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.

Author Summary Epilepsy is increasingly recognized as a network disorder characterized by recurrent seizures as well as broad-ranging cognitive difficulties and affective dysfunction. Our manuscript reviews recent literature highlighting brain network substrates of cognitive and affective dysfunction in common epilepsy syndromes, namely temporal lobe epilepsy secondary to mesiotemporal sclerosis, extratemporal epilepsy secondary to malformations of cortical development, and idiopathic generalized epilepsy syndromes arising from subcortico-cortical pathophysiology. We discuss prior work that has indicated both shared and distinct brain network signatures of cognitive and affective dysfunction across the epilepsy spectrum, improves our knowledge of structure-function links and interindividual heterogeneity, and ultimately aids screening and monitoring of therapeutic strategies. Abstract Epilepsy is one of the most common chronic neurological conditions, traditionally defined as a disorder of recurrent seizures. Cognitive and affective dysfunction are increasingly recognized as core disease dimensions and can affect patient well-being, sometimes more than the seizures themselves. Connectome-based approaches hold immense promise for revealing mechanisms that contribute to dysfunction and to identify biomarkers. Our review discusses emerging multimodal neuroimaging and connectomics studies that highlight network substrates of cognitive/affective dysfunction in the common epilepsies. We first discuss work in drug-resistant epilepsy syndromes, that is, temporal lobe epilepsy, related to mesiotemporal sclerosis (TLE), and extratemporal epilepsy (ETE), related to malformations of cortical development. While these are traditionally conceptualized as ‘focal’ epilepsies, many patients present with broad structural and functional anomalies. Moreover, the extent of distributed changes contributes to difficulties in multiple cognitive domains as well as affective-behavioral challenges. We also review work in idiopathic generalized epilepsy (IGE), a subset of generalized epilepsy syndromes that involve subcortico-cortical circuits. Overall, neuroimaging and network neuroscience studies point to both shared and syndrome-specific connectome signatures of dysfunction across TLE, ETE, and IGE. Lastly, we point to current gaps in the literature and formulate recommendations for future research.

In systems neuroscience, most models posit that brain regions communicate information under constraints of efficiency. Yet, evidence for efficient communication in structural brain networks characterized by hierarchical organization and highly connected hubs remains sparse. The principle of efficient coding proposes that the brain transmits maximal information in a metabolically economical or compressed form to improve future behavior. To determine how structural connectivity supports efficient coding, we develop a theory specifying minimum rates of message transmission between brain regions to achieve an expected fidelity, and we test five predictions from the theory based on random walk communication dynamics. In doing so, we introduce the metric of compression efficiency, which quantifies the trade-off between lossy compression and transmission fidelity in structural networks. In a large sample of youth ( n = 1,042; age 8–23 years), we analyze structural networks derived from diffusion-weighted imaging and metabolic expenditure operationalized using cerebral blood flow. We show that structural networks strike compression efficiency trade-offs consistent with theoretical predictions. We find that compression efficiency prioritizes fidelity with development, heightens when metabolic resources and myelination guide communication, explains advantages of hierarchical organization, links higher input fidelity to disproportionate areal expansion, and shows that hubs integrate information by lossy compression. Lastly, compression efficiency is predictive of behavior—beyond the conventional network efficiency metric—for cognitive domains including executive function, memory, complex reasoning, and social cognition. Our findings elucidate how macroscale connectivity supports efficient coding and serve to foreground communication processes that utilize random walk dynamics constrained by network connectivity. Author Summary Macroscale communication between interconnected brain regions underpins most aspects of brain function and incurs substantial metabolic cost. Understanding efficient and behaviorally meaningful information transmission dependent on structural connectivity has remained challenging. We validate a model of communication dynamics atop the macroscale human structural connectome, finding that structural networks support dynamics that strike a balance between information transmission fidelity and lossy compression. Notably, this balance is predictive of behavior and explanatory of biology. In addition to challenging and reformulating the currently held view that communication occurs by routing dynamics along metabolically efficient direct anatomical pathways, our results suggest that connectome architecture and behavioral demands yield communication dynamics that accord to neurobiological and information theoretical principles of efficient coding and lossy compression.

Precisely how the anatomical structure of the brain supports a wide range of complex functions remains a question of marked importance in both basic and clinical neuroscience. Progress has been hampered by the lack of theoretical frameworks explaining how a structural network of relatively rigid interareal connections can produce a diverse repertoire of functional neural dynamics. Here, we address this gap by positing that the brain’s structural network architecture determines the set of accessible functional connectivity patterns according to predictions of network control theory. In a large developmental cohort of 823 youths aged 8 to 23 years, we found that the flexibility of a brain region’s functional connectivity was positively correlated with the proportion of its structural links extending to different cognitive systems. Notably, this relationship was mediated by nodes’ boundary controllability, suggesting that a region’s strategic location on the boundaries of modules may underpin the capacity to integrate information across different cognitive processes. Broadly, our study provides a mechanistic framework that illustrates how temporal flexibility observed in functional networks may be mediated by the controllability of the underlying structural connectivity. Author Summary Precisely how the relatively rigid white matter wiring of the human brain gives rise to a diverse repertoire of functional neural dynamics is not well understood. In this work, we combined tools from network science and control theory to address this question. Capitalizing on a large developmental cohort, we demonstrated that the ability of a brain region to flexibly change its functional module allegiance over time (i.e., its modular flexibility) was positively correlated with its proportion of anatomical edges projecting to multiple cognitive networks (i.e., its structural participation coefficient). Moreover, this relationship was strongly mediated by the region’s boundary controllability, a metric capturing its capacity to integrate information across multiple cognitive domains.