Burst coding despite unimodal interval distributions

The burst coding hypothesis posits that the occurrence of sudden high-frequency patterns of action potentials constitutes a salient syllable of the neural code. Many neurons, however, do not produce clearly demarcated bursts, an observation invoked to rule out the pervasiveness of this coding scheme across brain areas and cell types. Here we ask how identifiable spike-timing patterns have to be to preserve potent transmission of information. Should we expect that neurons avoid ambiguous patterns that are neither clearly bursts nor isolated spikes? We addressed these questions using information theory and computational simulations. By quantifying how information transmission depends on firing statistics, we found that the information transmitted is not strongly influenced by the presence of clearly demarcated modes in the interspike interval distribution, a feature often used to identify the presence of burst coding. Instead, we found that neurons having unimodal interval distributions were still able to ascribe different meanings to bursts and isolated spikes. In this regime, information transmission depends on properties of the synapses as well as the length and relative frequency of bursts. Furthermore, we found that common metrics used to quantify burstiness were also unable to predict the degree with which bursts could be used to carry information. Our results provide guiding principles for the implementation of coding strategies based on spike-timing patterns, and show that even unimodal firing statistics can be consistent with a bivariate neural code.

EFFECT OF MEMBRANE DEPOLARISATION OF SUPRACHIASMATIC NUCLEUS NEURONS ON SPIKE ACTIVITY IN VITRO

The properties of spike activity of neurons of the suprachiasmatic nucleus during their membrane depolarisation in vitro are investigated on rat hypothalamic slices. Depolarisation of membrane caused an increase in activity of cells and a decrease in entropy log interspike interval distribution were used as a measure of spikes irregularity generation. Possible mechanisms of the effects are discussed.

ANALYSIS OF INTERSPIKE-INTERVALS FOR THE GENERAL CLASS OF INTEGRATE-AND-FIRE MODELS WITH PERIODIC DRIVE

We study one-dimensional integrate-and-fire models of the general type x˙ = F(t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F(t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle homeomorphism, we provide a detailed description of the regularity properties of the sequence of interspike-intervals and behaviour of the interspike-interval distribution.

Identification and Continuity of the Distributions of Burst-Length and Interspike Intervals in the Stochastic Morris-Lecar Neuron

Using the Morris-Lecar model neuron with a type II parameter set and K+-channel noise, we investigate the interspike interval distribution as increasing levels of applied current drive the model through a subcritical Hopf bifurcation. Our goal is to provide a quantitative description of the distributions associated with spiking as a function of applied current. The model generates bursty spiking behavior with sequences of random numbers of spikes (bursts) separated by interburst intervals of random length. This kind of spiking behavior is found in many places in the nervous system, most notably, perhaps, in stuttering inhibitory interneurons in cortex. Here we show several practical and inviting aspects of this model, combining analysis of the stochastic dynamics of the model with estimation based on simulations. We show that the parameter of the exponential tail of the interspike interval distribution is in fact continuous over the entire range of plausible applied current, regardless of the bifurcations in the phase portrait of the model. Further, we show that the spike sequence length, apparently studied for the first time here, has a geometric distribution whose associated parameter is continuous as a function of applied current over the entire input range. Hence, this model is applicable over a much wider range of applied current than has been thought.

Maximum Likelihood Decoding of Neuronal Inputs from an Interspike Interval Distribution

An expression for the probability distribution of the interspike interval of a leaky integrate-and-fire (LIF) model neuron is rigorously derived, based on recent theoretical developments in the theory of stochastic processes. This enables us to find for the first time a way of developing maximum likelihood estimates (MLE) of the input information (e.g., afferent rate and variance) for an LIF neuron from a set of recorded spike trains. Dynamic inputs to pools of LIF neurons both with and without interactions are efficiently and reliably decoded by applying the MLE, even within time windows as short as 25 msec.