Interspike Interval Research Articles

Synchrony of Spontaneous Burst Firing between Retinal Ganglion Cells Across Species.

Neurons communicate with other neurons in response to environmental changes. Their goal is to transmit information to their targets reliably. A burst, which consists of multiple spikes within a short time interval, plays an essential role in enhancing the reliability of information transmission through synapses. In the visual system, retinal ganglion cells (RGCs), the output neurons of the retina, show bursting activity and transmit retinal information to the lateral geniculate neuron of the thalamus. In this study, to extend our interest to the population level, the burstings of multiple RGCs were simultaneously recorded using a multi-channel recording system. As the first step in network analysis, we focused on investigating the pairwise burst correlation between two RGCs. Furthermore, to assess if the population bursting is preserved across species, we compared the synchronized bursting of RGCs between marmoset monkey (callithrix jacchus), one species of the new world monkeys and mouse (C57BL/6J strain). First, monkey RGCs showed a larger number of spikes within a burst, while the inter-spike interval, burst duration, and inter-burst interval were smaller compared with mouse RGCs. Monkey RGCs showed a strong burst synchronization between RGCs, whereas mouse RGCs showed no correlated burst firing. Monkey RGC pairs showed significantly higher burst synchrony and mutual information than mouse RGC pairs did. Comprehensively, through this study, we emphasize that two species have a different bursting activity of RGCs and different burst synchronization suggesting two species have distinctive retinal processing.

Does strict validation criteria for individual motor units alter population-based regression models of the motor unit pool?

The purpose of this study was to determine if the implementation of a strict validation procedure, designed to limit the inclusion of inaccuracies from the decomposition of surface electromyographic (sEMG) signals, affects population-based motor unit (MU) analyses. Four sEMG signals were obtained from the vastus lateralis of 59 participants during isometric contractions at different relative intensities [30%, 70%, and 100% of maximal voluntary contraction (MVC)], and its individual motor unit potential trains (MUPTs) were extracted. The MUPTs were then excluded (ISIval) based on the coefficient of variation and histogram of the interspike intervals (ISI), the absence of additional clusters that reveals missed or additional firings, and more. MU population-based regression models (i.e., modeling the entire motor unit pool) were performed between motor unit potential size (MUPSIZE), mean firing rate (MFR), and recruitment threshold (RT%) separately for DSDCOnly (includes all MUPTs without the additional validation performed) and ISIval data at each contraction intensity. The only significant difference in regression coefficients between DSDCOnly and ISIval was for the intercepts of the MUPSIZE/MFR at 100% MVC. The validation had no other significant effect on any of the other regression coefficients for each of the contraction intensities. Our findings suggest that even though the decomposition of surface signals leads to some inaccuracies, these errors have limited effects on the regression models used to estimate the behavior of the whole pool. Therefore, we propose that motor unit population-based regression models may be robust enough to overcome decomposition-induced errors at the individual MU level.

Contribution of T-Type Calcium Channels to Spinal Cord Injury-Induced Hyperexcitability of Nociceptors.

A hyperexcitable state and spontaneous activity of nociceptors have been suggested to play a critical role in the development of chronic neuropathic pain following spinal cord injury (SCI). In male rats, we employed the action potential-clamp technique to determine the underlying ionic mechanisms responsible for driving SCI-nociceptors to a hyperexcitable state and for triggering their spontaneous activity. We found that the increased activity of low voltage activated T-type calcium channels induced by the injury sustains the bulk (∼60-70%) of the inward current active at subthreshold voltages during the interspike interval in SCI-nociceptors, with a modest contribution (∼10-15%) from tetrodotoxin (TTX)-sensitive and TTX-resistant sodium channels and hyperpolarization-activated cyclic nucleotide-gated (HCN) channels. In current-clamp recordings, inhibition of T-type calcium channels with 1 μm TTA-P2 reduced both the spontaneous and the evoked firing in response to current injections in SCI-nociceptors to a level similar to sham-nociceptors. Electrophysiology in vitro was then combined with the conditioned place preference (CPP) paradigm to determine the relationship between the increased activity of T-type channels in SCI-nociceptors and chronic neuropathic pain following SCI. The size of the interspike T-type calcium current recorded from nociceptors isolated from SCI rats showing TTA-P2-induced CPP (responders) was ∼6 fold greater than the interspike T-type calcium current recorded from nociceptors isolated from SCI rats without TTA-P2-induced CPP (non-responders). Taken together, our data suggest that the increased activity of T-type calcium channels induced by the injury plays a primary role in driving SCI-nociceptors to a hyperexcitable state and contributes to chronic neuropathic pain following SCI.SIGNIFICANCE STATEMENT Chronic neuropathic pain is a major comorbidity of spinal cord injury (SCI), affecting up to 70-80% of patients. Anticonvulsant and tricyclic antidepressant drugs are first line analgesics used to treat SCI-induced neuropathic pain, but their efficacy is very limited. A hyperexcitable state and spontaneous activity of SCI-nociceptors have been proposed as a possible underlying cause for the development of chronic neuropathic pain following SCI. Here, we show that the increased activity of T-type calcium channels induced by the injury plays a major role in driving SCI-nociceptors to a hyperexcitable state and for promoting their spontaneous activity, suggesting that T-type calcium channels may represent a pharmacological target to treat SCI-induced neuropathic pain.

Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons.

The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects and nonstationary responses of the population activity to rapidly changing stimuli. Here we derive low-dimensional firing-rate models for homogeneous populations of neurons modeled as time-dependent renewal processes. The class of renewal neurons includes integrate-and-fire models driven by white noise and has been frequently used to model neuronal refractoriness and spike synchronization dynamics. The derivation is based on an eigenmode expansion of the associated refractory density equation, which generalizes previous spectral methods for Fokker-Planck equations to arbitrary renewal models. We find a simple relation between the eigenvalues characterizing the timescales of the firing rate dynamics and the Laplace transform of the interspike interval density, for which explicit expressions are available for many renewal models. Retaining only the first eigenmode already yields a reliable low-dimensional approximation of the firing-rate dynamics that captures spike synchronization effects and fast transient dynamics at stimulus onset. We explicitly demonstrate the validity of our model for a large homogeneous population of Poisson neurons with absolute refractoriness and other renewal models that admit an explicit analytical calculation of the eigenvalues. The eigenmode expansion presented here provides a systematic framework for alternative firing-rate models in computational neuroscience based on spiking neuron dynamics with refractoriness.

Cocaine memory reactivation induces functional adaptations within parvalbumin interneurons in the rat medial prefrontal cortex.

Substance use disorder is a complex disease created in part by maladaptive learning and memory mechanisms following repeated drug use. Exposure to drug-associated stimuli engages prefrontal cortex circuits, and dysfunction of the medial prefrontal cortex (mPFC) is thought to underlie drug-seeking behaviors. Growing evidence supports a role for parvalbumin containing fast-spiking interneurons (FSI) in modulating prefrontal cortical microcircuit activity by influencing the balance of excitation and inhibition, which can influence learning and memory processes. Most parvalbumin FSIs within layer V of the prelimbic mPFC are surrounded by specialized extracellular matrix structures called perineuronal nets (PNN). Previous work by our group found that cocaine exposure altered PNN-surrounded FSI function, and pharmacological removal of PNNs reduced cocaine-seeking behavior. However, the role of FSIs and associated constituents (parvalbumin and PNNs) in cocaine-related memories was not previously explored and is still unknown. Here, we found that reactivation of a cocaine conditioned place preference memory produced changes in cortical PNN-surrounded parvalbumin FSIs, including decreased parvalbumin intensity, increased parvalbumin cell axis diameter, decreased intrinsic excitability, and increased excitatory synaptic input. Further investigation of intrinsic properties revealed changes in the interspike interval, membrane capacitance, and afterhyperpolarization recovery time. Changes in these specific properties suggest an increase in potassium-mediated currents, which was validated with additional electrophysiological analysis. Collectively, our results indicate that cocaine memory reactivation induces functional adaptations in PNN-surrounded parvalbumin neurons, which likely alters cortical output to promote cocaine-seeking behavior.

Stochastic Spiking-Bursting Excitability and Transition to Chaos in a Discrete-Time Neuron Model

The randomly forced Rulkov neuron model with the discontinuous 2D-map is considered. We study the phenomena of the stochastic excitement: (i) noise-induced spiking in the parametric zone where the equilibrium is a single attractor; (ii) stochastic generation of the spiking in bistability zone; (iii) noise-induced bursting in the parametric zone where the deterministic model exhibits the tonic spiking. These stochastic effects are investigated numerically by means of probability density functions and mean values of interspike (interburst) intervals. For the parametric study of these noise-induced transformations, we suggest an analytical approach taking into account the stochastic sensitivity of attractors and peculiarities of deterministic phase portraits. In this analysis, we study the mutual arrangement of confidence domains and superthreshold zones near deterministic attractors. This approach gives a prediction of the onset of the noise-induced excitement in the form of the transitions quiescence-spiking or spiking-bursting. A relationship of these phenomena with the order-chaos transformations are discussed.

Stochastic sensitivity analysis of volcanic activity

In the present paper, we study the stochastically induced behavior of a nonlinear volcanic model containing three prognostic variables: the plug velocity u, the pressure p under the plug, and the conduit volume V. The nouvelle phenomena of noise‐induced transitions from the equilibrium to the cycle in the bistability parametric zone and noise‐induced excitement with the generation of spike oscillations in the monostability zone are found in the presence of N‐shaped friction force. To study these phenomena numerically, we used the computations of random solutions, the phase trajectories and time series, the statistics of interspike intervals, and the mean square variations. To study these phenomena analytically, we applied the stochastic sensitivity function technique and the confidence domains method. This approach is used to predict the noise‐induced transition from a “dormant volcano” state to the “active volcano” mode. From the physical point of view, the volcano is capable to become active under the influence of external noises in the friction force, which model various compositions and properties of volcanic rocks. What is more, the volcanic plug can pop out when its slipping becomes heavy, and the volcano can erupt.

Distribution of VTA Glutamate and Dopamine Terminals, and their Significance in CA1 Neural Network Activity

Reciprocal connection between the ventral tegmental area (VTA) and the hippocampus forms a loop that controls information entry into long-term memory. Compared with the widely studied VTA dopamine system, VTA glutamate terminals are anatomically dominant in the hippocampus and less understood. The current study employs anterograde and retrograde labeling of VTA dopamine and glutamate neurons to map the distribution of their terminals within the layers of the hippocampus. Also, functional tracing of VTA dopamine and glutamate projections to the hippocampus was performed by photostimulation of VTA cell bodies during CA1 extracellular voltage sampling in vivo. VTA dopamine terminals predominantly innervate the CA1 basal dendrite layer and modulate the firing rate of active putative neurons. In contrast, anatomical dominance of VTA glutamate terminals in the CA1 pyramidal cell and apical dendrite layers suggests the possible involvement of these terminals in excitability regulation. In support of these outcomes, photostimulation of VTA dopamine neurons increased the firing rate but not intrinsic excitability parameters for putative pyramidal units. Conversely, activation of VTA glutamate neurons increased CA1 network firing rate and burst rate. In addition, VTA glutamate inputs reduced the interspike and interburst intervals for putative CA1 neurons. Taken together, we deduced that layer-specific distribution of presynaptic dopamine and glutamate terminals in the hippocampus determinines VTA modulation (dopamine) or regulation (glutamate) of excitability in the CA1 neural network.

Effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise.

The behavior of a stochastic perfect integrate-and-fire (PIF) model of neurons is considered. The effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing Lévy-type subordinator. Using a first-passage-time formulation, we find exact expressions for the output interspike interval (ISI) statistics. Particularly, it is shown that at some parameter regimes the ISI density exhibits a multimodal structure. Moreover, it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current μ, i.e., the ISI's regularity is maximized at an intermediate value of μ. The features of spike statistics, analytically revealed in our study, are compared with previously obtained results for a perfect integrate-and-fire neuron model driven by dichotomous noise (without subordination).

Analysis of temperature-dependent abnormal bursting patterns of neurons in Aplysia.

Temperature affects the firing pattern and electrical activity of neurons in animals, eliciting diverse responses depending on neuronal cell type. However, the mechanisms underlying such diverse responses are not well understood. In the present study, we performed in vitro recording of abdominal ganglia cells of Aplysia juliana, and analyzed their burst firing patterns. We identified atypical bursting patterns dependent on temperature that were totally different from classical bursting patterns observed in R15 neurons of A. juliana. We classified these abnormal bursting patterns into type 1 and type 2; type 1 abnormal single bursts are composed of two kinds of spikes with a long interspike interval (ISI) followed by short ISI regular firing, while type 2 abnormal single bursts are composed of complex multiplets. To investigate the mechanism underlying the temperature dependence of abnormal bursting, we employed simulations using a modified Plant model and determined that the temperature dependence of type 2 abnormal bursting is related to temperature-dependent scaling factors and activation or inactivation of potassium or sodium channels.

Greater fatigability and motor unit discharge variability in human type 2 diabetes.

This study determined the discharge characteristics of motor units from two lower limb muscles before and after fatiguing exercise in people with type 2 diabetes (T2D) with no symptoms of polyneuropathy and activity‐matched controls. Seventeen people with T2D (65.0 ± 5.6 years; 8 women) and 17 controls (63.6 ± 4.5 years; 8 women) performed: (a) intermittent, isometric contractions at 50% maximal voluntary isometric contraction (MVIC) sustained to failure with the ankle dorsiflexors, and (b) a dynamic fatiguing task (30% MVIC load) for 6 min with the knee extensors. Before and after the fatiguing tasks, motor unit characteristics (including coefficient of variation (CV) of interspike intervals (ISI)) were quantified from high‐density electromyography and muscle contractile properties were assessed via electrical stimulation. Fatigability was ~50% greater for people with T2D than controls for the dorsiflexors (time‐to‐failure: 7.3 ± 4.1 vs. 14.3 ± 9.1 min, p = .010) and knee extensors (power reduction: 56.7 ± 11.9 vs. 31.5 ± 25.5%, p < .001). The CV of ISI was greater for the T2D than control group for the tibialis anterior (23.1 ± 11.0 vs. 21.3 ± 10.7%, p < .001) and vastus lateralis (27.8 ± 20.2 vs. 24.5 ± 16.1%, p = .011), but these differences did not change after the fatiguing exercises. People with T2D had greater reductions in the electrically evoked twitch amplitude of the dorsiflexors (8.5 ± 5.1 vs. 4.0 ± 3.4%·min‐1, p = .013) and knee extensors (49.1 ± 10.0 vs. 31.8 ± 15.9%, p = .004) than controls. Although motor unit activity was more variable in people with T2D than controls, the greater fatigability of the T2D group for lower limb muscles was due to mechanisms involving disruption of contractile function of the exercising muscles rather than motor unit behavior.

Evaluation of Frequency-Dependent Effects of Deep Brain Stimulation in a Cortex-Basal Ganglia-Thalamus Network Model of Parkinson's Disease.

Parkinson's disease (PD) is a chronic neurodegenerative disease whose motor symptoms are accompanied by an exaggerated power in the alpha-beta (7-35Hz) band and an increased synchronization of neurons encompassing the cortex-basal ganglia-thalamus network. Currently, deep brain stimulation (DBS) is used as an effective therapy for reducing the excessive power and synchrony observed in brain circuits, thereby ameliorating the PD symptoms. In the present study, we used a biologically plausible computational model of cortex-basal ganglia-thalamus network, which represents both healthy and PD conditions, to systematically investigate the effects of DBS frequency on the model outputs. DBS was applied to the subthalamic nucleus (STN) at different stimulation frequencies (40Hz to 300Hz). Spike train variability and spectral power in the 7-35Hz band were measured from the several nuclei represented in the model. In addition, the magnitude squared coherence between the nuclei was assessed. An increased DBS frequency tended to produce interspike intervals (ISIs) with higher variability as compared to PD condition. Also, DBS significantly reduced the alpha-beta power for almost all brain nuclei. The median of the magnitude-squared coherence matrix (which is a metric of global network synchronization) decreased significantly with the increase of DBS frequency.

Revealing Spectrum Features of Stochastic Neuron Spike Trains

Power spectra of spike trains reveal important properties of neuronal behavior. They exhibit several peaks, whose shape and position depend on applied stimuli and intrinsic biophysical properties, such as input current density and channel noise. The position of the spectral peaks in the frequency domain is not straightforwardly predictable from statistical averages of the interspike intervals, especially when stochastic behavior prevails. In this work, we provide a model for the neuronal power spectrum, obtained from Discrete Fourier Transform and expressed as a series of expected value of sinusoidal terms. The first term of the series allows us to estimate the frequencies of the spectral peaks to a maximum error of a few Hz, and to interpret why they are not harmonics of the first peak frequency. Thus, the simple expression of the proposed power spectral density (PSD) model makes it a powerful interpretative tool of PSD shape, and also useful for neurophysiological studies aimed at extracting information on neuronal behavior from spike train spectra.

Mean-reverting neuronal model based on two alternating patterns

A neuronal action potential model based on the generalised two-state Ornstein–Uhlenbeck process is studied. The model well describes all phases of a neuronal spike cycle, and the intrinsic parameters of the model have clear specification. Laplace transforms of a firing time are obtained explicitly. Formulae for the mean interspike intervals and their variances, as well as for the average duration of the relative refractory period are also obtained.

Realization of artificial synapse and inverter based on oxide electric-double-layer transistor gated by a chitosan biopolymer electrolyte

Low-voltage transparent zinc oxide (ZnO) thin-film transistor with chitosan biopolymer electrolyte as a gate dielectric was fabricated at room temperature and characterized. Due to an electric-double-layer (EDL) effect near the chitosan/ZnO interface through mobile-proton migration, the transistor exhibits a good performance with a carrier mobility of 7.88 cm2 V−1 s−1, a threshold voltage of 1.0 V, an on-off current ratio of 5 × 104, a subthreshold slope of 135 mV Dec−1, and an operating voltage of less than 3 V, respectively. Based on the EDL transistor, the excitatory post-synaptic current and paired-pulse facilitation (PPF) behavior of biological synapses are mimicked, and PPF index is related to the inter-spike interval of the paired pulse. Furthermore, the resistor-loaded inverter based on the transistor was built, showing a high voltage gain of ∼4 at a low supply voltage of 3 V, a small delay, a large noise margin and a low power consumption. The EDL transistor may find potential applications in portable electronics and synaptic electronics.

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

A mathematical model of the biochemical reaction with nonlinear recycling of the product into substrate is considered. The main control parameter of this model is the substrate injection rate, which is subject to random disturbances. We study noise-induced oscillations in the parameter zones where the system is bistable and exhibit a coexistence of the equilibrium and limit cycle, or two stable cycles (birhythmicity). Phenomena of the generation of noisy birhythmicity and ‘stochastic preference’ of attractors are studied on the basis of the stochastic sensitivity function technique, confidence domains method, and statistics of interspike intervals.

Periodicity Pitch Perception.

This study presents a computational model to reproduce the biological dynamics of “listening to music.” A biologically plausible model of periodicity pitch detection is proposed and simulated. Periodicity pitch is computed across a range of the auditory spectrum. Periodicity pitch is detected from subsets of activated auditory nerve fibers (ANFs). These activate connected model octopus cells, which trigger model neurons detecting onsets and offsets; thence model interval-tuned neurons are innervated at the right interval times; and finally, a set of common interval-detecting neurons indicate pitch. Octopus cells rhythmically spike with the pitch periodicity of the sound. Batteries of interval-tuned neurons stopwatch-like measure the inter-spike intervals of the octopus cells by coding interval durations as first spike latencies (FSLs). The FSL-triggered spikes synchronously coincide through a monolayer spiking neural network at the corresponding receiver pitch neurons.

Orexin enhances firing activities in the gigantocellular reticular nucleus through the activation of non-selective cationic conductance

Orexin/hypocretin has been implicated in central motor control. The gigantocellular reticular nucleus (Gi), a key element of the brainstem motor inhibitory system, also receives orexinergic innervations. However, the modulations of orexin on the neuronal activities and the underlying cellular mechanisms in Gi neurons remain unknown. Here, through whole-cell patch-clamp recordings, we first observed that orexin increased the firing frequency in Gi neurons. Interestingly, a postsynaptic depolarization elicited by orexin was observed in the presence of tetrodotoxin, without altering the input resistance of Gi neurons at around −60 mV. Moreover, through comparing the current-frequency curves constructed by identical current injections from equal membrane potentials, we found that orexin also increased the repetitive firing ability of Gi neurons. This action appeared to be caused by the shortening of inter-spike intervals, without altering the waveform of individual action potentials. We finally revealed that activation of the non-selective cationic conductance contributed to the orexin-elicited excitation in Gi neurons. Together, these results suggest that orexin may facilitate Gi-mediated motor functions through enhancing the neuronal activities of Gi neurons.

Spikes and Nets (S&amp;N): A New Fast, Parallel Computing, Point Process Software for Multineuronal Discharge and Connectivity Analysis

SN however, the aim of this work was to develop an easy to use, fast, short learning curve, multi-platform and parallel computing software able to manage a large number of neuronal spike train files to detect discharge patterns, connectivity, and time-dependent changes. A set of the most used spike train methods to perform single and multi-neuronal discharge pattern recognition and functional connectivity analysis were implemented in an easy-to-use, standalone, Matlab-based software toolbox: spikes and nets (S&N). The methods included for single and multi-neuronal discharge pattern analysis are raster plot, interspike intervals distribution, multiparametric burst, auto-correlation, auto-spectral, fractal, poincare, and phases. For functional connectivity analysis, cross-correlation and joint interval scatter diagram were implemented. Additionally, time segmentation analysis is available to detect temporal changes for all methods. S&N efficiently handles large numbers of neuronal discharge files at once with fast and automatic archiving of both analytical and graphical results which makes it suitable for multi-electrode array data. S&N applies up to 11 different analytical methods, including automatic file segmentation for time-dependent changes detection, and generates publication quality graphs. The developed toolbox is multi-platform and reads universal spike train files with any temporal resolution, able to process also ECG, EEG or similar data files.

Neuronal Transmission of Subthreshold Periodic Stimuli Via Symbolic Spike Patterns.

We study how sensory neurons detect and transmit a weak external stimulus. We use the FitzHugh–Nagumo model to simulate the neuronal activity. We consider a sub-threshold stimulus, i.e., the stimulus is below the threshold needed for triggering action potentials (spikes). However, in the presence of noise the neuron that perceives the stimulus fires a sequence of action potentials (a spike train) that carries the stimulus’ information. To yield light on how the stimulus’ information can be encoded and transmitted, we consider the simplest case of two coupled neurons, such that one neuron (referred to as neuron 1) perceives a subthreshold periodic signal but the second neuron (neuron 2) does not perceive the signal. We show that, for appropriate coupling and noise strengths, both neurons fire spike trains that have symbolic patterns (defined by the temporal structure of the inter-spike intervals), whose frequencies of occurrence depend on the signal’s amplitude and period, and are similar for both neurons. In this way, the signal information encoded in the spike train of neuron 1 propagates to the spike train of neuron 2. Our results suggest that sensory neurons can exploit the presence of neural noise to fire spike trains where the information of a subthreshold stimulus is encoded in over expressed and/or in less expressed symbolic patterns.