Neuronal Spike Timing Adaptation Described with a Fractional Leaky Integrate-and-Fire Model

Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

Download Full-text

Generalized Integrate-and-Fire Models of Neuronal Activity Approximate Spike Trains of a Detailed Model to a High Degree of Accuracy

Journal of Neurophysiology ◽

10.1152/jn.00190.2004 ◽

2004 ◽

Vol 92 (2) ◽

pp. 959-976 ◽

Cited By ~ 158

Author(s):

Renaud Jolivet ◽

Timothy J. Lewis ◽

Wulfram Gerstner

Keyword(s):

Cortical Neurons ◽

Direct Reduction ◽

Spike Trains ◽

Model Parameters ◽

Detailed Model ◽

Fire Model ◽

Integrate And Fire ◽

Fire Models ◽

Wide Range ◽

Simple Models

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance-based model to 2 variants of integrate-and-fire models. In the first variant (nonlinear integrate-and-fire model), parameters depend on the instantaneous membrane potential, whereas in the second variant, they depend on the time elapsed since the last spike [Spike Response Model (SRM)]. The direct reduction links features of the simple models to biophysical features of the full conductance-based model. To quantitatively test the predictive power of the SRM and of the nonlinear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70–80 percent of the spikes in the full model (with temporal precision of ±2 ms) over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the SRM and the nonlinear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

Download Full-text

Stimulus-Dependent Correlations in Threshold-Crossing Spiking Neurons

Neural Computation ◽

10.1162/neco.2009.07-08-830 ◽

2009 ◽

Vol 21 (8) ◽

pp. 2269-2308 ◽

Cited By ~ 16

Author(s):

Yoram Burak ◽

Sam Lewallen ◽

Haim Sompolinsky

Keyword(s):

Ganglion Cells ◽

Retinal Ganglion ◽

Qualitative Properties ◽

Fire Model ◽

Integrate And Fire ◽

Threshold Crossing ◽

Cross Correlations ◽

Bursting Events ◽

The One ◽

The Relationship

We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with gaussian statistics, we evaluate the cross-correlation of spike trains in pairs of model neurons with different thresholds. This correlation function tends to be asymmetric in time, indicating a preference for the neuron with the lower threshold to fire before the one with the higher threshold, even if their inputs are identical. The relationship between these results and spike statistics in other models of neural activity is explored. In particular, we compare our model with an integrate-and-fire model in which the membrane voltage resets following each spike. The qualitative properties of spike cross-correlations, emerging from the threshold-crossing model, are similar to those of bursting events in the integrate-and-fire model. This is particularly true for generalized integrate-and-fire models in which spikes tend to occur in bursts, as observed, for example, in retinal ganglion cells driven by a rapidly fluctuating visual stimulus. The threshold-crossing model thus provides a simple, analytically tractable description of event onsets in these neurons.

Download Full-text

Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity

Journal of Neurophysiology ◽

10.1152/jn.00686.2005 ◽

2005 ◽

Vol 94 (5) ◽

pp. 3637-3642 ◽

Cited By ~ 547

Author(s):

Romain Brette ◽

Wulfram Gerstner

Keyword(s):

Simple Model ◽

Expressive Power ◽

Detailed Model ◽

Fire Model ◽

Integrate And Fire ◽

Conductance States ◽

Effective Description ◽

High Conductance

We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. We describe a systematic method to estimate its parameters with simple electrophysiological protocols (current-clamp injection of pulses and ramps) and apply it to a detailed conductance-based model of a regular spiking neuron. Our simple model predicts correctly the timing of 96% of the spikes (±2 ms) of the detailed model in response to injection of noisy synaptic conductances. The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.

Download Full-text

A Computational Model as Neurodecoder Based on Synchronous Oscillation in the Visual Cortex

Neural Computation ◽

10.1162/089976603322362419 ◽

2003 ◽

Vol 15 (10) ◽

pp. 2399-2418 ◽

Cited By ~ 5

Author(s):

Zhao Songnian ◽

Xiong Xiaoyun ◽

Yao Guozheng ◽

Fu Zhi

Keyword(s):

Visual Cortex ◽

Computational Model ◽

Visual Information ◽

Spike Trains ◽

Spike Timing ◽

Contour Detection ◽

System Level ◽

Neuronal Spike ◽

Neuronal Spike Trains ◽

External Stimuli

Based on synchronized responses of neuronal populations in the visual cortex to external stimuli, we proposed a computational model consisting primarily of a neuronal phase-locked loop (NPLL) and multiscaled operator. The former reveals the function of synchronous oscillations in the visual cortex. Regardless of which of these patterns of the spike trains may be an average firing-rate code, a spike-timing code, or a rate-time code, the NPLL can decode original visual information from neuronal spike trains modulated with patterns of external stimuli, because a voltage-controlled oscillator (VCO), which is included in the NPLL, can precisely track neuronal spike trains and instantaneous variations, that is, VCO can make a copy of an external stimulus pattern. The latter, however, describes multi-scaled properties of visual information processing, but not merely edge and contour detection. In this study, in which we combined NPLL with a multiscaled operator and maximum likelihood estimation, we proved that the model, as a neurodecoder, implements optimum algorithm decoding visual information from neuronal spike trains at the system level. At the same time, the model also obtains increasingly important supports, which come from a series of experimental results of neurobiology on stimulus-specific neuronal oscillations or synchronized responses of the neuronal population in the visual cortex. In addition, the problem of how to describe visual acuity and multiresolution of vision by wavelet transform is also discussed. The results indicate that the model provides a deeper understanding of the role of synchronized responses in decoding visual information.

Download Full-text

Exact Event-Driven Implementation for Recurrent Networks of Stochastic Perfect Integrate-and-Fire Neurons

Neural Computation ◽

10.1162/neco_a_00346 ◽

2012 ◽

Vol 24 (12) ◽

pp. 3145-3180 ◽

Cited By ~ 2

Author(s):

Thibaud Taillefumier ◽

Jonathan Touboul ◽

Marcelo Magnasco

Keyword(s):

Intrinsic Noise ◽

Spike Timing ◽

Temporal Coding ◽

Recurrent Networks ◽

Neural Noise ◽

Integrate And Fire ◽

Discretization Schemes ◽

Event Driven ◽

Random Variability

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks’ dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Download Full-text