Interspike Interval Research Articles

Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction

The Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and large amplitudes. In the parametric analysis of the stochastic excitement, we use the analytical method of confidence domains based on the stochastic sensitivity technique. Analyzing a mutual arrangement of the confidence ellipses and separatrices, we estimate the critical intensity of the noise that causes the excitation. The phenomena of stochastic P-bifurcations and coherence resonances are discovered and studied by probability density functions and the statistics of interspike intervals.

Periodicity Pitch Perception Part III: Sensibility and Pachinko Volatility.

Neuromorphic computer models are used to explain sensory perceptions. Auditory models generate cochleagrams, which resemble the spike distributions in the auditory nerve. Neuron ensembles along the auditory pathway transform sensory inputs step by step and at the end pitch is represented in auditory categorical spaces. In two previous articles in the series on periodicity pitch perception an extended auditory model had been successfully used for explaining periodicity pitch proved for various musical instrument generated tones and sung vowels. In this third part in the series the focus is on octopus cells as they are central sensitivity elements in auditory cognition processes. A powerful numerical model had been devised, in which auditory nerve fibers (ANFs) spike events are the inputs, triggering the impulse responses of the octopus cells. Efficient algorithms are developed and demonstrated to explain the behavior of octopus cells with a focus on a simple event-based hardware implementation of a layer of octopus neurons. The main finding is, that an octopus' cell model in a local receptive field fine-tunes to a specific trajectory by a spike-timing-dependent plasticity (STDP) learning rule with synaptic pre-activation and the dendritic back-propagating signal as post condition. Successful learning explains away the teacher and there is thus no need for a temporally precise control of plasticity that distinguishes between learning and retrieval phases. Pitch learning is cascaded: At first octopus cells respond individually by self-adjustment to specific trajectories in their local receptive fields, then unions of octopus cells are collectively learned for pitch discrimination. Pitch estimation by inter-spike intervals is shown exemplary using two input scenarios: a simple sinus tone and a sung vowel. The model evaluation indicates an improvement in pitch estimation on a fixed time-scale.

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.

The nonlinear mechanisms underlying the various stochastic dynamics evoked from different bursting patterns in a neuronal model

The stochastic dynamics such as coherence resonance (CR) and anti-CR show that noise plays constructive roles in the nervous system, which are always evoked from the resting-state or the nearby coexisting behaviors instead of bursting. In the present paper, various stochastic dynamics are evoked from different bursting patterns and the corresponding nonlinear mechanisms are presented. Anti-CR, transition from CR to anti-CR, and non-CR characterized by the coefficient of variation (CV) of interspike intervals are induced by noise from the “Homoclinic/Homoclinic” bursting, “Fold/Big Homoclinic” bursting with quiescent state, and “Fold/Big Homoclinic” bursting with subthreshold oscillations, respectively, which are determined by different stochastic transition regularities between the burst/spike and quiescent state/subthreshold oscillations within the stochastic bursting. The more transitions from spike to subthreshold oscillations to form long duration of subthreshold oscillations evoked by noise near a homoclinic orbit bifurcation, noise-induced more transition from quiescent state to spikes prior to a fold bifurcation, and frequent transitions between spikes and quiescent state are the dominant dynamical mechanisms for the anti-CR, CR, and non-CR, respectively. More detailed causes for the three different stochastic dynamics can be acquired through building relationships between the transitions and the different nonlinear dynamics of the fast subsystem such as the bifurcations, coexisting behaviors, attraction domains, and the distance between the trajectory of bursting and the bifurcation point or border between attraction domains. The comprehensive viewpoint and nonlinear mechanism for the various stochastic dynamics of the different bursting patterns extend the occurrence conditions for the CR or anti-CR and presents modulation measures and potential functions of bursting neurons receiving synaptic noise.

Synchronization mode transitions induced by chaos in modified Morris–Lecar neural systems with weak coupling

Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak electrical and chemical coupling are, respectively, investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period-2 synchronization of the action potential is transformed to desynchronization first, and then to period-3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The corresponding inter-spike interval shows the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period-2 synchronization region in the parameters plane is, while the larger the period-3 synchronization region will be. For the star-coupled neural network, in the presence of weak electrical coupling, it can exhibit the completely synchronized mode, desynchronized mode, and drum head mode under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized mode cannot be observed. Our results might provide novel insights into synchronization modes transition and related biological experiments.

Large coefficient of variation of inter-spike intervals induced by noise current in the resonate-and-fire model neuron.

Neuronal spike variability is a statistical property associated with the noise environment. Considering a linearised Hodgkin-Huxley model, we investigate how large spike variability can be induced in a typical stellate cell when submitted to constant and noise current amplitudes. For low noise current, we observe only periodic firing (active) or silence activities. For intermediate noise values, in addition to only active or inactive periods, we also identify a single transition from an initial spike-train (active) to silence dynamics over time, where the spike variability is low. However, for high noise current, we find intermittent active and silence periods with different values. The spike intervals during active and silent states follow the exponential distribution, which is similar to the Poisson process. For non-maximal noise current, we observe the highest values of inter-spike variability. Our results suggest sub-threshold oscillations as a possible mechanism for the appearance of high spike variability in a single neuron due to noise currents.

Transience of the Retinal Output Is Determined by a Great Variety of Circuit Elements.

Retinal ganglion cells (RGCs) encrypt stimulus features of the visual scene in action potentials and convey them toward higher visual centers in the brain. Although there are many visual features to encode, our recent understanding is that the ~46 different functional subtypes of RGCs in the retina share this task. In this scheme, each RGC subtype establishes a separate, parallel signaling route for a specific visual feature (e.g., contrast, the direction of motion, luminosity), through which information is conveyed. The efficiency of encoding depends on several factors, including signal strength, adaptational levels, and the actual efficacy of the underlying retinal microcircuits. Upon collecting inputs across their respective receptive field, RGCs perform further analysis (e.g., summation, subtraction, weighting) before they generate the final output spike train, which itself is characterized by multiple different features, such as the number of spikes, the inter-spike intervals, response delay, and the rundown time (transience) of the response. These specific kinetic features are essential for target postsynaptic neurons in the brain in order to effectively decode and interpret signals, thereby forming visual perception. We review recent knowledge regarding circuit elements of the mammalian retina that participate in shaping RGC response transience for optimal visual signaling.

Spectrum dependency to rate and spike timing in neuronal spike trains

BackgroundSpike trains are series of interspike intervals in a specific order that can be characterized by their probability distributions and order in time which refer to the concepts of rate and spike timing features. Periodic structure in the spike train can be reflected in oscillatory activities. Thus, there is a direct link between oscillator activities and the spike train. The proposed methods are to investigate the dependency of emerging oscillatory activities to the rate and the spike timing features. MethodFirst, the circular statistics methods were compared to Fast Fourier Transform for best estimation of spectra. Second, two statistical tests were introduced to help make decisions regarding the dependency of spectrum, or individual frequencies, onto rate and spike timing. Third, the methodology is applied to in-vivo recordings of basal ganglia neurons in mouse, primate, and human. Finally, this novel framework is shown to allow the investigation of subsets of spikes contributing to individual oscillators. ResultsUse of circular statistical methods, in comparison to FFT, minimizes spectral leakage. Using virtual spike trains, the Rate versus Timing Dependency Spectrum Test (or RTDs-Test) permits identifying spectral spike trains solely dependent on the rate feature from those that are also dependent on the spike timing feature. Similarly, the Rate versus Timing Dependency Frequency Test (or RTDf-Test), allows to identify individual oscillators with partial dependency on spike timing. Dependency on spike timing was found for all in-vivo recordings but only in few frequencies. The mapping in frequency and time of dependencies showed a dynamical process that may be organizing the basal ganglia function. ConclusionsThe methodology may improve our understanding of the emergence of oscillatory activities and, possibly, the relation between oscillatory activities and circuitry functions.

Coexisting neuronal coding strategies in the barrel cortex.

During tactile sensation by rodents, whisker movements across surfaces generate complex whisker motions, including discrete, transient stick-slip events, which carry information about surface properties. The characteristics of these events and how the brain encodes this tactile information remain enigmatic. We found that cortical neurons show a mixture of synchronized and nontemporally correlated spikes in their tactile responses. Synchronous spikes convey the magnitude of stick-slip events by numerous aspects of temporal coding. These spikes show preferential selectivity for kinetic and kinematic whisker motion. By contrast, asynchronous spikes in each neuron convey the magnitude of stick-slip events by their discharge rates, response probability, and interspike intervals. We further show that the differentiation between these two types of activity is highly dependent on the magnitude of stick-slip events and stimulus and response history. These results suggest that cortical neurons transmit multiple components of tactile information through numerous coding strategies.

Decoding Vagus-Nerve Activity with Carbon Nanotube Sensors in Freely Moving Rodents.

The vagus nerve is the largest autonomic nerve and a major target of stimulation therapies for a wide variety of chronic diseases. However, chronic recording from the vagus nerve has been limited, leading to significant gaps in our understanding of vagus nerve function and therapeutic mechanisms. In this study, we use a carbon nanotube yarn (CNTY) biosensor to chronically record from the vagus nerves of freely moving rats for over 40 continuous hours. Vagal activity was analyzed using a variety of techniques, such as spike sorting, spike-firing rates, and interspike intervals. Many spike-cluster-firing rates were found to correlate with food intake, and the neural-firing rates were used to classify eating and other behaviors. To our knowledge, this is the first chronic recording and decoding of activity in the vagus nerve of freely moving animals enabled by the axon-like properties of the CNTY biosensor in both size and flexibility and provides an important step forward in our ability to understand spontaneous vagus-nerve function.

Human motoneuron firing behavior and single motor unit F-wave

In motor control studies, the F-wave (a recurrent discharge evoked by an axonal antidromic volley) widely used for obtaining information on motoneuron pool behavior. However, such F-wave using is a matter of discussion and still has been not validated experimentally. The aim of the present study was investigation of F-wave properties of single firing motor units (MUs) in healthy humans, the properties, which could give evidence for F-wave origin in motoneuron soma and, therefore, could be used for estimation of a relation between MU firing and motoneuron firing behavior. In total, 91 MUs in five muscles of six healthy subjects, during gentle voluntary contractions, were studied. Peri-stimulus time histograms of single MUs were plotted. None of them revealed statistically significant increasing in MU firing probability at the F-wave latency. Analysis of relationships between characteristics of motoneuron firing behavior (mean firing frequency and target interspike interval duration) and properties of F-waves showed their independence. At the same time, it was found that F-waves were recorded in MUs, whose axons possessed the marked supernormal period in excitability recovery cycle after a discharge. Thus, the present results are in contrast to that which should be expected if the F-wave originated in the motoneuronal soma and could provide evidence for motoneuron firing behavior.

Super-mode noise suppression of a silicon hybrid mode-locked ring laser using a symmetric Fabry–Perot filter

In this research, we propose a harmonically mode-locked hybrid silicon laser by introducing intracavity reflectors (ICRs) to suppress super-mode noise. Using a delay differential equation model, the dynamics, phase noise, and timing jitter of the proposed structure (PS) and the without-ICR structure (WOICRS) are investigated. The simulation results show a significant increase of 20 GHz harmonic regime of PS compared to WOICRS. Additionally, this regime of PS can be achieved at a lower current than WOICRS. The phase noise of the PS is improved to about 8 dB. Given the better selectivity of optical modes in PS, the phase noise is reduced compared to that of with-intracavity structure. Furthermore, numerical results show that timing jitter reduction has periodic behavior by changing the harmonic inter-spike interval time. The analyses demonstrate that harmonic mode-locking of a long cavity laser is a valid strategy for reducing phase noise and timing jitter. The simulation results of WOICRS are in a good agreement with experimental results.

Electrophysiological measures from human iPSC-derived neurons are associated with schizophrenia clinical status and predict individual cognitive performance

Neurons derived from human induced pluripotent stem cells (hiPSCs) have been used to model basic cellular aspects of neuropsychiatric disorders, but the relationship between the emergent phenotypes and the clinical characteristics of donor individuals has been unclear. We analyzed RNA expression and indices of cellular function in hiPSC-derived neural progenitors and cortical neurons generated from 13 individuals with high polygenic risk scores (PRSs) for schizophrenia (SCZ) and a clinical diagnosis of SCZ, along with 15 neurotypical individuals with low PRS. We identified electrophysiological measures in the patient-derived neurons that implicated altered Na+ channel function, action potential interspike interval, and gamma-aminobutyric acid-ergic neurotransmission. Importantly, electrophysiological measures predicted cardinal clinical and cognitive features found in these SCZ patients. The identification of basic neuronal physiological properties related to core clinical characteristics of illness is a potentially critical step in generating leads for novel therapeutics.

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture.

Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

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).

Analysis of Regularized Poisson GLM Spike-Train Modeling

This paper introduces a method for modeling and analyzing neural impulse sequences. In this paper, we define the response value of a scale-independent neuron and construct the correlation graph of the neuron under the response value. The minimum cut algorithm is applied continuously to obtain the maximum group of neurons. According to the characteristics of the firing of neurons, a Poisson-process based model is proposed to mathematically model the neural coding, and the gradient descent method is used to optimize it. Through the modeling analysis method, information such as maximum neuron group and Inter-spike-Interval (ISI) can be effectively analyzed according to neuron impulse sequence.

Reliability‐aware design of temporal neuromorphic encoder for image recognition

AbstractVery large scale integration (VLSI)‐based neuromorphic systems have been evolving quickly in recent years. These systems have been used in complex cognitive tasks such as image classification and pattern recognition. A neuromorphic encoder is an essential component in a neuromorphic system, which converts sensory data into spike trains. The advancement in CMOS technology nodes leads to various reliability issues. Bias temperature instability (BTI) and hot carrier injection (HCI) are major reliability issues in analog/mixed VLSI circuits. This paper implements a temporal neuromorphic encoder, and a corresponding mathematical model is derived for image processing applications. The relationship between an input image pixel value and output of the encoder, that is, interspike interval (ISI), is found to be exponential. The impact of BTI and HCI on the temporal neuromorphic encoder is analyzed. The degradation analysis revealed a loss of encoding functionality for which three mitigation techniques are discussed. Finally, a reliability‐aware neuromorphic encoder is proposed to minimize the effect of degradation over its lifetime. The power consumption of conventional and proposed reliability‐aware neuromorphic encoders is also presented.

Neurophysiological Characterization of Posteromedial Hypothalamus in Anaesthetized Patients.

Deep brain stimulation (DBS) requires a precise localization, which is especially difficult at the hypothalamus, because it is usually performed in anesthetized patients. We aimed to characterize the neurophysiological properties posteromedial hypothalamus (PMH), identified by the best neurophysiological response to electrical stimulation. We obtained microelectrode recordings from four patients with intractable aggressivity operated under general anesthesia. We pooled data from 1.5 mm at PMH, 1.5 mm upper (uPMH) and 1.5 mm lower (lPMH). We analyzed 178 units, characterized by the mean action potential (mAP). Only 11% were negative. We identified the next types of units: P1N1 (30.9%), N1P1N2 (29.8%), P1P2N1 (16.3%), N1P1 and N1N2P1 (6.2%) and P1N1P2 (5.0%). Besides, atypical action potentials (amAP) were recorded in 11.8%. PMH was highly different in cell composition from uPMH and lPMH, exhibiting also a higher percentage of amAP. Different kinds of cells shared similar features for the three hypothalamic regions. Although features for discharge pattern did not show region specificity, the probability mass function of inter-spike interval were different for all the three regions. Comparison of the same kind of mAP with thalamic neurons previously published demonstrate that most of cells are different for derivatives, amplitude and/or duration of repolarization and depolarization phases and also for the first phase, demonstrating a highly specificity for both brain centers. Therefore, the different properties described for PMH can be used to positively refine targeting, even under general anesthesia. Besides, we describe by first time the presence of atypical extracellular action potentials.

Nicotine Exposure during Adolescence Leads to Changes of Synaptic Plasticity and Intrinsic Excitability of Mice Insular Pyramidal Cells at Later Life.

To find satisfactory treatment for nicotine addiction, synaptic and cellular mechanisms should be investigated comprehensively. Synaptic transmission, plasticity and intrinsic excitability in various brain regions are known to be altered by acute nicotine exposure. However, it has not been addressed whether and how nicotine exposure during adolescence alters these synaptic events and intrinsic excitability in the insular cortex in adulthood. To address this question, we performed whole-cell patch-clamp recordings to examine the effects of adolescent nicotine exposure on synaptic transmission, plasticity and intrinsic excitability in layer V pyramidal neurons (PNs) of the mice insular cortex five weeks after the treatment. We found that excitatory synaptic transmission and potentiation were enhanced in these neurons. Following adolescent nicotine exposure, insular layer V PNs displayed enhanced intrinsic excitability, which was reflected in changes in relationship between current strength and spike number, inter-spike interval, spike current threshold and refractory period. In addition, spike-timing precision evaluated by standard deviation of spike timing was decreased following nicotine exposure. Our data indicate that adolescent nicotine exposure enhances synaptic transmission, plasticity and intrinsic excitability in layer V PNs of the mice insular cortex at later life, which might contribute to severe nicotine dependence in adulthood.

Transition from Anti-coherence resonance to coherence resonance for mixed-mode oscillations and period-1 firing of nervous system

Identification of dynamics of the mixed-mode oscillations (MMOs), which exhibit transition between oscillations with large and small amplitudes, is very important for nonlinear physics. In this paper, the MMOs with transition between subthreshold oscillations and spikes are investigated in a neuron model. In the absence of noise, the MMOs appear between the resting state and period-1 firing with increasing depolarization current. After introducing white noise, coherence resonance (CR) is evoked from the resting state and non-CR is induced from period-1 firing far from the MMOs, which is consistent with the traditional viewpoint. However, an interesting result that a transition from anti-CR to CR is evoked by noise from both the MMOs and the period-1 firing near the MMOs is acquired, which is characterized by the increase, decrease and increase again of the coefficient of variations of interspike intervals (ISIs) with increasing noise intensity. At small noise intensity, more subthreshold oscillations are evoked by noise to reduce the firing frequency, resulting in faster increase of standard deviation (SD) of ISIs than that of mean value of ISIs, which is the cause for the anti-CR. The decrease of SD is faster for middle noise intensity and is lower for strong noise intensity, which is the cause for the CR. The different stochastic responses of MMOs and period-1 firing nearby at different levels of noise insanity are the dynamical mechanism for the transition from anti-CR to CR. Such results present potential functions of the MMOs and period-1 firing on information processing in the nervous system with noise and extend the conditions for the CR and anti-CR phenomena, which enriches the contents of nonlinear dynamics.