Astrocytes as a mechanism for contextually-guided network dynamics and function.

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales, may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably compared to dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results fuel the notion that neuron-astrocyte interactions in the brain benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.

Using network control theory to study the dynamics of the structural connectome.

Network control theory (NCT) is a simple and powerful tool for studying how network topology informs and constrains dynamics. Compared to other structure-function coupling approaches, the strength of NCT lies in its capacity to predict the patterns of external control signals that may alter dynamics in a desired way. We have extensively developed and validated the application of NCT to the human structural connectome. Through these efforts, we have studied (i) how different aspects of connectome topology affect neural dynamics, (ii) whether NCT outputs cohere with empirical data on brain function and stimulation, and (iii) how NCT outputs vary across development and correlate with behavior and mental health symptoms. In this protocol, we introduce a framework for applying NCT to structural connectomes following two main pathways. Our primary pathway focuses on computing the control energy associated with transitioning between specific neural activity states. Our second pathway focuses on computing average controllability, which indexes nodes' general capacity to control dynamics. We also provide recommendations for comparing NCT outputs against null network models. Finally, we support this protocol with a Python-based software package called network control theory for python (nctpy).

Uncovering the biological basis of control energy: Structural and metabolic correlates of energy inefficiency in temporal lobe epilepsy.

Network control theory is increasingly used to profile the brain's energy landscape via simulations of neural dynamics. This approach estimates the control energy required to simulate the activation of brain circuits based on structural connectome measured using diffusion magnetic resonance imaging, thereby quantifying those circuits' energetic efficiency. The biological basis of control energy, however, remains unknown, hampering its further application. To fill this gap, investigating temporal lobe epilepsy as a lesion model, we show that patients require higher control energy to activate the limbic network than healthy volunteers, especially ipsilateral to the seizure focus. The energetic imbalance between ipsilateral and contralateral temporolimbic regions is tracked by asymmetric patterns of glucose metabolism measured using positron emission tomography, which, in turn, may be selectively explained by asymmetric gray matter loss as evidenced in the hippocampus. Our investigation provides the first theoretical framework unifying gray matter integrity, metabolism, and energetic generation of neural dynamics.

Functional control of oscillator networks.

Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators' parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators' phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.

Path-dependent dynamics induced by rewiring networks of inertial oscillators.

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when the network structure is time varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain may exhibit these properties simultaneously. It is thus relevant to ask how time-varying network connectivity impacts synchronization in systems that can exhibit multistability. To address this question, we study how the dynamics of coupled Kuramoto oscillators with inertia are affected when the topology of the underlying network changes in time. We show that hysteretic synchronization behavior in networks of coupled inertial oscillators can be driven by changes in connection topology alone. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony that remain even after the network returns to its initial configuration, and we show that these changes are robust to a wide range of network perturbations. Our findings highlight that the specific progression of network topology over time, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.

Brain network dynamics during working memory are modulated by dopamine and diminished in schizophrenia.

Dynamical brain state transitions are critical for flexible working memory but the network mechanisms are incompletely understood. Here, we show that working memory performance entails brain-wide switching between activity states using a combination of functional magnetic resonance imaging in healthy controls and individuals with schizophrenia, pharmacological fMRI, genetic analyses and network control theory. The stability of states relates to dopamine D1 receptor gene expression while state transitions are influenced by D2 receptor expression and pharmacological modulation. Individuals with schizophrenia show altered network control properties, including a more diverse energy landscape and decreased stability of working memory representations. Our results demonstrate the relevance of dopamine signaling for the steering of whole-brain network dynamics during working memory and link these processes to schizophrenia pathophysiology.

Data-driven control of complex networks.

Our ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice. In this paper we overcome this limitation, and develop a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of data, where the unknown network is stimulated with arbitrary and possibly random inputs. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy data and in the presence of nonlinear dynamics, as they arise in power grid and brain networks.

Time-evolving controllability of effective connectivity networks during seizure progression.

Over one third of the estimated 3 million people with epilepsy in the United States are medication resistant. Responsive neurostimulation from chronically implanted electrodes provides a promising treatment alternative to resective surgery. However, determining optimal personalized stimulation parameters, including when and where to intervene to guarantee a positive patient outcome, is a major open challenge. Network neuroscience and control theory offer useful tools that may guide improvements in parameter selection for control of anomalous neural activity. Here we use a method to characterize dynamic controllability across consecutive effective connectivity (EC) networks based on regularized partial correlations between implanted electrodes during the onset, propagation, and termination regimes of 34 seizures. We estimate regularized partial correlation adjacency matrices from 1-s time windows of intracranial electrocorticography recordings using the Graphical Least Absolute Shrinkage and Selection Operator (GLASSO). Average and modal controllability metrics calculated from each resulting EC network track the time-varying controllability of the brain on an evolving landscape of conditionally dependent network interactions. We show that average controllability increases throughout a seizure and is negatively correlated with modal controllability throughout. Our results support the hypothesis that the energy required to drive the brain to a seizure-free state from an ictal state is smallest during seizure onset, yet we find that applying control energy at electrodes in the seizure onset zone may not always be energetically favorable. Our work suggests that a low-complexity model of time-evolving controllability may offer insights for developing and improving control strategies targeting seizure suppression.

Brain network dynamics fingerprints are resilient to data heterogeneity.

CONTEXT: Large multi-site neuroimaging datasets have significantly advanced our quest to understand brain-behavior relationships and to develop biomarkers of psychiatric and neurodegenerative disorders. Yet, such data collections come at a cost, as the inevitable differences across samples may lead to biased or erroneous conclusions. OBJECTIVE: We aim to validate the estimation of individual brain network dynamics fingerprints and appraise sources of variability in large resting-state functional magnetic resonance imaging (rs-fMRI) datasets by providing a novel point of view based on data-driven dynamical models. APPROACH: Previous work has investigated this critical issue in terms of effects on static measures, such as functional connectivity and brain parcellations. Here, we utilize dynamical models (Hidden Markov models - HMM) to examine how diverse scanning factors in multi-site fMRI recordings affect our ability to infer the brain's spatiotemporal wandering between large-scale networks of activity. Specifically, we leverage a stable HMM trained on the Human Connectome Project (homogeneous) dataset, which we then apply to an heterogeneous dataset of traveling subjects scanned under a multitude of conditions. MAIN RESULTS: Building upon this premise, we first replicate previous work on the emergence of non-random sequences of brain states. We next highlight how these time-varying brain activity patterns are robust subject-specific fingerprints. Finally, we suggest these fingerprints may be used to assess which scanning factors induce high variability in the data. SIGNIFICANCE: These results demonstrate that we can i) use large scale dataset to train models that can be then used to interrogate subject-specific data, ii) recover the unique trajectories of brain activity changes in each individual, but also iii) urge caution as our ability to infer such patterns is affected by how, where and when we do so.

Path-dependent connectivity, not modularity, consistently predicts controllability of structural brain networks.

The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the communication dynamics that can emerge therefrom is not well understood. In addition to offering insight into the structure-function relationship of networked systems, such an understanding is a critical step toward the ability to manipulate the brain's large-scale dynamical activity in a targeted manner. We investigate the role of community structure in the controllability of structural brain networks. At the region level, we find that certain network measures of community structure are sometimes statistically correlated with measures of linear controllability. However, we then demonstrate that this relationship depends on the distribution of network edge weights. We highlight the complexity of the relationship between community structure and controllability by performing numerical simulations using canonical graph models with varying mesoscale architectures and edge weight distributions. Finally, we demonstrate that weighted subgraph centrality, a measure rooted in the graph spectrum, and which captures higher order graph architecture, is a stronger and more consistent predictor of controllability. Our study contributes to an understanding of how the brain's diverse mesoscale structure supports transient communication dynamics.

Models of communication and control for brain networks: distinctions, convergence, and future outlook.

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

Gene coexpression patterns predict opiate-induced brain-state transitions.

Opioid addiction is a chronic, relapsing disorder associated with persistent changes in brain plasticity. Reconfiguration of neuronal connectivity may explain heightened abuse liability in individuals with a history of chronic drug exposure. To characterize network-level changes in neuronal activity induced by chronic opiate exposure, we compared FOS expression in mice that are morphine-naïve, morphine-dependent, or have undergone 4 wk of withdrawal from chronic morphine exposure, relative to saline-exposed controls. Pairwise interregional correlations in FOS expression data were used to construct network models that reveal a persistent reduction in connectivity strength following opiate dependence. Further, we demonstrate that basal gene expression patterns are predictive of changes in FOS correlation networks in the morphine-dependent state. Finally, we determine that regions of the hippocampus, striatum, and midbrain are most influential in driving transitions between opiate-naïve and opiate-dependent brain states using a control theoretic approach. This study provides a framework for predicting the influence of specific therapeutic interventions on the state of the opiate-dependent brain.

Control of brain network dynamics across diverse scales of space and time.

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow timescales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast timescales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.

Learning in brain-computer interface control evidenced by joint decomposition of brain and behavior.

OBJECTIVE: Motor imagery-based brain-computer interfaces (BCIs) use an individual's ability to volitionally modulate localized brain activity, often as a therapy for motor dysfunction or to probe causal relations between brain activity and behavior. However, many individuals cannot learn to successfully modulate their brain activity, greatly limiting the efficacy of BCI for therapy and for basic scientific inquiry. Formal experiments designed to probe the nature of BCI learning have offered initial evidence that coherent activity across spatially distributed and functionally diverse cognitive systems is a hallmark of individuals who can successfully learn to control the BCI. However, little is known about how these distributed networks interact through time to support learning. APPROACH: Here, we address this gap in knowledge by constructing and applying a multimodal network approach to decipher brain-behavior relations in motor imagery-based brain-computer interface learning using magnetoencephalography. Specifically, we employ a minimally constrained matrix decomposition method - non-negative matrix factorization - to simultaneously identify regularized, covarying subgraphs of functional connectivity, to assess their similarity to task performance, and to detect their time-varying expression. MAIN RESULTS: We find that learning is marked by diffuse brain-behavior relations: good learners displayed many subgraphs whose temporal expression tracked performance. Individuals also displayed marked variation in the spatial properties of subgraphs such as the connectivity between the frontal lobe and the rest of the brain, and in the temporal properties of subgraphs such as the stage of learning at which they reached maximum expression. From these observations, we posit a conceptual model in which certain subgraphs support learning by modulating brain activity in sensors near regions important for sustaining attention. To test this model, we use tools that stipulate regional dynamics on a networked system (network control theory), and find that good learners display a single subgraph whose temporal expression tracked performance and whose architecture supports easy modulation of sensors located near brain regions important for attention. SIGNIFICANCE: The nature of our contribution to the neuroscience of BCI learning is therefore both computational and theoretical; we first use a minimally-constrained, individual specific method of identifying mesoscale structure in dynamic brain activity to show how global connectivity and interactions between distributed networks supports BCI learning, and then we use a formal network model of control to lend theoretical support to the hypothesis that these identified subgraphs are well suited to modulate attention.

Optimization of energy state transition trajectory supports the development of executive function during youth.

Executive function develops during adolescence, yet it remains unknown how structural brain networks mature to facilitate activation of the fronto-parietal system, which is critical for executive function. In a sample of 946 human youths (ages 8-23y) who completed diffusion imaging, we capitalized upon recent advances in linear dynamical network control theory to calculate the energetic cost necessary to activate the fronto-parietal system through the control of multiple brain regions given existing structural network topology. We found that the energy required to activate the fronto-parietal system declined with development, and the pattern of regional energetic cost predicts unseen individuals' brain maturity. Finally, energetic requirements of the cingulate cortex were negatively correlated with executive performance, and partially mediated the development of executive performance with age. Our results reveal a mechanism by which structural networks develop during adolescence to reduce the theoretical energetic costs of transitions to activation states necessary for executive function.

Adolescents are known for taking risks, from driving too fast to experimenting with drugs and alcohol. Such behaviors tend to decrease as individuals move into adulthood. Most people in their mid-twenties have greater self-control than they did as teenagers. They are also often better at planning, sustaining attention, and inhibiting impulsive behaviors. These skills, which are known as executive functions, develop over the course of adolescence. Executive functions rely upon a series of brain regions distributed across the frontal lobe and the lobe that sits just behind it, the parietal lobe. Fiber tracts connect these regions to form a fronto-parietal network. These fiber tracts are also referred to as white matter due to the whitish fatty material that surrounds and insulates them. Cui et al. now show that changes in white matter networks have implications for teen behavior. Almost 950 healthy young people aged between 8 and 23 years underwent a type of brain scan called diffusion-weighted imaging that visualizes white matter. The scans revealed that white matter networks in the frontal and parietal lobes mature over adolescence. This makes it easier for individuals to activate their fronto-parietal networks by decreasing the amount of energy required. Cui et al. show that a computer model can predict the maturity of a person's brain based on the energy needed to activate their fronto-parietal networks. These changes help explain why executive functions improve during adolescence. This in turn explains why behaviors such as risk-taking tend to decrease with age. That said, adults with various psychiatric disorders, such as ADHD and psychosis, often show impaired executive functions. In the future, it may be possible to reduce these impairments by applying magnetic fields to the scalp to reduce the activity of specific brain regions. The techniques used in the current study could help reveal which brain regions to target with this approach.

Fragility Limits Performance in Complex Networks.

While numerous studies have suggested that large natural, biological, social, and technological networks are fragile, convincing theories are still lacking to explain why natural evolution and human design have failed to optimize networks and avoid fragility. In this paper we provide analytical and numerical evidence that a tradeoff exists in networks with linear dynamics, according to which general measures of robustness and performance are in fact competitive features that cannot be simultaneously optimized. Our findings show that large networks can either be robust to variations of their weights and parameters, or efficient in responding to external stimuli, processing noise, or transmitting information across long distances. As illustrated in our numerical studies, this performance tradeoff seems agnostic to the specific application domain, and in fact it applies to simplified models of ecological, neuronal, and traffic networks.

A practical guide to methodological considerations in the controllability of structural brain networks.

OBJECTIVE: Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool from the physical and engineering sciences that can provide insights regarding that relationship; it formalizes the study of how the dynamics of a complex system can arise from its underlying structure of interconnected units. APPROACH: Given the recent use of network control theory in neuroscience, it is now timely to offer a practical guide to methodological considerations in the controllability of structural brain networks. Here we provide a systematic overview of the framework, examine the impact of modeling choices on frequently studied control metrics, and suggest potentially useful theoretical extensions. We ground our discussions, numerical demonstrations, and theoretical advances in a dataset of high-resolution diffusion imaging with 730 diffusion directions acquired over approximately 1 h of scanning from ten healthy young adults. MAIN RESULTS: Following a didactic introduction of the theory, we probe how a selection of modeling choices affects four common statistics: average controllability, modal controllability, minimum control energy, and optimal control energy. Next, we extend the current state-of-the-art in two ways: first, by developing an alternative measure of structural connectivity that accounts for radial propagation of activity through abutting tissue, and second, by defining a complementary metric quantifying the complexity of the energy landscape of a system. We close with specific modeling recommendations and a discussion of methodological constraints. SIGNIFICANCE: Our hope is that this accessible account will inspire the neuroimaging community to more fully exploit the potential of network control theory in tackling pressing questions in cognitive, developmental, and clinical neuroscience.

White Matter Network Architecture Guides Direct Electrical Stimulation through Optimal State Transitions.

Optimizing direct electrical stimulation for the treatment of neurological disease remains difficult due to an incomplete understanding of its physical propagation through brain tissue. Here, we use network control theory to predict how stimulation spreads through white matter to influence spatially distributed dynamics. We test the theory's predictions using a unique dataset comprising diffusion weighted imaging and electrocorticography in epilepsy patients undergoing grid stimulation. We find statistically significant shared variance between the predicted activity state transitions and the observed activity state transitions. We then use an optimal control framework to posit testable hypotheses regarding which brain states and structural properties will efficiently improve memory encoding when stimulated. Our work quantifies the role that white matter architecture plays in guiding the dynamics of direct electrical stimulation and offers empirical support for the utility of network control theory in explaining the brain's response to stimulation.

RE: Warnings and caveats in brain controllability.

The use of network control theory to analyze the organization of white matter fibers in the human brain has the potential to enable mechanistic theories of cognition, and to inform the development of novel diagnostics and treatments for neurological disease and psychiatric disorders (Gu et al., 2015). The recent article (Tu et al., 2018) aims to challenge several of the contributions of (Gu et al., 2015), and particularly the conclusions that brain networks are theoretically controllable from single regions, and that brain networks feature no specific controllability profiles when compared to random network models. Here we provide additional theoretical arguments in support of (Gu et al., 2015) and against the results and methodologies used in (Tu et al., 2018), thus settling that (i) brain networks are controllable from a single region, (ii) brain networks require large control energy, and (iii) brain networks feature distinctive controllability properties with respect to a class of random network models.

Sex differences in network controllability as a predictor of executive function in youth.

Executive function is a quintessential human capacity that emerges late in development and displays different developmental trends in males and females. Sex differences in executive function in youth have been linked to vulnerability to psychopathology as well as to behaviors that impinge on health, wellbeing, and longevity. Yet, the neurobiological basis of these differences is not well understood, in part due to the spatiotemporal complexity inherent in patterns of brain network maturation supporting executive function. Here we test the hypothesis that sex differences in impulsivity in youth stem from sex differences in the controllability of structural brain networks as they rewire over development. Combining methods from network neuroscience and network control theory, we characterize the network control properties of structural brain networks estimated from diffusion imaging data acquired in males and females in a sample of 879 youth aged 8-22 years. We summarize the control properties of these networks by estimating average and modal controllability, two statistics that probe the ease with which brain areas can drive the network towards easy versus difficult-to-reach states. We find that females have higher modal controllability in frontal, parietal, and subcortical regions while males have higher average controllability in frontal and subcortical regions. Furthermore, controllability profiles in males are negatively related to the false positive rate on a continuous performance task, a common measure of impulsivity. Finally, we find associations between average controllability and individual differences in activation during an n-back working memory task. Taken together, our findings support the notion that sex differences in the controllability of structural brain networks can partially explain sex differences in executive function. Controllability of structural brain networks also predicts features of task-relevant activation, suggesting the potential for controllability to represent context-specific constraints on network state more generally.