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

Snatch trajectory of elite level girevoy (Kettlebell) sport athletes and its implications to strength and conditioning coaching

Girevoy sport (GS) has developed only recently in the West, resulting in a paucity of English scientific literature available. The aim was to document kettlebell trajectory of GS athletes performing the kettlebell snatch. Four elite GS athletes (age = 29-47 years, body mass = 68.3-108.1 kg, height 1.72-1.89 m) completed one set of 16 repetitions with a 32.1 kg kettlebell. Trajectory was captured with the VICON motion analysis system (250 Hz) and analysed with VICON Nexus (1.7.1). The kettlebell followed a ‘C’ shape trajectory in the sagittal plane. Mean peak velocity in the upwards phase was 4.03 ± 0.20 m s –1, compared to 3.70 ± 0.30 m s–1 during the downwards phase, and mean radial error across the sagittal and frontal planes was 0.022 ± 0.006 m. Low error in the movement suggests consistent trajectory is important to reduce extraneous movement and improve efficiency. While the kettlebell snatch and swing both require large anterior-posterior motion, the snatch requires the kettlebell to be held stationary overhead. Therefore, a different coaching application is required to that of a barbell snatch

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

SCS 21: ≤ (n)

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.htm

The \u3ci\u3ePhycodnaviridae\u3c/i\u3e: The Story of How Tiny Giants Rule the World

The family Phycodnaviridae encompasses a diverse and rapidly expanding collection of large icosahedral, dsDNA viruses that infect algae. These lytic and lysogenic viruses have genomes ranging from 160 to 560 kb. The family consists of six genera based initially on host range and supported by sequence comparisons. The family is monophyletic with branches for each genus, but the phycodnaviruses have evolutionary roots that connect them with several other families of large DNA viruses, referred to as the nucleocytoplasmic large DNA viruses (NCLDV).The phycodnaviruses have diverse genome structures, some with large regions of noncoding sequence and others with regions of ssDNA. The genomes of members in three genera in the Phycodnaviridae have been sequenced. The genome analyses have revealed more than 1000 unique genes, with only 14 homologous genes in common among the three genera of phycodnaviruses sequenced to date. Thus, their gene diversity far exceeds the number of so-called core genes. Not much is known about the replication of these viruses, but the consequences of these infections on phytoplankton have global affects, including influencing geochemical cycling and weather patterns

The \u3ci\u3ePhycodnaviridae\u3c/i\u3e: The Story of How Tiny Giants Rule the World

The family Phycodnaviridae encompasses a diverse and rapidly expanding collection of large icosahedral, dsDNA viruses that infect algae. These lytic and lysogenic viruses have genomes ranging from 160 to 560 kb. The family consists of six genera based initially on host range and supported by sequence comparisons. The family is monophyletic with branches for each genus, but the phycodnaviruses have evolutionary roots that connect them with several other families of large DNA viruses, referred to as the nucleocytoplasmic large DNA viruses (NCLDV).The phycodnaviruses have diverse genome structures, some with large regions of noncoding sequence and others with regions of ssDNA. The genomes of members in three genera in the Phycodnaviridae have been sequenced. The genome analyses have revealed more than 1000 unique genes, with only 14 homologous genes in common among the three genera of phycodnaviruses sequenced to date. Thus, their gene diversity far exceeds the number of so-called core genes. Not much is known about the replication of these viruses, but the consequences of these infections on phytoplankton have global affects, including influencing geochemical cycling and weather patterns

Shear-Wave Splitting and Mantle Flow Beneath the Colorado Plateau and its Boundary with the Great Basin

Shear-wave splitting measurements from SKS and SKKS phases show fast polarization azimuths that are subparallel to North American absolute plate motion within the central Rio Grande Rift (RGR) and Colorado Plateau (CP) through to the western rim of the CP, with anisotropy beneath the CP and central RGR showing a remarkably consistent pattern with a mean fast azimuth of 4 degrees +/- degrees 6 E of N. Approaching the rim from the southeast, fast anisotropic directions become north-northeast-south-southwest (NNE-SSW), rotate counter clockwise to north-south in the CP-GB transition, and then to NNW-SSE in the western Great Basin ( GB). This change is coincident with uppermost mantle S-wave velocity perturbations that vary from +4% beneath the western CP and the eastern edge of the Marysvale volcanic field to about -8% beneath the GB. Corresponding delay times average 1.5 sec beneath the central CP, decrease to approximately 0.8 sec near the CP-GB transition, and increase to about 1.2 sec beneath the GB. For the central CP, we suggest anisotropy predominantly controlled by North American plate motion above the asthenosphere. The observed pattern of westward-rotating anisotropy from the western CP through the CP-GB transition may be influenced to asthenospheric flow around a CP lithospheric keel and/or by vertical flow arising from edge-driven small-scale convection. The anisotropic transition from the CP to the GB thus marks a first-order change from absolute plate motion dominated lithosphere-asthenosphere shear to a new regime controlled by regional flow processes. The NNW-SSE anisotropic fast directions of split SKS waves in the eastern GB area are part of a broad circular pattern of seismic anisotropic fast direction in the central GB that has recently been hypothesized to be due to toroidal flow around the sinking Juan de Fuca-Gorda slab.National Science Foundation EAR 9706094, 9707188, 9707190, 0207812Los Alamos National Laboratory Institute of Geophysics and Planetary PhysicsNational Science Foundation Cooperative EAR-000430Department of Energy National Nuclear Security AdministrationGeological Science

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