Functional triplet motifs underlie accurate predictions of single-trial responses in populations of tuned and untuned V1 neurons.

Visual stimuli evoke activity in visual cortical neuronal populations. Neuronal activity can be selectively modulated by particular visual stimulus parameters, such as the direction of a moving bar of light, resulting in well-defined trial averaged tuning properties. However, given any single stimulus parameter, a large number of neurons in visual cortex remain unmodulated, and the role of this untuned population is not well understood. Here, we use two-photon calcium imaging to record, in an unbiased manner, from large populations of layer 2/3 excitatory neurons in mouse primary visual cortex to describe co-varying activity on single trials in neuronal populations consisting of both tuned and untuned neurons. Specifically, we summarize pairwise covariability with an asymmetric partial correlation coefficient, allowing us to analyze the resultant population correlation structure, or functional network, with graph theory. Using the graph neighbors of a neuron, we find that the local population, including both tuned and untuned neurons, are able to predict individual neuron activity on a moment to moment basis, while also recapitulating tuning properties of tuned neurons. Variance explained in total population activity scales with the number of neurons imaged, demonstrating larger sample sizes are required to fully capture local network interactions. We also find that a specific functional triplet motif in the graph results in the best predictions, suggesting a signature of informative correlations in these populations. In summary, we show that unbiased sampling of the local population can explain single trial response variability as well as trial-averaged tuning properties in V1, and the ability to predict responses is tied to the occurrence of a functional triplet motif.

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

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.

Ensemble stacking mitigates biases in inference of synaptic connectivity.

A promising alternative to directly measuring the anatomical connections in a neuronal population is inferring the connections from the activity. We employ simulated spiking neuronal networks to compare and contrast commonly used inference methods that identify likely excitatory synaptic connections using statistical regularities in spike timing. We find that simple adjustments to standard algorithms improve inference accuracy: A signing procedure improves the power of unsigned mutual-information-based approaches and a correction that accounts for differences in mean and variance of background timing relationships, such as those expected to be induced by heterogeneous firing rates, increases the sensitivity of frequency-based methods. We also find that different inference methods reveal distinct subsets of the synaptic network and each method exhibits different biases in the accurate detection of reciprocity and local clustering. To correct for errors and biases specific to single inference algorithms, we combine methods into an ensemble. Ensemble predictions, generated as a linear combination of multiple inference algorithms, are more sensitive than the best individual measures alone, and are more faithful to ground-truth statistics of connectivity, mitigating biases specific to single inference methods. These weightings generalize across simulated datasets, emphasizing the potential for the broad utility of ensemble-based approaches.