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. The waveform of the membrane potential and the contribution of each current change as the models are perturbed. To represent these changes over a range of the perturbation control parameter, we compute and display the distributions of these waveforms. We illustrate these procedures in six examples of bursting model neurons with similar activity but that differ as much as threefold in their conductance densities. These visualization methods provide heuristic insight into why individual neurons or networks with similar behavior can respond widely differently to perturbations.

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. We argue that the brain, as a dynamical system, is self-regulated at the boundary between stable and unstable regimes, allowing it in particular to maintain high susceptibility to stimuli. To test this hypothesis, we performed stability analysis of high-density electrocorticography recordings covering an entire cerebral hemisphere in monkeys during reversible loss of consciousness. We show that, during loss of consciousness, the number of eigenmodes at the edge of instability decreases smoothly, independently of the type of anesthetic and specific features of brain activity. The eigenmodes drift back toward the unstable line during recovery of consciousness. Furthermore, we show that stability is an emergent phenomenon dependent on the correlations among activity in different cortical regions rather than signals taken in isolation. These findings support the conclusion that dynamics at the edge of instability are essential for maintaining consciousness and provide a novel and principled measure that distinguishes between the conscious and the unconscious brain.

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. Consistent with the hypothesis we show that while the subject is awake, many modes of neuronal activity oscillations are found at the edge of instability. As the subject becomes anesthetized, we observe statistically significant increase in the stability of neuronal dynamics, most prominently observed for high frequency oscillations. Stabilization was not observed in phase randomized surrogates constructed to preserve the spectral signatures of each channel of neuronal activity. Thus, stability analysis offers a novel way of quantifying changes in neuronal activity that characterize loss of consciousness induced by general anesthetics.

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. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC) led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration) and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior.