Interspike Interval Sequences Research Articles

Multiplexed temporal coding of electric communication signals in mormyrid fishes

The coding of stimulus information into patterns of spike times occurs widely in sensory systems. Determining how temporally coded information is decoded by central neurons is essential to understanding how brains process sensory stimuli. Mormyrid weakly electric fishes are experts at time coding, making them an exemplary organism for addressing this question. Mormyrids generate brief, stereotyped electric pulses. Pulse waveform carries information about sender identity, and it is encoded into submillisecond-to-millisecond differences in spike timing between receptors. Mormyrids vary the time between pulses to communicate behavioral state, and these intervals are encoded into the sequence of interspike intervals within receptors. Thus, the responses of peripheral electroreceptors establish a temporally multiplexed code for communication signals, one consisting of spike timing differences between receptors and a second consisting of interspike intervals within receptors. These signals are processed in a dedicated sensory pathway, and recent studies have shed light on the mechanisms by which central circuits can extract behaviorally relevant information from multiplexed temporal codes. Evolutionary change in the anatomy of this pathway is related to differences in electrosensory perception, which appears to have influenced the diversification of electric signals and species. However, it remains unknown how this evolutionary change relates to differences in sensory coding schemes, neuronal circuitry and central sensory processing. The mormyrid electric communication pathway is a powerful model for integrating mechanistic studies of temporal coding with evolutionary studies of correlated differences in brain and behavior to investigate neural mechanisms for processing temporal codes.

Passage-time coding with a timing kernel inferred from irregular cortical spike sequences

In vivo cortical neurons exhibit highly irregular spike sequences. However, the computational implications of this irregular firing with respect to neural codings are not yet fully understood. Recently, we formulated neuronal firing as a stochastic process to translate the firing rate determined by synaptic input into an irregular sequence of inter-spike intervals (ISIs). We previously determined that steady-state distributions of ISIs obey a power-law in the majority of neurons recorded from the sensorimotor cortex of a rat performing a forelimb-movement task. This observation led us to a hypothesis for a neural code with irregular spiking, which we termed as ‘constrained maximization of firing-rate entropy’ (CMFE). This hypothesis asserts that noisy neuronal activity maximizes steady-state firing-rate entropy under the joint constraints of energy consumption and uncertainty over output spike trains. CMFE previously assumed that the values of the rate parameters in two successive ISIs are random and uncorrelated with each other. However, this is an oversimplification and is unrealistic. In addition, the CMFE hypothesis seems to contradict our perception that the firing-rate distribution is dependent on external stimuli. Therefore, it is necessary to explore a rate-coding scheme that can resolve these issues. In this study, we review the concept of CMFE and extend it to incorporate the correlated nature of a firing rate sequence in a biological nervous system. We introduced passage-time coding of stimulus with the timing kernel inferred from irregular cortical spike sequences in our previous study. We showed how the timing kernel determines the amount of information in spike sequences.

Efficient modeling of neural activity using coupled renewal processes

Generalized Linear Models (GLMs) are stochastic models that have been successfully used to model neural activity of single cells and populations. Typically, this requires the spike train to be binned into a binary time series that is modeled as a Bernoulli-type GLM. Unless a loss in temporal precision is acceptable, the bin size has to be chosen on the order of milliseconds. This renders an application to long-term recordings infeasible for computational reasons. We propose a new, binning-free application of the GLM framework to model neural activity by noting that spike trains can equally be characterized by the sequence of continuous-valued inter-spike intervals (ISIs). It was shown that single-neuron spike trains can often be sufficiently modeled as a non-stationary renewal process. Here, we focus on the Gamma distribution for the inter-spike intervals as it allows the accommodation of a relative refractory period and includes the inhomogeneous Poisson process as a special case. We generalize the idea of a modulated Gamma process to the population level by including cross-couplings between the neurons in case of recordings from multiple neurons in parallel. In a Gamma-GLM, each observed inter-spike interval is modeled as a sample from a Gamma distribution whose mean can vary with time, e.g. through modulation by an external stimulus. Traditionally, ISIs are assumed to be independent. However, this renewal assumption can be relaxed by conditioning on the durations of previous intervals. An inter-neuron coupling is introduced by additionally conditioning on the times of spikes of the other neurons. The Gamma distribution and other canonical distributions for inter-spike intervals are part of the exponential family so that efficient maximum likelihood solutions for all model parameters can be obtained using the framework of Generalized Linear Models. Considering the ratio between bin sizes for time-discrete models and the typical length of cortical inter-spike intervals, the computational demand can be reduced by several orders of magnitude. Goodness-of-fit is assessed by adapting standard tests for point process models and evaluating spike prediction performance based on cross-validation. We demonstrate the versatility of the coupled Gamma model for estimating functional connectivity from multi-electrode recordings. With a data set obtained from multi-electrode recordings of the visual system of the awake monkey, we show that the test power of the Gamma-GLM for detecting functional connectivity links is comparable to the performance of a classical discrete-time GLM albeit requiring much less computational time and memory resources. Using the two models on the same data set, we are able to estimate the unknown, underlying connection density of the network. Finally, we discuss general limitations of coupled Gamma-GLMs on the type of interactions that can be faithfully represented and discuss similarities to other binning-free models, in particular Cox’s proportional hazards model.

Inferring ion channel densities from spike data

In high density multiple electrode array recordings, it is now possible to simultaneously measure spiking activity of a large number of single neurons in cultures. However, the connectivity and synaptic weights are not accessible, which makes it difficult to make a good comparison with simulated data. In fact, the spike pattern of a neuron strongly depends on its input, whereas the effect of changes in ion channel densities often makes only a small difference. Thus, to infer neuronal properties from such data, one needs to take into account its synaptic inputs. We stimulated a reduced neuron model based on the model of [1] with different Poisson spike trains and randomly permuted the synaptic weights, keeping the sum of weights constant. We then locally compared interspike interval (ISI) sequences between pairs of the resulting spike trains. This was done by ranking ISIs according to their lengths around different points in time, calculating the difference of those ranks and summing up the absolute value of the difference vector. We chose to compare ranks instead of absolute values as they depend less on the firing rate of the neuron. As a

Biophysical information representation in temporally correlated spike trains

Spike trains commonly exhibit interspike interval (ISI) correlations caused by spike-activated adaptation currents. Here we investigate how the dynamics of adaptation currents can represent spike pattern information generated from stimulus inputs. By analyzing dynamical models of stimulus-driven single neurons, we show that the activation states of the correlation-inducing adaptation current are themselves statistically independent from spike to spike. This paradoxical finding suggests a biophysically plausible means of information representation. We show that adaptation independence is elicited by input levels that produce regular, non-Poisson spiking. This adaptation-independent regime is advantageous for sensory processing because it does not require sensory inferences on the basis of multivariate conditional probabilities, reducing the computational cost of decoding. Furthermore, if the kinetics of postsynaptic activation are similar to the adaptation, the activation state information can be communicated postsynaptically with no information loss, leading to an experimental prediction that simple synaptic kinetics can decorrelate the correlated ISI sequence. The adaptation-independence regime may underly efficient weak signal detection by sensory afferents that are known to exhibit intrinsic correlated spiking, thus efficiently encoding stimulus information at the limit of physical resolution.

Nonlinear temporal organization of neuronal discharge in the basal ganglia of Parkinson's disease patients

Previous electrophysiological studies of the basal ganglia in Parkinson's disease (PD) patients have utilized linear analyses in time-or-frequency domains to characterize neuronal discharge patterns. However, these measures do not fully describe the non-linear features of discharge rates and oscillatory activities of basal ganglia neurons.In this original research, we investigate whether non-linear temporal organizations exist in the inter-spike interval series of neurons recorded in the globus pallidus or the subthalamic nucleus in PD patients undergoing surgery for the implantation of deep brain stimulating electrodes.Our data indicate that in approximately 80% of globus pallidus and subthalamic neurons, the raw inter-spike interval sequences have lower entropy values than those observed after shuffling of the original series. This is the first report establishing non-linear temporal organization as a common feature of neuronal discharge in the basal ganglia of PD patients.

Chaos game representation of human pallidal spike trains

Many studies have demonstrated the presence of scale invariance and long-range correlation in animal and human neuronal spike trains. The methodologies to extract the fractal or scale-invariant properties, however, do not address the issue as to the existence within the train of fine temporal structures embedded in the global fractal organisation. The present study addresses this question in human spike trains by the chaos game representation (CGR) approach, a graphical analysis with which specific temporal sequences reveal themselves as geometric structures in the graphical representation. The neuronal spike train data were obtained from patients whilst undergoing pallidotomy. Using this approach, we observed highly structured regions in the representation, indicating the presence of specific preferred sequences of interspike intervals within the train. Furthermore, we observed that for a given spike train, the higher the magnitude of its scaling exponent, the more pronounced the geometric patterns in the representation and, hence, higher probability of occurrence of specific subsequences. Given its ability to detect and specify in detail the preferred sequences of interspike intervals, we believe that CGR is a useful adjunct to the existing set of methodologies for spike train analysis.

Chaotic control of Hindmarsh-Rose neuron by delayed self-feedback

The control problems of chaotic dynamical patterns of single Hindmarsh-Rose neuron model are studied by using delayed feedback self-control method. Taking gain factor and time delay as controlling parameters respectively, in some ranges of the combination of gain factor and time-delay, we find that the chaotic burst pattern of inter-spike interval sequences of H-R neuron can be controlled to a single_spike period, double_spikes period, 3_or 4_spikes period pattern or multi-period of these patterns for inter-spike interval as the results of numerical simulation analysis. Choice of delay is in-dependent and doesn't rely on the period of unstable periodic orbits embedded within chaotic attractor. The chaotic burst orbit will be controlled to a certain type of periodic patterns of inter-spike interval automatically.

Temporal spike pattern learning

Sensory systems pass information about an animal's environment to higher nervous system units through sequences of action potentials. When these action potentials have essentially equivalent wave forms, all information is contained in the interspike intervals (ISIs) of the spike sequence. How do neural circuits recognize and read these ISI sequences? We address this issue of temporal sequence learning by a neuronal system utilizing spike timing dependent plasticity (STDP). We present a general architecture of neural circuitry that can perform the task of ISI recognition. The essential ingredients of this neural circuit, which we refer to as "interspike interval recognition unit" (IRU) are (i) a spike selection unit, the function of which is to selectively distribute input spikes to downstream IRU circuitry; (ii) a time-delay unit that can be tuned by STDP; and (iii) a detection unit, which is the output of the IRU and a spike from which indicates successful ISI recognition by the IRU. We present two distinct configurations for the time-delay circuit within the IRU using excitatory and inhibitory synapses, respectively, to produce a delayed output spike at time t_{0}+tau(R) in response to the input spike received at time t_{0} . R is the tunable parameter of the time-delay circuit that controls the timing of the delayed output spike. We discuss the forms of STDP rules for excitatory and inhibitory synapses, respectively, that allow for modulation of R for the IRU to perform its task of ISI recognition. We then present two specific implementations for the IRU circuitry, derived from the general architecture that can both learn the ISIs of a training sequence and then recognize the same ISI sequence when it is presented on subsequent occasions.

Management of synchronized network activity by highly active neurons

Increasing evidence supports the idea that spontaneous brain activity may have an important functional role. Cultured neuronal networks provide a suitable model system to search for the mechanisms by which neuronal spontaneous activity is maintained and regulated. This activity is marked by synchronized bursting events (SBEs)—short time windows (hundreds of milliseconds) of rapid neuronal firing separated by long quiescent periods (seconds). However, there exists a special subset of rapidly firing neurons whose activity also persists between SBEs. It has been proposed that these highly active (HA) neurons play an important role in the management (i.e. establishment, maintenance and regulation) of the synchronized network activity. Here, we studied the dynamical properties and the functional role of HA neurons in homogeneous and engineered networks, during early network development, upon recovery from chemical inhibition and in response to electrical stimulations. We found that their sequences of inter-spike intervals (ISI) exhibit long time correlations and a unimodal distribution. During the network's development and under intense inhibition, the observed activity follows a transition period during which mostly HA neurons are active. Studying networks with engineered geometry, we found that HA neurons are precursors (the first to fire) of the spontaneous SBEs and are more responsive to electrical stimulations.

Slow chaotic changes in the excitability of the auditory units

We explored the statistical properties of the spontaneous and evoked firing activity in the brainstem auditory units of the grass frog (Rana t temporaria). We estimated the properties of spontaneous firing using the following functions: interspike interval distribution, hazard function, autocorrelation functions for original and shifted sequence of interspike intervals, function of interdependence of neighboring intervals. The dependences of Fano and Allans factors upon the values of counting time (window size) were also obtained. We observed a considerable deviation of the spontaneous activity from the renewal process for the majority of units located both in the dorsal medullar nucleus (homolog of cochlear nucleus in the mammals) and in torus semicircularis (homolog of inferior colliculus). The negative correlation between the neighboring short interspike intervals was typical for some (mainly toral) units. However, generally week but quite reliable positive correlation between neighboring intervals was typical for the great majority of neurons. The values of Fano and Allan factors were close to 1 at window size less than 100‐500 ms and increased in proportion to some power for larger window sizes. The exponents of these power dependences were different for different units.

Intrinsic mechanisms of spike frequency adaption lead to negative serial correlations of inter-spike intervals

Event Abstract Back to Event Intrinsic mechanisms of spike frequency adaption lead to negative serial correlations of inter-spike intervals Farzad Farkhooi1, 2*, Martin P. Nawrot1, 2, Hermann Cuntz3 and Eilif Muller4 1 Freie Universitat Berlin , Germany 2 BCCN Berlin, Germany 3 University College London, United Kingdom 4 Ecole Polytechnique Federale de Lausanne , Switzerland It has been reported that many neurons in various different systems illustrate a pattern of negative serial dependence between adjacent inter-spike intervals, when measured under stationary firing rates (for review see [3]). We studied a biophysical model of spike frequency adaptation with M-type currents, which are caused by slow, voltage-dependent, high-threshold potassium channels ([2] and [4]). This model in the presence of white noise current injection exhibited serial negative correlation between inter-spike interval sequences. We analysed the dependency of serial correlation on the input statistics, this result shows in the physiological spiking frequency range, the inter-spike serial correlation is a persistence phenomena. We investigate the generality of this effect with two different phenomenological Integrate-and-Fire neuron models with spike frequency adaptation proposed in [5] and [1]. Both models captured the negative serial correlation between subsequent intervals. We describe the relationship of the input statistics with the observed serial dependency between the inter-spike intervals. We compare both models with respect to produced inter-spike serial correlation and their input coefficient of variation. Furthermore, we showed the strength of the observed correlation is rate dependent for both models. We argue that the feature of negatively correlated intervals is likely to be a neuron intrinsic property caused by cellular mechanisms that underlie spike frequency adaptation and the particular input statistics affects the modulation of the negative serial dependency between two following spiking intervals.

Nonlinear analysis of discharge patterns in monkey basal ganglia

Spontaneous discharge of basal ganglia neurons is often analyzed with time- or frequency-domain methods. However, it has been shown that sequences of inter-spike interval series are not fully described by such linear procedures. We therefore carried out a characterization of the nonlinear features of spontaneous discharge of neurons in the primate basal ganglia. We studied the spontaneous activity of neurons in the subthalamic nucleus (22 cells), as well as neurons in the external and internal pallidal segments (53 and 39 cells, respectively), recorded with standard extracellular recording methods in two awake Rhesus monkeys. As a measure of the statistical irregularity of neuronal discharge, we compared the approximate entropy of inter-spike interval sequences with that of shuffled representations of the same data. In all three basal ganglia structures, approximately 95% of the original data showed lower approximate entropy values than the shuffled data, suggesting a temporal organization in the original sequence. Fano factor analysis confirmed the presence of a temporal organization of inter-spike interval sequences, and indicated the presence of self-similarity in the great majority of them. In addition, Hurst exponent analysis showed that the inter-spike interval series are persistent. Hurst exponents often differ between short and long scaling ranges. Subsequent principal component analyses allowed us to identify three distinct patterns of the temporal evolution of inter-spike interval sequences in the phase space. These types were found in varying distributions in all three nuclei. Our analyses demonstrate that the discharge of most neurons in the basal ganglia of awake monkeys has nonlinear features that may be important for information coding in the basal ganglia.

Neural Circuitry for Recognizing Interspike Interval Sequences

Sensory systems present environmental information to central nervous system as sequences of action potentials or spikes. How do animals recognize these sequences carrying information about their world? We present a biologically inspired neural circuit designed to enable spike pattern recognition. This circuit is capable of training itself on a given interspike interval (ISI) sequence and is then able to respond to presentations of the same sequence. The essential ingredients of the recognition circuit are (a) a tunable time delay circuit, (b) a spike selection unit, and (c) a tuning mechanism using spike timing dependent plasticity of inhibitory synapses. We have investigated this circuit using Hodgkin-Huxley neuron models connected by realistic excitatory and inhibitory synapses. It is robust in the presence of noise represented as jitter in the spike times of the ISI sequence.

Dynamical Heterogeneity of Suprachiasmatic Nucleus Neurons Based on Regularity and Determinism

The suprachiasmatic nucleus (SCN) is known to be the master biological clock in mammals. Despite the periodic mean firing rate, interspike interval (ISI) patterns of SCN neurons are quite complex and irregular. The aim of the present study was to investigate the existence of nonlinear determinism in the complex ISI patterns of SCN neurons. ISI sequences were recorded from 173 neurons in rat hypothalamic slice preparations using a cell-attached patch recording technique. Their correlation dimensions (D2) were estimated, and were then compared with those of the randomly-shuffled surrogate data. We found that only 16 neurons (16/173) exhibited deterministic ISI patterns of spikes. In addition, clustering analysis revealed that SCN neurons could be divided into two subgroups of neurons each having distinct values of coefficient of variation (CV) and skewness (SK). Interestingly, most deterministic SCN neurons (14/16) belonged to the group of irregularly spiking neurons having large CV and SK values. To see if the neuronal coupling mediated by the gamma-aminobutyric acid (GABA), the major neurotransmitter in the SCN, contributed to the deterministic nature, we examined the effect of the GABAA receptor antagonist bicuculline on D2 values of 56 SCN neurons. 8 SCN neurons which were originally stochastic became to exhibit deterministic characteristics after the bicuculline application. This result suggests that the deterministic nature of the SCN neurons arises not from GABAergic synaptic interactions, but likely from properties inherent to neurons themselves.

Fractal Stochastic Modeling of Spiking Activity in Suprachiasmatic Nucleus Neurons

Individual neurons in the suprachiasmatic nucleus (SCN), the master biological clock in mammals, autonomously produce highly complex patterns of spikes. We have shown that most (approximately 90%) SCN neurons exhibit truly stochastic interspike interval (ISI) patterns. The aim of this study was to understand the stochastic nature of the firing patterns in SCN neurons by analyzing the ISI sequences of 150 SCN neurons in hypothalamic slices. Fractal analysis, using the periodogram, Fano factor, and Allan factor, revealed the presence of a 1/f-type power-law (fractal) behavior in the ISI sequences. This fractal nature was persistent after the application of the GABAA receptor antagonist bicuculline, suggesting that the fractal stochastic activity is an intrinsic property of individual SCN neurons. Based on these physiological findings, we developed a computational model for the stochastic SCN neurons to find that their stochastic spiking activity was best described by a gamma point process whose mean firing rate was modulated by a fractal binomial noise. Taken together, we suggest that SCN neurons generate temporal spiking patterns using the fractal stochastic point process.

Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction

The nonlinear prediction method based on the interspike interval (ISI) reconstruction is applied to the ISI sequence of noisy pulse trains and the detection of the deterministic structure is performed. It is found that this method cannot discriminate between the noisy periodic pulse train and the noisy chaotic one when noise-induced pulses exist. When the noise-induced pulses are eliminated by the grouping of ISI sequence with the genetic algorithm, the chaotic structure of the chaotic firings becomes clear, and the noisy chaotic pulse train could be discriminated from the periodic one.

Long-range temporal correlations in the spontaneous spiking of neurons in the hippocampal-amygdala complex of humans

The spontaneous or background discharge patterns of in vivo single neuron is mostly considered as neuronal noise, which is assumed to be devoid of any correlation between successive inter-spike-intervals (ISI). Such random fluctuations are modeled only statistically by stochastic point process, lacking any temporal correlation. In this study, we have investigated the nature of spontaneous irregular fluctuations of single neurons from human hippocampus-amygdala complex by three different methods: (i) detrended fluctuation analysis (DFA), (ii) multiscale entropy (MSE), (iii) rate estimate convergence. Both the DFA and MSE analysis showed the presence of long-range power-law correlation over time in the ISI sequences. Moreover, we observed that the individual spike trains presented non-random structure on longer time-scales and showed slow convergence of rate estimates with increasing counting time. This power-law correlation and the slow convergence of statistical moments were eliminated by randomly shuffling the ISIs even though the distributions of ISIs were preserved. Thus the power-law relationship arose from long-term correlations among ISIs that were destroyed by shuffling the data. Further, we found that neurons which showed long-range correlations also showed statistically significant correlated firing as measured by correlation coefficient or mutual information function. The presence of long-range correlations indicates the history-effect or memory in the firing pattern by the associative formation of a neuronal assembly.

Study on nonlinear characteristics of two synchronizing uncoupled Hindmarsh-Rose neurons

Modulating the current input of two uncoupled Hindmarsh-Rose neurons by using the membrane potential of Hindmarsh-Rose neuron under different initial conditions, the evolution mechanism of synchronization process of the two neurons is revealed by analyzing interspike interval sequences. When periodic stimulation is u sed, the full synchronization is realized in two identical neurons, and the sync hronized response of modulated neurons can be different from the stimulation sig nal; and phase synchronization can be obtained in two neurons with different par ameters:two neurons with small parameter mismatch can be synchronized to the per iodic response different from the stimulation signal, and two neurons with big p arameter mismatch can only be synchronized to the response in phase synchronizat ion with stimulation signal. When chaotic stimulation is used, two systems can o nly be synchronized to the response being in phase synchronization with stimulat ion signal. Obviously, chaotic stimulation is more helpful in encoding and deco ding information. Analyzing the relation between the largest condition Lyapunov exponents and the stimulation strength shows that when the largest condition Lya punov exponents of the two systems are both negative is the necessary condition for synchronization. The chaotic stimulation signal can more easily synchronize two neurons than periodic stimulation signal, implying that the effect of chaoti c stimulation is stronger than periodic one, and the experiments also confirm th is conclusion.

When does interval coding occur?

During the stationary portion of neuron's spiking response to a stimulus, the stimulus could be coded in the average rate and, more elaborately, in the statistics of the sequence of interspike intervals. We use information processing theory to explicitly define when interval coding occurs and quantify the coding gain beyond rate coding provided by the interval code. We explicitly find the interval distribution commensurate with average rate coding. When we analyzed optomotor neural responses recorded from the crayfish eye, we found little interval coding occurring despite stimulus-induced changes from a unimodal to a bimodal interval distribution.