Non-Markov negative correlation between interspike intervals in mammalian sympathetic efferent discharges

Nonrenewal spike train statistics: causes and functional consequences on neural coding

Many neurons display significant patterning in their spike trains (e.g. oscillations, bursting), and there is accumulating evidence that information is contained in these patterns. In many cases, this patterning is caused by intrinsic mechanisms rather than external signals. In this review, we focus on spiking activity that displays nonrenewal statistics (i.e. memory that persists from one firing to the next). Such statistics are seen in both peripheral and central neurons and appear to be ubiquitous in the CNS. We review the principal mechanisms that can give rise to nonrenewal spike train statistics. These are separated into intrinsic mechanisms such as relative refractoriness and network mechanisms such as coupling with delayed inhibitory feedback. Next, we focus on the functional roles for nonrenewal spike train statistics. These can either increase or decrease information transmission. We also focus on how such statistics can give rise to an optimal integration timescale at which spike train variability is minimal and how this might be exploited by sensory systems to maximize the detection of weak signals. We finish by pointing out some interesting future directions for research in this area. In particular, we explore the interesting possibility that synaptic dynamics might be matched with the nonrenewal spiking statistics of presynaptic spike trains in order to further improve information transmission.

Serial correlation in neural spike trains: experimental evidence, stochastic modeling, and single neuron variability

The activity of spiking neurons is frequently described by renewal point process models that assume the statistical independence and identical distribution of the intervals between action potentials. However, the assumption of independent intervals must be questioned for many different types of neurons. We review experimental studies that reported the feature of a negative serial correlation of neighboring intervals, commonly observed in neurons in the sensory periphery as well as in central neurons, notably in the mammalian cortex. In our experiments we observed the same short-lived negative serial dependence of intervals in the spontaneous activity of mushroom body extrinsic neurons in the honeybee. To model serial interval correlations of arbitrary lags, we suggest a family of autoregressive point processes. Its marginal interval distribution is described by the generalized gamma model, which includes as special cases the log-normal and gamma distributions, which have been widely used to characterize regular spiking neurons. In numeric simulations we investigated how serial correlation affects the variance of the neural spike count. We show that the experimentally confirmed negative correlation reduces single-neuron variability, as quantified by the Fano factor, by up to 50%, which favors the transmission of a rate code. We argue that the feature of a negative serial correlation is likely to be common to the class of spike-frequency-adapting neurons and that it might have been largely overlooked in extracellular single-unit recordings due to spike sorting errors.

A stochastic model for neuronal bursting

A new stochastic model for bursting of neuronal firing is proposed. It is based on stochastic diffusion and related to the first passage time problem. However, the model is not of renewal type. Its form and parameters are physiologically interpretable. Parametric and non-parametric inferential issues are discussed.

Stochastic model neuron without resetting of dendritic potential: application to the olfactory system

A two-dimensional neuronal model, in which the membrane potential of the dendrite evolves independently from that at the trigger zone of the axon, is proposed and studied. In classical one-dimensional neuronal models the dendritic and axonal potentials cannot be distinguished, and thus they are reset to resting level after firing of an action potential, whereas in the present model the dendritic potential is not reset. The trigger zone is modelled by a simplified leaky integrator (RC circuit) and the dendritic compartment can be described by any of the classical one-dimensional neuronal models. The new model simulates observed features of the firing dynamics which are not displayed by classical models, namely positive correlation between interspike intervals and endogenous bursting. It gives a more natural account of features already accounted for in previous models, such as the absence of an upper limit for the coefficient of variation of intervals (i.e. irregular firing). It allows the first- and second-order neurons of the olfactory system to be described with the same basic assumptions, which was not the case in one-point models. Nevertheless it keeps the main qualitative properties found previously, such as the existence of three regimens of firing with increasing stimulus concentration and the sigmoid shape of the firing frequency of first-order neurons as a function of the logarithm of stimulus concentration.

Effects of afterhyperpolarization on neuronal firing

Stein's model for a neuron is studied. This model is modified to take into account the effects of afterhyperpolarization on the neuronal firing. The relative refractory phase, following the absolute one, is modelled by a time-increasing amplitude of postsynaptic potentials and it is also incorporated into the model. Besides the simulation of the model, some theoretical results and approximation methods are derived. Afterhyperpolarization tends to preserve the linearity of the frequency transfer characteristic and it has a limited effect on the moments of the interspike intervals in general. The main effects are seen at high firing rates and in the removal of short intervals in the interspike interval histogram.