Mechanisms for Frequency Control in Neuronal Competition Models

Curtu, Rodica; Shpiro, Asya; Rubin, Nava; Rinzel, John

doi:10.1137/070705842

Cited by 67 publications

(112 citation statements)

References 33 publications

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“…This suggests that our basic results on how the release and escape mechanisms shape the HCO's PRC can apply to a wide variety of HCOs models that share similar dynamical properties. Note that this family of models also includes population or competition models such as the binocular rivalry models examined in Shpiro et al (2007), Curtu et al (2008) and Seely and Chow (2011) and the spike-rate-based CPG model in Varkonyi et al (2008). Indeed, in Appendix A and B, we show that the PRCs for Morris-Lecar-based HCOs with intrinsically oscillatory cells (Skinner et al 1994) and the Wang-Rinzel model for the release and escape mechanisms have the same basic shapes as those described here.…”

Section: Discussionsupporting

confidence: 52%

“…When the HCO exhibits release-type behavior at lower values of I, f decreases with I; when the HCO exhibits escape-type behavior at higher values of I, f increases with I. This dependence of the f -I curve of HCOs on the mechanism of oscillation was pointed out in Shpiro et al (2007), Curtu et al (2008) and Daun et al (2009).…”

Section: Half-center Oscillations Involving Both Release and Escape Mmentioning

confidence: 78%

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Phase response properties of half-center oscillators

Zhang

Lewis

2013

J Comput Neurosci

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We examine the phase response properties of half-center oscillators (HCOs) that are modeled by a pair of Morris-Lecar-type neurons connected by strong fast inhibitory synapses. We find that the two basic mechanisms for half-center oscillations, "release" and "escape", give rise to strikingly different phase response curves (PRCs). Release-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the active to the suppressed state, and PRCs are dominated by a large negative peak (phase delays) at corresponding phases. On the other hand, escape-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the suppressed to the active state, and PRCs are dominated by a large positive peak (phase advances) at corresponding phases. By analyzing the phase space structure of Morris-Lecar-type HCO models with fast synaptic dynamics, we identify the dynamical mechanisms underlying the shapes of the PRCs. To demonstrate the significance of the different shapes of the PRCs for the release-type and escape-type HCOs, we link the shapes of the PRCs to the different frequency modulation properties of release-type

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Section: Discussionsupporting

confidence: 52%

Section: Half-center Oscillations Involving Both Release and Escape Mmentioning

confidence: 78%

Phase response properties of half-center oscillators

Zhang

Lewis

2013

J Comput Neurosci

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“…These propositions are satisfied because of a combination of competition (from attentional modulation and mutual inhibition), recurrent excitation (from attentional modulation), and slow adaptation (6,38,39). Levelt's proposition IV, in particular, depends on having some degree of recurrent excitation (38,39).…”

Section: Discussionmentioning

confidence: 99%

“…Changing the mapping between stimulus intensity (e.g., contrast) and neural input strength would scale and/or warp the x axis in Figs. 5 and 7 (38,39).…”

Section: Mutual Inhibition Supports Eye Dominance and Attention Stabimentioning

confidence: 99%

Attention model of binocular rivalry

Rankin

Rinzel

et al. 2017

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

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When the corresponding retinal locations in the two eyes are presented with incompatible images, a stable percept gives way to perceptual alternations in which the two images compete for perceptual dominance. As perceptual experience evolves dynamically under constant external inputs, binocular rivalry has been used for studying intrinsic cortical computations and for understanding how the brain regulates competing inputs. Converging behavioral and EEG results have shown that binocular rivalry and attention are intertwined: binocular rivalry ceases when attention is diverted away from the rivalry stimuli. In addition, the competing image in one eye suppresses the target in the other eye through a pattern of gain changes similar to those induced by attention. These results require a revision of the current computational theories of binocular rivalry, in which the role of attention is ignored. Here, we provide a computational model of binocular rivalry. In the model, competition between two images in rivalry is driven by both attentional modulation and mutual inhibition, which have distinct selectivity (feature vs. eye of origin) and dynamics (relatively slow vs. relatively fast). The proposed model explains a wide range of phenomena reported in rivalry, including the three hallmarks: (i) binocular rivalry requires attention; (ii) various perceptual states emerge when the two images are swapped between the eyes multiple times per second; (iii) the dominance duration as a function of input strength follows Levelt's propositions. With a bifurcation analysis, we identified the parameter space in which the model's behavior was consistent with experimental results.B inocular rivalry is a visual phenomenon in which perception alternates between incompatible monocular images presented to the two eyes. During binocular rivalry, perceptual experience evolves dynamically while the external inputs are held constant. Binocular rivalry thereby provides an opportunity to gain insights about the intrinsic cortical computations underlying visual perception (1, 2).In conventional models of binocular rivalry, the competition between two percepts has been characterized as mutual inhibition between two populations of neurons selective for each of the two stimuli (3-11). Notwithstanding the differences in their details, these models consider the neural processing underlying binocular rivalry to be an automatic process. These models predict, therefore, that the dynamics of binocular rivalry are influenced mainly by bottom-up sensory inputs.Converging experimental evidence has shown, however, that binocular rivalry also depends on attention (for a review, see ref.12). First, EEG has been used to measure a neural correlate of the perceptual alternations during binocular rivalry when observers pay attention to the rival stimuli (13). However, this rivalry-induced modulation of the EEG signal is largely or entirely eliminated when attention is diverted away from the stimuli (14). Second, behavioral experiments comparing the perceptual cons...

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“…We do not discuss more exotic possibilities here. Curtu [26,27] and Curtu et al [28] have analysed the bifurcations of a rate model for a network with two identical nodes (Z 2 symmetry) in considerable detail. Even in this case there is a richer range of dynamic behaviour than equilibria and periodic states arising from local bifurcation.…”

mentioning

confidence: 99%

Symmetry-Breaking in a Rate Model for a Biped Locomotion Central Pattern Generator

Stewart

2014

Symmetry

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The timing patterns of animal gaits are produced by a network of spinal neurons called a Central Pattern Generator (CPG). Pinto and Golubitsky studied a four-node CPG for biped dynamics in which each leg is associated with one flexor node and one extensor node, with Z 2 × Z 2 symmetry. They used symmetric bifurcation theory to predict the existence of four primary gaits and seven secondary gaits. We use methods from symmetric bifurcation theory to investigate local bifurcation, both steady-state and Hopf, for their network architecture in a rate model. Rate models incorporate parameters corresponding to the strengths of connections in the CPG: positive for excitatory connections and negative for inhibitory ones. The three-dimensional space of connection strengths is partitioned into regions that correspond to the first local bifurcation from a fully symmetric equilibrium. The partition is polyhedral, and its symmetry group is that of a tetrahedron. It comprises two concentric tetrahedra, subdivided by various symmetry planes. The tetrahedral symmetry arises from the structure of the eigenvalues of the connection matrix, which is involved in, but not equal to, the Jacobian of the rate model at bifurcation points. Some of the results apply to rate equations on more general networks.

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Mechanisms for Frequency Control in Neuronal Competition Models

Cited by 67 publications

References 33 publications

Phase response properties of half-center oscillators

Phase response properties of half-center oscillators

Attention model of binocular rivalry

Symmetry-Breaking in a Rate Model for a Biped Locomotion Central Pattern Generator

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