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

Abstract

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.

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

“…The oldest report that is known to the authors is in the activity of motoneurons in humans (Hagiwara 1949). Subsequent studies have found nonrenewal spiking statistics in retinal cat retinal ganglion cells (Kuffler et al 1957;Rodieck 1967;Levine 1980), cat superior olivary neurons (Goldberg et al 1964;Tsuchitani and Johnson 1985), cat peripheral auditory fibers (Lowen and Teich 1992), cat cochlear nuclear neurons (Goldberg and Greenwood 1966), cat medullary sympathetic neurons (Lewis et al 2001), cat sympathetic efferent fibers (Floyd et al 1982), pigeon vestibular afferents (Correia and Landolt 1977), weakly electric fish electroreceptor neurons (Longtin and Racicot 1997;Chacron et al 2000;Ratnam and Nelson 2000;Chacron et al 2001b;Chacron et al 2005b;Gussin et al 2007), paddlefish electroreceptors (Bahar et al 2001;Neiman and Russell 2001;Neiman and Russell 2004), catfish electroreceptors (Schäfer et al 1995), weakly electric fish electrosensory pyramidal neurons (Doiron et al 2003;Chacron et al 2007), honeybee mushroom body neurons (Farkhooi et al 2009), grasshopper auditory neurons (Schwalger et al 2010), primate spinothalamic neurons (Surmeier et al 1989), rat mesencephalic reticular neurons (Lansky and Radil 1987), primate somatosensory cortical neurons (Yamamoto and Nakahama 1983;Lebedev and Nelson 1996;Nawrot et al 2007), as well as rat entorhinal cortical pyramidal and interneurons (Engel et al 2008). We note that the last five studies challenge the notion that cortical neurons can be described by a renewal process such as the Poisson process and shall return to this point later.…”

“…Several investigators have reported nonrenewal spike train statistics in the form of a negative ISI serial correlation coefficient at lag 1 that is significantly different from zero (Kuffler et al 1957;Goldberg et al 1964;Yamamoto and Nakahama 1983;Tsuchitani and Johnson 1985;Schäfer et al 1995;Chacron et al 2000;Chacron et al 2007;Nawrot et al 2007;Engel et al 2008;Farkhooi et al 2009). As mentioned above, this implies that ISIs that are shorter than average tend to be followed by ISIs that are longer than average and vice versa, thus giving rise to patterning in the spike train.…”

“…While it is frequently assumed that cortical neurons can be modeled by Poisson processes with a refractory period (Shadlen and Newsome 1998;Kara et al 2000) due to their high variability (Softky and Koch 1993), this view is being challenged more and more (Engel et al 2008;Farkhooi et al 2009;Maimon and Assad 2009). In particular, recent studies have found that cortical neurons could display nonrenewal spike train statistics in vivo (Engel et al 2008).…”

“…In particular, recent studies have found that cortical neurons could display nonrenewal spike train statistics in vivo (Engel et al 2008). A more recent paper has argued that it is possible that nonrenewal spike train statistics are far more prevalent in cortical neurons than was originally thought and might have been missed in extracellular recordings due to missed spikes (Farkhooi et al 2009). Intracellular recordings from cortical neurons have shown that they can display significant patterning in their spiking activities (Engel et al 2008), and further studies are needed to test this hypothesis.…”

Onset of negative interspike interval correlations in adapting neurons

“…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].…”