Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles

The firing of an action potential by a biological neuron represents a dramatic transition from small-scale linear stochastics (subthreshold voltage fluctuations) to gross-scale nonlinear dynamics (birth of a 1-ms voltage spike). In populations of neurons we see similar, but slower, switch-like there-and-back transitions between low-firing background states and high-firing activated states. These state transitions are controlled by varying levels of input current (single neuron), varying amounts of GABAergic drug (anesthesia), or varying concentrations of neuromodulators and neurotransmitters (natural sleep), and all occur within a milieu of unrelenting biological noise. By tracking the altering responsiveness of the excitable membrane to noisy stimulus, we can infer how close the neuronal system (single unit or entire population) is to switching threshold. We can quantify this “nearness to switching” in terms of the altering eigenvalue structure: the dominant eigenvalue approaches zero, leading to a growth in correlated, low-frequency power, with exaggerated responsiveness to small perturbations, the responses becoming larger and slower as the neural population approaches its critical point–-this is critical slowing. In this chapter we discuss phase-transition predictions for both single-neuron and neural-population models, comparing theory with laboratory and clinical measurement

Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion

In this chapter we describe a continuum model for the cortex that includes both axon-to-dendrite chemical synapses and direct neuron-to-neuron gap-junction diffusive synapses. The effectiveness of chemical synapses is determined by the voltage of the receiving dendrite V relative to its Nernst reversal potential Vrev. Here we explore two alternative strategies for incorporating dendritic reversal potentials, and uncover surprising differences in their stability properties and model dynamics. In the “slow-soma” variant, the (Vrev - V) weighting is applied after the input flux has been integrated at the dendrite, while for “fast-soma”, the weighting is applied directly to the input flux, prior to dendritic integration. For the slow-soma case, we find that–-provided the inhibitory diffusion (via gap-junctions) is sufficiently strong–-the cortex generates stationary Turing patterns of cortical activity. In contrast, the fast-soma destabilizes in favor of standing-wave spatial structures that oscillate at low-gamma frequency ( 30-Hz); these spatial patterns broaden and weaken as diffusive coupling increases, and disappear altogether at moderate levels of diffusion. We speculate that the slow- and fast-soma models might correspond respectively to the idling and active modes of the cortex, with slow-soma patterns providing the default background state, and emergence of gamma oscillations in the fast-soma case signaling the transition into the cognitive state

Instabilities of the cortex during natural sleep

The electrical signals generated by the human cortex during sleep have been widely studied over the last 50 years. The electroencephalogram (EEG) observed during natural sleep exhibits structures with frequencies from 0.5 Hz to over 50 Hz and complicated waveforms such as spindles and K-complexes. Understanding has been enhanced by comprehensive intra-cellular measurements from the cortex and thalamus such as those performed by Steriade et al [1] and Sanchez-Vives and McCormick [2]. Models of the cerebal cortex have been developed in order to explain many of the features observed. These can be classified in terms of individual neuron models or collective models. Since we wish to compare predictions with gross features of the human EEG, we choose a collective model, where we average over a population of neurons in macrocolumns. A number of models of this form have been developed recently; that developed at Waikato draws from a number of different sources to describe the temporal and spatial dynamics of the system

C60 adsorption on an aperiodically modulated Cu surface

Copper deposited on the ve-fold surface of icosahedral Al-Pd-Mn forms domains of a structure whose surface has a one-dimensional aperiodic modulation. It is shown that C60 deposited on this aperiodic film has highly reduced mobility as compared to C60 deposited on periodic Cu surfaces. This fnding is explained in terms of the recently proposed structural model of this system

Simulating the Impact of X-ray Heating during the Cosmic Dawn

Upcoming observations of the 21-cm signal from the Epoch of Reionization will soon provide the first direct detection of this era. This signal is influenced by many astrophysical effects, including long range X-ray heating of the intergalactic gas. During the preceding Cosmic Dawn era the impact of this heating on the 21-cm signal is particularly prominent, especially before spin temperature saturation. We present the largest-volume (349\,Mpc comoving=244~$h^{-1}$Mpc) full numerical radiative transfer simulations to date of this epoch that include the effects of helium and multi-frequency heating, both with and without X-ray sources. We show that X-ray sources contribute significantly to early heating of the neutral intergalactic medium and, hence, to the corresponding 21-cm signal. The inclusion of hard, energetic radiation yields an earlier, extended transition from absorption to emission compared to the stellar-only case. The presence of X-ray sources decreases the absolute value of the mean 21-cm differential brightness temperature. These hard sources also significantly increase the 21-cm fluctuations compared the common assumption of temperature saturation. The 21-cm differential brightness temperature power spectrum is initially boosted on large scales, before decreasing on all scales. Compared to the case of the cold, unheated intergalactic medium, the signal has lower rms fluctuations and increased non-Gaussianity, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. Images of the 21-cm signal with resolution around 11~arcmin still show fluctuations well above the expected noise for deep integrations with the SKA1-Low, indicating that direct imaging of the X-ray heating epoch could be feasible.Comment: 13 pages, 8 figure

A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep

Previous studies have shown that activated cortical states (awake and rapid eye-movement (REM) sleep), are associated with increased cholinergic input into the cerebral cortex. However, the mechanisms that underlie the detailed dynamics of the cortical transition from slow-wave to REM sleep have not been quantitatively modeled. How does the sequence of abrupt changes in the cortical dynamics (as detected in the electrocorticogram) result from the more gradual change in subcortical cholinergic input? We compare the output from a continuum model of cortical neuronal dynamics with experimentally-derived rat electrocorticogram data. The output from the computer model was consistent with experimental observations. In slow-wave sleep, 0.5–2-Hz oscillations arise from the cortex jumping between “up” and “down” states on the stationary-state manifold. As cholinergic input increases, the upper state undergoes a bifurcation to an 8-Hz oscillation. The coexistence of both oscillations is similar to that found in the intermediate stage of sleep of the rat. Further cholinergic input moves the trajectory to a point where the lower part of the manifold in not available, and thus the slow oscillation abruptly ceases (REM sleep). The model provides a natural basis to explain neuromodulator-induced changes in cortical activity, and indicates that a cortical phase change, rather than a brainstem “flip-flop”, may describe the transition from slow-wave sleep to REM

Feasibility of reduced gravity experiments involving quiescent, uniform particle cloud combustion

The study of combustible particle clouds is of fundamental scientific interest as well as a practical concern. The principal scientific interests are the characteristic combustion properties, especially flame structure, propagation rates, stability limits, and the effects of stoichiometry, particle type, transport phenomena, and nonadiabatic processes on these properties. The feasibility tests for the particle cloud combustion experiment (PCCE) were performed in reduced gravity in the following stages: (1) fuel particles were mixed into cloud form inside a flammability tube; (2) when the concentration of particles in the cloud was sufficiently uniform, the particle motion was allowed to decay toward quiescence; (3) an igniter was energized which both opened one end of the tube and ignited the suspended particle cloud; and (4) the flame proceeded down the tube length, with its position and characteristic features being photographed by high-speed cameras. Gravitational settling and buoyancy effects were minimized because of the reduced gravity enviroment in the NASA Lewis drop towers and aircraft. Feasibility was shown as quasi-steady flame propagation which was observed for fuel-rich mixtures. Of greatest scientific interest is the finding that for near-stoichiometric mixtures, a new mode of flame propagation was observed, now called a chattering flame. These flames did not propagate steadily through the tube. Chattering modes of flame propagation are not expected to display extinction limits that are the same as those for acoustically undisturbed, uniform, quiescent clouds. A low concentration of fuel particles, uniformly distributed in a volume, may not be flammable but may be made flammable, as was observed, through induced segregation processes. A theory was developed which showed that chattering flame propagation was controlled by radiation from combustion products which heated the successive discrete laminae sufficiently to cause autoignition

What can a mean-field model tell us about the dynamics of the cortex?

In this chapter we examine the dynamical behavior of a spatially homogeneous two-dimensional model of the cortex that incorporates membrane potential, synaptic flux rates and long- and short-range synaptic input, in two spatial dimensions, using parameter sets broadly realistic of humans and rats. When synaptic dynamics are included, the steady states may not be stable. The bifurcation structure for the spatially symmetric case is explored, identifying the positions of saddle–node and sub- and supercritical Hopf instabilities. We go beyond consideration of small-amplitude perturbations to look at nonlinear dynamics. Spatially-symmetric (breathing mode) limit cycles are described, as well as the response to spatially-localized impulses. When close to Hopf and saddle–node bifurcations, such impulses can cause traveling waves with similarities to the slow oscillation of slow-wave sleep. Spiral waves can also be induced. We compare model dynamics with the known behavior of the cortex during natural and anesthetic-induced sleep, commenting on the physiological significance of the limit cycles and impulse responses

Macular Bioaccelerometers on Earth and in Space

Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth