Noise in Integrate-and-Fire Neurons: From Stochastic Input to Escape Rates

2000 ◽  
Vol 12 (2) ◽  
pp. 367-384 ◽  
Author(s):  
Hans E. Plesser ◽  
Wulfram Gerstner
Keyword(s):  
Membrane Potential ◽  
Diffusion Approximation ◽  
Hazard Function ◽  
Time Dependent ◽  
Integrate And Fire ◽  
Probability Current ◽  
Periodic Input ◽  
Stochastic Input ◽  
Free Membrane ◽  
Noise Models

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.

A frequency-resolved mutual information rate and its application to neural systems

2015 ◽  
Vol 113 (5) ◽  
pp. 1342-1357 ◽  
Author(s):  
Davide Bernardi ◽  
Benjamin Lindner
Keyword(s):  
Mutual Information ◽  
Information Filtering ◽  
Coherence Function ◽  
Time Dependent ◽  
Information Rate ◽  
Qualitative Behavior ◽  
Theoretical Problem ◽  
Neural Firing ◽  
Integrate And Fire ◽  
Model Free

The encoding and processing of time-dependent signals into sequences of action potentials of sensory neurons is still a challenging theoretical problem. Although, with some effort, it is possible to quantify the flow of information in the model-free framework of Shannon's information theory, this yields just a single number, the mutual information rate. This rate does not indicate which aspects of the stimulus are encoded. Several studies have identified mechanisms at the cellular and network level leading to low- or high-pass filtering of information, i.e., the selective coding of slow or fast stimulus components. However, these findings rely on an approximation, specifically, on the qualitative behavior of the coherence function, an approximate frequency-resolved measure of information flow, whose quality is generally unknown. Here, we develop an assumption-free method to measure a frequency-resolved information rate about a time-dependent Gaussian stimulus. We demonstrate its application for three paradigmatic descriptions of neural firing: an inhomogeneous Poisson process that carries a signal in its instantaneous firing rate; an integrator neuron (stochastic integrate-and-fire model) driven by a time-dependent stimulus; and the synchronous spikes fired by two commonly driven integrator neurons. In agreement with previous coherence-based estimates, we find that Poisson and integrate-and-fire neurons are broadband and low-pass filters of information, respectively. The band-pass information filtering observed in the coherence of synchronous spikes is confirmed by our frequency-resolved information measure in some but not all parameter configurations. Our results also explicitly show how the response-response coherence can fail as an upper bound on the information rate.

Ca2+-activated Cl− current in cultured myenteric neurons from murine proximal colon

2003 ◽  
Vol 284 (4) ◽  
pp. C839-C847 ◽  
Author(s):  
Sok Han Kang ◽  
Pieter Vanden Berghe ◽  
Terence K. Smith
Keyword(s):  
Membrane Potential ◽  
Channel Blocker ◽  
Reversal Potential ◽  
Outward Current ◽  
Proximal Colon ◽  
Time Dependent ◽  
Equilibrium Potential ◽  
Resting Membrane Potential ◽  
Myenteric Neurons ◽  
Whole Cell Patch Clamp

Whole cell patch-clamp recordings were made from cultured myenteric neurons taken from murine proximal colon. The micropipette contained Cs+ to remove K+ currents. Depolarization elicited a slowly activating time-dependent outward current ( I tdo), whereas repolarization was followed by a slowly deactivating tail current ( I tail). I tdo and I tail were present in ∼70% of neurons. We identified these currents as Cl− currents ( I Cl), because changing the transmembrane Cl− gradient altered the measured reversal potential ( E rev) of both I tdo and I tail with that for I tailshifted close to the calculated Cl− equilibrium potential ( E Cl). I Cl are Ca2+-activated Cl− current [ I Cl(Ca)] because they were Ca2+dependent. E Cl, which was measured from the E rev of I Cl(Ca) using a gramicidin perforated patch, was −33 mV. This value is more positive than the resting membrane potential (−56.3 ± 2.7 mV), suggesting myenteric neurons accumulate intracellular Cl−. ω-Conotoxin GIVA [0.3 μM; N-type Ca2+ channel blocker] and niflumic acid [10 μM; known I Cl(Ca) blocker], decreased the I Cl(Ca). In conclusion, these neurons have I Cl(Ca) that are activated by Ca2+entry through N-type Ca2+ channels. These currents likely regulate postspike frequency adaptation.

Protective effect of the dimer of 16,16-diMePGB1 against KCN-induced mitochondrial failure in hepatocytes

1992 ◽  
Vol 263 (2) ◽  
pp. C405-C411 ◽  
Author(s):  
Y. Park ◽  
T. M. Devlin ◽  
D. P. Jones
Keyword(s):  
Membrane Potential ◽  
Protective Effect ◽  
Ion Transport ◽  
Mitochondrial Membrane Potential ◽  
Mitochondrial Function ◽  
Mitochondrial Membrane ◽  
Time Dependent ◽  
Dependent Manner ◽  
Protective Effects ◽  
Cellular Swelling

The dimer and trimer of 16,16-dimethyl-15-dehydroprostaglandin B1 (16,16-diMePGB1) previously have been shown to have protective effects on mitochondrial function. To examine the potential mechanisms involved in protection against mitochondrial failure, we have studied the effects of the dimer of 16,16-diMe-PGB1 (dicalciphor) on mitochondrial function in hepatocytes exposed to KCN. Addition of micromolar concentrations of dicalciphor provided substantial protection against KCN-induced toxicity in a concentration- and time-dependent manner. Dicalciphor, however, had no effect on total or mitochondrial ATP losses in KCN-treated cells. The dimer prevented the marked loss of mitochondrial membrane potential (delta psi) and delta pH that occurs as a result of KCN treatment and prevented KCN-induced loading of phosphate in mitochondria. Furthermore, the dimer of 16,16-diMePGB1 also prevented KCN-induced mitochondrial and cellular swelling. These results demonstrate that dicalciphor protects against KCN-induced damage and that this protection is associated with regulation of specific mitochondrial ion transport functions.

On some time-non-homogeneous diffusion approximations to queueing systems

1987 ◽  
Vol 19 (4) ◽  
pp. 974-994 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Approximation ◽  
Busy Period ◽  
Queueing Systems ◽  
Time Dependent ◽  
Single Server ◽  
Time Varying ◽  
Diffusion Approximations ◽  
Linear Drift ◽  
Transition Functions ◽  
Fcfs Discipline

Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

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.

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