Input-Dependent Wave Attenuation in a Critically-Balanced Model of Cortex

Abstract

A number of studies have suggested that many properties of brain activity can be understood in terms of critical systems. However it is still not known how the long-range susceptibilities characteristic of criticality arise in the living brain from its local connectivity structures. Here we prove that a dynamically critically-poised model of cortex acquires an infinitely-long ranged susceptibility in the absence of input. When an input is presented, the susceptibility attenuates exponentially as a function of distance, with an increasing spatial attenuation constant (i.e., decreasing range) the larger the input. This is in direct agreement with recent results that show that waves of local field potential activity evoked by single spikes in primary visual cortex of cat and macaque attenuate with a characteristic length that also increases with decreasing contrast of the visual stimulus. A susceptibility that changes spatial range with input strength can be thought to implement an input-dependent spatial integration: when the input is large, no additional evidence is needed in addition to the local input; when the input is weak, evidence needs to be integrated over a larger spatial domain to achieve a decision. Such input-strength-dependent strategies have been demonstrated in visual processing. Our results suggest that input-strength dependent spatial integration may be a natural feature of a critically-balanced cortical network.

Adaptive scales of integration and response latencies in a critically-balanced model of the primary visual cortex

“…In physics, the relationship between the spatial and temporal frequencies in a system is known as the dispersion relation. Yan and Magnasco [ 27 ] have shown that the dispersion relation of the system considered in this paper and described by Eq (1) is elliptical, c 2 k 2 + ω 2 = 1, where k and ω are the spatial and temporal frequencies, respectively, and c is a constant. If our theory is correct, multielectrode array recordings in V1 should reveal elliptic dispersion relations.…”

“…Let be the activity vector for a network of neurons which evolve in time according to the normal form equation: In this model, originally proposed by Yan and Magnasco [ 27 ], neurons interact with one another through a skew-symmetric connectivity matrix A . The cubic-nonlinear term in the model is purely local and does not couple the activity states of distinct neurons, while the external input to the system may depend on time and have a complex spatial pattern.…”

“…In contrast to hyperbolic fixed points [ 29 ], where the linearization of the system fully describes the topological structure of the local solution, dynamics on center manifolds are not dominated by the linearization. This leads to complex nonlinear behavior where nonlinear terms and input parameters play a crucial role in determining the properties of the system such as relaxation timescales and correlation lengths [ 27 ]. In the model presented in this paper, the center manifold is full dimensional, and thus the rich, complex behavior we will be discussing is not surprising.…”

D-Serine and Glycine Differentially Control Neurotransmission during Visual Cortex Critical Period

“…Remarkably, a recent study provides fMRI data supporting the latter hypothesis [ 68 ]. By demonstrating that activation of GlyRs along the L5PyNs dendrite enables efficient shunt of synaptic inputs while maintaining the E-I balance intact, the present study shed light on a mechanism that likely participates in the selective wave attenuation of sensory inputs, known to be necessary for the adaptation of inputs intensity to visual processing [ 69 ].…”

Renormalization of Collective Modes in Large-Scale Neural Dynamics

“…We have previoiusly argued that homeostatic mechanisms, such as those seeking to balance excitation and inhibition, will result in many dynamical modes of the system posing themselves close to the boundary between stability and instability [15]. Near the onset of instability, the spatial layout of such dynamical modes is determined as eigenvectors of a connectivity matrix [16]; their transient activation is then consistent with the eigenvalue of such an eigenvector being driven through the instability line, and back [14,17].…”