Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density

Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a delay. We investigate here, how does the presence of inhibitory feedback affect the output firing statistics. Using binding neuron (BN) as a model, we derive analytically the exact expressions for the output interspike intervals (ISI) probability density, mean output ISI and coefficient of variation as functions of model's parameters for the case of threshold 2. Using the leaky integrate-and-fire (LIF) model, as well as the BN model with higher thresholds, these statistical quantities are found numerically. In contrast to the previously studied situation of no feedback, the ISI probability densities found here both for BN and LIF neuron become bimodal and have discontinuity of jump type. Nevertheless, the presence of inhibitory delayed feedback was not found to affect substantially the output ISI coefficient of variation. The ISI coefficient of variation found ranges between 0.5 and 1. It is concluded that introduction of delayed inhibitory feedback can radically change neuronal output firing statistics. This statistics is as well distinct from what was found previously (Vidybida and Kravchuk, 2009) by a similar method for excitatory neuron with delayed feedback.     

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker–Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).     

Human Exposure to Malathion during a Possible Vector-Control Intervention against West Nile Virus. II: Evaluation of the Toxicological Risks Using a Probabilistic Approach

In order to prevent the propagation of West Nile Virus (WNV), insecticide sprayings have been carried out in several locations in North America since 1999 with the objective of controlling the mosquito populations that transmit this pathogen. An attempt to quantitatively compare the risk of developing a health response to WNV infection with the toxicological risk of insecticides is presented here. First, the acute and subchronic environmental concentrations resulting from repeated spraying events were modeled according to a reasonable worst-case spraying sequence established in an intervention program proposed by the Government of Quebec (Canada). Second, probability density functions (PDF) were established for some exposure parameters according to the data for the concerned population, when feasible. Monte Carlo analyses were performed by incorporating these PDF into the equations used to calculate the daily absorbed doses resulting from the exposure scenarios presented in the companion article (this issue). The results showed that for a significant proportion of the population, aerial and, to a lesser extent, ground sprayings of malathion can generate acute and subchronic exposure that may exceed some levels of toxicological concern based on the USEPA's reference values. Indeed, in the case of acute exposure following aerial spraying for infants, toddlers, and children, these proportions were respectively 37.1%, 59.5%, and 32.8% of the individuals, and 27.3%, 41.3%, and 24.9% following subchronic exposure. For ground spraying, these values were 12.5%, 24.2%, 8.8%; and 9.8%, 16.5%, and 7.4%. These results allowed the comparison of the probability of exceeding a level of toxicological concern for malathion exposure with the probability of developing WNV symptoms. This comparison shows that in some circumstances, the toxicological risk of malathion may exceed the infectious risk of WNV.