Interspike Interval Distribution Research Articles

The Cross-Correlation Between Spikes and Local Field Potentials at Different Running Speeds During Entorhinal Cortex Inactivation

Understanding neural spike dynamics and their interaction with local field potentials is crucial for deciphering neural connectivity. This study utilizes data generously shared by Zutshi et al. in 2022 (PMID: 34890566) to investigate spike characteristics and their cross-correlation with local field potentials. Our findings reveal significant shifts in the interspike interval (ISI) distributions during the medial entorhinal cortex (mEC) inactivation, with the instantaneous burst frequency exhibiting an overall decrease and preference for lower frequencies. These differences in the spike distributions were observed in individual cells, accompanied by changes in mean firing rates. Further exploration of the cross-correlation between spike multiunit activity (MUA) and the theta rhythm uncovers distinct coupling patterns. In the control cases, spikes closely align with theta peaks, whereas this alignment is disrupted during the mEC inactivation. Notably, we find that the strength of this cross-correlation is amplified at higher running speeds. This research enhances our understanding of neural dynamics, shedding light on the intricate relationship between spikes, local field potentials, and running speed, with potential implications for neural connectivity studies. R01MH126236 1R01MH109548-01A1. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Stochasticity in the synchronization of strongly coupled spiking oscillators

Synchronization of electrical oscillators is a crucial step toward practical implementation of oscillator-based and bio-inspired computing. Here, we report the emergence of an unusual stochastic pattern in coupled spiking Mott nanodevices. Although a moderate capacitive coupling results in a deterministic alternating spiking, increasing the coupling strength leads counterintuitively to stochastic disruptions of the alternating spiking sequence. The disruptions of the deterministic spiking sequence are a direct consequence of the small intrinsic stochasticity in electrical triggering of the insulator–metal transition. Although the stochasticity is subtle in individual nanodevices, it becomes dramatically enhanced just in a single pair of coupled oscillators and, thus, dominates the synchronization. This is different from the stochasticity and multimodal coupling, appearing due to collective effects in large oscillator networks. The stochastic spiking pattern in Mott nanodevices results in a discrete inter-spike interval distribution resembling those in biological neurons. Our results advance the understanding of the emergent synchronization properties in spiking oscillators and provide a platform for hardware-level implementation of probabilistic computing and biologically plausible electronic devices.

The Effects of Insulin on Spike Activity of the Suprachiasmatic Nucleus Neurones and Functional State of Afferent Inputs from the Arcuate Nucleus in Rats

In experiments on the sagittal hypothalamic slices of male Wistar rats, the effects of 15 nM insulin on the level of spike activity, parameters of spike information coding by the suprachiasmatic nucleus neurones, and functional state of afferent inputs to the neurones from the arcuate nucleus were studied. Application of insulin induced a decrease in the frequency of action potential generation and an increase in the entropy of interspike interval distribution in 33.3% of neurones recorded; in 12% of cells, the responses of opposite direction were found; in the remaining 54.7% neurones, spike activity did not change. The responses of the entropy of interspike interval distribution suggest the related changes in a degree of interspike interval irregularity induced by insulin. To characterise afferent inputs to the suprachiasmatic nucleus neurones from the arcuate nucleus, electrophysiological technique of the construction and analysis of the peristimulus time histogram (PSTH) was used. Statistically significant responses to the stimulation of the arcuate nucleus were recorded in 24 of 38 neurones of the suprachiasmatic nucleus. In 6 of the neurones, the responses were in the form of a short-latency (20 ms) excitation, in 1 neurone in the form of a long-latency excitation, in 6 neurones in the form of a short-latency inhibition; in 11 neurones complex two- or three-phase responses in the form of different compositions of excitation and inhibition were observed. Application of 15 nM insulin induced a qualitative transformation of the responses (disappearing of the initial responses or emergence of new responses) in 5 neurones initially responded to stimulation, and in 1 neurone initially not responded to stimulation of the arcuate nucleus. Statistically significant changes in the latency or duration of the responses in the presence of insulin were not found. The results of the study suggest the ability of insulin to influence the activity level and the spike code of a respectively numerous population of neurones in the suprachiasmatic nucleus circadian oscillator as well as modulate the functional state of afferent inputs to the circadian oscillator from hypothalamic arcuate nucleus playing an important role in the control of appetite and metabolism.

Intermittent chaotic spiking in the van der Pol–FitzHugh–Nagumo system with inertia

The van der Pol–FitzHugh–Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast to the standard 2D van der Pol–FitzHugh–Nagumo model driven by noise, the inter-spike intervals distribution displays a complex arrangement of sharp peaks related to the unstable periodic orbits of the chaotic attractor. For many ranges of parameters controlling the excitability of the system, we observe that chaotic mixed-mode states consist of lapses of nearly regular spiking interleaved by others of highly irregular one. We explore here the emergence of these structures and show their correspondence to the intermittent transitions to chaos. In fact, the average residence times in the nearly-periodic firing state, obey the same scaling law – as a function of the control parameter – than the one at the onset of type I intermittency for dynamical systems in the vicinity of a saddle node bifurcation. We hypothesize that this scenario is also present in a variety of slow-fast neuron models characterized by the coexistence of a two-dimensional fast manifold and a one-dimensional slow one.

Distribution of Interspike Intervals of a Neuron with Inhibitory Autapse Stimulated with a Renewal Process

In this paper, we study analytically the impact of an inhibitory autapse on neuronal activity. In order to do this, we formulate conditions on a set of non-adaptive spiking neuron models with delayed feedback inhibition, instead of considering a particular neuronal model. The neuron is stimulated with a stochastic point renewal process of excitatory impulses. Probability density function (PDF) [Formula: see text] of output interspike intervals (ISIs) of such a neuron is found exactly without any approximations made. It is expressed in terms of ISIs PDF for the input renewal stream and ISIs PDF for that same neuron without any feedback. Obtained results are applied to a subset of neuronal models with threshold 2 when the time intervals between input impulses are distributed according to the Erlang-2 distribution. In that case, we have found explicitly the model-independent initial part of ISIs PDF [Formula: see text] defined at some initial interval [Formula: see text] of ISI values.

Quantitative properties of the creation and activation of a cell-intrinsic duration-encoding engram.

The engram encoding the interval between the conditional stimulus (CS) and the unconditional stimulus (US) in eyeblink conditioning resides within a small population of cerebellar Purkinje cells. CSs activate this engram to produce a pause in the spontaneous firing rate of the cell, which times the CS-conditional blink. We developed a Bayesian algorithm that finds pause onsets and offsets in the records from individual CS-alone trials. We find that the pause consists of a single unusually long interspike interval. Its onset and offset latencies and their trial-to-trial variability are proportional to the CS-US interval. The coefficient of variation (CoV = σ/μ) are comparable to the CoVs for the conditional eye blink. The average trial-to-trial correlation between the onset latencies and the offset latencies is close to 0, implying that the onsets and offsets are mediated by two stochastically independent readings of the engram. The onset of the pause is step-like; there is no decline in firing rate between the onset of the CS and the onset of the pause. A single presynaptic spike volley suffices to trigger the reading of the engram; and the pause parameters are unaffected by subsequent volleys. The Fano factors for trial-to-trial variations in the distribution of interspike intervals within the intertrial intervals indicate pronounced non-stationarity in the endogenous spontaneous spiking rate, on which the CS-triggered firing pause supervenes. These properties of the spontaneous firing and of the engram read out may prove useful in finding the cell-intrinsic, molecular-level structure that encodes the CS-US interval.

Input-output consistency in integrate and fire interconnected neurons

Interspike intervals describe the output of neurons. Signal transmission in a neuronal network implies that the output of some neurons becomes the input of others. The output should reproduce the main features of the input to avoid a distortion when it becomes the input of other neurons, that is input and output should exhibit some sort of consistency. In this paper, we consider the question: how should we mathematically characterize the input in order to get a consistent output? Here we interpret the consistency by requiring the reproducibility of the input tail behaviour of the interspike intervals distributions in the output. Our answer refers to a system of interconnected neurons with stochastic perfect integrate and fire units. In particular, we show that the class of regularly-varying vectors is a possible choice to obtain such consistency. Some further necessary technical hypotheses are added.

Different coding characteristics between flight and freezing in dorsal periaqueductal gray of mice during exposure to innate threats.

Flight and freezing are two vital defensive behaviors that mice display to avoid natural enemies. When they are exposed to innate threats, visual cues are processed and transmitted by the visual system into the emotional nuclei and finally transmitted to the periaqueductal gray (PAG) to induce defensive behaviors. However, how the dorsal PAG (dPAG) encodes the two defensive behaviors is unclear. Multi-array electrodes were implanted in the dPAG nuclei of C57BL/6 mice. Two kinds of visual stimuli (looming and sweeping) were used to induce defensive behaviors in mice. Neural signals under different defense behaviors were recorded, and the encoding characteristics of the two behaviors were extracted and analyzed from spike firing and frequency oscillations. Finally, synchronization of neural activity during the defense process was analyzed. The neural activity between flight and freezing behaviors showed different firing patterns, and the differences in the inter-spike interval distribution were mainly reflected in the 2-10ms period. The frequency band activities under both defensive behaviors were concentrated in the theta band; the active frequency of flight was ~8 to 10Hz, whereas that of freezing behavior was ~6 to 8Hz. The network connection density under both defense behaviors was significantly higher than the period before and after defensive behavior occurred, indicating that there was a high synchronization of neural activity during the defense process. The dPAG nuclei of mice have different coding features between flight and freezing behaviors; during strong looming stimulation, fast neuro-instinctive decision making is required while encountering weak sweeping stimulation, and computable planning late behavior is predicted in the early stage. The frequency band activities under both defensive behaviors were concentrated in the theta band. There was a high synchronization of neural activity during the defense process, which may be a key factor triggering different defensive behaviors.

The Effects of Background Noise on a Biophysical Model of Olfactory Bulb Mitral Cells

The spiking activity of mitral cells (MC) in the olfactory bulb is a key attribute in olfactory sensory information processing to downstream cortical areas. A more detailed understanding of the modulation of MC spike statistics could shed light on mechanistic studies of olfactory bulb circuits and olfactory coding. We study the spike response of a recently developed single-compartment biophysical MC model containing seven known ionic currents and calcium dynamics subject to constant current input with background white noise. We observe rich spiking dynamics even with constant current input, including multimodal peaks in the interspike interval distribution (ISI). Although weak-to-moderate background noise for a fixed current input does not change the firing rate much, the spike dynamics can change dramatically, exhibiting non-monotonic spike variability not commonly observed in standard neuron models. We explain these dynamics with a phenomenological model of the ISI probability density function. Our study clarifies some of the complexities of MC spiking dynamics.

A hybrid artificial neural network for the generation of critical fluctuations and inter-spike intervals

The recently introduced [Contoyiannis et al., 2021] hybrid artificial neural network can simulate the dynamics of membrane potential fluctuations of real neurons based on fundamental principles of Physics. Here, we propose a temporal description of the membrane potential fluctuations, which resembles the soliton solutions in φ4 field theory. Within this framework, kink-antikink dynamics are associated with spike generation. Furthermore, we show that the simulation can also reproduce the distribution of inter-spike intervals of biological neurons in their critical state [Kosmidis et al., 2018]. A proposal for the intermittency origin of these fluctuations is discussed.

Dynamics of a semiconductor laser with feedback and modulation: experiments and model comparison.

We study experimentally and numerically the dynamics of a semiconductor laser near threshold, subject to optical feedback and sinusoidal current modulation. The laser operates in the low frequency fluctuation (LFF) regime where, without modulation, the intensity shows sudden spikes at irregular times. Under particular modulation conditions the spikes lock to the modulation and their timing becomes highly regular. While the modulated LFF dynamics has received a lot of attention, an in-depth comparison with the predictions of the Lang-Kobayashi (LK) model has not yet been performed. Here we use the LK model to simulate the laser dynamics and use the Fano factor to quantify the regularity of the timing of the spikes. The Fano factor is calculated by counting the number of spikes in successive segments of the intensity time-series and keeps information about temporal order in the spike sequence that is lost when the analysis is based on the distribution of inter-spike intervals. Here we compare the spike timing regularity in experimental and in simulated spike sequences as a function of the modulation amplitude and frequency and find a good qualitative agreement. We find that in both experiments and simulation for appropriate conditions the spike timing can be highly regular, as revealed by very small values of the Fano factor.

A Stochastic Leaky-Integrate-and-Fire Neuron Model With Floating Gate-Based Technology for Fast and Accurate Population Coding

An analytical model has been developed for stochastic leaky-integrate-and-fire (LIF) neurons with floating gate (FG) technology. The stochastic behaviors have been modeled extensively for both individual neurons and populations of neurons. In the FG LIF neurons, the electron injection is governed by the tunneling process through the gate oxide, leading to the exponential distributions of the injection time and inter spike interval (ISI) stochasticity. The concept of the population coding is demonstrated by simulating the stochastic behaviors of the populations of the FG LIF neurons. The ISI stochasticity enables encoding of the input signals to the population outputs. Spike-to-spike stochasticity improves the signal-to-noise ratio of the population outputs. Moreover, the shape of the ISI distribution can be controlled by adjusting the number of electrons to spike (NES). Exponential-like ISI distributions are realized by reducing the NES. With the exponential-like ISI distributions, the population of fast spiking neurons increases significantly (more than 10% of neurons spiking twice faster than the mean ISI), potentially contributing to the fast computation. Finally, step-by-step procedures have been proposed to design the FG LIF neurons exhibiting the desired neuron characteristics including operation voltage (0.5 V to 3 V), leaky time constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$( { &lt; } 1~ {\mathrm {\mu }}\text{s}$ </tex-math></inline-formula> to >10 ms), ISI mean (in the range of 6 orders of magnitude) and stochasticity ~0 % to ~60 %) as well as the type of the distribution (exponential-like to Gaussian-like).

Microscopic theory of intrinsic timescales in spiking neural networks

A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including spectra and, correspondingly, autocorrelation times. We develop a theory for self-consistent second-order single-neuron statistics in block-structured sparse random networks of spiking neurons. In particular, the theory predicts the neuron-level autocorrelation times, also known as intrinsic timescales, of the neuronal activity. The theory is based on an extension of dynamic mean-field theory from rate networks to spiking networks, which is validated via simulations. It accounts for both static variability, e.g. due to a distributed number of incoming synapses per neuron, and temporal fluctuations of the input. We apply the theory to balanced random networks of generalized linear model neurons, balanced random networks of leaky integrate-and-fire neurons, and a biologically constrained network of leaky integrate-and-fire neurons. For the generalized linear model network with an error function nonlinearity, a novel analytical solution of the colored noise problem allows us to obtain self-consistent firing rate distributions, single-neuron power spectra, and intrinsic timescales. For the leaky integrate-and-fire networks, we derive an approximate analytical solution of the colored noise problem, based on the Stratonovich approximation of the Wiener-Rice series and a novel analytical solution for the free upcrossing statistics. Again closing the system self-consistently, in the fluctuation-driven regime this approximation yields reliable estimates of the mean firing rate and its variance across neurons, the inter-spike interval distribution, the single-neuron power spectra, and intrinsic timescales.

Changes of discharge properties of neurons from dorsomedial hypothalamic nuclei during aging in rats

The hypothalamus is a vital brain center that is participated in the integration of the endocrine and nervous systems and control of the homeostasis and aging. Spontaneous firing activity from single neurons of the dorsomedial hypothalamic nucleus (DMN) was studied extracellularly in vivo in urethane-anaesthetized rats. The discharge patterns of the majority of DMN neurons were irregular, including periods of relatively stable activity interrupted by pauses. Based on the features of interval interspike histogram, we have selected neurons with an irregular arrhythmic activity (50% in young, 46% in adult and 44% in aged rats), with a constant rhythmic activity (18% of neurons in young, 19% in adult and 23% in aged rats), with a wide interspike interval distribution (22% in young, 26% in adult and 25% in aged rats) and cells with bursts of two or three spikes (10% in young, 9% in adult and 8% in aged rats). The firing rate of DMN neurons was 2.5 ± 0.12 Hz in young and 2.4 ± 0.21 Hz in adult rats and significantly decreased to 1.8 ± 0.17 Hz in aged rats.

Neural burst codes disguised as rate codes

The burst coding hypothesis posits that the occurrence of sudden high-frequency patterns of action potentials constitutes a salient syllable of the neural code. Many neurons, however, do not produce clearly demarcated bursts, an observation invoked to rule out the pervasiveness of this coding scheme across brain areas and cell types. Here we ask how detrimental ambiguous spike patterns, those that are neither clearly bursts nor isolated spikes, are for neuronal information transfer. We addressed this question using information theory and computational simulations. By quantifying how information transmission depends on firing statistics, we found that the information transmitted is not strongly influenced by the presence of clearly demarcated modes in the interspike interval distribution, a feature often used to identify the presence of burst coding. Instead, we found that neurons having unimodal interval distributions were still able to ascribe different meanings to bursts and isolated spikes. In this regime, information transmission depends on dynamical properties of the synapses as well as the length and relative frequency of bursts. Furthermore, we found that common metrics used to quantify burstiness were unable to predict the degree with which bursts could be used to carry information. Our results provide guiding principles for the implementation of coding strategies based on spike-timing patterns, and show that even unimodal firing statistics can be consistent with a bivariate neural code.

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.

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.

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.

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.

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.