Circuit function is more robust to changes in synaptic than intrinsic conductances.

Circuit function results from both intrinsic conductances of network neurons and the synaptic conductances that connect them. In models of neural circuits, different combinations of maximal conductances can give rise to similar activity. We compared the robustness of a neural circuit to changes in their intrinsic versus synaptic conductances.

Gating of homeostatic regulation of intrinsic excitability produces cryptic long-term storage of prior perturbations.

Neurons and neuronal circuits must maintain their function throughout the life of the organism despite changing environments. Previous theoretical and experimental work suggests that neurons monitor their activity using intracellular calcium concentrations to regulate their intrinsic excitability. Models with multiple sensors can distinguish among different patterns of activity, but previous work using models with multiple sensors produced instabilities that lead the models' conductances to oscillate and then to grow without bound and diverge.

Repeated applications of high potassium elicit long-term changes in a motor circuit from the crab, .

We examined the effects of altered extracellular potassium concentration on the output of the well-studied pyloric circuit in the crab, . Pyloric neurons initially become quiescent, then recover spiking and bursting activity in high potassium saline (2.5x[K]).

Temperature compensation in a small rhythmic circuit.

Temperature affects the conductances and kinetics of the ionic channels that underlie neuronal activity. Each membrane conductance has a different characteristic temperature sensitivity, which raises the question of how neurons and neuronal circuits can operate robustly over wide temperature ranges. To address this, we employed computational models of the pyloric network of crabs and lobsters.

Author Correction: Single-trial classification of awareness state during anesthesia by measuring critical dynamics of global brain activity.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Single-trial classification of awareness state during anesthesia by measuring critical dynamics of global brain activity.

In daily life, in the operating room and in the laboratory, the operational way to assess wakefulness and consciousness is through responsiveness. A number of studies suggest that the awake, conscious state is not the default behavior of an assembly of neurons, but rather a very special state of activity that has to be actively maintained and curated to support its functional properties. Thus responsiveness is a feature that requires active maintenance, such as a homeostatic mechanism to balance excitation and inhibition.

Visualization of currents in neural models with similar behavior and different conductance densities.

Conductance-based models of neural activity produce large amounts of data that can be hard to visualize and interpret. We introduce visualization methods to display the dynamics of the ionic currents and to display the models' response to perturbations. To visualize the currents' dynamics, we compute the percent contribution of each current and display them over time using stacked-area plots.

Complex spatiotemporal behavior and coherent excitations in critically-coupled chains of neural circuits.

We investigate a critically-coupled chain of nonlinear oscillators, whose dynamics displays complex spatiotemporal patterns of activity, including regimes in which glider-like coherent excitations move about and interact. The units in the network are identical simple neural circuits whose dynamics is given by the Wilson-Cowan model and are arranged in space along a one-dimensional lattice with nearest neighbor interactions. The interactions follow an alternating sign rule, and hence the "synaptic matrix" embodying them is tridiagonal antisymmetric and has purely imaginary (critical) eigenvalues.

Complex behavior in chains of nonlinear oscillators.

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally.

Nonlinear resonances and multi-stability in simple neural circuits.

This article describes a numerical procedure designed to tune the parameters of periodically driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic solutions available to the system within a range of the parameters that define the driving. The procedure is applied to a problem of interest in computational neuroscience: a circuit composed of two interacting populations of neurons under external periodic forcing.

Loss of Consciousness Is Associated with Stabilization of Cortical Activity.

Unlabelled: What aspects of neuronal activity distinguish the conscious from the unconscious brain? This has been a subject of intense interest and debate since the early days of neurophysiology. However, as any practicing anesthesiologist can attest, it is currently not possible to reliably distinguish a conscious state from an unconscious one on the basis of brain activity. Here we approach this problem from the perspective of dynamical systems theory.

Parameter estimation, nonlinearity, and Occam's razor.

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple harmonic function. In order to identify if a recorded time series is the result of a nonlinear system responding to a simpler forcing, we develop a discrete nonlinear transformation for time series based on synchronization techniques.

Dynamical criticality during induction of anesthesia in human ECoG recordings.

In this work we analyze electro-corticography (ECoG) recordings in human subjects during induction of anesthesia with propofol. We hypothesize that the decrease in responsiveness that defines the anesthetized state is concomitant with the stabilization of neuronal dynamics. To test this hypothesis, we performed a moving vector autoregressive analysis and quantified stability of neuronal dynamics using eigenmode decomposition of the autoregressive matrices, independently fitted to short sliding temporal windows.

Temperature induced syllable breaking unveils nonlinearly interacting timescales in birdsong motor pathway.

The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy.

Average dynamics of a driven set of globally coupled excitable units.

We investigate the behavior of the order parameter describing the collective dynamics of a large set of driven, globally coupled excitable units. We derive conditions on the parameters of the system that allow to bound the degree of synchrony of its solutions. We describe a regime where time dependent nonsynchronous dynamics occurs and, yet, the average activity displays low dimensional, temporally complex behavior.

Low-dimensional dynamical model for the diversity of pressure patterns used in canary song.

During song production, oscine birds produce large air sac pressure pulses. During those pulses, energy is transferred to labia located at the juncture between the bronchii and the trachea, inducing the high frequency labial oscillations which are responsible for airflow modulations, i.e.