Nonequilibrium Green's Functions for Functional Connectivity in the Brain

Neural signal propagation atlas of Caenorhabditis elegans

Establishing how neural function emerges from network properties is a fundamental problem in neuroscience1. Here, to better understand the relationship between the structure and the function of a nervous system, we systematically measure signal propagation in 23,433 pairs of neurons across the head of the nematode Caenorhabditis elegans by direct optogenetic activation and simultaneous whole-brain calcium imaging. We measure the sign (excitatory or inhibitory), strength, temporal properties and causal direction of signal propagation between these neurons to create a functional atlas. We find that signal propagation differs from model predictions that are based on anatomy. Using mutants, we show that extrasynaptic signalling not visible from anatomy contributes to this difference. We identify many instances of dense-core-vesicle-dependent signalling, including on timescales of less than a second, that evoke acute calcium transients-often where no direct wired connection exists but where relevant neuropeptides and receptors are expressed. We propose that, in such cases, extrasynaptically released neuropeptides serve a similar function to that of classical neurotransmitters. Finally, our measured signal propagation atlas better predicts the neural dynamics of spontaneous activity than do models based on anatomy. We conclude that both synaptic and extrasynaptic signalling drive neural dynamics on short timescales, and that measurements of evoked signal propagation are crucial for interpreting neural function.

Structure and function in artificial, zebrafish and human neural networks

Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.

Nonequilibrium Green's Functions for Functional Connectivity in the Brain

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a continuous-variable network of neurons. We show how the connectivity is related to the measurable response functions, and provide two illustrative examples via numerical calculations, inspired from Caenorhabditis elegans.