Not One, but Many Critical States: A Dynamical Systems Perspective

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Pattern forming mechanisms of color vision

While our understanding of the way single neurons process chromatic stimuli in the early visual pathway has advanced significantly in recent years, we do not yet know how these cells interact to form stable representations of hue. Drawing on physiological studies, we offer a dynamical model of how the primary visual cortex tunes for color, hinged on intracortical interactions and emergent network effects. After detailing the evolution of network activity through analytical and numerical approaches, we discuss the effects of the model's cortical parameters on the selectivity of the tuning curves. In particular, we explore the role of the model's thresholding nonlinearity in enhancing hue selectivity by expanding the region of stability, allowing for the precise encoding of chromatic stimuli in early vision. Finally, in the absence of a stimulus, the model is capable of explaining hallucinatory color perception via a Turing-like mechanism of biological pattern formation.

Critical Drift in a Neuro-Inspired Adaptive Network

It has been postulated that the brain operates in a self-organized critical state that brings multiple benefits, such as optimal sensitivity to input. Thus far, self-organized criticality has typically been depicted as a one-dimensional process, where one parameter is tuned to a critical value. However, the number of adjustable parameters in the brain is vast, and hence critical states can be expected to occupy a high-dimensional manifold inside a high-dimensional parameter space. Here, we show that adaptation rules inspired by homeostatic plasticity drive a neuro-inspired network to drift on a critical manifold, where the system is poised between inactivity and persistent activity. During the drift, global network parameters continue to change while the system remains at criticality.

Local Dirac Synchronization on networks

We propose Local Dirac Synchronization that uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely while the other modes are interacting non-linearly, leading to a collectively synchronized state when the coupling constant of the model is increased. Local Dirac Synchronization is characterized by discontinuous transitions and the emergence of a rhythmic coherent phase. In this rhythmic phase, one of the two complex order parameters oscillates in the complex plane at a slow frequency (called emergent frequency) in the frame in which the intrinsic frequencies have zero average. Our theoretical results obtained within the annealed approximation are validated by extensive numerical results on fully connected networks and sparse Poisson and scale-free networks. Local Dirac Synchronization on both random and real networks, such as the connectome of Caenorhabditis Elegans, reveals the interplay between topology (Betti numbers and harmonic modes) and non-linear dynamics. This unveils how topology might play a role in the onset of brain rhythms.

Subcritical escape waves in schooling fish

Theoretical physics predicts optimal information processing in living systems near transitions (or pseudo-critical points) in their collective dynamics. However, focusing on potential benefits of proximity to a critical point, such as maximal sensitivity to perturbations and fast dissemination of information, commonly disregards possible costs of criticality in the noisy, dynamic environmental contexts of biological systems. Here, we find that startle cascades in fish schools are subcritical (not maximally responsive to environmental cues) and that distance to criticality decreases when perceived risk increases. Considering individuals' costs related to two detection error types, associated to both true and false alarms, we argue that being subcritical, and modulating distance to criticality, can be understood as managing a trade-off between sensitivity and robustness according to the riskiness and noisiness of the environment. Our work emphasizes the need for an individual-based and context-dependent perspective on criticality and collective information processing and motivates future questions about the evolutionary forces that brought about a particular trade-off.

Toward a Unified Analysis of the Brain Criticality Hypothesis: Reviewing Several Available Tools

The study of the brain criticality hypothesis has been going on for about 20 years, various models and methods have been developed for probing this field, together with large amounts of controversial experimental findings. However, no standardized protocol of analysis has been established so far. Therefore, hoping to make some contributions to standardization of such analysis, we review several available tools used for estimating the criticality of the brain in this paper.

Early functional changes associated with alpha-synuclein proteinopathy in engineered human neural networks

A patterned spread of proteinopathy represents a common characteristic of many neurodegenerative diseases. In Parkinson's disease (PD), misfolded forms of α-synuclein proteins accumulate in hallmark pathological inclusions termed Lewy bodies and Lewy neurites. Such protein aggregates seem to affect selectively vulnerable neuronal populations in the substantia nigra and to propagate within interconnected neuronal networks. Research findings suggest that these proteinopathic inclusions are present at very early time points in disease development, even before clear behavioral symptoms of dysfunction arise. In this study, we investigate the early pathophysiology developing after induced formation of such PD-related α-synuclein inclusions in a physiologically relevant in vitro setup using engineered human neural networks. We monitor the neural network activity using multielectrode arrays (MEAs) for a period of 3 wk following proteinopathy induction to identify associated changes in network function, with a special emphasis on the measure of network criticality. Self-organized criticality represents the critical point between resilience against perturbation and adaptational flexibility, which appears to be a functional trait in self-organizing neural networks, both in vitro and in vivo. We show that although developing pathology at early onset is not clearly manifest in standard measurements of network function, it may be discerned by investigating differences in network criticality states.