Spiking and bursting activity in stochastic recurrent networks

Pyramidal neurons in mammalian cortical layer 5 (L5) send long-range projections to other cortical areas and subcortical structures. Understanding the outputs of the cortex thus requires understanding the activity of these neurons. Thick-tufted L5 pyramidal neurons generate two types of action potentials: 1) the classic sodium-potassium action potentials (Na-K APs) generated at the axon hillock, which propagate down the axon to trigger neurotransmitter release and backpropagate across the soma and dendritic tree, and 2) slow calcium spikes in the apical dendrite, triggered by the coincidence of a back-propagating Na-K AP and dendritic depolarization [Larkum et al., 1999]. These calcium spikes can then trigger a burst of Na-K APs. Somatostatin-positive Martinotti interneurons, which specifically target the apical dendrite, can gate dendrite-dependent bursts. Dendrite-dependent bursting has been proposed as a mechanism for coincidence detection [Larkum, 2013], multiplexed spike-burst sensory coding [Naud and Sprekeler, 2018], and provide a substrate for powerful and biologically plausible learning algorithms, e.g., [Greedy et al., 2022, Payeur et al., 2021]. Understanding these theoretically requires a theory for the joint spiking and bursting activity in cortical networks.

Here, we study a simple stochastic model of dendrite-dependent bursting. Using tools from statistical field theory, we develop the joint probability density functional of spikes and bursts in recurrent networks. This allows the prediction of mean spike and burst rates, as well as pairwise and higher-order correlations between spikes and bursts. We show how somatic vs dendritic-targeting connectivity shapes population activity. Our approach opens new avenues to investigating how bursting nonlinearities interact with network structure to shape population activity