Neuronal Interspike Intervals Research Articles

Bifurcation and negative self-feedback mechanisms for enhanced spike-timing precision of inhibitory interneurons

<abstract> <p>A high spike-timing precision characterized by a small variation in interspike intervals of neurons is important for information processing in various brain functions. An experimental study on fast-spiking interneurons has shown that inhibitory autapses functioning as negative self-feedback can enhance spike-timing precision. In the present paper, bifurcation and negative self-feedback mechanisms for the enhanced spike-timing precision to stochastic modulations are obtained in two theoretical models, presenting theoretical explanations to the experimental finding. For stochastic spikes near both the saddle-node bifurcation on an invariant cycle (SNIC) and the subcritical Hopf (SubH) bifurcation with classes 1 and 2 excitabilities, respectively, enhanced spike-timing precision appears in large ranges of the conductance and the decaying rate of inhibitory autapses, closely matching the experimental observation. The inhibitory autaptic current reduces the membrane potential after a spike to a level lower than that in the absence of inhibitory autapses and the threshold to evoke the next spike, making it more difficult for stochastic modulations to affect spike timings, and thereby enhancing spike-timing precision. In addition, firing frequency near the SubH bifurcation is more robust than that near the SNIC bifurcation, resulting in a higher spike-timing precision for the SubH bifurcation. The bifurcation and negative self-feedback mechanisms for the enhanced spike-timing precision present potential measures to modulate the neuronal dynamics or the autaptic parameters to adjust the spike-timing precision.</p> </abstract>

Noise induces continuous and noncontinuous transitions in neuronal interspike intervals range

Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to model firing patterns of neurons subject to noise. In this work, we consider perturbing noise in the adaptive exponential integrate-and-fire (AEIF) neuron. The AEIF is a two- dimensional model that describes different neuronal firing patterns by varying its parameters. Noise is added in the equation related to the membrane potential. We show that a noise current can induce continuous and noncontinuous transitions in neuronal interspike intervals. Moreover, we show that the noncontinuous transition occurs mainly for parameters close to the border between tonic spiking and burst activities of the neuron without noise

Synchronous behaviour in network model based on human cortico-cortical connections

Objective: We consider a network topology according to the cortico-cortical connection network of the human brain, where each cortical area is composed of a random network of adaptive exponential integrate-and-fire neurons. Approach: Depending on the parameters, this neuron model can exhibit spike or burst patterns. As a diagnostic tool to identify spike and burst patterns we utilise the coefficient of variation of the neuronal inter-spike interval. Main results: In our neuronal network, we verify the existence of spike and burst synchronisation in different cortical areas. Significance: Our simulations show that the network arrangement, i.e. its rich-club organisation, plays an important role in the transition of the areas from desynchronous to synchronous behaviours.

Distribution of transition times in a stochastic model of excitable cell: Insights into the cell-intrinsic mechanisms of randomness in neuronal interspike intervals.

In this paper, we develop an analytical approach to studying random patterns of activity in excitable cells. Our analytical approach uses a two-state stochastic model of excitable system based on the electrophysiological properties of refractoriness and restitution, which characterize cell recovery after excitation. By applying the notion of probability density flux, we derive the distributions of transition times between states and the distribution of interspike interval (ISI) durations for a constant applied stimulus. The derived ISI distribution is unimodal and, provided that the time spent in the excited state is constant, can be approximated by a Rayleigh peak followed by an exponential tail. We then explore the role of the model parameters in determining the shape of the derived distributions and the ISI coefficient of variation. Finally, we use our analytical results to study simulation results from the stochastic Morris-Lecar neuron and from a three-state extension of the proposed stochastic model, which is capable of reproducing multimodal ISI histograms.

Dynamic Properties of Purkinje Cells Having Different Electrophysiological Parameters: a Model Study

Simple spikes and complex spikes are two distinguishing features in neurons of the cerebellar cortex; the motor learning and memory processes are dependent on these firing patterns. In our research, the detailed firing behaviors of Purkinje cells were investigated using a computer compartmental neuronal model. By means of application of numerical stimuli, the abundant dynamical properties involved in the multifarious firing patterns (such as the Max-Min potentials of each spike and period-adding/perioddoubling bifurcations) appeared. Neuronal interspike interval (ISI) diagrams, frequency diagrams, and current-voltage diagrams for different ions were plotted. Finally, Poincare mapping was used as a theoretical method to markedly distinguish timing of the above firing patterns. Our simulation results indicated that firing of Purkinje cells varies dynamically depending on different electrophysiological parameters of these neurons, and the respective properties may play significant roles in the formation of the mentioned characteristics of dynamical firings in the coding strategy for information processing and learning.

On the Continuous Differentiability of Inter-Spike Intervals of Synaptically Connected Cortical Spiking Neurons in a Neuronal Network

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.

A unified description of cerebellar inter-spike interval distributions and variabilities using summation of Gaussians

Neuronal inter-spike intervals (ISIs) have previously been described as Poisson, Gamma, inverse Gaussian or other unimodal distributions. We analyzed ISIs of rhythmic and arrhythmic neuronal spike trains in cerebellum recorded from freely behaving rats, and found that their distributions can be described as the summation or integration of multiple Gaussian distributions. The ISIs of rhythmic cerebellar Purkinje cells have a main Gaussian peak at a basic firing interval and exponentially reduced peaks at multiples of this firing period. ISIs of arrhythmic Purkinje cells can be modeled as the integration of multiple Gaussian distributions centered at continuous intervals with exponentially reduced peak amplitudes. The sources of variability are directly related to the relative timing of action potentials between neighboring cells since we show that irregularities of discharge in one cell are associated with the previous history of its discharge in time relative to another cell. Through relative phase analyses, we demonstrate that the shape and the mathematical form of the ISI distributions in cerebellum are direct result of dynamic interactions in the nearby neuronal network, in addition to intrinsic firing properties. The analysis in this paper provides a unified description of cerebellar inter-spike interval distributions which deviate from the usual Poisson assumptions. Our results suggest the existence of an intrinsic rhythmicity in cells exhibiting arrhythmic spike trains in cerebellum, and may identify an important source of variability in neuronal firing patterns that is relevant to the mechanism of neural computation in cerebellum.

Optimal Signal Estimation in Neuronal Models

We study optimal estimation of a signal in parametric neuronal models on the basis of interspike interval data. Fisher information is the inverse asymptotic variance of the best estimator. Its dependence on the parameter value indicates accuracy of estimation. Our models assume that the input signal is estimated from neuronal output interspike interval data where the frequency transfer function is sigmoidal. If the coefficient of variation of the interspike interval is constant with respect to the signal, the Fisher information is unimodal, and its maximum for the most estimable signal can be found. We obtain a general result and compare the signal producing maximal Fisher information with the inflection point of the sigmoidal transfer function in several basic neuronal models.

Decreased neuronal burst discharge near site of seizure onset in epileptic human temporal lobes.

We examined auto-correlation and interval distribution characteristics of neuronal discharge from patients with complex partial seizures. The objective was to compare the interictal firing patterns of neurons in mesial temporal structures ipsilateral to the site of seizure onset with firing patterns of neurons in homologous contralateral structures. Spontaneous interictal recordings of 258 single neurons were acquired from 23 patients. A "burst area" measure was derived from the neuronal auto-correlation to assess the likelihood of grouped action potential discharge (burst discharge). Large burst area measures indicate a tendency for single neuronal burst discharge, but do not disclose information about interspike intervals within bursts. Although several measures based on single neuronal interspike interval distributions showed no overall difference between hemispheres, burst area was significantly reduced in mesial temporal structures ipsilateral to the site of seizure onset. Possible mechanisms of decreased burst discharge in epileptogenic regions include selective loss of burst-discharging neurons and increased recurrent inhibition.

A method of neuronal spike train study based on autoregressive analysis

The method of autoregressive (AR) analysis for neuronal spike trains (NST) is proposed in the paper. The AR model and the Green's function as well as the power spectral density function are used to process and analyse the neuronal interspike interval (ISI) sequences of cat's first somatosensory area of cortex (SI area) under various situations. With these methods the characteristics of the ISI sequence such as the AR order and parameters, memory property, correlativity and periodicity etc. can be extracted.

Reflection of plasticity of two monosynaptically interconnected neurons in the statistical characteristics of their spike discharge

1. Principles governing a change in cross-correlation histograms (CCH) of spike trains of monosynaptically interconnected neurons, and values calculated from the principal peak for troughs of CCH were investigated by methods of mathematical and biomathematical models of neuronal interaction to assess the degree of dependence between spike trains due to the action of direct and reciprocal connections, in the presence of changes in the efficiency of interneuronal connections and excitability of the neurons and of the action of independent random afferent synaptic inflows on them. 2. The amplitude of the principal peak (trough) of the normalized CCH of the spike trains of monosynaptically interconnected neurons increases both with an increase in amplitude of the corresponding excitatory (inhibitory) postsynaptic potential and with an increase in the mean interspike interval of any neuron, due to a decrease in the range of random exogenous oscillations of its membrane potential or elevation of its thresholds of spike generation. The increase in amplitudes of the principal peak of the CCH has a limit determined by the minimal of the average interspike intervals of the interconnected neurons. 3. It is impossible to establish the true physiological cause of the modification of CCH of the spike trains of monosynaptically interconnected neurons purely from the character of that modification observed in the course of the experiment. The character of changes in the mean interspike intervals of the test neurons must also be taken into account. 4. An increase in amplitude of the principal peak or trough of the normalized CCH of the spike trains of the neurons, accompanied by reduction of their mean interspike intervals, is an unambiguous sign of an increase in the efficiency of a monosynaptic excitatory or inhibitory connection between neurons, i.e., an increase in the amplitude of the corresponding excitatory (or inhibitory) postsynaptic potential.

A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions

We consider the classic Stein (1965) model for stochastic neuronal firing under random synaptic input. Our treatment includes the additional effect of synaptic reversal potentials. We develop and employ two numerical methods (in addition to Monte Carlo simulations) to study the relation of the various parameters of the model to the shape of the theoretical interspike interval distribution. Contrary to the results of Tuckwell (1979) we are unable to account, on the basis of substantial synaptic inhibition and with parameter settings in the known physiologic range, for experimental interspike interval distributions which exhibit large coefficients of variation or bimodality. We therefore introduce a time varying threshold into the model, which readily allows for such distributions and which has physiological justification.

Serial dependencies and markov properties of neuronal interspike intervals from rat cerebellum

Using three different approaches, each with different theoretical assumptions, we showed that mammalian neuronal spike trains contain serial ordering. We demonstrated that: (1) when intervals are categorized according to whether their durations are short, medium, or long, sequential groupings of adjacent interval categories exhibit Markov dependencies, extending to at least the 4th order; (2) the observed incidence of specified patterns of these groups of adjacent interval categories differs from the independent case, based on Chi square goodness-of-fit tests, and by using similar procedures; (3) there is divergence from independence when adjacent interval patterns are described in terms of relative lengths of adjacent intervals. The statistical indicators of serial dependence were significantly greater when applied to the original data than when applied to the same data after shuffling. Each of these approaches leads to the notion that “information” is carried in clusters of adjacent intervals (“bytes” or “words”) and moreover, we can identify which specific patterns of interspike intervals contribute most to the statistical significance (i.e., those clusters that are potential candidates for “information carriers”). In most of the ten neurons, the “memory” of the system appears to be at least 36–45 msecs.

Single neuron sequential interspike intervals: Measurement, teleprocessing, and analysis

Successive neuronal interspike intervals (ISI) were measured sequentially. Code numbers, each one characteristic of an experimental manipulation, were added to the measured ISI. The resulting file was sent automatically through MODEM and telephone to an UNIVAC 1110 computer by way of a microprocessor system. The UNIVAC computer was programmed to extract each code number from the ISI file and to create a descriptive index by use of a set of questions to the experimenter, each one depending on the code number encountered in the ISI file. Each element of the descriptive index contained, as pointer, the address of the very ISI where the manipulation started or ended. From these data, a classical spike rate versus time diagram as well as a sequential probability density function were computed and some spike train characteristics were automatically estimated from an autocorrelogram and a serial correlogram. An example is given to illustrate the results obtained with the system.

A comparison of two techniques for analyzing neuronal interspike intervals: Autocorrelation and relative interval coding

Only two theoretical approaches for serial order analysis of spike trains seem to be practical and to preserve a degree of the sequential ordering of the intervals. We herein compared these approaches, employing the two common techniques for autocorrelation and a group of relative interval coding techniques, using 4 short, idealized trains of spike intervals. The relative interval coding approach seemed to be more sensitive for accurately specifying and analyzing serial order. The autocorrelation methods create ambiguity because of inherent “partitioning” effects in the computation and because the interrelations among peaks in the correlogram can be deceptive.

Higher-order patterns of neuronal interspike intervals (trigrams and quadgrams) analyzed as self-adjusting sets of ratios.

The present study proposes a new technique designed to disclose patterns of intervals, and which allows to make probabilistic statements about sequential arrangement of three, four and five intervals. It discloses patterns of intervals since it reduces the number of possible relationships between sequential intervals to only three alternatives by assuming that the first interval in a sequential pair can be either smaller than, equal to or larger than the second interval. The rationale of this technique is based on the assumption that information is carried by discrete patterns rather than statistical parameters such as the mean, standard deviation, etc., a contention strongly supported by experimental evidence.

A technique that discloses complex (sequential) multiphasic patterns in trains of increasing or decreasing neuronal interspike intervals

As the first step in correlating the output of single neurons with changes in the grass behavior of the organism or with changes in the electroencephalogram, we developed a technique that discloses complex, multiphasic patterns of increasing or decreasing neuronal interspike intervals. These sequential patterns are composed of as many as 15 intervals. The basic component of the patterns consisted of simple biphasic patterns that have been previously correlated with changes in the electroencephalogram that were produced by I.V. injection of 7–10 mg. pentobarbital.

The differential spectrum of neuronal interspike intervals: a one-dimensional analysis of sequential relationships

The differential spectrum of neuronal interspike intervals: a one-dimensional analysis of sequential relationships

The Interdependence Series Matrix; A Method for Determining the Serial Dependence of Neuronal Interspike Intervals

In the present study we propose a new technique of analysis of neuronal interspike intervals which we termed the interdependence series matrix. This method is based on the concept of serial correlation, and gives an estimate of the relationship between a particular interval and an interval that is removed from it by a fixed number of other intervals specified by a particular lag value.

A new analysis of neuronal interspike intervals based on inequality tests.

In an attempt to define patterns in the output of a neuron in the central nervous system, an inequality test for differences in the width of adjacent pairs of interspike intervals was performed using a digital computer. The results of the tests, whether the first interval was longer (+), shorter (-), or the same duration (0) as the second, were arranged into a conditional probability matrix which showed the sequential relationships between three adjacent intervals. The probabilities can be denned as the transition probabilities for an output of a neuron going from one state to another. Significant diagram patterns emerged.