Neurons often display complex patterns of action potential firing in response to a wide variety of inputs. Correlations amongst the interspike interval sequence are often seen in experimental data from sensory neurons including electroreceptor afferents from weakly electric fish. Here we review some of our recent computational,
theoretical, and experimental results on the mechanism by which negative interspike interval correlations increase information transfer: noise shaping. This mechanism might explain the behavioral hypersensitivity displayed by weakly electric fish when detecting prey.
Many of the stochastic neuron models employed in the neurobiological
literature generate renewal point processes, i.e., successive
intervals between spikes are statistically uncorrelated. Recently,
however, much experimental evidence for positive and negative
correlations in the interspike interval (ISI) sequence of real neurons
has been accumulated. It has been shown that these correlations can
have implications for neuronal functions. We study a leaky
integrate-and-fire (LIF) model with a dynamical threshold or an
adaptation current both of which lead to negative correlations. Conditions are identified where these models are equivalent. The ISI statistics, the serial correlation coefficient, and the power spectrum of the spike train, are numerically investigated for various parameter sets.
The pyramidal cells of weakly electric fish respond to environmental broadband electrical stimuli. They have recently been shown to exhibit oscillations in mean firing rate in response to global stimuli that affect the whole body simultaneously similar to communication stimuli for these animals. In contrast, for spatially localized stimuli such as those produced by prey, the firing rate simply fluctuates around a constant mean. This switch in coding strategy relies on delayed negative (inhibitory) feedback connections in the neural network. We first summarize these experimental findings, as well as our mathematical modeling of this effect using a globally-coupled delayed inhibitory network of leaky
integrate-and-fire neurons (LIF's). Here we study the mechanism of the transition from oscillatory to non-oscillatory firing states in such networks. This is done using simulations of a simpler network of LIF's with current based Gaussian white noise stimuli, rather than conductance based bandlimited Gaussian stimuli. We focus on the effect of feedback gain, current bias, and stimulus intensity
on the oscillation under global conditions, and see how the decrease of these parameters brings on a response characteristic of the local case. These simulations are performed for a fixed amount of individual synaptic noise to each cell. We also show how insights into these results can be obtained from the analysis of stimulus-induced oscillations in a simpler rate model description of this spatially-extended excitable system.