Interspike Interval Density Research Articles

Rosetta stone for the population dynamics of spiking neuron networks.

Populations of spiking neuron models have densities of their microscopic variables (e.g., single-cell membrane potentials) whose evolution fully capture the collective dynamics of biological networks, even outside equilibrium. Despite its general applicability, the Fokker-Planck equationgoverning such evolution is mainly studied within the borders of the linear response theory, although alternative spectral expansion approaches offer some advantages in the study of the out-of-equilibrium dynamics. This is mainly due to the difficulty in computing the state-dependent coefficients of the expanded system of differential equations. Here, we address this issue by deriving analytic expressions for such coefficients by pairing perturbative solutions of the Fokker-Planck approach with their counterparts from the spectral expansion. A tight relationship emerges between several of these coefficients and the Laplace transform of the interspike interval density (i.e., the distribution of first-passage times). "Coefficients" like the current-to-rate gain function, the eigenvalues of the Fokker-Planck operator and its eigenfunctions at the boundaries are derived without resorting to integral expressions. For the leaky integrate-and-fire neurons, the coupling terms between stationary and nonstationary modes are also worked out paving the way to accurately characterize the critical points and the relaxation timescales in networks of interacting populations.

Neural activity of the subthalamic nucleus during voluntary movements in patients with Parkinson’s disease

Microelectrode recording (MER) during electrode implantation for deep brain stimulation (DBS) can determine the boundaries of the subthalamic nucleus (STN), and track neural activity during rest and voluntary movement in Parkinson’s disease (PD) patients. However, the functional role of STN in motor control remains unclear, despite its effectiveness in stimulation. Single unit activity of STN was recorded in 16 patients with PD during implantation of deep brain stimulation electrodes. Electromyograms of forearm muscles and a phonogram featuring verbal commands were simultaneously recorded with MER. The patients were instructed to perform motor tests involving clenching their hand into a fist. Out of the 560 neurons studied, 93 (16.6%) responded to motor tasks. The registered neurons were classified into three patterns using the hierarchical clustering method of histograms of interspike interval density — namely, tonic, burst, and pause patterns. Sensitive neurons were classified according to their responses, with activation (76.9%) and inhibition (23.1%) being the two identified types. In 90% of cases, neuron activation preceded movement. Of the responses, 53.8% were classified as tonic and 46.2% as phasic. Two thirds of inhibitory responses were advanced, occurring 0.2–0.3 seconds before movement onset. One third of neurons were activated after movement initiation with a delay of 0.05–0.2 seconds. 83.3% of the inhibitory neurons responded tonically, while the remaining 16.7% responded phasically. Notably, all phasic reactions occurred before the onset of movement. A comparison of the parameters of sensitive and non-sensitive neurons revealed several differences. The findings suggest a potential physiological distinction between the two neuron types. All three patterns of activity were present in both types of neurons, but sensitive neurons exhibited a wider representation of pause neurons (57.9% vs. 49.5%). Additionally, burst and pause neurons responded to movements that featured significantly lower variance of multiple activity parameters, such as firing rate, burst index, mean burst length, and oscillation scores in the 8–12 and 12–20 Hz range. The distribution of sensitive neurons along the electrode trajectory through the subthalamic nucleus was analyzed. Sensitive neurons were located significantly more dorsally compared to non-sensitive neurons, and no sensitive pause cells were observed in the ventral half of the STN. Based on our findings, it is presumed that the pause pattern plays a critical role in both motor control and its related disorders in Parkinson’s disease. A diverse range of neuronal responses suggests a high degree of heterogeneity among STN neurons implicated in motor control. The presence of both delayed and advanced neural responses suggests that STN involvement in motor control encompasses both the preparation and initiation of movement, as well as the regulation of ongoing movements via afferent feedback. The range of neural responses aligns with the dynamic model of basal ganglia, which suggests that STN can perform distinct functional roles during different stages of movement, including initiation, control, and completion.

An integrate-and-fire approach to Ca2+ signaling. Part I: Renewal model

In computational neuroscience integrate-and-fire models capture the spike generation by a subthreshold dynamics supplemented by a simple fire-and-reset rule; they allow for a numerically efficient and analytically tractable description of stochastic single cell as well as network dynamics. Stochastic spiking is also a prominent feature of Ca2+ signaling which suggests to adopt the integrate-and-fire approach for this fundamental biophysical process. The model introduced here consists of two components describing 1) activity of clusters of inositol-trisphosphate receptor channels and 2) dynamics of the global Ca2+ concentrations in the cytosol. The cluster dynamics is given in terms of a cyclic Markov chain, capturing the puff, i.e., the punctuated release of Ca2+ from intracellular stores. The cytosolic Ca2+ concentration is described by an integrate-and-fire dynamics driven by the puff current. For the cyclic Markov chain we derive expressions for the statistics of the interpuff interval, the single-puff strength and the puff current assuming constant cytosolic Ca2+. The latter condition is often well approximated because cytosolic Ca2+ varies much slower than the cluster activity does. Furthermore, because the detailed two-component model is numerically expensive to simulate and difficult to treat analytically, we develop an analytical framework to approximate the driving puff current of the stochastic cytosolic Ca2+ dynamics by a temporally uncorrelated Gaussian noise. This approximation reduces our two-component system to an integrate-and-fire model with a nonlinear drift function and a multiplicative Gaussian white noise, a model that is known to generate a renewal spike train, i.e., a point process with statistically independent interspike intervals. The model allows for fast numerical simulations, permits to derive analytical expressions for the rate of Ca2+ spiking and the coefficient of variation of the interspike interval, and to approximate the interspike interval density and the spike train power spectrum. Comparison of these statistics to experimental data is discussed.

Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

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

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

Firing statistics in the bistable regime of neurons with homoclinic spike generation.

Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixed point and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This paper focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential-a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.

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.

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).

MODELING REFRACTORINESS FOR STOCHASTICALLY DRIVEN SINGLE NEURONS

A description of the sequence of interspike intervals and of the subsequent firing times for single neurons is performed by means of an instantaneous return pro- cess in the presence of refractoriness. Every interspike interval consists of an absolute refractory period of fixed duration followed by a period of relative refractoriness whose duration is described by the first-passage time of the modeling diffusion process through a generally time-dependent threshold. In the cases of Wiener and Ornstein-Uhlenbeck processes, the interspike probability density functions and some of its statistical fea- tures are explicitly obtained for special monotonically non-increasing thresholds. 1 Introduction Stochastic models for neuronal firing in the presence of refractoriness have been the object of various investigations. The first attempt to study the effect of refractoriness in a point process is made in (22) and in (25) in which the authors consider the role played by the dead time in determining the distribution of the output when the input obeys a given distribution. Successively, an instantaneous return process, constructed on a diffusion, has been considered aiming to a quantitative description of neuron's membrane potential behavior. Within such a context, the presence of refractoriness has been included in two different ways. The first way assumes that the firing threshold acts as an elastic barrier that is partially transparent, i.e. such that its behavior is intermediate between total absorption and total reflection (cf. (3), (4), (5), (20)). Alternatively, the return process paradigm for the description of the time course of the membrane potential is analyzed by assuming that the neuronal refractoriness period is a random variable with a pre-assigned probability density (cf. (1), (10), (11), (15), (23)). Recently, in (2) and (16), the Wiener neuronal model in the presence of constant and of exponentially distributed refractoriness has been considered, and expressions for output distributions and for interspike interval densities have been obtained in closed form. Customarily, the firing threshold has been viewed in the literature as a constant which may not be appropriate, especially for rapidly firing cells (cf. (7), (13), (14), (26)). Indeed, when a neuron releases an action potential, it becomes temporarily incapable of responding to further input signals. In fact, for a period of time, of the order of one or two milliseconds, the neuron is unable to respond to any stimuli (absolute refractory period). After that, for several successive milliseconds its sensitivity to the incoming stimuli is normally reduced, in some cases increasing successively. This type of after-firing behavior (after potentials) may last up to about 100 msec. In the present context we focus our attention on a constant absolute refractory period followed by a period of relative refractoriness that we model as a random variable. Hence, after a spike release, we assume that the neuron is unable to fire again during the absolute refractory period, while the firing threshold is assumed to decrease progressively as the inhibitory effect of the previous spike fades away.

Bimodality of the interspike interval distributions for subordinated diffusion models of integrate-and-fire neurons

A subordinated Langevin process, with a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, is considered as a generalization of the conventional perfect and leaky integrate-and-fire neuron models. The parent process is given by standard Brownian motion. The effect of the random activity of synaptic inputs, which arises from other neurons forming local and distant networks, is modeled via a Lévy exponent of the subordinator. Using a first-passage-time formulation in an external force field, we find exact expressions for the Laplace transform of the output interspike interval (ISI) density. More detailed analysis is presented on the properties of the ISI distribution in the case of the Lévy exponent which corresponds to the truncated double-order time-fractional diffusion equation for the probability density of the membrane potential. Particularly, it is shown that at some parameter regimes the ISI density exhibits a bimodal structure. Moreover, it is demonstrated that the ISIs regularity is maximized at an intermediate value of the mean input current.

Memory-induced resonancelike suppression of spike generation in a resonate-and-fire neuron model.

The behavior of a stochastic resonate-and-fire neuron model based on a reduction of a fractional noise-driven generalized Langevin equation (GLE) with a power-law memory kernel is considered. The effect of temporally correlated random activity of synaptic inputs, which arise from other neurons forming local and distant networks, is modeled as an additive fractional Gaussian noise in the GLE. Using a first-passage-time formulation, in certain system parameter domains exact expressions for the output interspike interval (ISI) density and for the survival probability (the probability that a spike is not generated) are derived and their dependence on input parameters, especially on the memory exponent, is analyzed. In the case of external white noise, it is shown that at intermediate values of the memory exponent the survival probability is significantly enhanced in comparison with the cases of strong and weak memory, which causes a resonancelike suppression of the probability of spike generation as a function of the memory exponent. Moreover, an examination of the dependence of multimodality in the ISI distribution on input parameters shows that there exists a critical memory exponent α_{c}≈0.402, which marks a dynamical transition in the behavior of the system. That phenomenon is illustrated by a phase diagram describing the emergence of three qualitatively different structures of the ISI distribution. Similarities and differences between the behavior of the model at internal and external noises are also discussed.

Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise.

A neuron receives input from other neurons via electrical pulses, so-called spikes. The pulse-like nature of the input is frequently neglected in analytical studies; instead, the input is usually approximated to be Gaussian. Recent experimental studies have shown, however, that an assumption underlying this approximation is often not met: Individual presynaptic spikes can have a significant effect on a neuron's dynamics. It is thus desirable to explicitly account for the pulse-like nature of neural input, i.e. consider neurons driven by a shot noise - a long-standing problem that is mathematically challenging. In this work, we exploit the fact that excitatory shot noise with exponentially distributed weights can be obtained as a limit case of dichotomous noise, a Markovian two-state process. This allows us to obtain novel exact expressions for the stationary voltage density and the moments of the interspike-interval density of general integrate-and-fire neurons driven by such an input. For the special case of leaky integrate-and-fire neurons, we also give expressions for the power spectrum and the linear response to a signal. We verify and illustrate our expressions by comparison to simulations of leaky-, quadratic- and exponential integrate-and-fire neurons.

Response to a periodic stimulus in a perfect integrate-and-fire neuron model driven by colored noise.

The output interspike interval statistics of a stochastic perfect integrate-and-fire neuron model driven by an additive exogenous periodic stimulus is considered. The effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise. Using a first-passage-time formulation, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime, and their dependence on input parameters (e.g., the noise correlation time and amplitude as well as the frequency of an input current) is analyzed. It is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects, such as sign reversals of the interspike interval correlations versus noise-switching rate as well as versus the frequency of periodic forcing, a power-law-like decay of oscillations of the serial correlation coefficients in the long-lag limit, amplification of the output signal modulation in the instantaneous firing rate of the neural response, etc. The features of spike statistics in the limits of slow and fast noises are also discussed.

Statistics of a leaky integrate-and-fire model of neurons driven by dichotomous noise.

The behavior of a stochastic leaky integrate-and-fire model of neurons is considered. The effect of temporally correlated random neuronal input is modeled as a colored two-level (dichotomous) Markovian noise. Relying on the Riemann method, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived, and their dependence on noise parameters (such as correlation time and amplitude) is analyzed. Particularly, noise-induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established. The features of spike statistics, analytically revealed in our study, are compared with recently obtained results for a perfect integrate-and-fire neuron model.

The effect of positive interspike interval correlations on neuronal information transmission.

Experimentally it is known that some neurons encode preferentially information about low-frequency (slow) components of a time-dependent stimulus while others prefer intermediate or high-frequency (fast) components. Accordingly, neurons can be categorized as low-pass, band-pass or high-pass information filters. Mechanisms of information filtering at the cellular and the network levels have been suggested. Here we propose yet another mechanism, based on noise shaping due to spontaneous non-renewal spiking statistics. We compare two integrate-and-fire models with threshold noise that differ solely in their interspike interval (ISI) correlations: the renewal model generates independent ISIs, whereas the non-renewal model exhibits positive correlations between adjacent ISIs. For these simplified neuron models we analytically calculate ISI density and power spectrum of the spontaneous spike train as well as approximations for input-output cross-spectrum and spike-train power spectrum in the presence of a broad-band Gaussian stimulus. This yields the spectral coherence, an approximate frequency-resolved measure of information transmission. We demonstrate that for low spiking variability the renewal model acts as a low-pass filter of information (coherence has a global maximum at zero frequency), whereas the non-renewal model displays a pronounced maximum of the coherence at non-vanishing frequency and thus can be regarded as a band-pass filter of information.

Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity.

A major source of random variability in cortical networks is the quasi-random arrival of presynaptic action potentials from many other cells. In network studies as well as in the study of the response properties of single cells embedded in a network, synaptic background input is often approximated by Poissonian spike trains. However, the output statistics of the cells is in most cases far from being Poisson. This is inconsistent with the assumption of similar spike-train statistics for pre- and postsynaptic cells in a recurrent network. Here we tackle this problem for the popular class of integrate-and-fire neurons and study a self-consistent statistics of input and output spectra of neural spike trains. Instead of actually using a large network, we use an iterative scheme, in which we simulate a single neuron over several generations. In each of these generations, the neuron is stimulated with surrogate stochastic input that has a similar statistics as the output of the previous generation. For the surrogate input, we employ two distinct approximations: (i) a superposition of renewal spike trains with the same interspike interval density as observed in the previous generation and (ii) a Gaussian current with a power spectrum proportional to that observed in the previous generation. For input parameters that correspond to balanced input in the network, both the renewal and the Gaussian iteration procedure converge quickly and yield comparable results for the self-consistent spike-train power spectrum. We compare our results to large-scale simulations of a random sparsely connected network of leaky integrate-and-fire neurons (Brunel, 2000) and show that in the asynchronous regime close to a state of balanced synaptic input from the network, our iterative schemes provide an excellent approximations to the autocorrelation of spike trains in the recurrent network.

Global dynamics of a stochastic neuronal oscillator

Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

Characterizing mixed mode oscillations shaped by noise and bifurcation structure

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude, and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh–Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and resets and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.

The effects of stochastic and deterministic adaptation currents on interspike interval histograms and correlations

Event Abstract Back to Event The effects of stochastic and deterministic adaptation currents on interspike interval histograms and correlations Tilo Schwalger1*, Karin Fisch2, Jan Benda2 and Benjamin Lindner1 1 MPI for the Physics of Complex Systems, MPI, Germany 2 Ludwig-Maximilians-Universität München, Division of Neurobiology, Department Biology II, Germany The spiking patterns of neurons can be often highly variable. In many cases, the origin of this neural noise is not known and might be difficult to access directly. Here, we explore the possibility to distinguish between two different kinds of intrinsic noise solely by measuring the interspike interval (ISI) statistics of a neuron. Specifically, we consider adaptive neuron models in which fluctuations (channel noise) are either associated with fast ionic currents or with slow adaptation currents that are observed in many neurons. We show by means of analytical techniques and extensive numerical simulations that the shape of the ISI histograms and the ISI correlations are markedly different in both cases: For fast current fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian and the ISI correlations are negative. In contrast, for stochastic adaptation currents, the density is more peaked and has a heavier tail than an inverse Gaussian density and the serial correlations are positive. For the theoretical analysis we use an analytically tractable integrate-and-fire model. The results are qualitatively confirmed by simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics Keywords: computational neuroscience Conference: Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010. Presentation Type: Poster Abstract Topic: Bernstein Conference on Computational Neuroscience Citation: Schwalger T, Fisch K, Benda J and Lindner B (2010). The effects of stochastic and deterministic adaptation currents on interspike interval histograms and correlations. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. doi: 10.3389/conf.fncom.2010.51.00016 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 22 Sep 2010; Published Online: 23 Sep 2010. * Correspondence: Dr. Tilo Schwalger, MPI for the Physics of Complex Systems, MPI, Dresden, Germany, tilo.schwalger@epfl.ch Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Tilo Schwalger Karin Fisch Jan Benda Benjamin Lindner Google Tilo Schwalger Karin Fisch Jan Benda Benjamin Lindner Google Scholar Tilo Schwalger Karin Fisch Jan Benda Benjamin Lindner PubMed Tilo Schwalger Karin Fisch Jan Benda Benjamin Lindner Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

A First-Order Nonhomogeneous Markov Model for the Response of Spiking Neurons Stimulated by Small Phase-Continuous Signals

We present a first-order nonhomogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval density to be expressed as products of two separate functions, one of which describes only the neuron characteristics and the other of which describes only the signal characteristics. The approximation shows particularly clearly that signal autocorrelations and cross-correlations arise as natural features of the interspike-interval density and are particularly clear for small signals and moderate noise. We show that this model simplifies the design of spiking neuron cross-correlation systems and describe a four-neuron mutual inhibition network that generates a cross-correlation output for two input signals.