The non-capacitor model of leaky integrate-and-fire VO2 neuron with the thermal mechanism of the membrane potential

We analyze the effect of noise in integrate-and-fire neurons driven by time-dependent input and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard function that has a gaussian dependence on the distance between the (noise-free) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.

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

Neural Computation ◽

10.1162/neco.2009.09-08-853 ◽

2009 ◽

Vol 21 (8) ◽

pp. 2114-2122 ◽

Cited By ~ 22

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.

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Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model

Biosystems ◽

10.1016/j.biosystems.2006.03.003 ◽

2007 ◽

Vol 87 (1) ◽

pp. 49-57 ◽

Cited By ~ 12

Author(s):

Junko Inoue ◽

Shinji Doi

Keyword(s):

Membrane Potential ◽

Coefficient Of Variation ◽

Neuron Model ◽

Lower Boundary ◽

Interspike Intervals ◽

Integrate And Fire ◽

Sensitive Dependence ◽

Integrate And Fire Neuron

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Calculation of Interspike Intervals for Integrate-and-Fire Neurons with Poisson Distribution of Synaptic Inputs

Neural Computation ◽

10.1162/089976600300015141 ◽

2000 ◽

Vol 12 (8) ◽

pp. 1789-1820 ◽

Cited By ~ 24

Author(s):

A. N. Burkitt ◽

G. M. Clark

Keyword(s):

Membrane Potential ◽

Probability Density ◽

Poisson Distribution ◽

Conditional Probability ◽

Conditional Probability Density ◽

Interspike Intervals ◽

Translational Invariance ◽

Postsynaptic Response ◽

Arrival Times ◽

Integrate And Fire

We present a new technique for calculating the interspike intervals of integrate-and-fire neurons. There are two new components to this technique. First, the probability density of the summed potential is calculated by integrating over the distribution of arrival times of the afferent post-synaptic potentials (PSPs), rather than using conventional stochastic differential equation techniques. A general formulation of this technique is given in terms of the probability distribution of the inputs and the time course of the postsynaptic response. The expressions are evaluated in the gaussian approximation, which gives results that become more accurate for large numbers of small-amplitude PSPs. Second, the probability density of output spikes, which are generated when the potential reaches threshold, is given in terms of an integral involving a conditional probability density. This expression is a generalization of the renewal equation, but it holds for both leaky neurons and situations in which there is no time-translational invariance. The conditional probability density of the potential is calculated using the same technique of integrating over the distribution of arrival times of the afferent PSPs. For inputs with a Poisson distribution, the known analytic solutions for both the perfect integrator model and the Stein model (which incorporates membrane potential leakage) in the diffusion limit are obtained. The interspike interval distribution may also be calculated numerically for models that incorporate both membrane potential leakage and a finite rise time of the postsynaptic response. Plots of the relationship between input and output firing rates, as well as the coefficient of variation, are given, and inputs with varying rates and amplitudes, including inhibitory inputs, are analyzed. The results indicate that neurons functioning near their critical threshold, where the inputs are just sufficient to cause firing, display a large variability in their spike timings.

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How Sample Paths of Leaky Integrate-and-Fire Models Are Influenced by the Presence of a Firing Threshold

Neural Computation ◽

10.1162/neco_a_00143 ◽

2011 ◽

Vol 23 (7) ◽

pp. 1743-1767 ◽

Cited By ~ 7

Author(s):

Maria Teresa Giraudo ◽

Priscilla E. Greenwood ◽

Laura Sacerdote

Keyword(s):

Membrane Potential ◽

Diffusion Process ◽

Fixed Time ◽

Firing Time ◽

Fire Model ◽

Integrate And Fire ◽

Sample Paths ◽

The Mean ◽

First Time

Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t1 and of a diffusion process conditioned to cross the boundary for the first time at t1. This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.

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On a Stochastic Leaky Integrate-and-Fire Neuronal Model

Neural Computation ◽

10.1162/neco_a_00023 ◽

2010 ◽

Vol 22 (10) ◽

pp. 2558-2585 ◽

Cited By ~ 18

Author(s):

A. Buonocore ◽

L. Caputo ◽

E. Pirozzi ◽

L.M. Ricciardi

Keyword(s):

Membrane Potential ◽

Probability Density ◽

Time Course ◽

First Passage Time ◽

Passage Time ◽

Neuronal Model ◽

Resting Potential ◽

Uhlenbeck Process ◽

Integrate And Fire ◽

Stochastic Framework

The leaky integrate-and-fire neuronal model proposed in Stevens and Zador ( 1998 ), in which time constant and resting potential are postulated to be time dependent, is revisited within a stochastic framework in which the membrane potential is mathematically described as a gauss-diffusion process. The first-passage-time probability density, miming in such a context the firing probability density, is evaluated by either the Volterra integral equation of Buonocore, Nobile, and Ricciardi ( 1987 ) or, when possible, by the asymptotics of Giorno, Nobile, and Ricciardi ( 1990 ). The model examined here represents an extension of the classic leaky integrate-and-fire one based on the Ornstein-Uhlenbeck process in that it is in principle compatible with the inclusion of some other physiological characteristics such as relative refractoriness. It also allows finer tuning possibilities in view of its accounting for certain qualitative as well as quantitative features, such as the behavior of the time course of the membrane potential prior to firings and the computation of experimentally measurable statistical descriptors of the firing time: mean, median, coefficient of variation, and skewness. Finally, implementations of this model are provided in connection with certain experimental evidence discussed in the literature.

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Measurement of spontaneous neuronal membrane activity by time lapse confocal microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100141238 ◽

1995 ◽

Vol 53 ◽

pp. 972-973

Author(s):

R H. Selinfreund ◽

A. H. Cornell-Bell

Keyword(s):

Membrane Potential ◽

Confocal Microscopy ◽

Patch Clamp ◽

Electrical Activity ◽

Time Lapse ◽

Neuronal Firing ◽

Neuronal Membrane ◽

Pituitary Cells ◽

Patch Clamp Recording ◽

Spontaneous Electrical Activity

Cellular electrophysiological properties are normally monitored by standard patch clamp techniques . The combination of membrane potential dyes with time-lapse laser confocal microscopy provides a more direct, least destructive rapid method for monitoring changes in neuronal electrical activity. Using membrane potential dyes we found that spontaneous action potential firing can be detected using time-lapse confocal microscopy. Initially, patch clamp recording techniques were used to verify spontaneous electrical activity in GH4\C1 pituitary cells. It was found that serum depleted cells had reduced spontaneous electrical activity. Brief exposure to the serum derived growth factor, IGF-1, reconstituted electrical activity. We have examined the possibility of developing a rapid fluorescent assay to measure neuronal activity using membrane potential dyes. This neuronal regeneration assay has been adapted to run on a confocal microscope. Quantitative fluorescence is then used to measure a compounds ability to regenerate neuronal firing.The membrane potential dye di-8-ANEPPS was selected for these experiments. Di-8- ANEPPS is internalized slowly, has a high signal to noise ratio (40:1), has a linear fluorescent response to change in voltage.

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Fluorescent potentiometric dyes for membrane-potential imaging

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100168566 ◽

1994 ◽

Vol 52 ◽

pp. 166-167

Author(s):

Leslie M. Loew

Keyword(s):

Membrane Potential ◽

Single Cells ◽

Quantitative Imaging ◽

Optical Recording ◽

Biological Processes ◽

Major Focus ◽

The Past ◽

Excitable Systems ◽

Major Application ◽

The Impact

A major application of potentiometric dyes has been the multisite optical recording of electrical activity in excitable systems. After being championed by L.B. Cohen and his colleagues for the past 20 years, the impact of this technology is rapidly being felt and is spreading to an increasing number of neuroscience laboratories. A second class of experiments involves using dyes to image membrane potential distributions in single cells by digital imaging microscopy - a major focus of this lab. These studies usually do not require the temporal resolution of multisite optical recording, being primarily focussed on slow cell biological processes, and therefore can achieve much higher spatial resolution. We have developed 2 methods for quantitative imaging of membrane potential. One method uses dual wavelength imaging of membrane-staining dyes and the other uses quantitative 3D imaging of a fluorescent lipophilic cation; the dyes used in each case were synthesized for this purpose in this laboratory.

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