Failure of adaptive self-organized criticality during epileptic seizure attacks

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimal in the critical state. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.     

Perspective: network-guided pattern formation of neural dynamics

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain''s network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatio-temporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.     

Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.     

Global self-organization of the cellular metabolic structure

Background

Over many years, it has been assumed that enzymes work either in an isolated way, or organized in small catalytic groups. Several studies performed using “metabolic networks models” are helping to understand the degree of functional complexity that characterizes enzymatic dynamic systems. In a previous work, we used “dissipative metabolic networks” (DMNs) to show that enzymes can present a self-organized global functional structure, in which several sets of enzymes are always in an active state, whereas the rest of molecular catalytic sets exhibit dynamics of on-off changing states. We suggested that this kind of global metabolic dynamics might be a genuine and universal functional configuration of the cellular metabolic structure, common to all living cells. Later, a different group has shown experimentally that this kind of functional structure does, indeed, exist in several microorganisms.

Methodology/Principal Findings

Here we have analyzed around 2.500.000 different DMNs in order to investigate the underlying mechanism of this dynamic global configuration. The numerical analyses that we have performed show that this global configuration is an emergent property inherent to the cellular metabolic dynamics. Concretely, we have found that the existence of a high number of enzymatic subsystems belonging to the DMNs is the fundamental element for the spontaneous emergence of a functional reactive structure characterized by a metabolic core formed by several sets of enzymes always in an active state.

Conclusions/Significance

This self-organized dynamic structure seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. To better understand cellular functionality, it will be crucial to structurally characterize these enzymatic self-organized global structures.     

Dynamics of a hybrid system of a brain neural network and an artificial nonlinear oscillator

In the brain, many functional modules interact with each other to execute complex information processing. Understanding the nature of these interactions is necessary for understanding how the brain functions. In this study, to mimic interacting modules in the brain, we constructed a hybrid system mutually coupling a hippocampal CA3 network as an actual brain module and a radial isochron clock (RIC) simulated by a personal computer as an artificial module. Return map analysis of the CA3-RIC system's dynamics showed the mutual entrainment and complex dynamics dependent on the coupling modes. The phase response curve of CA3 was modeled regarding the CA3 as a nonlinear oscillator. Using the phase response curves of CA3 and RIC, we reconstructed return maps of the hybrid system's dynamics. Although the reconstructed return maps almost agreed with the experimental data, there were deviations dependent on the coupling mode. In particular, we noted that the deviation was smaller under the bidirectional coupling conditions than during the one-way coupling from RIC to CA3. These results suggest that brain modules may flexibly change their dynamical properties through interaction with other modules.     

Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons

Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing.     

Nonlinear Dynamics of Emotion-Cognition Interaction: When Emotion Does not Destroy Cognition?

Emotion (i.e., spontaneous motivation and subsequent implementation of a behavior) and cognition (i.e., problem solving by information processing) are essential to how we, as humans, respond to changes in our environment. Recent studies in cognitive science suggest that emotion and cognition are subserved by different, although heavily integrated, neural systems. Understanding the time-varying relationship of emotion and cognition is a challenging goal with important implications for neuroscience. We formulate here the dynamical model of emotion-cognition interaction that is based on the following principles: (1) the temporal evolution of cognitive and emotion modes are captured by the incoming stimuli and competition within and among themselves (competition principle); (2) metastable states exist in the unified emotion-cognition phase space; and (3) the brain processes information with robust and reproducible transients through the sequence of metastable states. Such a model can take advantage of the often ignored temporal structure of the emotion-cognition interaction to provide a robust and generalizable method for understanding the relationship between brain activation and complex human behavior. The mathematical image of the robust and reproducible transient dynamics is a Stable Heteroclinic Sequence (SHS), and the Stable Heteroclinic Channels (SHCs). These have been hypothesized to be possible mechanisms that lead to the sequential transient behavior observed in networks. We investigate the modularity of SHCs, i.e., given a SHS and a SHC that is supported in one part of a network, we study conditions under which the SHC pertaining to the cognition will continue to function in the presence of interfering activity with other parts of the network, i.e., emotion.     

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others.     

Creative dynamics approach to neural intelligence

The thrust of this paper is to introduce and discuss a substantially new type of dynamical system for modelling biological behavior. The approach was motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks — their rigid behavior compared with even simplest biological systems. This approach exploits a novel paradigm in nonlinear dynamics based upon the concept of terminal attractors and repellers. It was demonstrated that non-Lipschitzian dynamics based upon the failure of Lipschitz condition exhibits a new qualitative effect — a multi-choice response to periodic external excitations. Based upon this property, a substantially new class of dynamical systems — the unpredictable systems — was introduced and analyzed. These systems are represented in the form of coupled activation and learning dynamical equations whose ability to be spontaneously activated is based upon two pathological characteristics. Firstly, such systems have zero Jacobian. As a result of that, they have an infinite number of equilibrium points which occupy curves, surfaces or hypersurfaces. Secondly, at all these equilibrium points, the Lipschitz conditions fails, so the equilibrium points become terminal attractors or repellers depending upon the sign of the periodic excitation. Both of these pathological characteristics result in multi-choice response of unpredictable dynamical systems. It has been shown that the unpredictable systems can be controlled by sign strings which uniquely define the system behaviors by specifying the direction of the motions in the critical points. By changing the combinations of signs in the code strings the system can reproduce any prescribed behavior to a prescribed accuracy. That is why the unpredictable systems driven by sign strings are extremely flexible and are highly adaptable to environmental changes. It was also shown that such systems can serve as a powerful tool for temporal pattern memories and complex pattern recognition. It has been demonstrated that new architecture of neural networks based upon non-Lipschitzian dynamics can be utilized for modelling more complex patterns of behavior which can be associated with phenomenological models of creativity and neural intelligence.     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.     

Water: the bloodstream of the biosphere

Water, the bloodstream of the biosphere, determines the sustainability of living systems. The essential role of water is expanded in a conceptual model of energy dissipation, based on the water balance of whole landscapes. In this model, the underlying role of water phase changes--and their energy-dissipative properties--in the function and the self-organized development of natural systems is explicitly recognized. The energy-dissipating processes regulate the ecological dynamics within the Earth's biosphere, in such a way that the development of natural systems is never allowed to proceed in an undirected or random way. A fundamental characteristic of self-organized development in natural systems is the increasing role of cyclic processes while loss processes are correspondingly reduced. This gives a coincidental increase in system efficiency, which is the basis of growing stability and sustainability. Growing sustainability can be seen as an increase of ecological efficiency, which is applicable at all levels up to whole landscapes. Criteria for necessary changes in society and for the design of the measures that are necessary to restore sustainable landscapes and waters are derived.     

The role of ecological factors in controlling vegetation dynamics on long temporal scales

Abstract

The pattern of change in the Holocene forests of Europe is outlined and discussed in the light of external and internal forcing factors. Forests are seen as non-linear, dynamic systems, that are, at any point in time, unique and changing. In the absence of human activity, potential forcing factors during the Holocene include (i) climate, (ii) soil development, and (iii) internal forest dynamics. Climate is influential through exerting control on the floristic pool from which forests developed. Current results indicate that the role of soil development is likely to have been minor, but may have slowed rate of invasion and increase of some mid- and late-Holocene forest dominants. Forest change following spread and increase then forces soil change. Internal processes of forest dynamics include competition among existing species, and interactions between existing species and potential invading species. The patterns of interaction may be detectable through rates of change and patterns of increase seen in pollen records. Such processes are seen as being the dominant influence on the pattern of change and the development of forest. Forested systems, such as those in Europe, are strongly influenced by historical events, such as the mid-Holocene decline of elm. Forest composition is likely to be similar, in the broadest terms, from one interglacial to another, but always to vary in detail. The interaction of individuals, populations and environmental variables ensures that, although deterministic, prediction of change will always be difficult.     

Embedding Responses in Spontaneous Neural Activity Shaped through Sequential Learning

Recent experimental measurements have demonstrated that spontaneous neural activity in the absence of explicit external stimuli has remarkable spatiotemporal structure. This spontaneous activity has also been shown to play a key role in the response to external stimuli. To better understand this role, we proposed a viewpoint, “memories-as-bifurcations,” that differs from the traditional “memories-as-attractors” viewpoint. Memory recall from the memories-as-bifurcations viewpoint occurs when the spontaneous neural activity is changed to an appropriate output activity upon application of an input, known as a bifurcation in dynamical systems theory, wherein the input modifies the flow structure of the neural dynamics. Learning, then, is a process that helps create neural dynamical systems such that a target output pattern is generated as an attractor upon a given input. Based on this novel viewpoint, we introduce in this paper an associative memory model with a sequential learning process. Using a simple Hebbian-type learning, the model is able to memorize a large number of input/output mappings. The neural dynamics shaped through the learning exhibit different bifurcations to make the requested targets stable upon an increase in the input, and the neural activity in the absence of input shows chaotic dynamics with occasional approaches to the memorized target patterns. These results suggest that these dynamics facilitate the bifurcations to each target attractor upon application of the corresponding input, which thus increases the capacity for learning. This theoretical finding about the behavior of the spontaneous neural activity is consistent with recent experimental observations in which the neural activity without stimuli wanders among patterns evoked by previously applied signals. In addition, the neural networks shaped by learning properly reflect the correlations of input and target-output patterns in a similar manner to those designed in our previous study.     

Broadband Criticality of Human Brain Network Synchronization

Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.     

How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models

Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual''s Voronoi neighbors. The models include a tunable parameter that controls an individual''s relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.