Diverse Community Structures in the Neuronal-Level Connectome of the Drosophila Brain

Augmenting flexibility: mutual inhibition between inhibitory neurons expands functional diversity

Recent advances in microcircuit analysis of nervous systems have revealed a plethora of mutual connections between inhibitory interneurons across many different species and brain regions. The abundance of these mutual connections has not been fully explained. Strikingly, we show that neural circuits with mutually inhibitory connections are able to rapidly and flexibly switch between distinct functions. That is, multiple functions coexist for a single set of synaptic weights. Here, we develop a theoretical framework to explain how inhibitory recurrent circuits give rise to this flexibility and show that mutual inhibition doubles the number of cusp bifurcations in small neural circuits. As a concrete example, we study a class of functional motifs we call coupled recurrent inhibitory and recurrent excitatory loops (CRIRELs). These CRIRELs have the advantage of being both multi-functional and controllable, performing a plethora of functions, including decisions, memory, toggle, and so forth. Finally, we demonstrate how mutual inhibition maximizes storage capacity for larger networks.

Heterogeneous and higher-order cortical connectivity undergirds efficient, robust, and reliable neural codes

We hypothesized that the heterogeneous architecture of biological neural networks provides a substrate to regulate the well-known tradeoff between robustness and efficiency, thereby allowing different subpopulations of the same network to optimize for different objectives. To distinguish between subpopulations, we developed a metric based on the mathematical theory of simplicial complexes that captures the complexity of their connectivity by contrasting its higher-order structure to a random control and confirmed its relevance in several openly available connectomes. Using a biologically detailed cortical model and an electron microscopic dataset, we showed that subpopulations with low simplicial complexity exhibit efficient activity. Conversely, subpopulations of high simplicial complexity play a supporting role in boosting the reliability of the network as a whole, softening the robustness-efficiency tradeoff. Crucially, we found that both types of subpopulations can and do coexist within a single connectome in biological neural networks, due to the heterogeneity of their connectivity.

Cell morphologies in the nervous system: Glia steal the limelight

Neurons and glia have distinct yet interactive functions but are both characterized by branching morphology. Dendritic trees have been digitally traced for over 40 years in many animal species, anatomical regions, and neuron types. Recently, long-range axons also are being reconstructed throughout the brain of many organisms from invertebrates to primates. In contrast, less attention has been paid until lately to glial morphology. Thus, although glia and neurons are similarly abundant in the nervous systems of humans and most animal models, glia have traditionally been much less represented than neurons in morphological reconstruction repositories such as NeuroMorpho.Org. This is rapidly changing with the advent of high-throughput glia tracing. NeuroMorpho.Org introduced glial cells in 2017 and today they constitute nearly a third of the database content. It took NeuroMorpho.Org 10 years to collect the first 40,000 neurons and now that amount of data can be produced in a single publication. This not only demonstrates the spectacular technological progress in data production, but also demands a corresponding advancement in informatics processing. At the same time, these publicly available data also open new opportunities for quantitative analysis and computational modeling to identify universal or cell-type-specific design principles in the cellular architecture of nervous systems. As a first application, we demonstrated that supervised machine learning of tree geometry classifies neurons and glia with practically perfect accuracy. Furthermore, we discovered a new morphometric biomarker capable of robustly separating these cell classes across multiple species, brain regions, and experimental preparations, with only sparse sampling of branch measurements.

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Extended Anderson Criticality in Heavy-Tailed Neural Networks

We investigate the emergence of complex dynamics in networks with heavy-tailed connectivity by developing a non-Hermitian random matrix theory. We uncover the existence of an extended critical regime of spatially multifractal fluctuations between the quiescent and active phases. This multifractal critical phase combines features of localization and delocalization and differs from the edge of chaos in classical networks by the appearance of universal hallmarks of Anderson criticality over an extended region in phase space. We show that the rich nonlinear response properties of the extended critical regime can account for a variety of neural dynamics such as the diversity of timescales, providing a computational advantage for persistent classification in a reservoir setting.