Energetic Constraints Produce Self-sustained Oscillatory Dynamics in Neuronal Networks

EEG spectral attractors identify a geometric core of brain dynamics

Multidimensional reconstruction of brain attractors from electroencephalography (EEG) data enables the analysis of geometric complexity and interactions between signals in state space. Utilizing resting-state data from young and older adults, we characterize periodic (traditional frequency bands) and aperiodic (broadband exponent) attractors according to their geometric complexity and shared dynamical signatures, which we refer to as a geometric cross-parameter coupling. Alpha and aperiodic attractors are the least complex, and their global shapes are shared among all other frequency bands, affording alpha and aperiodic greater predictive power. Older adults show lower geometric complexity but greater coupling, resulting from dedifferentiation of gamma activity. The form and content of resting-state thoughts were further associated with the complexity of attractor dynamics. These findings support a process-developmental perspective on the brain's dynamic core, whereby more complex information differentiates out of an integrative and global geometric core.

Metabolic energetics underlying attractors in neural models

Neural population modeling, including the role of neural attractors, is a promising tool for understanding many aspects of brain function. We propose a modeling framework to connect the abstract variables used in modeling to recent cellular-level estimates of the bioenergetic costs of different aspects of neural activity, measured in ATP consumed per second per neuron. Based on recent work, an empirical reference for brain ATP use for the awake resting brain was estimated as ∼2 × 109 ATP/s-neuron across several mammalian species. The energetics framework was applied to the Wilson-Cowan (WC) model of two interacting populations of neurons, one excitatory (E) and one inhibitory (I). Attractors were considered to exhibit steady-state behavior and limit cycle behavior, both of which end when the excitatory stimulus ends, and sustained activity that persists after the stimulus ends. The energy cost of limit cycles, with oscillations much faster than the average neuronal firing rate of the population, is tracked more closely with the firing rate than the limit cycle frequency. Self-sustained firing driven by recurrent excitation, though, involves higher firing rates and a higher energy cost. As an example of a simple network in which each node is a WC model, a combination of three nodes can serve as a flexible circuit element that turns on with an oscillating output when input passes a threshold and then persists after the input ends (an "on-switch"), with moderate overall ATP use. The proposed framework can serve as a guide for anchoring neural population models to plausible bioenergetics requirements.NEW & NOTEWORTHY This work bridges two approaches for understanding brain function: cellular-level studies of the metabolic energy costs of different aspects of neural activity and neural population modeling, including the role of neural attractors. The proposed modeling framework connects energetic costs, in ATP consumed per second per neuron, to the more abstract variables used in neural population modeling. In particular, this work anchors potential neural attractors to physiologically plausible bioenergetics requirements.

Cognition is entangled with metabolism: relevance for resting-state EEG-fMRI

The brain is a living organ with distinct metabolic constraints. However, these constraints are typically considered as secondary or supportive of information processing which is primarily performed by neurons. The default operational definition of neural information processing is that (1) it is ultimately encoded as a change in individual neuronal firing rate as this correlates with the presentation of a peripheral stimulus, motor action or cognitive task. Two additional assumptions are associated with this default interpretation: (2) that the incessant background firing activity against which changes in activity are measured plays no role in assigning significance to the extrinsically evoked change in neural firing, and (3) that the metabolic energy that sustains this background activity and which correlates with differences in neuronal firing rate is merely a response to an evoked change in neuronal activity. These assumptions underlie the design, implementation, and interpretation of neuroimaging studies, particularly fMRI, which relies on changes in blood oxygen as an indirect measure of neural activity. In this article we reconsider all three of these assumptions in light of recent evidence. We suggest that by combining EEG with fMRI, new experimental work can reconcile emerging controversies in neurovascular coupling and the significance of ongoing, background activity during resting-state paradigms. A new conceptual framework for neuroimaging paradigms is developed to investigate how ongoing neural activity is "entangled" with metabolism. That is, in addition to being recruited to support locally evoked neuronal activity (the traditional hemodynamic response), changes in metabolic support may be independently "invoked" by non-local brain regions, yielding flexible neurovascular coupling dynamics that inform the cognitive context. This framework demonstrates how multimodal neuroimaging is necessary to probe the neurometabolic foundations of cognition, with implications for the study of neuropsychiatric disorders.

Aperiodic measures of neural excitability are associated with anticorrelated hemodynamic networks at rest: A combined EEG-fMRI study

The hallmark of resting EEG spectra are distinct rhythms emerging from a broadband, aperiodic background. This aperiodic neural signature accounts for most of total EEG power, although its significance and relation to functional neuroanatomy remains obscure. We hypothesized that aperiodic EEG reflects a significant metabolic expenditure and therefore might be associated with the default mode network while at rest. During eyes-open, resting-state recordings of simultaneous EEG-fMRI, we find that aperiodic and periodic components of EEG power are only minimally associated with activity in the default mode network. However, a whole-brain analysis identifies increases in aperiodic power correlated with hemodynamic activity in an auditory-salience-cerebellar network, and decreases in aperiodic power are correlated with hemodynamic activity in prefrontal regions. Desynchronization in residual alpha and beta power is associated with visual and sensorimotor hemodynamic activity, respectively. These findings suggest that resting-state EEG signals acquired in an fMRI scanner reflect a balance of top-down and bottom-up stimulus processing, even in the absence of an explicit task.

Functional Weight of Somatic and Cognitive Networks and Asymmetry of Compensatory Mechanisms: Collaboration or Divergency among Hemispheres after Cerebrovascular Accident?

The human brain holds highly sophisticated compensatory mechanisms relying on neuroplasticity. Neuronal degeneracy, redundancy, and brain network organization make the human nervous system more robust and evolvable to continuously guarantee an optimal environmental-related homeostasis. Nevertheless, after injury, restitution processes appear dissimilar, depending on the pathology. Following a cerebrovascular accident, asymmetry, within- and across-network compensation and interhemispheric inhibition are key features to functional recovery. In moderate-to-severe stroke, neurological outcome is often poor, and little is known about the paths that enable either an efficient collaboration among hemispheres or, on the contrary, an antagonism of adaptative responses. In this review, we aim to decipher key issues of ipsilesional and contralesional hemispheric functioning allowing the foundations of effective neurorehabilitation strategies.

Simple models including energy and spike constraints reproduce complex activity patterns and metabolic disruptions

In this work, we introduce new phenomenological neuronal models (eLIF and mAdExp) that account for energy supply and demand in the cell as well as the inactivation of spike generation how these interact with subthreshold and spiking dynamics. Including these constraints, the new models reproduce a broad range of biologically-relevant behaviors that are identified to be crucial in many neurological disorders, but were not captured by commonly used phenomenological models. Because of their low dimensionality eLIF and mAdExp open the possibility of future large-scale simulations for more realistic studies of brain circuits involved in neuronal disorders. The new models enable both more accurate modeling and the possibility to study energy-associated disorders over the whole time-course of disease progression instead of only comparing the initially healthy status with the final diseased state. These models, therefore, provide new theoretical and computational methods to assess the opportunities of early diagnostics and the potential of energy-centered approaches to improve therapies.

Neurons, even “at rest”, require a constant supply of energy to function. They cannot sustain high-frequency activity over long periods because of regulatory mechanisms, such as adaptation or sodium channels inactivation, and metabolic limitations. These limitations are especially severe in many neuronal disorders, where energy can become insufficient and make the neuronal response change drastically, leading to increased burstiness, network oscillations, or seizures. Capturing such behaviors and impact of energy constraints on them is an essential prerequisite to study disorders such as Parkinson’s disease and epilepsy. However, energy and spiking constraints are not present in any of the standard neuronal models used in computational neuroscience. Here we introduce models that provide a simple and scalable way to account for these features, enabling large-scale theoretical and computational studies of neurological disorders and activity patterns that could not be captured by previously used models. These models provide a way to study energy-associated disorders over the whole time-course of disease progression, and they enable a better assessment of energy-centered approaches to improve therapies.

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Structural plasticity, characterized by the formation and elimination of synapses, plays a big role in learning and long-term memory formation in the brain. The majority of the synapses in the neocortex occur between the axonal boutons and dendritic spines. Therefore, understanding the dynamics of the dendritic spine growth and elimination can provide key insights to the mechanisms of structural plasticity. In addition to learning and memory formation, the connectivity of neural networks affects cognition, perception, and behavior. Unsurprisingly, psychiatric and neurological disorders such as schizophrenia and autism are accompanied by pathological alterations in spine morphology and synapse numbers. Hence, it is vital to develop a model to understand the mechanisms governing dendritic spine dynamics throughout the lifetime. Here, we applied the density dependent Ricker population model to investigate the feasibility of ecological population concepts and mathematical foundations in spine dynamics. The model includes “immigration,” which is based on the filopodia type transient spines, and we show how this effect can potentially stabilize the spine population theoretically. For the long-term dynamics we employed a time dependent carrying capacity based on the brain's metabolic energy allocation. The results show that the mathematical model can explain the spine density fluctuations in the short-term and also account for the long term trends in the developing brain during synaptogenesis and pruning.