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

Abstract

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.

Onset of negative interspike interval correlations in adapting neurons

“…In their work, Chacron et al demonstrated that a slow external noise leaves relatively intact the short-range correlations, while destroying negative correlations at large lags, giving rise to small and slowly decaying positive correlations which dominate the asymptotic regime. On the other hand, across different neural systems it has been observed that the only significant SCC corresponds to the lag 1 [19,23], which reinforces the idea that a slow external noise would be an important part of the incoming signal, in addition to fast fluctuations. Theoretically, the analysis of the spike-count variance for IF neuron models driven by slow fluctuations were successfully carried out via a quasistatic approximation [34,36].…”

“…The external current is composed by a static input and fast fluctuations. For this system, the dependence of the adaptation current on the past history, through the initial states of the adaptation process, facilitates the development of correlations between successive ISIs [6,[13][14][15]19]. In the regime of slight adaptation, we have shown that correlations share a general structure across different models.…”

“…After some calculus [it is convenient to leave unevaluated all integrals in τ i in the transition density from s n to s n+k , for posterior evaluation in Eq. (19)], the average between successive ISIs is given, up to first order in α (and/or ε ), by…”

“…First, they modify the tuning curve between signals and responses or the input-output relationship mentioned above, which helps to match dynamic ranges [2][3][4][5][6]. Second, they introduce negative correlations between successive interspike intervals (ISIs) in stationary neural spike trains [6,[13][14][15]19]. While the first effect reflects the modification of the mean spike count, the second effect implies a strong change in its variance (and higher-order properties).…”

“…This change * urdapile@ib.cnea.gov.ar arises from the fact that the presence of negative correlations in a point process reduces the long-term variability in the counting process that defines the rate code [20]. Taken together, both effects deeply affect the encoding reliability [19,[21][22][23][24]. The presence of negative correlations also affects the coding capabilities of other related schemes; for example, coding of slowly varying signals through a mechanism called noise shaping [25][26][27] (demonstrated for negative correlations arising from a history-dependent threshold, but also valid for spikerelated adaptation currents), or adaptation-based independent codes [28].…”