Deterministic excitable media under Poisson drive: Power law responses, spiral waves, and dynamic range

Ribeiro, Tiago L.; Copelli, Mauro

doi:10.1103/physreve.77.051911

Cited by 20 publications

(21 citation statements)

References 54 publications

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“…These two requirements are exactly balanced at the point of the phase transition. A similar effect has also been demonstrated recently in a randomly driven network model, where the stability and sensitivity to input was maximized at a transition from a quiescent regimen to a state with propagating, self-sustained activity (Ribeiro and Copelli, 2008). Since such behavior is also seen in cultured networks (see below), this may be a state which neural networks without an external drive generally adopt during development.…”

Section: Developmental Significancesupporting

confidence: 74%

Early-Stage Waves in the Retinal Network Emerge Close to a Critical State Transition between Local and Global Functional Connectivity

Hennig¹,

Adams²,

Willshaw³

et al. 2009

J. Neurosci.

132

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A novel, biophysically realistic model for early-stage, acetylcholine-mediated retinal waves is presented. In this model, neural excitability is regulated through a slow after-hyperpolarization (sAHP) operating on two different temporal scales. As a result, the simulated network exhibits competition between a desynchronizing effect of spontaneous, cell-intrinsic bursts, and the synchronizing effect of synaptic transmission during retinal waves. Cell-intrinsic bursts decouple the retinal network through activation of the sAHP current, and we show that the network is capable of operating at a transition point between purely local and global functional connectedness, which corresponds to a percolation phase transition. Multielectrode array recordings show that, at this point, the properties of retinal waves are reliably predicted by the model. These results indicate that early spontaneous activity in the developing retina is regulated according to a very specific principle, which maximizes randomness and variability in the resulting activity patterns.

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Section: Developmental Significancesupporting

confidence: 74%

Early-Stage Waves in the Retinal Network Emerge Close to a Critical State Transition between Local and Global Functional Connectivity

Hennig¹,

Adams²,

Willshaw³

et al. 2009

J. Neurosci.

132

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show abstract

“…This signal compression property, or enhancement of dynamic range, is a general property of excitable media and has proven very robust against variations in the topology of the medium and the level of modeling, from cellular automata to compartmental conductance-based models [21][22][23][24][25][26][27][28][29][30][31][32][33]. Furthermore, the idea that dynamic range can be enhanced in neuronal excitable media has received support from experiments in very different setups [34,35], which again suggests that the phenomenon is robust.…”

Section: Introductionmentioning

confidence: 99%

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

2012

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We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

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“…This result is very robust because, as mentioned previously, it depends on very few properties of excitable media. Enhancement of dynamic range has been observed in models which in their details are very different from the one described in Section 16.1.1, from deterministic excitable media (one- [26,29], two- [27,28,31] and three-dimensional networks [31]) to a detailed conductance-based model of the retina [32]. In fact, one can look at a smaller scale and consider the dendritic tree of a single neuron.…”

Section: Enhancement Of Dynamic Rangementioning

confidence: 99%

“…The exponent 1∕ h can be different for more structured topologies [15,37] and deterministic models [31,38], but the fact that it is always less than unity means that lowstimulus response is amplified and dynamic range is enhanced at the critical point (as compared to a linear response in the subcritical regime).…”

Section: Nonlinear Collective Response and Maximal Dynamic Range At Cmentioning

confidence: 99%

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Criticality at Work: How Do Critical Networks Respond to Stimuli?

Copelli¹

2014

Criticality in Neural Systems

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IntroductionMost models of critical neuronal networks have in common the theoretical ingredient of separation of time scales, according to which the interval between neuronal avalanches is much longer than their duration. This framework has proven useful for several reasons, among which are the possibilities of learning from an extensive literature on models of self-organized criticality and of comparing results with data obtained from some experimental setups. The brain of a freely behaving animal, however, is often found to operate away from this regime, thereby raising doubts about the relevance of criticality for brain function. In this chapter, two questions aimed at this direction are reviewed. From a theoretical perspective, how could criticality be harnessed by neuronal networks for processing incoming stimuli? From an experimental perspective, how could we know that the brain during natural behavior is critical?In 2003, the idea that the brain (as a dynamical system) sits at (or fluctuates around) a critical point received compelling experimental support from Dietmar Plenz's lab: cortical slices show spontaneous activity in ''bursts'' with the very peculiar feature of not having a characteristic size. As described in the now-classic paper by Beggs and Plenz [1], the probability distributions of size (s) and duration (d) of these neuronal avalanches were experimentally measured and shown to be compatible with power laws, respectively, P(s) ∼ s −3∕2 and P(d) ∼ d −2 . In the following, I will briefly review how this experimental result is connected with the theoretical idea of a critical brain (a much more expanded review can be found e.g., in Ref.[2]). Phase Transition in a Simple ModelIn order to do that, let us consider a very simple model of activity (e.g., spike) propagation in a network of connected neurons. We will make the drastic simplification that a neuron can be modeled by a finite set of states: if s i (t) = 0, neuron i is in a Criticality in Neural Systems, First Edition. Edited by Dietmar Plenz and Ernst Niebur.

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Deterministic excitable media under Poisson drive: Power law responses, spiral waves, and dynamic range

Cited by 20 publications

References 54 publications

Early-Stage Waves in the Retinal Network Emerge Close to a Critical State Transition between Local and Global Functional Connectivity

Early-Stage Waves in the Retinal Network Emerge Close to a Critical State Transition between Local and Global Functional Connectivity

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

Criticality at Work: How Do Critical Networks Respond to Stimuli?

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