Emergent cortical circuit dynamics contain dense, interwoven ensembles of spike sequences

Abstract

Temporal codes are theoretically powerful encoding schemes, but their precise form in the neocortex remains unknown in part because of the large number of possible codes and the difficulty in disambiguating informative spikes from statistical noise. A biologically plausible and computationally powerful temporal coding scheme is the Hebbian assembly phase sequence (APS), which predicts reliable propagation of spikes between functionally related assemblies of neurons. Here, we sought to measure the inherent capacity of neocortical networks to produce reliable sequences of spikes, as would be predicted by an APS code. To record microcircuit activity, the scale at which computation is implemented, we used two-photon calcium imaging to densely sample spontaneous activity in murine neocortical networks ex vivo. We show that the population spike histogram is sufficient to produce a spatiotemporal progression of activity across the population. To more comprehensively evaluate the capacity for sequential spiking that cannot be explained by the overall population spiking, we identify statistically significant spike sequences. We found a large repertoire of sequence spikes that collectively comprise the majority of spiking in the circuit. Sequences manifest probabilistically and share neuron membership, resulting in unique ensembles of interwoven sequences characterizing individual spatiotemporal progressions of activity. Distillation of population dynamics into its constituent sequences provides a way to capture trial-to-trial variability and may prove to be a powerful decoding substrate in vivo. Informed by these data, we suggest that the Hebbian APS be reformulated as interwoven sequences with flexible assembly membership due to shared overlapping neurons.NEW & NOTEWORTHY Neocortical computation occurs largely within microcircuits comprised of individual neurons and their connections within small volumes (<500 μm³). We found evidence for a long-postulated temporal code, the Hebbian assembly phase sequence, by identifying repeated and co-occurring sequences of spikes. Variance in population activity across trials was explained in part by the ensemble of active sequences. The presence of interwoven sequences suggests that neuronal assembly structure can be variable and is determined by previous activity.

Keywords: Hebbian assembly; circuit dynamics; neocortex; spike sequences; temporal structure.

Fig. 1.

Structured, emergent dynamics in neocortical populations A: representative field of view showing imaged neurons spanning all cortical lamina. B: 2 sample spontaneous events of activity. C: post-event time histogram (PETH) of population showing a fast rise in activity and slower decay (means ± SD). D: accumulation of variance across the population. Each circle is a neuron (all data sets included; n = 11). For each neuron, spikes were pooled across all events aligned to the start of each event. Overlaid running, means ± SE in blue. E: mean global progression is a product of the population PETH; representative mean global progression (MGP) from data and MGP generated from an inhomogeneous Poisson population. MGPs in each case have unique ordering but similar structure. Normalized activity of neurons sorted by their mean spike time; spikes convolved with a 60-ms Gaussian window for visualization; color map from Niccoli (2012).

Fig. 2.

Identification of spike sequences. A: illustration of sequence identification method (details in materials and methods). Candidate sequences are constructed, and a sequence score is computed from weighted spike trains. The sequence was accepted if score was significantly larger than scores from surrogate spike trains. B: spike sequences of each length. Single-example columns: spike trains from 1 event (sequence spikes outlined in green); average columns: normalized spike weight across all sequences and all events showing strong sequential structure. C: no. of sequences identified across all data sets (data), trial-shuffled data sets (trial shuffle), sequences identified with randomly sorted candidate sequences (random) and surrogate spikes replicating population PETH (inhom). Boxes show median and interquartile range (IQR). Whisker length computed with default MATLAB settings (2.7 × SD × IQR).

Fig. 3.

Sequences converge onto high-membership neurons with low-variance spiking. A: sequence membership of a neuron vs. mean sequence position (note log scale on ordinate axis). Majority of neurons initiate few sequences, and a minority participate promiscuously at the end of sequences, leading to broad convergence onto a small subset of neurons. Marginal distributions are at left and bottom; color gradient is from Niccoli (2012). B: promiscuous neurons have more precise spike times relative to event onset. Each neuron variance was z-scored according to its mean spike time quantile (see inset). Mean variance shown with bootstrapped 95% confidence intervals. C: illustrative example of shared neurons between sequences. Directed graph showing sequences that share every neuron (unordered) with another sequence. Each node (n = 855) is a sequence (size corresponds to sequence length); edges lead from 1 sequence to another in which the target contains all neurons of the source.

Fig. 4.

Long sequences are bounded by the duration and variance of population activity. A: distributions of onset times for each sequence length. Short sequences occur throughout MGP; long sequences are temporally coupled to peak activity (see Fig. 1C). Only sequences in which 75% of neurons were active in an event were included. Box and whisker plots are displayed as in Fig. 2C. B: running means ± SD of sequence score against sequence onset time. Short sequences are robustly reliable over time; longer sequences lose reliability in conjunction with accumulation of variability (Fig. 1D).

Fig. 5.

Sequences comprise a large fraction of population activity. A: total population spiking and spiking categorized as either sequence or nonsequence spiking (means ± SD). B: sequences track population activity; more spikes belong to sequences when more neurons are spiking (means ± SE). Uniform probability of sequence spikes was generated by shuffling spikes in each event. C: active sequences, within any 1 event, are less common yet show similar evolution in time as the average of events (means ± SD).

Fig. 6.

Single trails of MGP are composed of unique subsets of interwoven sequences A: 2 example rasters with overlaid active sequences. Neurons sorted according to MGP; events exhibit unique (top: blue; bottom: orange) and overlapping (green) sequences. B: distribution of shared sequence spikes between event pairs. Low overall overlap, with many events sharing nearly no sequences. C: sequence spikes occur closer to expected MGP position (P = 1.1 × 10⁻³, 2-way ANOVA). Box and whiskers plots displayed as in Fig. 2C. D: all sequences show strong pooling at the end of long sequences (black bar is mean, gray dots are for each data set); active sequences show balanced convergence and divergence throughout event (means ± SE; gray points show each time point across all events).

Fig. 7.

Sequence composition of MGP suggests an interwoven assembly phase sequence framework. A: distinct, nonoverlapping assemblies (neuron color) underlie propagation of activity. Traditionally, the hypothesis is interpreted as dynamics being driven by a concatenated feedforward assembly phase sequence. Assemblies are defined by the group of coactive neurons in a time window, and noise intrinsic to each assembly leads to trial-to-trial variability. B: in our suggested revision, based on our data analysis, neurons belong to many assemblies, and probabilistic activation of sequences underlies propagation of activity. Neuron color denotes single-trial assembly membership. Arrows denote underlying sequences; gray neurons and arrows are inactive in this trial. Assemblies are defined by the ensemble of active sequences.