Interspike Interval Research Articles

Temporal Correlates to Monaural Edge Pitch in the Distribution of Interspike Interval Statistics in the Auditory Nerve.

Pitch is a perceptual attribute enabling perception of melody. There is no consensus regarding the fundamental nature of pitch and its underlying neural code. A stimulus which has received much interest in psychophysical and computational studies is noise with a sharp spectral edge. High-pass (HP) or low-pass (LP) noise gives rise to a pitch near the edge frequency (monaural edge pitch; MEP). The simplicity of this stimulus, combined with its spectral and autocorrelation properties, make it an interesting stimulus to examine spectral versus temporal cues that could underly its pitch. We recorded responses of single auditory nerve (AN) fibers in chinchilla to MEP-stimuli varying in edge frequency. Temporal cues were examined with shuffled autocorrelogram (SAC) analysis. Correspondence between the population’s dominant interspike interval and reported pitch estimates was poor. A fuller analysis of the population interspike interval distribution, which incorporates not only the dominant but all intervals, results in good matches with behavioral results, but not for the entire range of edge frequencies that generates pitch. Finally, we also examined temporal structure over a slower time scale, intermediate between average firing rate and interspike intervals, by studying the SAC envelope. We found that, in response to a given MEP stimulus, this feature also systematically varies with edge frequency, across fibers with different characteristic frequency (CF). Because neural mechanisms to extract envelope cues are well established, and because this cue is not limited by coding of stimulus fine-structure, this newly identified slower temporal cue is a more plausible basis for pitch than cues based on fine-structure.

Frontal Cortex Neuron Type Classification with Deep Learning and Recurrence Plot

One of the goals of neural decoding in neuroscience is to create Brain-Computer Interfaces (BCI) that use nerve signals. In this context, we are interested in the activity of nerve cells. It is possible to classify nerve cells as excitatory or inhibitors by evaluating individual extra-cellular measurements taken from the frontal cortex of rats. Classification of neurons with only spike timing values has not been studied before, with deep learning, without knowing all of the wave properties and the intercellular interactions. In this study, inter-spike interval values of individual neuronal spike sequences were converted into recurrence plot images to analyze as point processing, image features were extracted using the pre-trained AlexNet with CNN deep learning method, and frontal cortex nerve cell type classification was made. Kernel classification, SVM, Naive Bayes, Ensemble, decision trees classification methods were used. The accuracy, sensitivity and specificity evaluate the proposed methods. A success of more than 81% has been achieved. Thus, the cell type is defined automatically. It has been observed that the ISI properties of spike trains can carry out information on cell type and thus neural network activity. Under these circumstances, these values are significant and important for neuroscientists.

Proposal of phase noise and jitter reduction in a long-ring hybrid silicon mode-locked laser by intracavity reflectors.

We propose a harmonically hybrid silicon mode-locked ring laser using intracavity reflectors (ICRs) to suppress supermode noise. The dynamic and noise properties of the structure are investigated using a delay differential equation model. The results of the dynamic show that a 20 GHz harmonic regime of the structure is significantly increased compared to a without intracavity-reflector structure. Additionally, the phase noise of the proposed structure (PS) is improved to about 8 dB. Furthermore, an analysis shows that timing jitter reduction has periodic behavior by changing the harmonic inter-spike interval time (TISI).

Models of stochastic hbox {Ca}^{2+} spiking

Complexity and limited knowledge render it impractical to write down the equations describing a cellular system completely. Cellular biophysics uses hypotheses-based modelling instead. How can we set up models with predictive power beyond the experimental examples used to develop them? The two textbook systems of cellular biophysics, hbox {Ca}^{2+} signalling and neuronal membrane potential dynamics, both face this question. Both systems also have a non-equilibrium feature in common: on different time scales and for different observables, they exhibit stochastic spiking, i.e., sequences of stereotypical events that are separated by statistically distributed intervals, the interspike intervals (ISI). Here we review recent progress on the description of hbox {Ca}^{2+} spikes in terms of blips, puffs and cellular hbox {Ca}^{2+} spikes and focus on stochastic models that can explain the statistics of the single ISIs, in particular its mean and variance and the cell-to-cell variability of these statistics. We also review models of the stochastic integrate-and-fire type and measures like the spike-train power spectrum or the serial correlation coefficient that are used to describe neuronal spike trains. These concepts from computational neuroscience might be applicable for understanding long-term memory effects in hbox {Ca}^{2+} spiking that extend beyond a single ISI, such as cumulative refractoriness.

Variability and Randomness of the Instantaneous Firing Rate.

The apparent stochastic nature of neuronal activity significantly affects the reliability of neuronal coding. To quantify the encountered fluctuations, both in neural data and simulations, the notions of variability and randomness of inter-spike intervals have been proposed and studied. In this article we focus on the concept of the instantaneous firing rate, which is also based on the spike timing. We use several classical statistical models of neuronal activity and we study the corresponding probability distributions of the instantaneous firing rate. To characterize the firing rate variability and randomness under different spiking regimes, we use different indices of statistical dispersion. We find that the relationship between the variability of interspike intervals and the instantaneous firing rate is not straightforward in general. Counter-intuitively, an increase in the randomness (based on entropy) of spike times may either decrease or increase the randomness of instantaneous firing rate, in dependence on the neuronal firing model. Finally, we apply our methods to experimental data, establishing that instantaneous rate analysis can indeed provide additional information about the spiking activity.

Dynamical robustness and firing modes in multilayer memristive neural networks of nonidentical neurons

On the basis of Hindmarsh-Rose neuron model, dynamical robustness and the transition of firing modes of multilayer memristive neural network consisting of nonidentical neurons have been investigated in detail. The dynamic effects of memristive synapses coupling which are either cubic order flux or quadratic flux are detected. Our results suggest that for the cubic order flux-controlled memristors increasing electromagnetic induction parameter and parameter of memristor show the tendency to spoil the dynamical robustness of the multilayer memristive neural network. For quadratic flux-controlled memristors, weak electromagnetic induction can spoil the dynamical robustness while strong electromagnetic induction and parameter of memristor have little influence on dynamical robustness. We found that the ratio of inactive neurons switches the firing patterns of the active neuron among periodic bursting, chaotic bursting and spiking-like. In the case of memristive synapse coupling by cubic order flux-controlled memristors, chaotic bursting alternates with period bursting as the ratio of inactive neurons is increased, and the chaotic bursting occupy a large range of the ratio of inactive neurons. In the case of memristive synapse coupling by quadratic flux-controlled memristors, the main firing pattern of the active neuron is chaotic bursting. The distribution of interspike interval can be broadly classified into two groups: those that are long interspike intervals and those that are short interspike intervals. The dynamics of multilayer memristive neural network is also verified in the circuits built on Multisim. These results could give new mechanism explanation for aging transition by applying electromagnetic field to neural network.

Statistical moments of the interspike intervals for a neuron model driven by trichotomous noise.

The influence of a colored three-level input noise (trichotomous noise) on the spike generation of a perfect integrate-and-fire (PIF) model of neurons is studied. Using a first-passage-time formulation, exact expressions for the Laplace transform of the output interspike interval (ISI) density and for the statistical moments of the ISIs (such as the coefficient of variation, the skewness, the serial correlation coefficient, and the Fano factor) are derived. To model the anomalous subdiffusion that can arise from, e.g., the trapping properties of dendritic spines, the model is extended by including a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, and exact formulas for ISI statistics are given for this case as well. Particularly, it is shown that at some parameter regimes, the ISI density exhibits a three-modal structure. The results for the extended model show that the ISI serial correlation coefficient and the Fano factor are nonmonotonic with respect to the input current, which indicates that at an intermediate value of the input current the variability of the output spike trains is minimal. Similarities and differences between the behavior of the presented models and the previously investigated PIF models driven by dichotomous noise are also discussed.

Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding.

Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in the membrane of a nerve cell provides an important example. The contributions of independent noise sources to the variability of action potential timing have not previously been studied at the level of molecular transitions within a conductance-based model ion-state graph. Here we study a stochastic Langevin model for the Hodgkin-Huxley (HH) system based on a detailed representation of the underlying channel state Markov process, the "[Formula: see text]D model" introduced in (Pu and Thomas in Neural Computation 32(10):1775-1835, 2020). We show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean return time (MRT) phase reduction developed in (Cao et al. in SIAM JApplMath 80(1):422-447, 2020) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt and Galán in PhysRevLett 109(11):118101, 2012) from the stationary voltage clamp case to the current clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. Finally, we demonstrate that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike detection threshold. We find a small but significant increase in ISI variance, the higher the spike detection voltage, both for simulated stochastic HH data and for voltage traces recorded in in vitro experiments. In contrast, the IPI variance is invariant with respect to the choice of isochron used as a trigger for counting "spikes."

The length of tibialis anterior does not influence force steadiness during submaximal isometric contractions with the dorsiflexors

ABSTRACT The purpose of the study was to assess the influence of short, intermediate, and long muscle lengths on dorsiflexor force steadiness and the discharge characteristics of motor units in tibialis anterior during submaximal isometric contractions. Steady contractions were performed at 5 target forces (5, 10, 20, 40, and 60% maximal voluntary contraction, MVC) for 3 ankle angles (75°, 90°, and 105°). MVC force was less (p = 0.043) at the smallest joint angle compared with the other two angles. The absolute (standard deviation) and normalised amplitudes (coefficient of variation) of the force fluctuations were similar for all 3 ankle angles at each target force. The coefficient of variation for force decreased progressively from 5% to 20% MVC force and then it plateaued at 40% and 60% MVC force. At all target forces, the mean discharge rate (MDR) of the motor units at 75° was greater than at 90° (p = 0.006) and 105° (p = 0.034). Moreover, the MDR was similar for 5% and 10% MVC forces and then increased gradually until 60% MVC force (p < 0.005). The variability in discharge times (coefficient of variation for interspike interval) and variability in neural drive (coefficient of variation of filtered cumulative spike train) were similar at all ankle angles. Variability in neural drive had a greater influence on force steadiness than did the variability in discharge times. Changes in ankle-joint angle did not influence either the normalised amplitude force fluctuations during steady submaximal contractions or the underlying modulation of the discharge characteristics of motor units in tibialis anterior.

The Effect of Low-Dose Atropine on Alpha Ganglion Cell Signaling in the Mouse Retina.

Low-dose atropine helps to control myopia progression with few side effects. However, the impact of atropine, a non-selective muscarinic Acetylcholine (ACh) receptor antagonist, on retinal ganglion cells (RGCs) remains unclear. After immersing the cornea and adjacent conjunctiva of enucleated eyes in 0.05% (approximately 800 μM) atropine solution for 30 min, the atropine concentration reached in the retina was below 2 μM. After direct superfusion of the retina with 1 μM atropine (considering that the clinical application of 0.05% atropine eye drops will be diluted over time due to tear flow for 30 min), no noticeable changes in the morphology of ON and OFF alpha RGCs (αRGCs) were observed. Atropine affected the light-evoked responses of ON and OFF αRGCs in a dose- and time-dependent fashion. Direct application of less than 100 μM atropine on the retina did not affect light-evoked responses. The time latency of light-induced responses of ON or OFF αRGCs did not change after the application of 0.05–100 μM atropine for 5 min. However, 50 μM atropine extended the threshold of joint inter-spike interval (ISI) distribution of the RGCs. These results indicated that low-dose atropine (<0.5 μM; equal to 1% atropine topical application) did not interfere with spike frequency, the pattern of synchronized firing between OFF αRGCs, or the threshold of joint ISI distribution of αRGCs. The application of atropine unmasked inhibition to induce ON responses from certain OFF RGCs, possibly via the GABAergic pathway, potentially affecting visual information processing.

Kcns3 deficiency disrupts Parvalbumin neuron physiology in mouse prefrontal cortex: Implications for the pathophysiology of schizophrenia

The unique fast spiking (FS) phenotype of cortical parvalbumin-positive (PV) neurons depends on the expression of multiple subtypes of voltage-gated potassium channels (Kv). PV neurons selectively express Kcns3, the gene encoding Kv9.3 subunits, suggesting that Kcns3 expression is critical for the FS phenotype. KCNS3 expression is lower in PV neurons in the neocortex of subjects with schizophrenia, but the effects of this alteration are unclear, because Kv9.3 subunit function is poorly understood. Therefore, to assess the role of Kv9.3 subunits in PV neuron function, we combined gene expression analyses, computational modeling, and electrophysiology in acute slices from the cortex of Kcns3-deficient mice.Kcns3 mRNA levels were ~ 50% lower in cortical PV neurons from Kcns3-deficient relative to wildtype mice. While silent per se, Kv9.3 subunits are believed to amplify the Kv2.1 current in Kv2.1-Kv9.3 channel complexes. Hence, to assess the consequences of reducing Kv9.3 levels, we simulated the effects of decreasing the Kv2.1-mediated current in a computational model. The FS cell model with reduced Kv2.1 produced spike trains with irregular inter-spike intervals, or stuttering, and greater Na+ channel inactivation. As in the computational model, PV basket cells (PVBCs) from Kcns3-deficient mice displayed spike trains with strong stuttering, which depressed PVBC firing. Moreover, Kcns3 deficiency impaired the recruitment of PVBC firing at gamma frequency by stimuli mimicking synaptic input observed during cortical UP states. Our data indicate that Kv9.3 subunits are critical for PVBC physiology and suggest that KCNS3 deficiency in schizophrenia could impair PV neuron firing, possibly contributing to deficits in cortical gamma oscillations in the illness.

A reliability assessment approach for a Hodgkin-Huxley neuron circuit

The performance of the Hodgkin-Huxley neuron circuits used in novel communication and computer systems depends on its capacitors. Thus, degradation of capacitors in neuron circuits may have significant impact on reliability of the neuron. In this paper, a simulation-based reliability assessment approach was developed for a Hodgkin-Huxley neuron circuit to consider the degradation of capacitors. SPICE simulation, neural information coding method, and degradation modelling of capacitors are integrated to assess impact of capacitors on the given neuron circuit. A MOS-based Hodgkin-Huxley neuron circuit is simulated to obtain output waveforms with degraded capacitors. It has been found that the output waveform of the selected neuron changes significantly with capacitors' degradation. In the total operation range of the neuron, degradation of capacitors may result in significant errors and loss of neural information. Capacitor's degradation elevates the duty ratio threshold for generating voltage spikes, and would lead to higher values of the inter-spike interval, regardless of variation of input period and duty cycle. However, by limitation of the input range and duty ration, information carried by S-Space code is transmitted correctly.

A Tantalum Disulfide Charge-Density-Wave Stochastic Artificial Neuron for Emulating Neural Statistical Properties.

Artificial neuronal devices that functionally resemble biological neurons are important toward realizing advanced brain emulation and for building bioinspired electronic systems. In this Communication, the stochastic behaviors of a neuronal oscillator based on the charge-density-wave (CDW) phase transition of a 1T-TaS2 thin film are reported, and the capability of this neuronal oscillator to generate spike trains with statistical features closely matching those of biological neurons is demonstrated. The stochastic behaviors of the neuronal device result from the melt-quench-induced reconfiguration of CDW domains during each oscillation cycle. Owing to the stochasticity, numerous key features of the Hodgkin-Huxley description of neurons can be realized in this compact two-terminal neuronal oscillator. A statistical analysis of the spike train generated by the artificial neuron indicates that it resembles the neurons in the superior olivary complex of a mammalian nervous system, in terms of its interspike interval distribution, the time-correlation of spiking behavior, and its response to acoustic stimuli.

Cues to monaural edge pitch in single auditory nerve fibers

The spectral edge of a bandlimited noise can create a pitch sensation, called “edge pitch,” which is slightly mismatched to the edge frequency. This pitch is usually speculated to reflect neural lateral inhibition but could also reflect temporal cues. We looked for such cues recording responses of single auditory nerve fibers in the anesthetized chinchilla to edge pitch stimuli. For every stimulus, we compute shuffled autocorrelograms for all recorded fibers and pool them in a population interval distribution (PID) from which we obtain the most common interval. We also quantify the slower “envelope” fluctuations in firing resulting from cochlear bandpass filtering of the bandlimited noise stimulus. Single fibers shows systematic temporal changes related to the spectral edge of the stimulus when it does not cover the fiber's frequency filter. Across the population of fibers, the estimated pitch based on the dominant interspike interval shows trends that are similar, qualitatively and quantitatively, to those observed behaviorally. Slower envelope fluctuations also systematically vary with the relationship of edge frequency to fiber CF, and are another potential temporal cue to the presence of the edge frequency. We conclude that temporal cues to edge-pitch are present in the auditory nerve at multiple time scales.

Non-uniform Effects of Nociceptive Stimulation to Motoneurones during Experimental Muscle Pain

Nociceptive stimulation is predicted to uniformly inhibit motoneurone pools of painful muscles and those producing painful movements. Although reduced motoneurone discharge rate during pain provides some evidence, recent data show evidence of increased excitability of some motoneurones. These observations suggest non-uniform effects of nociception on motoneurone excitability. More direct measures are required, but this is difficult to assess as few measures enable in vivo evaluation of motoneurone excitability in humans. We investigated changes in motoneurone excitability during experimental pain using two methods in separate experiments: (i) estimation of the time-course of motoneurone afterhyperpolarization (AHP) from interval death rate analysis of interspike intervals of single motor unit discharge; and (ii) probability of early motoneurone discharge to a descending volley excited using transcranial magnetic stimulation (TMS). Tibialis anterior motor units were recorded with fine-wire electrodes before, during and after painful infusion of 5% hypertonic saline into the muscle. Activation of 17 units (16 participants) could be used for AHP analysis. Data show shortened (n = 11) and lengthened (n = 6) AHP time-course. Increased (n = 6) and decreased (n = 6) probability of early motoneurone discharge were observed in the TMS experiment. These convergent observations suggest non-uniform effects of nociceptive stimulation on motoneurone pools. This does not support the hypothesis that nociceptive input induces uniform inhibition of painful muscle. Instead, interpretation of results implies redistribution of activity between motor units, with possible benefit for unloading painful tissues. This finding supports an interpretation that differs from the generally accepted view in pain physiology regarding adaptation to motor function in pain.

Propagation of spiking regularity in feedforward networks with recurrent connections

The regularity of the inter-spike intervals (ISIs) gives a critical window into how the information is coded temporally in the cortex. Previous researches mostly adopt pure feedforward networks (FFNs) to study how the network structure affects spiking regularity propagation, which ignore the role of local dynamics within the layer. In this paper, we construct an FFN with recurrent connections and investigate the propagation of spiking regularity. We argue that an FFN with recurrent connections serves as a basic circuit to explain that the regularity increases as spikes propagate from middle temporal visual areas to higher cortical areas. We find that the reduction of regularity is related to the decreased complexity of the shared activity co-fluctuations. We show in simulations that there is an appropriate excitation–inhibition ratio maximizing the regularity of deeper layers. Furthermore, it is demonstrated that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight. Our work provides a critical link between cortical circuit structure and realistic spiking regularity.

Inferring phenomenological models of first passage processes.

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.

Phasic Neuronal Firing in the Rodent Nucleus of the Solitary Tract ex vivo.

Phasic pattern of neuronal activity has been previously described in detail for magnocellular vasopressin neurons in the hypothalamic paraventricular and supraoptic nuclei. This characteristic bistable pattern consists of alternating periods of electrical silence and elevated neuronal firing, implicated in neuropeptide release. Here, with the use of multi-electrode array recordings ex vivo, we aimed to study the firing pattern of neurons in the nucleus of the solitary tract (NTS) – the brainstem hub for homeostatic, cardio-vascular, and metabolic processes. Our recordings from the mouse and rat hindbrain slices reveal the phasic activity pattern to be displayed by a subset of neurons in the dorsomedial NTS subjacent to the area postrema (AP), with the inter-spike interval distribution closely resembling that reported for phasic magnocellular vasopressin cells. Additionally, we provide interspecies comparison, showing higher phasic frequency and firing rate of phasic NTS cells in mice compared to rats. Further, we describe daily changes in their firing rate and pattern, peaking at the middle of the night. Last, we reveal these phasic cells to be sensitive to α2 adrenergic receptors activation and to respond to electrical stimulation of the AP. This study provides a comprehensive description of the phasic neuronal activity in the rodent NTS and identifies it as a potential downstream target of the AP noradrenergic system.

A low-cost computational approach to analyze spiking activity in cockroach sensory neurons.

Undergraduates use a spike sorting routine developed in Octave to analyze the spiking activity generated from mechanical stimulation of spines of cockroach legs with the inexpensive SpikerBox amplifier and the free software Audacity. Students learn the procedures involved in handling the cockroaches and recording extracellular action potentials (spikes) with the SpikerBox apparatus as well as the importance of spike sorting for analysis in neuroscience. The spike sorting process requires students to choose the spike threshold and spike selection criteria and interact with the clustering process that forms the groups of similar spikes. Once the spike groups are identified, interspike intervals and neuron firing frequencies can be calculated and analyzed. A classic neurophysiology lab exercise is thus adapted to be interdisciplinary for underrepresented students in a small rural college.

The probability density function of interspike intervals in an FHN model with α-stable noise

In this paper, we expand the paradigmatic Fitzhugh–Nagumo (FHN) model by including α-stable noise and study the firing rate and coherence resonance via probability density function (PDF) of the interspike intervals (ISIs). In the previous work, different indicators and measurements are given to illustrate the firing rate and coherence resonance. However, we find that they can be described simply by the PDF of ISIs, which contains the underlying information of spiking neuron signals. For example, the width of the peak of the PDF of ISIs can characterize the phenomenon of coherence resonance. The narrower width of peak stands for the better coherence resonance.