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

2004 ◽  
Vol 92 (2) ◽  
pp. 959-976 ◽  
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.

scholarly journals Predicting spike timing in highly synchronous auditory neurons at different sound levels

2013 ◽  
Vol 110 (7) ◽  
pp. 1672-1688 ◽  
Author(s):  
Bertrand Fontaine ◽  
Victor Benichoux ◽  
Philip X. Joris ◽  
Romain Brette
Keyword(s):  
Temporal Structure ◽  
Spike Trains ◽  
Sound Level ◽  
Spike Timing ◽  
Spike Threshold ◽  
Integrate And Fire ◽  
Fire Models ◽  
Wide Range

A challenge for sensory systems is to encode natural signals that vary in amplitude by orders of magnitude. The spike trains of neurons in the auditory system must represent the fine temporal structure of sounds despite a tremendous variation in sound level in natural environments. It has been shown in vitro that the transformation from dynamic signals into precise spike trains can be accurately captured by simple integrate-and-fire models. In this work, we show that the in vivo responses of cochlear nucleus bushy cells to sounds across a wide range of levels can be precisely predicted by deterministic integrate-and-fire models with adaptive spike threshold. Our model can predict both the spike timings and the firing rate in response to novel sounds, across a large input level range. A noisy version of the model accounts for the statistical structure of spike trains, including the reliability and temporal precision of responses. Spike threshold adaptation was critical to ensure that predictions remain accurate at different levels. These results confirm that simple integrate-and-fire models provide an accurate phenomenological account of spike train statistics and emphasize the functional relevance of spike threshold adaptation.

Including Long-Range Dependence in Integrate-and-Fire Models of the High Interspike-Interval Variability of Cortical Neurons

2004 ◽  
Vol 16 (10) ◽  
pp. 2125-2195 ◽  
Author(s):  
B. Scott Jackson
Keyword(s):  
Long Range ◽  
Cortical Neurons ◽  
Interspike Interval ◽  
Spike Trains ◽  
High Variability ◽  
Long Range Dependence ◽  
Interspike Intervals ◽  
Integrate And Fire ◽  
Fire Models ◽  
Output Spike

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (non-Poissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have longrange dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

scholarly journals Event-Driven Simulations of Nonlinear Integrate-and-Fire Neurons

2007 ◽  
Vol 19 (12) ◽  
pp. 3226-3238 ◽  
Author(s):  
Arnaud Tonnelier ◽  
Hana Belmabrouk ◽  
Dominique Martinez
Keyword(s):  
Neural Networks ◽  
Spiking Neural Networks ◽  
Synaptic Currents ◽  
Fire Model ◽  
Integrate And Fire ◽  
Fire Models ◽  
Event Driven

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.

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

2005 ◽  
Vol 94 (5) ◽  
pp. 3637-3642 ◽  
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.

scholarly journals Inferring Biological Mechanisms by Data-Based Mathematical Modelling: Compartment-Specific Gene Activation during Sporulation in Bacillus subtilis as a Test Case

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Dagmar Iber
Keyword(s):  
Bacillus Subtilis ◽  
Gene Activation ◽  
Experimental Information ◽  
Specific Gene ◽  
Model Parameters ◽  
Test Case ◽  
Detailed Model ◽  
Wide Range ◽  
Technical Advances ◽  
Biological Functionality

Biological functionality arises from the complex interactions of simple components. Emerging behaviour is difficult to recognize with verbal models alone, and mathematical approaches are important. Even few interacting components can give rise to a wide range of different responses, that is, sustained, transient, oscillatory, switch-like responses, depending on the values of the model parameters. A quantitative comparison of model predictions and experiments is therefore important to distinguish between competing hypotheses and to judge whether a certain regulatory behaviour is at all possible and plausible given the observed type and strengths of interactions and the speed of reactions. Here I will review a detailed model for the transcription factor , a regulator of cell differentiation during sporulation in Bacillus subtilis. I will focus in particular on the type of conclusions that can be drawn from detailed, carefully validated models of biological signaling networks. For most systems, such detailed experimental information is currently not available, but accumulating biochemical data through technical advances are likely to enable the detailed modelling of an increasing number of pathways. A major challenge will be the linking of such detailed models and their integration into a multiscale framework to enable their analysis in a larger biological context.

Physiological Gain Leads to High ISI Variability in a Simple Model of a Cortical Regular Spiking Cell

1997 ◽  
Vol 9 (5) ◽  
pp. 971-983 ◽  
Author(s):  
Todd W. Troyer ◽  
Kenneth D. Miller
Keyword(s):  
Steady State ◽  
Cortical Neurons ◽  
Cortical Cell ◽  
Firing Frequency ◽  
Cell Physiology ◽  
State Behavior ◽  
Integrate And Fire ◽  
Wide Range ◽  
Visual Cortical

To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky & Koch, 1993), it is critical to examine the dynamics of their neuronal integration, as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick, Connors, Lighthall, & Prince, 1985). After setting RC parameters, the postspike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency versus injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory [Formula: see text] and random walk pictures that have previously been proposed. When ISIs are dominated by postspike recovery,[Formula: see text] arguments hold and spiking is regular; after the “memory” of the last spike becomes negligible, spike threshold crossing is caused by input variance around a steady state and spiking is Poisson. In integrate-and-fire neurons matched to cortical cell physiology, steady-state behavior is predominant, and ISIs are highly variable at all physiological firing rates and for a wide range of inhibitory and excitatory inputs.

scholarly journals Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model

2009 ◽  
Vol 21 (8) ◽  
pp. 2114-2122 ◽  
Author(s):  
Jonathan Touboul
Keyword(s):  
Membrane Potential ◽  
Cortical Neurons ◽  
Large Scale ◽  
Quadratic Model ◽  
Fixed Amount ◽  
Cutoff Value ◽  
Fire Model ◽  
Integrate And Fire ◽  
Large Scale Simulations ◽  
Adaptation Variable

The quadratic adaptive integrate-and-fire model (Izhikevich, 2003 , 2007 ) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value Vc or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing Vc can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008 ) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005 ). Hence, these models are robust to changes in the cutoff value.

The Ornstein-Uhlenbeck Process Does Not Reproduce Spiking Statistics of Neurons in Prefrontal Cortex

1999 ◽  
Vol 11 (4) ◽  
pp. 935-951 ◽  
Author(s):  
Shigeru Shinomoto ◽  
Yutaka Sakai ◽  
Shintaro Funahashi
Keyword(s):  
Prefrontal Cortex ◽  
Order Statistics ◽  
Cortical Neurons ◽  
Biological Data ◽  
Higher Order Statistics ◽  
Uhlenbeck Process ◽  
Fire Model ◽  
Integrate And Fire ◽  
Spike Sequences ◽  
Ornstein Uhlenbeck Process

Cortical neurons of behaving animals generate irregular spike sequences. Recently, there has been a heated discussion about the origin of this irregularity. Softky and Koch (1993) pointed out the inability of standard single-neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible. Shadlen and Newsome (1994), on the other hand, demonstrated that a standard leaky integrate-and-fire model can reproduce the irregularity if the inhibition is balanced with the excitation. Motivated by this discussion, we attempted to determine whether the Ornstein-Uhlenbeck process, which is naturally derived from the leaky integration assumption, can in fact reproduce higher-order statistics of biological data. For this purpose, we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher-order statistics of the interspike intervals. Consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient, which are, respectively, a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution. It is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values. This fact suggests that the leaky integrate-and-fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons.

Hybrid Integrate-and-Fire Model of a Bursting Neuron

2003 ◽  
Vol 15 (12) ◽  
pp. 2843-2862 ◽  
Author(s):  
Barbara J. Breen ◽  
William C. Gerken ◽  
Robert J. Butera
Keyword(s):  
Bifurcation Analysis ◽  
Original Model ◽  
Full Model ◽  
Single Neurons ◽  
Tonic Firing ◽  
Fire Model ◽  
Integrate And Fire ◽  
Bursting Neuron ◽  
Computational Speed ◽  
Wide Range

We present a reduction of a Hodgkin-Huxley (HH)—style bursting model to a hybridized integrate-and-fire (IF) formalism based on a thorough bifurcation analysis of the neuron's dynamics. The model incorporates HH-style equations to evolve the subthreshold currents and includes IF mechanisms to characterize spike events and mediate interactions between the subthreshold and spiking currents. The hybrid IF model successfully reproduces the dynamic behavior and temporal characteristics of the full model over a wide range of activity, including bursting and tonic firing. Comparisons of timed computer simulations of the reduced model and the original model for both single neurons and moderate lysized networks (n ≤ 500) show that this model offers improvement in computational speed over the HH-style bursting model.

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