Role of Graph Architecture in Controlling Dynamical Networks with Applications to Neural Systems

Contributions of network structure, chemoarchitecture and diagnostic categories to transitions between cognitive topographies

The mechanisms linking the brain's network structure to cognitively relevant activation patterns remain largely unknown. Here, by leveraging principles of network control, we show how the architecture of the human connectome shapes transitions between 123 experimentally defined cognitive activation maps (cognitive topographies) from the NeuroSynth meta-analytic database. Specifically, we systematically integrated large-scale multimodal neuroimaging data from functional magnetic resonance imaging, diffusion tractography, cortical morphometry and positron emission tomography to simulate how anatomically guided transitions between cognitive states can be reshaped by neurotransmitter engagement or by changes in cortical thickness. Our model incorporates neurotransmitter-receptor density maps (18 receptors and transporters) and maps of cortical thickness pertaining to a wide range of mental health, neurodegenerative, psychiatric and neurodevelopmental diagnostic categories (17,000 patients and 22,000 controls). The results provide a comprehensive look-up table charting how brain network organization and chemoarchitecture interact to manifest different cognitive topographies, and establish a principled foundation for the systematic identification of ways to promote selective transitions between cognitive topographies.

Sleep Deprivation Effects on Brain State Dynamics Are Associated With Dopamine D2 Receptor Availability Via Network Control Theory

BACKGROUND

Sleep deprivation (SD) negatively affects brain function. Most brain imaging studies have investigated the effects of SD on static brain function. SD effects on functional brain dynamics and their relationship with molecular changes remain relatively unexplored.

METHODS

We used functional magnetic resonance imaging to examine resting-brain state dynamics after one night of SD compared with rested wakefulness (N = 41) and assessed the association of brain state dynamics with striatal brain dopamine D2 receptor availability measured by positron emission tomography [11C]raclopride using network control theory.

RESULTS

SD reduced dwell time and persistence probabilities, with the strongest effects in two brain states, one characterized by high default mode network and low dorsal attention network activity and the other by high frontoparietal network and low somatomotor network activity. Using network control theory, we showed that after SD, there was an overall increase in the control energy required for brain state transitions, with effects varying for different brain state transitions. Control energy requirement was negatively associated with transition probabilities under SD and restful wakefulness and accounted for SD-induced changes in transition probabilities. Alteration in the energy landscape was associated with SD-induced changes in striatal D2 receptor distribution.

CONCLUSIONS

These findings demonstrate altered occurrence of internally and externally oriented brain states following acute SD and suggest an association with energy requirements for brain state transitions modulated by striatal D2 receptors.

Controllability in attention deficit hyperactivity disorder brains

The role of network metrics in exploring brain networks of mental illness is crucial. This study focuses on quantifying a node controllability index (CA-scores) and developing a novel framework for studying the dysfunction of attention deficit hyperactivity disorder (ADHD) brains. By analyzing fMRI data from 143 healthy controls and 102 ADHD patients, the controllability metric reveals distinct differences in nodes (brain regions) and subsystems (functional modules). There are significantly atypical CA-scores in the Rolandic operculum, superior medial orbitofrontal cortex, insula, posterior cingulate gyrus, supramarginal gyrus, angular gyrus, precuneus, heschl gyrus, and superior temporal gyrus of ADHD patients. A comparison with measures of connection strength, eigenvector centrality, and topology entropy suggests that the controllability index may be more effective in identifying abnormal regions in ADHD brains. Furthermore, our controllability index could be extended to investigate functional networks associated with other psychiatric disorders.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-10063-z.

Detection of minimal extended driver nodes in energetic costs reduction

Structures of complex networks are fundamental to system dynamics, where node state and connectivity patterns determine the cost of a control system, a key aspect in unraveling complexity. However, minimizing the energy required to control a system with the fewest input nodes remains an open problem. This study investigates the relationship between the structure of closed-connected function modules and control energy. We discovered that small structural adjustments, such as adding a few extended driver nodes, can significantly reduce control energy. Thus, we propose MInimal extended driver nodes in Energetic costs Reduction (MIER). Next, we transform the detection of MIER into a multi-objective optimization problem and choose an NSGA-II algorithm to solve it. Compared with the baseline methods, NSGA-II can approximate the optimal solution to the greatest extent. Through experiments using synthetic and real data, we validate that MIER can exponentially decrease control energy. Furthermore, random perturbation tests confirm the stability of MIER. Subsequently, we applied MIER to three representative scenarios: regulation of differential expression genes affected by cancer mutations in the human protein-protein interaction network, trade relations among developed countries in the world trade network, and regulation of body-wall muscle cells by motor neurons in Caenorhabditis elegans nervous network. The results reveal that the involvement of MIER significantly reduces control energy required for these original modules from a topological perspective. Additionally, MIER nodes enhance functionality, supplement key nodes, and uncover potential mechanisms. Overall, our work provides practical computational tools for understanding and presenting control strategies in biological, social, and neural systems.

A network control theory pipeline for studying the dynamics of the structural connectome

Network control theory (NCT) is a simple and powerful tool for studying how network topology informs and constrains the dynamics of a system. 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 the dynamics of a system in a desired way. An interesting development for NCT in the neuroscience field is its application to study behavior and mental health symptoms. To date, NCT has been validated to study different aspects of the human structural connectome. NCT outputs can be monitored throughout developmental stages to study the effects of connectome topology on neural dynamics and, separately, to test the coherence of empirical datasets with brain function and stimulation. Here, we provide a comprehensive pipeline for applying NCT to structural connectomes by following two procedures. The main procedure focuses on computing the control energy associated with the transitions between specific neural activity states. The second procedure focuses on computing average controllability, which indexes nodes' general capacity to control the dynamics of the system. We provide recommendations for comparing NCT outputs against null network models, and we further support this approach with a Python-based software package called 'network control theory for python'. The procedures in this protocol are appropriate for users with a background in network neuroscience and experience in dynamical systems theory.

The mechanics of correlated variability in segregated cortical excitatory subnetworks

Understanding the genesis of shared trial-to-trial variability in neuronal population activity within the sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since it likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in the mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells. Furthermore, our findings provide theoretical support for recent experimental observations showing that cortical inhibition forms structural and functional subnetworks with excitatory cells, in contrast to the classical view that inhibition is a nonspecific blanket suppression of local excitation.

From Connectivity to Controllability: Unraveling the Brain Biomarkers of Major Depressive Disorder

Major Depressive Disorder (MDD) is a significant neurological condition associated with aberrations in brain functional networks. Traditional studies have predominantly analyzed these from a network topology perspective. However, given the brain's dynamic and complex nature, exploring its mechanisms from a network control standpoint provides a fresh and insightful framework. This research investigates the integration of network controllability and machine learning to pinpoint essential biomarkers for MDD using functional magnetic resonance imaging (fMRI) data. By employing network controllability methods, we identify crucial brain regions that are instrumental in facilitating transitions between brain states. These regions demonstrate the brain's ability to navigate various functional states, emphasizing the utility of network controllability metrics as potential biomarkers. Furthermore, these metrics elucidate the complex dynamics of MDD and support the development of precision medicine strategies that incorporate machine learning to improve the precision of diagnostics and the efficacy of treatments. This study underscores the value of merging machine learning with network neuroscience to craft personalized interventions that align with the unique pathological profiles of individuals, ultimately enhancing the management and treatment of MDD.

Graph Analysis of the Visual Cortical Network during Naturalistic Movie Viewing Reveals Increased Integration and Decreased Segregation Following Mild TBI

Traditional neuroimaging methods have identified alterations in brain activity patterns following mild traumatic brain injury (mTBI), particularly during rest, complex tasks, and normal vision. However, studies using graph theory to examine brain network changes in mTBI have produced varied results, influenced by the specific networks and task demands analyzed. In our study, we employed functional MRI to observe 17 mTBI patients and 54 healthy individuals as they viewed a simple, non-narrative underwater film, simulating everyday visual tasks. This approach revealed significant mTBI-related changes in network connectivity, efficiency, and organization. Specifically, the mTBI group exhibited higher overall connectivity and local network specialization, suggesting enhanced information integration without overwhelming the brain's processing capabilities. Conversely, these patients showed reduced network segregation, indicating a less compartmentalized brain function compared to healthy controls. These patterns were consistent across various visual cortex subnetworks, except in primary visual areas. Our findings highlight the potential of using naturalistic stimuli in graph-based neuroimaging to understand brain network alterations in mTBI and possibly other conditions affecting brain integration.

Control adjustment costs limit goal flexibility: Empirical evidence and a computational account

A cornerstone of human intelligence is the ability to flexibly adjust our cognition and behavior as our goals change. For instance, achieving some goals requires efficiency, while others require caution. Adapting to these changing goals require corresponding adjustments in cognitive control (e.g., levels of attention, response thresholds). However, adjusting our control to meet new goals comes at a cost: we are better at achieving a goal in isolation than when transitioning between goals. The source of these control adjustment costs remains poorly understood, and the bulk of our understanding of such costs comes from settings in which participants transition between discrete task sets, rather than performance goals. Across four experiments, we show that adjustments in continuous control states incur a performance cost, and that a dynamical systems model can explain the source of these costs. Participants performed a single cognitively demanding task under varying performance goals (e.g., to be fast or to be accurate). We modeled control allocation to include a dynamic process of adjusting from one's current control state to a target state for a given performance goal. By incorporating inertia into this adjustment process, our model accounts for our empirical findings that people under-shoot their target control state more (i.e., exhibit larger adjustment costs) when (a) goals switch rather than remain fixed over a block (Study 1); (b) target control states are more distant from one another (Study 2); (c) less time is given to adjust to the new goal (Study 3); and (d) when anticipating having to switch goals more frequently (Study 4). Our findings characterize the costs of adjusting control to meet changing goals, and show that these costs can emerge directly from cognitive control dynamics. In so doing, they shed new light on the sources of and constraints on flexibility in human goal-directed behavior.

Controlling the human connectome with spatially diffuse input signals

The human brain is never at "rest"; its activity is constantly fluctuating over time, transitioning from one brain state-a whole-brain pattern of activity-to another. Network control theory offers a framework for understanding the effort - energy - associated with these transitions. One branch of control theory that is especially useful in this context is "optimal control", in which input signals are used to selectively drive the brain into a target state. Typically, these inputs are introduced independently to the nodes of the network (each input signal is associated with exactly one node). Though convenient, this input strategy ignores the continuity of cerebral cortex - geometrically, each region is connected to its spatial neighbors, allowing control signals, both exogenous and endogenous, to spread from their foci to nearby regions. Additionally, the spatial specificity of brain stimulation techniques is limited, such that the effects of a perturbation are measurable in tissue surrounding the stimulation site. Here, we adapt the network control model so that input signals have a spatial extent that decays exponentially from the input site. We show that this more realistic strategy takes advantage of spatial dependencies in structural connectivity and activity to reduce the energy (effort) associated with brain state transitions. We further leverage these dependencies to explore near-optimal control strategies such that, on a per-transition basis, the number of input signals required for a given control task is reduced, in some cases by two orders of magnitude. This approximation yields network-wide maps of input site density, which we compare to an existing database of functional, metabolic, genetic, and neurochemical maps, finding a close correspondence. Ultimately, not only do we propose a more efficient framework that is also more adherent to well-established brain organizational principles, but we also posit neurobiologically grounded bases for optimal control.

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).

Alprazolam modulates persistence energy during emotion processing in first-degree relatives of individuals with schizophrenia: a network control study

Schizophrenia is marked by deficits in facial affect processing associated with abnormalities in GABAergic circuitry, deficits also found in first-degree relatives. Facial affect processing involves a distributed network of brain regions including limbic regions like amygdala and visual processing areas like fusiform cortex. Pharmacological modulation of GABAergic circuitry using benzodiazepines like alprazolam can be useful for studying this facial affect processing network and associated GABAergic abnormalities in schizophrenia. Here, we use pharmacological modulation and computational modeling to study the contribution of GABAergic abnormalities toward emotion processing deficits in schizophrenia. Specifically, we apply principles from network control theory to model persistence energy - the control energy required to maintain brain activation states - during emotion identification and recall tasks, with and without administration of alprazolam, in a sample of first-degree relatives and healthy controls. Here, persistence energy quantifies the magnitude of theoretical external inputs during the task. We find that alprazolam increases persistence energy in relatives but not in controls during threatening face processing, suggesting a compensatory mechanism given the relative absence of behavioral abnormalities in this sample of unaffected relatives. Further, we demonstrate that regions in the fusiform and occipital cortices are important for facilitating state transitions during facial affect processing. Finally, we uncover spatial relationships (i) between regional variation in differential control energy (alprazolam versus placebo) and (ii) both serotonin and dopamine neurotransmitter systems, indicating that alprazolam may exert its effects by altering neuromodulatory systems. Together, these findings provide a new perspective on the distributed emotion processing network and the effect of GABAergic modulation on this network, in addition to identifying an association between schizophrenia risk and abnormal GABAergic effects on persistence energy during threat processing.

Computational modelling in disorders of consciousness: Closing the gap towards personalised models for restoring consciousness

Disorders of consciousness are complex conditions characterised by persistent loss of responsiveness due to brain injury. They present diagnostic challenges and limited options for treatment, and highlight the urgent need for a more thorough understanding of how human consciousness arises from coordinated neural activity. The increasing availability of multimodal neuroimaging data has given rise to a wide range of clinically- and scientifically-motivated modelling efforts, seeking to improve data-driven stratification of patients, to identify causal mechanisms for patient pathophysiology and loss of consciousness more broadly, and to develop simulations as a means of testing in silico potential treatment avenues to restore consciousness. As a dedicated Working Group of clinicians and neuroscientists of the international Curing Coma Campaign, here we provide our framework and vision to understand the diverse statistical and generative computational modelling approaches that are being employed in this fast-growing field. We identify the gaps that exist between the current state-of-the-art in statistical and biophysical computational modelling in human neuroscience, and the aspirational goal of a mature field of modelling disorders of consciousness; which might drive improved treatments and outcomes in the clinic. Finally, we make several recommendations for how the field as a whole can work together to address these challenges.

Identifying properties of pattern completion neurons in a computational model of the visual cortex

Neural ensembles are found throughout the brain and are believed to underlie diverse cognitive functions including memory and perception. Methods to activate ensembles precisely, reliably, and quickly are needed to further study the ensembles' role in cognitive processes. Previous work has found that ensembles in layer 2/3 of the visual cortex (V1) exhibited pattern completion properties: ensembles containing tens of neurons were activated by stimulation of just two neurons. However, methods that identify pattern completion neurons are underdeveloped. In this study, we optimized the selection of pattern completion neurons in simulated ensembles. We developed a computational model that replicated the connectivity patterns and electrophysiological properties of layer 2/3 of mouse V1. We identified ensembles of excitatory model neurons using K-means clustering. We then stimulated pairs of neurons in identified ensembles while tracking the activity of the entire ensemble. Our analysis of ensemble activity quantified a neuron pair's power to activate an ensemble using a novel metric called pattern completion capability (PCC) based on the mean pre-stimulation voltage across the ensemble. We found that PCC was directly correlated with multiple graph theory parameters, such as degree and closeness centrality. To improve selection of pattern completion neurons in vivo, we computed a novel latency metric that was correlated with PCC and could potentially be estimated from modern physiological recordings. Lastly, we found that stimulation of five neurons could reliably activate ensembles. These findings can help researchers identify pattern completion neurons to stimulate in vivo during behavioral studies to control ensemble activation.

The mechanics of correlated variability in segregated cortical excitatory subnetworks

Understanding the genesis of shared trial-to-trial variability in neural activity within sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since this variability likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells.

Reduced emergent character of neural dynamics in patients with a disrupted connectome

High-level brain functions are widely believed to emerge from the orchestrated activity of multiple neural systems. However, lacking a formal definition and practical quantification of emergence for experimental data, neuroscientists have been unable to empirically test this long-standing conjecture. Here we investigate this fundamental question by leveraging a recently proposed framework known as "Integrated Information Decomposition," which establishes a principled information-theoretic approach to operationalise and quantify emergence in dynamical systems - including the human brain. By analysing functional MRI data, our results show that the emergent and hierarchical character of neural dynamics is significantly diminished in chronically unresponsive patients suffering from severe brain injury. At a functional level, we demonstrate that emergence capacity is positively correlated with the extent of hierarchical organisation in brain activity. Furthermore, by combining computational approaches from network control theory and whole-brain biophysical modelling, we show that the reduced capacity for emergent and hierarchical dynamics in severely brain-injured patients can be mechanistically explained by disruptions in the patients' structural connectome. Overall, our results suggest that chronic unresponsiveness resulting from severe brain injury may be related to structural impairment of the fundamental neural infrastructures required for brain dynamics to support emergence.

Transitions between cognitive topographies: contributions of network structure, neuromodulation, and disease

Patterns of neural activity underlie human cognition. Transitions between these patterns are orchestrated by the brain's network architecture. What are the mechanisms linking network structure to cognitively relevant activation patterns? Here we implement principles of network control to investigate how the architecture of the human connectome shapes transitions between 123 experimentally defined cognitive activation maps (cognitive topographies) from the NeuroSynth meta-analytic engine. We also systematically incorporate neurotransmitter receptor density maps (18 receptors and transporters) and disease-related cortical abnormality maps (11 neurodegenerative, psychiatric and neurodevelopmental diseases; N = 17 000 patients, N = 22 000 controls). Integrating large-scale multimodal neuroimaging data from functional MRI, diffusion tractography, cortical morphometry, and positron emission tomography, we simulate how anatomically-guided transitions between cognitive states can be reshaped by pharmacological or pathological perturbation. Our results provide a comprehensive look-up table charting how brain network organisation and chemoarchitecture interact to manifest different cognitive topographies. This computational framework establishes a principled foundation for systematically identifying novel ways to promote selective transitions between desired cognitive topographies.

Input node placement restricting the longest control chain in controllability of complex networks

The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is an inherent trade-off between minimizing the number of inputs and control energy. To better understand this trade-off, we study the problem of identifying a minimum set of input nodes such that controllabililty is ensured while restricting the length of the longest control chain. The longest control chain is the maximum distance from input nodes to any network node, and recent work found that reducing its length significantly reduces control energy. We map the longest control chain-constraint minimum input problem to finding a joint maximum matching and minimum dominating set. We show that this graph combinatorial problem is NP-complete, and we introduce and validate a heuristic approximation. Applying this algorithm to a collection of real and model networks, we investigate how network structure affects the minimum number of inputs, revealing, for example, that for many real networks reducing the longest control chain requires only few or no additional inputs, only the rearrangement of the input nodes.

Optimal Control Costs of Brain State Transitions in Linear Stochastic Systems

The brain is a system that performs numerous functions by controlling its states. Quantifying the cost of this control is essential as it reveals how the brain can be controlled based on the minimization of the control cost, and which brain regions are most important to the optimal control of transitions. Despite its great potential, the current control paradigm in neuroscience uses a deterministic framework and is therefore unable to consider stochasticity, severely limiting its application to neural data. Here, to resolve this limitation, we propose a novel framework for the evaluation of control costs based on a linear stochastic model. Following our previous work, we quantified the optimal control cost as the minimal Kullback-Leibler divergence between the uncontrolled and controlled processes. In the linear model, we established an analytical expression for minimal cost and showed that we can decompose it into the cost for controlling the mean and covariance of brain activity. To evaluate the utility of our novel framework, we examined the significant brain regions in the optimal control of transitions from the resting state to seven cognitive task states in human whole-brain imaging data of either sex. We found that, in realizing the different transitions, the lower visual areas commonly played a significant role in controlling the means, while the posterior cingulate cortex commonly played a significant role in controlling the covariances.SIGNIFICANCE STATEMENT The brain performs many cognitive functions by controlling its states. Quantifying the cost of this control is essential as it reveals how the brain can be optimally controlled in terms of the cost, and which brain regions are most important to the optimal control of transitions. Here, we built a novel framework to quantify control cost that takes account of stochasticity of neural activity, which is ignored in previous studies. We established the analytical expression of the stochastic control cost, which enables us to compute the cost in high-dimensional neural data. We identified the significant brain regions for the optimal control in cognitive tasks in human whole-brain imaging data.

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.

Changes in dynamic transitions between integrated and segregated states underlie visual hallucinations in Parkinson's disease

Hallucinations are a core feature of psychosis and common in Parkinson's. Their transient, unexpected nature suggests a change in dynamic brain states, but underlying causes are unknown. Here, we examine temporal dynamics and underlying structural connectivity in Parkinson's-hallucinations using a combination of functional and structural MRI, network control theory, neurotransmitter density and genetic analyses. We show that Parkinson's-hallucinators spent more time in a predominantly Segregated functional state with fewer between-state transitions. The transition from integrated-to-segregated state had lower energy cost in Parkinson's-hallucinators; and was therefore potentially preferable. The regional energy needed for this transition was correlated with regional neurotransmitter density and gene expression for serotoninergic, GABAergic, noradrenergic and cholinergic, but not dopaminergic, receptors. We show how the combination of neurochemistry and brain structure jointly shape functional brain dynamics leading to hallucinations and highlight potential therapeutic targets by linking these changes to neurotransmitter systems involved in early sensory and complex visual processing.

The expanding horizons of network neuroscience: From description to prediction and control

The field of network neuroscience has emerged as a natural framework for the study of the brain and has been increasingly applied across divergent problems in neuroscience. From a disciplinary perspective, network neuroscience originally emerged as a formal integration of graph theory (from mathematics) and neuroscience (from biology). This early integration afforded marked utility in describing the interconnected nature of neural units, both structurally and functionally, and underscored the relevance of that interconnection for cognition and behavior. But since its inception, the field has not remained static in its methodological composition. Instead, it has grown to use increasingly advanced graph-theoretic tools and to bring in several other disciplinary perspectives-including machine learning and systems engineering-that have proven complementary. In doing so, the problem space amenable to the discipline has expanded markedly. In this review, we discuss three distinct flavors of investigation in state-of-the-art network neuroscience: (i) descriptive network neuroscience, (ii) predictive network neuroscience, and (iii) a perturbative network neuroscience that draws on recent advances in network control theory. In considering each area, we provide a brief summary of the approaches, discuss the nature of the insights obtained, and highlight future directions.

Hierarchical Reinforcement Learning, Sequential Behavior, and the Dorsal Frontostriatal System

To effectively behave within ever-changing environments, biological agents must learn and act at varying hierarchical levels such that a complex task may be broken down into more tractable subtasks. Hierarchical reinforcement learning (HRL) is a computational framework that provides an understanding of this process by combining sequential actions into one temporally extended unit called an option. However, there are still open questions within the HRL framework, including how options are formed and how HRL mechanisms might be realized within the brain. In this review, we propose that the existing human motor sequence literature can aid in understanding both of these questions. We give specific emphasis to visuomotor sequence learning tasks such as the discrete sequence production task and the M × N (M steps × N sets) task to understand how hierarchical learning and behavior manifest across sequential action tasks as well as how the dorsal cortical-subcortical circuitry could support this kind of behavior. This review highlights how motor chunks within a motor sequence can function as HRL options. Furthermore, we aim to merge findings from motor sequence literature with reinforcement learning perspectives to inform experimental design in each respective subfield.

Information content of brain states is explained by structural constraints on state energetics

Signal propagation along the structural connectome of the brain induces changes in the patterns of activity. These activity patterns define global brain states and contain information in accordance with their expected probability of occurrence. Being the physical substrate upon which information propagates, the structural connectome, in conjunction with the dynamics, determines the set of possible brain states and constrains the transition between accessible states. Yet, precisely how these structural constraints on state transitions relate to their information content remains unexplored. To address this gap in knowledge, we defined the information content as a function of the activation distribution, where statistically rare values of activation correspond to high information content. With this numerical definition in hand, we studied the spatiotemporal distribution of information content in functional magnetic resonance imaging (fMRI) data from the Human Connectome Project during different tasks, and report four key findings. First, information content strongly depends on cognitive context; its absolute level and spatial distribution depend on the cognitive task. Second, while information content shows similarities to other measures of brain activity, it is distinct from both Neurosynth maps and task contrast maps generated by a general linear model applied to the fMRI data. Third, the brain's structural wiring constrains the cost to control its state, where the cost to transition into high information content states is larger than that to transition into low information content states. Finally, all state transitions-especially those to high information content states-are less costly than expected from random network null models, thereby indicating the brains marked efficiency. Taken together, our findings establish an explanatory link between the information contained in a brain state and the energetic cost of attaining that state, thereby laying important groundwork for our understanding of large-scale cognitive computations.

Control theory illustrates the energy efficiency in the dynamic reconfiguration of functional connectivity

The brain's functional connectivity fluctuates over time instead of remaining steady in a stationary mode even during the resting state. This fluctuation establishes the dynamical functional connectivity that transitions in a non-random order between multiple modes. Yet it remains unexplored how the transition facilitates the entire brain network as a dynamical system and what utility this mechanism for dynamic reconfiguration can bring over the widely used graph theoretical measurements. To address these questions, we propose to conduct an energetic analysis of functional brain networks using resting-state fMRI and behavioral measurements from the Human Connectome Project. Through comparing the state transition energy under distinct adjacent matrices, we justify that dynamic functional connectivity leads to 60% less energy cost to support the resting state dynamics than static connectivity when driving the transition through default mode network. Moreover, we demonstrate that combining graph theoretical measurements and our energy-based control measurements as the feature vector can provide complementary prediction power for the behavioral scores (Combination vs. Control: t = 9.41, p = 1.64e-13; Combination vs. Graph: t = 4.92, p = 3.81e-6). Our approach integrates statistical inference and dynamical system inspection towards understanding brain networks.

Informed MEG/EEG source imaging reveals the locations of interictal spikes missed by SEEG

Determining the accurate locations of interictal spikes has been fundamental in the presurgical evaluation of epilepsy surgery. Stereo-electroencephalography (SEEG) is able to directly record cortical activity and localize interictal spikes. However, the main caveat of SEEG techniques is that they have limited spatial sampling (covering <5% of the whole brain), which may lead to missed spikes originating from brain regions that were not covered by SEEG. To address this problem, we propose a SEEG-informed minimum-norm estimates (SIMNE) method by combining SEEG with magnetoencephalography (MEG) or EEG. Specifically, the spike locations determined by SEEG offer as a priori information to guide MEG source reconstruction. Both computer simulations and experiments using data from five epilepsy patients were conducted to evaluate the performance of SIMNE. Our results demonstrate that SIMNE generates more accurate source estimation than a traditional minimum-norm estimates method and reveals the locations of spikes missed by SEEG, which would improve presurgical evaluation of the epileptogenic zone.

Control energy assessment of spatial interactions among macro‐scale brain networks

Many recent studies have revealed that spatial interactions of functional brain networks derived from fMRI data can well model functional connectomes of the human brain. However, it has been rarely explored what the energy consumption characteristics are for such spatial interactions of macro‐scale functional networks, which remains crucial for the understanding of brain organization, behavior, and dynamics. To explore this unanswered question, this article presents a novel framework for quantitative assessment of energy consumptions of macro‐scale functional brain network's spatial interactions via two main effective computational methodologies. First, we designed a novel scheme combining dictionary learning and hierarchical clustering to derive macro‐scale consistent brain network templates that can be used to define a common reference space for brain network interactions and energy assessments. Second, the control energy consumption for driving the brain networks during their spatial interactions is computed from the viewpoint of the linear network control theory. Especially, the energetically favorable brain networks were identified and their energy characteristics were comprehensively analyzed. Experimental results on the Human Connectome Project (HCP) task‐based fMRI (tfMRI) data showed that the proposed methods can reveal meaningful, diverse energy consumption patterns of macro‐scale network interactions. In particular, those networks present remarkable differences in energy consumption. The energetically least favorable brain networks are stable and consistent across HCP tasks such as motor, language, social, and working memory tasks. In general, our framework provides a new perspective to characterize human brain functional connectomes by quantitative assessment for the energy consumption of spatial interactions of macro‐scale brain networks.

Structure-informed functional connectivity driven by identifiable and state-specific control regions

Describing how the brain anatomical wiring contributes to the emergence of coordinated neural activity underlying complex behavior remains challenging. Indeed, patterns of remote coactivations that adjust with the ongoing task-demand do not systematically match direct, static anatomical links. Here, we propose that observed coactivation patterns, known as functional connectivity (FC), can be explained by a controllable linear diffusion dynamics defined on the brain architecture. Our model, termed structure-informed FC, is based on the hypothesis that different sets of brain regions controlling the information flow on the anatomical wiring produce state-specific functional patterns. We thus introduce a principled framework for the identification of potential control centers in the brain. We find that well-defined, sparse, and robust sets of control regions, partially overlapping across several tasks and resting state, produce FC patterns comparable to empirical ones. Our findings suggest that controllability is a fundamental feature allowing the brain to reach different states.

Understanding how brain anatomy promotes particular patterns of coactivations among neural regions is a key challenge in neuroscience. This challenge can be addressed using network science and systems theory. Here, we propose that coactivations result from the diffusion of information through the network of anatomical links connecting brain regions, with certain regions controlling the dynamics. We translate this hypothesis into a model called structure-informed functional connectivity, and we introduce a framework for identifying control regions based on empirical data. We find that our model produces coactivation patterns comparable to empirical ones, and that distinct sets of control regions are associated with different functional states. These findings suggest that controllability is an important feature allowing the brain to reach different states.

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.

Working memory requires the brain to switch between cognitive states and activity patterns. Here, the authors show that the steering of these neural network dynamics is influenced by dopamine D1- and D2-receptor function and altered in schizophrenia.

Uncovering and classifying the role of driven nodes in control of complex networks

The widely used Maximum Matching (MM) method identifies the minimum driver nodes set to control biological and technological systems. Nevertheless, it is assumed in the MM approach that one driver node can send control signal to multiple target nodes, which might not be appropriate in certain complex networks. A recent work introduced a constraint that one driver node can control one target node, and proposed a method to identify the minimum target nodes set under such a constraint. We refer such target nodes to driven nodes. However, the driven nodes may not be uniquely determined. Here, we develop a novel algorithm to classify driven nodes in control categories. Our computational analysis on a large number of biological networks indicates that the number of driven nodes is considerably larger than the number of driver nodes, not only in all examined complete plant metabolic networks but also in several key human pathways, which firstly demonstrate the importance of use of driven nodes in analysis of real-world networks.

Structural control energy of resting-state functional brain states reveals less cost-effective brain dynamics in psychosis vulnerability

How the brain's white-matter anatomy constrains brain activity is an open question that might give insights into the mechanisms that underlie mental disorders such as schizophrenia. Chromosome 22q11.2 deletion syndrome (22q11DS) is a neurodevelopmental disorder with an extremely high risk for psychosis providing a test case to study developmental aspects of schizophrenia. In this study, we used principles from network control theory to probe the implications of aberrant structural connectivity for the brain's functional dynamics in 22q11DS. We retrieved brain states from resting-state functional magnetic resonance images of 78 patients with 22q11DS and 85 healthy controls. Then, we compared them in terms of persistence control energy; that is, the control energy that would be required to persist in each of these states based on individual structural connectivity and a dynamic model. Persistence control energy was altered in a broad pattern of brain states including both energetically more demanding and less demanding brain states in 22q11DS. Further, we found a negative relationship between persistence control energy and resting-state activation time, which suggests that the brain reduces energy by spending less time in energetically demanding brain states. In patients with 22q11DS, this behavior was less pronounced, suggesting a deficiency in the ability to reduce energy through brain activation. In summary, our results provide initial insights into the functional implications of altered structural connectivity in 22q11DS, which might improve our understanding of the mechanisms underlying the disease.

Critical Neural Networks Minimize Metabolic Cost

Brain dynamics show a rich spatiotemporal behavior whose stability is neither ordered nor chaotic, indicating that neural networks operate at intermediate stability regimes including critical dynamics represented by a negative power-law distribution of avalanche sizes with exponent α=−1.5. However, it is unknown which stability regimen allows global and local information transmission with reduced metabolic costs, which are measured in terms of synaptic potentials and action potentials. In this work, using a hierarchical neuron model with rich-club organization, we measure the average number of action potentials required to activate n different neurons (avalanche size). Besides, we develop a mathematical formula to represent the metabolic synaptic potential cost. We develop simulations variating the synaptic amplitude, synaptic time course (ms), and hub excitatory/inhibitory ratio. We compare different dynamic regimes in terms of avalanche sizes vs. metabolic cost. We also implement the dynamic model in a Drosophila and Erdos–Renyi networks to computer dynamics and metabolic costs. The results show that the synaptic amplitude and time course play a key role in information propagation. They can drive the system from subcritical to supercritical regimes. The later result promotes the coexistence of critical regimes with a wide range of excitation/inhibition hub ratios. Moreover, subcritical or silent regimes minimize metabolic cost for local avalanche sizes, whereas critical and intermediate stability regimes show the best compromise between information propagation and reduced metabolic consumption, also minimizing metabolic cost for a wide range of avalanche sizes.

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.

Modeling brain, symptom, and behavior in the winds of change

Neuropsychopharmacology addresses pressing questions in the study of three intertwined complex systems: the brain, human behavior, and symptoms of illness. The field seeks to understand the perturbations that impinge upon those systems, either driving greater health or illness. In the pursuit of this aim, investigators often perform analyses that make certain assumptions about the nature of the systems that are being perturbed. Those assumptions can be encoded in powerful computational models that serve to bridge the wide gulf between a descriptive analysis and a formal theory of a system's response. Here we review a set of three such models along a continuum of complexity, moving from a local treatment to a network treatment: one commonly applied form of the general linear model, impulse response models, and network control models. For each, we describe the model's basic form, review its use in the field, and provide a frank assessment of its relative strengths and weaknesses. The discussion naturally motivates future efforts to interlink data analysis, computational modeling, and formal theory. Our goal is to inspire practitioners to consider the assumptions implicit in their analytical approach, align those assumptions to the complexity of the systems under study, and take advantage of exciting recent advances in modeling the relations between perturbations and system function.

Network structure of cascading neural systems predicts stimulus propagation and recovery

OBJECTIVE

Many neural systems display spontaneous, spatiotemporal patterns of neural activity that are crucial for information processing. While these cascading patterns presumably arise from the underlying network of synaptic connections between neurons, the precise contribution of the network's local and global connectivity to these patterns and information processing remains largely unknown.

APPROACH

Here, we demonstrate how network structure supports information processing through network dynamics in empirical and simulated spiking neurons using mathematical tools from linear systems theory, network control theory, and information theory.

MAIN RESULTS

In particular, we show that activity, and the information that it contains, travels through cycles in real and simulated networks.

SIGNIFICANCE

Broadly, our results demonstrate how cascading neural networks could contribute to cognitive faculties that require lasting activation of neuronal patterns, such as working memory or attention.

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.

On the Nature of Explanations Offered by Network Science: A Perspective From and for Practicing Neuroscientists

Network neuroscience represents the brain as a collection of regions and inter-regional connections. Given its ability to formalize systems-level models, network neuroscience has generated unique explanations of neural function and behavior. The mechanistic status of these explanations and how they can contribute to and fit within the field of neuroscience as a whole has received careful treatment from philosophers. However, these philosophical contributions have not yet reached many neuroscientists. Here we complement formal philosophical efforts by providing an applied perspective from and for neuroscientists. We discuss the mechanistic status of the explanations offered by network neuroscience and how they contribute to, enhance, and interdigitate with other types of explanations in neuroscience. In doing so, we rely on philosophical work concerning the role of causality, scale, and mechanisms in scientific explanations. In particular, we make the distinction between an explanation and the evidence supporting that explanation, and we argue for a scale-free nature of mechanistic explanations. In the course of these discussions, we hope to provide a useful applied framework in which network neuroscience explanations can be exercised across scales and combined with other fields of neuroscience to gain deeper insights into the brain and behavior.

Cost-Aware Robust Control of Signed Networks by Using a Memetic Algorithm

The robust controllability (RC) of a complex system tries to select a set of dominating entities for the functional control of this entire system without uncertain disturbances, and the research on RC will help to understand the system's underlying functions. In this article, we introduce the control cost in signed networks and present a cost-aware robust control (CRC) problem in this scenario. The aim of CRC is to minimize the cost to control a set of dominating nodes and transform a set of unbalanced links into balanced ones, such that the signed network can be robustly controlled without uncertain unbalanced factors (like nodes and links). To solve this problem, we first model CRC as a constrained combination optimization problem, and then present a memetic algorithm with some problem-specific knowledge (like the neighbors of nodes, the constraints of CRC, and the fast computation of the cost under each optimization) to solve this problem on signed networks. The extensive experiments on both real social and biological networks assess that our algorithm outperforms several state-of-the-art RC algorithms.

Dynamic representations in networked neural systems

A group of neurons can generate patterns of activity that represent information about stimuli; subsequently, the group can transform and transmit activity patterns across synapses to spatially distributed areas. Recent studies in neuroscience have begun to independently address the two components of information processing: the representation of stimuli in neural activity and the transmission of information in networks that model neural interactions. Yet only recently are studies seeking to link these two types of approaches. Here we briefly review the two separate bodies of literature; we then review the recent strides made to address this gap. We continue with a discussion of how patterns of activity evolve from one representation to another, forming dynamic representations that unfold on the underlying network. Our goal is to offer a holistic framework for understanding and describing neural information representation and transmission while revealing exciting frontiers for future research.

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.

Network architectures supporting learnability

Human learners acquire complex interconnected networks of relational knowledge. The capacity for such learning naturally depends on two factors: the architecture (or informational structure) of the knowledge network itself and the architecture of the computational unit-the brain-that encodes and processes the information. That is, learning is reliant on integrated network architectures at two levels: the epistemic and the computational, or the conceptual and the neural. Motivated by a wish to understand conventional human knowledge, here, we discuss emerging work assessing network constraints on the learnability of relational knowledge, and theories from statistical physics that instantiate the principles of thermodynamics and information theory to offer an explanatory model for such constraints. We then highlight similarities between those constraints on the learnability of relational networks, at one level, and the physical constraints on the development of interconnected patterns in neural systems, at another level, both leading to hierarchically modular networks. To support our discussion of these similarities, we employ an operational distinction between the modeller (e.g. the human brain), the model (e.g. a single human's knowledge) and the modelled (e.g. the information present in our experiences). We then turn to a philosophical discussion of whether and how we can extend our observations to a claim regarding explanation and mechanism for knowledge acquisition. What relation between hierarchical networks, at the conceptual and neural levels, best facilitate learning? Are the architectures of optimally learnable networks a topological reflection of the architectures of comparably developed neural networks? Finally, we contribute to a unified approach to hierarchies and levels in biological networks by proposing several epistemological norms for analysing the computational brain and social epistemes, and for developing pedagogical principles conducive to curious thought. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

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.

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.

Neuronal Degeneration Impairs Rhythms Between Connected Microcircuits

Synchronization of neural activity across brain regions is critical to processes that include perception, learning, and memory. After traumatic brain injury (TBI), neuronal degeneration is one possible effect and can alter communication between neural circuits. Consequently, synchronization between neurons may change and can contribute to both lasting changes in functional brain networks and cognitive impairment in patients. However, fundamental principles relating exactly how TBI at the cellular scale affects synchronization of mesoscale circuits are not well understood. In this work, we use computational networks of Izhikevich integrate-and-fire neurons to study synchronized, oscillatory activity between clusters of neurons, which also adapt according to spike-timing-dependent plasticity (STDP). We study how the connections within and between these neuronal clusters change as unidirectional connections form between the two neuronal populations. In turn, we examine how neuronal deletion, intended to mimic the temporary or permanent loss of neurons in the mesoscale circuit, affects these dynamics. We determine synchronization of two neuronal circuits requires very modest connectivity between these populations; approximately 10% of neurons projecting from one circuit to another circuit will result in high synchronization. In addition, we find that synchronization level inversely affects the strength of connection between neuronal microcircuits - moderately synchronized microcircuits develop stronger intercluster connections than do highly synchronized circuits. Finally, we find that highly synchronized circuits are largely protected against the effects of neuronal deletion but may display changes in frequency properties across circuits with targeted neuronal loss. Together, our results suggest that strongly and weakly connected regions differ in their inherent resilience to damage and may serve different roles in a larger network.

Data-Driven Approaches to Neuroimaging Analysis to Enhance Psychiatric Diagnosis and Therapy

Combining advanced neuroimaging with novel computational methods in network science and machine learning has led to increasingly meaningful descriptions of structure and function in both the normal and the abnormal brain, thereby contributing significantly to our understanding of psychiatric disorders as circuit dysfunctions. Despite its marked potential for psychiatric care, this approach has not yet extended beyond the research setting to any clinically useful applications. Here we review current developments in the study of neuroimaging data using network models and machine learning methods, with a focus on their promise in offering a framework for clinical translation. We discuss 3 potential contributions of these methods to psychiatric care: 1) a better understanding of psychopathology beyond current diagnostic boundaries; 2) individualized prediction of treatment response and prognosis; and 3) formal theories to guide the development of novel interventions. Finally, we highlight current obstacles and sketch a forward-looking perspective of how the application of machine learning and network modeling methods should proceed to accelerate their potential transformation of clinically useful tools.

Controllability Ensured Leader Group Selection on Signed Multiagent Networks

Leader-follower controllability on signed multiagent networks is investigated in this paper. Specifically, we consider a dynamic signed multiagent network, where the agents interact via neighbor-based Laplacian feedback and the network allows positive and negative edges to capture cooperative and competitive interactions among agents. The agents are classified as either leaders or followers, thus forming a leader-follower signed network. To enable full control of the leader-follower signed network, controllability ensured leader group selection approaches are investigated in this paper, that is, identifying a small subset of nodes in the signed network, such that the selected nodes are able to drive the network to a desired behavior, even in the presence of antagonistic interactions. In particular, graphical characterizations of the controllability of signed networks are first developed based on the investigation of the interaction between network topology and agent dynamics. Since signed path and cycle graphs are basic building blocks for a variety of networks, the developed topological characterizations are then exploited to develop leader selection methods for signed path and cycle graphs to ensure leader-follower controllability. Along with illustrative examples, heuristic algorithms are also developed showing how leader selection methods developed for path and cycle graphs can be potentially extended to more general signed networks. In contrast to existing results that mainly focus on unsigned networks, this paper characterizes controllability and develops leader selection methods for signed networks. In addition, the developed results are generic, in the sense that they are not only applicable to signed networks but also to unsigned networks, since unsigned networks are a particular case of signed networks that only contain positive edges.

Stability of spontaneous, correlated activity in mouse auditory cortex

Neural systems can be modeled as complex networks in which neural elements are represented as nodes linked to one another through structural or functional connections. The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system’s topological organization and to better understand its function. Here, we used two-photon calcium imaging to record spontaneous activity from the same set of cells in mouse auditory cortex over the course of several weeks. We reconstruct functional networks in which cells are linked to one another by edges weighted according to the correlation of their fluorescence traces. We show that the networks exhibit modular structure across multiple topological scales and that these multi-scale modules unfold as part of a hierarchy. We also show that, on average, network architecture becomes increasingly dissimilar over time, with similarity decaying monotonically with the distance (in time) between sessions. Finally, we show that a small fraction of cells maintain strongly-correlated activity over multiple days, forming a stable temporal core surrounded by a fluctuating and variable periphery. Our work indicates a framework for studying spontaneous activity measured by two-photon calcium imaging using computational methods and graphical models from network science. The methods are flexible and easily extended to additional datasets, opening the possibility of studying cellular level network organization of neural systems and how that organization is modulated by stimuli or altered in models of disease.

Neurons coordinate their activity with one another, forming networks that help support adaptive, flexible behavior. Still, little is known about the organization of these networks at the cellular scale and their stability over time. Here, we reconstruct networks from calcium imaging data recorded in mouse primary auditory cortex. We show that these networks exhibit spatially constrained, hierarchical modular structure, which may facilitate specialized information processing. However, we show that connection weights and modular structure are also variable over time, changing on a timescale of days and adopting novel network configurations. Despite this, a small subset of neurons maintain their connections to one another and preserve their modular organization across time, forming a stable temporal core surrounded by a flexible periphery. These findings represent a conceptual bridge linking network analyses of macroscale and cellular-level neuroimaging data. They also represent a complementary approach to existing circuits- and systems-based interrogation of nervous system function, opening the door for deeper and more targeted analysis in the future.

A topology-dynamics-based control strategy for multi-dimensional complex networked dynamical systems

Complex systems are omnipresent and play a vital role in in our every-day lives. Adverse behavior of such systems has generated considerable interest in being able to control complex systems modeled as networks. Here, we propose a topology-dynamics-based approach for controlling complex systems modeled as networks of coupled multi-dimensional dynamical entities. For given dynamics and topology, we introduce an efficient scheme to identify in polynomial time a finite set of driver nodes, which – when endowed with the control function – steer the network to the desired behavior. We demonstrate the high suitability of our approach by controlling various networked multi-dimensional dynamics, coupled onto different topologies.