Self-Organized Criticality Model for Brain Plasticity

Arcangelis, L. de; Perrone-Capano, Carla; Herrmann, Hans J.

doi:10.1103/physrevlett.96.028107

Cited by 245 publications

(222 citation statements)

References 40 publications

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“…In a random network of size N with connectivity probability c, the critical parameter α is approximately equal to α cr N /c, where α cr N is obtained from the critical parameter region of the fully connected network of size c × N. If the connections in a partially connected random network are not chosen independently (for example, 'small-world' connectivity 18 ), even more accurate power laws than for the independent case with the same average connectivity are found. A similar phenomenon occurs in the grid network 19 which has been used to model criticality in electroencephalograph recordings.…”

Section: (4)mentioning

confidence: 99%

Dynamical synapses causing self-organized criticality in neural networks

2007

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Self-organized criticality 1 is one of the key concepts to describe the emergence of complexity in natural systems. The concept asserts that a system self-organizes into a critical state where system observables are distributed according to a power law. Prominent examples of self-organized critical dynamics include piling of granular media 2 , plate tectonics 3 and stick-slip motion 4 . Critical behaviour has been shown to bring about optimal computational capabilities 5 , optimal transmission 6 , storage of information 7 and sensitivity to sensory stimuli 8-10 . In neuronal systems, the existence of critical avalanches was predicted 11 and later observed experimentally 6,12,13 . However, whereas in the experiments generic critical avalanches were found, in the model of ref. 11 they only show up if the set of parameters is fine-tuned externally to a critical transition state. Here, we demonstrate analytically and numerically that by assuming (biologically more realistic) dynamical synapses 14 in a spiking neural network, the neuronal avalanches turn from an exceptional phenomenon into a typical and robust self-organized critical behaviour, if the total resources of neurotransmitter are sufficiently large.In multi-electrode recordings on slices of rat cortex and neuronal cultures 6,12 , neuronal avalanches were observed whose sizes were distributed according to a power law with an exponent of −3/2. The distribution was stable over a long period of time.Variations of the dynamical behaviour are induced by application or wash-out of neuromodulators. Qualitatively identical behaviour can be reached in models such as those in refs 11,15 by variations of a global connectivity parameter. In these models, criticality only shows up if the interactions are fixed precisely at a specific value or connectivity structure.Here, we study a model with activity-dependent depressive synapses and show that existence of several dynamical regimes can be reconciled with parameter-independent criticality. We find that synaptic depression causes the mean synaptic strengths to approach a critical value for a certain range of interaction parameters, whereas outside this range other dynamical behaviours are prevalent, see Fig. 1. We analytically derive an expression for the average coupling strengths among neurons and the average inter-spike intervals in a mean-field approach. The mean-field approximation is applicable here even in the critical state, because the quantities that are averaged do not exhibit power laws, but unimodal distributions. These mean values obey a self-consistency equation that allows us to identify the mechanism that drives the dynamics of the system towards the critical regime. Moreover, the critical regime induced by the synaptic dynamics is robust to parameter changes.Consider a network of N integrate-and-fire neurons. Each neuron is characterized by a membrane potential 0 < h i (t ) < θ. The neurons receive external inputs by a random process ξ τ ∈ {1,. . .,N} that selects a neuron ξ τ (t ) = i at a rate τ and a...

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Section: (4)mentioning

confidence: 99%

Dynamical synapses causing self-organized criticality in neural networks

2007

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“…Indeed, the finding of scale invariance does not exclude long-range or short-range heterogeneous corticocortical projections. Numerical simulations have shown that neuronal avalanches can arise at the critical state in models with scale-free (26), fully connected (27), random (28), and nearest-neighbor (18,26) topologies, although in each case the conditions to reach criticality can be different. In cortical cultures, the neuronal avalanches establish a functional small-world architecture with specific and highly diverse point-topoint connectivity between cortical sites that is, the network representing these site activations is densely interconnected, globally as well as locally (29).…”

Section: Scale Invariance In Time Nlfp Amplitude and Finite-size Scmentioning

confidence: 99%

Spontaneous cortical activity in awake monkeys composed of neuronal avalanches

Petermann

Thiagarajan

Lebedev

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

534

541

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Spontaneous neuronal activity is an important property of the cerebral cortex but its spatiotemporal organization and dynamical framework remain poorly understood. Studies in reduced systems-tissue cultures, acute slices, and anesthetized ratsshow that spontaneous activity forms characteristic clusters in space and time, called neuronal avalanches. Modeling studies suggest that networks with this property are poised at a critical state that optimizes input processing, information storage, and transfer, but the relevance of avalanches for fully functional cerebral systems has been controversial. Here we show that ongoing cortical synchronization in awake rhesus monkeys carries the signature of neuronal avalanches. Negative LFP deflections (nLFPs) correlate with neuronal spiking and increase in amplitude with increases in local population spike rate and synchrony. These nLFPs form neuronal avalanches that are scale-invariant in space and time and with respect to the threshold of nLFP detection. This dimension, threshold invariance, describes a fractal organization: smaller nLFPs are embedded in clusters of larger ones without destroying the spatial and temporal scale-invariance of the dynamics. These findings suggest an organization of ongoing cortical synchronization that is scale-invariant in its three fundamental dimensions-time, space, and local neuronal group size. Such scale-invariance has ontogenetic and phylogenetic implications because it allows large increases in network capacity without a fundamental reorganization of the system. neuronal synchronization ͉ resting state ͉ rhesus monkey ͉ spontaneous activity ͉ ongoing activity T he cerebral cortex displays spontaneous activity, also known as 'ongoing' or 'resting state' activity, which persists in the absence of sensory stimuli or motor outputs. The ongoing activity is a robust feature of cortical dynamics as it is only modulated to a small extent by stimulus presentation (1), but contributes significantly to the large variability observed in stimulus responses (2-5). In fact, ongoing activity has been found to reflect multiple aspects of neuronal processing. The activity is similar to that observed during stimulus presentation (1, 6-8), incorporates previously acquired information (9), and carries information about the underlying neuronal network [for review see (10)]. Indeed, correlations during resting state activity are altered in disease states such as schizophrenia or chronic pain (11, 12), which raises the question whether there is a general framework that describes the statistics in the spatiotemporal organization of this dynamics.Recently, we found that spontaneous cortical activity in slice cultures, acute slices, and in the anesthetized rat in vivo has a scale-invariant dynamics called neuronal avalanches (13)(14)(15). These spontaneous bursts of synchronized activity occur in clusters of sizes s (where s is the number of active sites in an electrode array) that distribute according to a power law with exponent ␣:where ␣ usually lies between ...

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“…Candidate mechanisms for leading the network into this state include competitive activity-dependent attachment and pruning (e.g. Bornholdt & Rohlf 2000;de Arcangelis et al 2006), short-term synaptic plasticity (Levina et al 2005) or some combination of homeostatic regulation of excitability and Hebbian learning (Hsu & Beggs 2006).…”

Section: Modelsmentioning

confidence: 99%

The criticality hypothesis: how local cortical networks might optimize information processing

Beggs

2007

Phil. Trans. R. Soc. A.

434

408

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Early theoretical and simulation work independently undertaken by Packard, Langton and Kauffman suggested that adaptability and computational power would be optimized in systems at the 'edge of chaos', at a critical point in a phase transition between total randomness and boring order. This provocative hypothesis has received much attention, but biological experiments supporting it have been relatively few. Here, we review recent experiments on networks of cortical neurons, showing that they appear to be operating near the critical point. Simulation studies capture the main features of these data and suggest that criticality may allow cortical networks to optimize information processing. These simulations lead to predictions that could be tested in the near future, possibly providing further experimental evidence for the criticality hypothesis.

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Self-Organized Criticality Model for Brain Plasticity

Cited by 245 publications

References 40 publications

Dynamical synapses causing self-organized criticality in neural networks

Dynamical synapses causing self-organized criticality in neural networks

Spontaneous cortical activity in awake monkeys composed of neuronal avalanches

The criticality hypothesis: how local cortical networks might optimize information processing

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