequency or ‘multiunit activity’ (MUA) is often used as a surrogate. Although MUA recordings allow one to monitor the activity of a large number of neurons, they do not allow identification of specific neuronal subtypes, the knowledge of which is often critical for understanding electrophysiological processes. Here, we explored whether prior knowledge of the single unit waveform of specific neuron types is sufficient to permit the use of MUA to monitor and distinguish differential activity of individual neuron types. We used an experimental and modeling approach to determine if components of the MUA can monitor medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs) in the mouse dorsal striatum. We demonstrate that when well-isolated spikes are recorded, the MUA at frequencies greater than 100Hz is correlated with single unit spiking, highly dependent on the waveform of each neuron type, and accurately reflects the timing and spectral signature of each neuron. However, in the absence of well-isolated spikes (the norm in most MUA recordings), the MUA did not typically contain sufficient information to permit accurate prediction of the respective population activity of MSNs and FSIs. Thus, even under ideal conditions for the MUA to reliably predict the moment-to-moment activity of specific local neuronal ensembles, knowledge of the spike waveform of the underlying neuronal populations is necessary, but not sufficient.     

Increased noise level of purkinje cell activities minimizes impact of their modulation during sensorimotor control

While firing rate is well established as a relevant parameter for encoding information exchanged between neurons, the significance of other parameters is more conjectural. Here, we show that regularity of neuronal spike activities affects sensorimotor processing in tottering mutants, which suffer from a mutation in P/Q-type voltage-gated calcium channels. While the modulation amplitude of the simple spike firing rate of their floccular Purkinje cells during optokinetic stimulation is indistinguishable from that of wild-types, the regularity of their firing is markedly disrupted. The gain and phase values of tottering's compensatory eye movements are indistinguishable from those of flocculectomized wild-types or from totterings with the flocculus treated with P/Q-type calcium channel blockers. Moreover, normal eye movements can be evoked in tottering when the flocculus is electrically stimulated with regular spike trains mimicking the firing pattern of normal simple spikes. This study demonstrates the importance of regularity of firing in Purkinje cells for neuronal information processing.     

Firing properties of substantia nigra dopaminergic neurons in freely moving rats

Single unit recordings were obtained from putative dopaminergic neurons in the substantia nigra of awake, freely moving rats. The cells exhibited waveforms, range of firing rates and types of firing patterns identical to those of identified DA neurons of anesthetized or paralyzed rats. Two firing patterns were observed: single spike activity and a bursting mode with spikes of progressively diminished amplitude and increased duration within each burst. The degree of burst firing varied considerably among the cells and individual cells sometimes switched from one pattern of firing (e.g. predominantly single spike) to another (e.g. bursting), although the determinants of these transitions are, at this time, unclear. Putative DA neurons were inhibited by i.v. apomorphine and excited by i.v. haloperidol. Haloperidol also reversed the apomorphine-induced inhibition of firing. Inhibitions and excitations were associated with a reduction and elevation, respectively, in burst firing. The effects of the two drugs were identical to their effects in immobilized rats. In several cases, a putative DA neuron was observed to fire all of its spikes in near coincidence with at least one other cell with identical electrophysiological characteristics. This form of interaction (i.e. presumed electrical coupling) between DA cells is only rarely observed in anesthetized or paralyzed rats and may play a significant role in the normal functioning of the nigrostriatal DA system.     

Predictive Coding of Dynamical Variables in Balanced Spiking Networks

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.     

Analysis of bursting in a thalamic neuron model

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgkin-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a–c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes. Received: 18 July 1993/Accepted in revised form: 22 January 1994     

Spike tranfer in statistical neuron assemblies. II. Neuron--nonlinear spike source]

The mathematical model of the neuron function is known to rely on space summing of excitement. The spikes contribute to the inner state of the neuron the farther from cell soma the synapses are located. The difference between excitatory and inhibitory effect results in spike firing if only neural firing threshold is achieved. The values of spike flux have been estimated on the basis of the model of CA3 sector of the Hippocampus and were found to be 15 divided by 35 imp/s.     

Modulation of a feeding neural circuit by microinjection of K+ channel expression genes into a single identified neuron in Aplysia kurodai

In Aplysia buccal ganglion expression genes for voltage-dependent K(+) channels (AKv1.1a) were injected into one of four electrically coupled multi-action (MA) neurons that directly inhibit jaw-closing (JC) motor neurons and may cooperatively generate their firing pattern during the feeding response. Following the DNA injection, the firing threshold increased and the spike frequency at the same current decreased in the current-induced excitation of the MA neuron; indicating a decrease in excitability of the MA neuron. This procedure also reduced the firing activity of MA neurons during the feeding-like rhythmic responses induced by the electrical nerve stimulation. Moreover, the firing pattern in JC motor neurons was remarkably changed, suggesting the effective contribution of a single MA neuron or electrically coupled MA neurons to the generation of the firing pattern in the JC motor neurons. This method appears useful for exploring the functional roles of specific neurons in complex neural circuits.     

The effects of temperature on signalling in ocellar neurons of the desert locust, <Emphasis Type="Italic">Schistocerca gregaria</Emphasis>

In Schistocerca gregaria ocellar pathways, large second-order L-neurons use graded potentials to communicate signals from the ocellar retina to third-order neurons in the protocerebrum. A third-order neuron, DNI, converts graded potentials into axonal spikes that have been shown in experiments at room temperature to be sparse and precisely timed. I investigated effects of temperature changes that a locust normally experiences on these signals. With increased temperature, response latency decreases and frequency responses of the neurons increase. Both the graded potential responses in the two types of neuron and the spikes in DNI report greater detail about a fluctuating light stimulus. Over a rise from 22 to 35°C the power spectrum of the L-neuron response encompasses higher frequencies and its information capacity increases from about 600 to 1,700 bits/s. DNI generates spikes more often during a repeated stimulus but at all temperatures it reports rapid decreases in light rather than providing a continual measure of light intensity. Information rate carried by spike trains increases from about 50 to 185 bits/s. At warmer temperatures, increased performance by ocellar interneurons may contribute to improved aerobatic performance by delivering spikes earlier and in response to smaller, faster light stimuli.     

Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability

The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.     

The effect of neural adaptation on population coding accuracy

Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.