Prelude. Cycle 1. Introduction. Cycle 2. Structure defines function. Cycle 3. Diversity of cortical functions is provided by inhibition. Cycle 4. Windows on the brain. Cycle 5. A system of rhythms: from simple to complex dynamics. Cycle 6. Synchronization by oscillation. Cycle 7. The brain's default state: self-organized oscillations in rest and sleep. Cycle 8. Perturbation of the default patterns by experience. Cycle 9. The gamma buzz: gluing by oscillations in the waking brain. Cycle 10. Perceptions and actions are brain state-dependent. Cycle 11. Oscillations in the "other cortex:" navigation in real and memory space. Cycle 12. Coupling of systems by oscillations. Cycle 13. The tough problem. References.

Rhythms of the brain

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

/pdf/dynamical-systems-in-neuroscience-51dkewn57v.pdf

Dynamical Systems in Neuroscience

Neuronal activity in the brain gives rise to transmembrane currents that can be measured in the extracellular medium. Although the major contributor of the extracellular signal is the synaptic transmembrane current, other sources — including Na+ and Ca2+ spikes, ionic fluxes through voltage- and ligand-gated channels, and intrinsic membrane oscillations — can substantially shape the extracellular field. High-density recordings of field activity in animals and subdural grid recordings in humans, combined with recently developed data processing tools and computational modelling, can provide insight into the cooperative behaviour of neurons, their average synaptic input and their spiking output, and can increase our understanding of how these processes contribute to the extracellular signal.

/pdf/the-origin-of-extracellular-fields-and-currents-eeg-ecog-lfp-2e79zygxj0.pdf

The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes

Interneurons of the hippocampus

EEG alpha oscillations: The inhibition–timing hypothesis

Instantaneous velocity fields and background suppression by filtered Rayleigh scattering

Glickfeld and colleagues (2009) suggested that single hippocampal interneurones generate field potentials at monosynaptic latencies. We pursued this obervation in simultaneous intracellular and multiple extracellular records from the CA3 region of rat hippocampal slices. We confirmed that interneurones evoked field potentials at monosynaptic latencies. Pyramidal cells initiated disynaptic inhibitory field potentials, but did not initiate detectable monosynaptic excitatory fields. We confirmed that inhibitory fields were GABAergic in nature and showed they were suppressed at low external Cl−, suggesting they originate at postsynaptic sites. Field potentials generated by a single interneurone were detected at multiple sites over distances of more than 800 μm along the stratum pyramidale of the CA3 region. We used arrays of extracellular electrodes to examine amplitude distributions of spontaneous inhibitory fields recorded at sites orthogonal to or along the CA3 stratum pyramidale. Cluster analysis of spatially distributed inhibitory field events let us separate events generated by interneurones terminating on distinct zones of somato-dendritic axis. Events generated at dendritic sites had similar amplitudes but occurred less frequently and had somewhat slower kinetics than perisomatic events generated near the stratum pyramidale. In records from multiple sites in the CA3 stratum pyramidale, we distinguished inhibitory fields that seemed to be initiated by interneurones with spatially distinct axonal arborisations.

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.2009.185918

Unitary inhibitory field potentials in the CA3 region of rat hippocampus

A low density of sodium atoms seeded into a hypersonic helium flow is used to quantitatively determine flow‐field properties. By observing fluorescence from a point as a single‐mode dye laser is tuned through the sodium D2 line, the absorption profile may be found. This profile is fitted to a properly weighted sum of Voigt functions to yield the velocity, temperature, and pressure at the observation point. The fluorescence is strong enough to use this technique for qualitative flow‐field visualization.

Hypersonic‐helium‐flow‐field measurements with the resonant Doppler velocimeter

This paper describes several flow visualization experiments carried out in Mach 3 and Mach 8 turbulent shear flows. The experimental technique was based on laser scattering from particles of H2O or CO2 condensate that form in the wind tunnel nozzle expansion process. The condensate particles vaporize extremely rapidly on entering the relatively hot fluid within a turbulent structure, so that a sharp vaporization interface marks the outer edge of the rotational shear layer fluid. Calculations indicate that the observed thin interface corresponds to a particle size of 10 nm or less, which is consistent with optical measurements, and that particles of this size track the fluid motions well. Further, calculations and experiments show that the freestream concentration of condensate required for flow visualization has only a small effect on the wind tunnel pressure distribution. Statistics based on the image data were compared to corresponding results from probe measurements and agreement was obtained in statistical measures of speed, scale, and orientation of the large-scale structures in the shear layer turbulence. The condensate-enhanced Rayleigh scattering technique is judged to be a useful tool for quantitative studies of shear layer structure, particularly for identifying the instantaneous boundary layer edge and for extracting comparative information on the large-scale structures represented there.

Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering

The presubiculum, located between hippocampus and entorhinal cortex, plays a fundamental role in representing spatial information, notably head direction. Little is known about GABAergic interneurons of this region. Here, we used three transgenic mouse lines, Pvalb-Cre, Sst-Cre, and X98, to examine distinct interneurons labeled with tdTomato or green fluorescent protein. The distribution of interneurons in presubicular lamina for each animal line was compared to that in the GAD67-GFP knock-in animal line. Labeling was specific in the Pvalb-Cre line with 87% of labeled interneurons immunopositive for parvalbumin (PV). Immunostaining for somatostatin (SOM) revealed good specificity in the X98 line with 89% of fluorescent cells, but a lesser specificity in Sst-Cre animals where only 71% of labeled cells were immunopositive. A minority of ∼6% of interneurons co-expressed PV and SOM in the presubiculum of Sst-Cre animals. The electrophysiological and morphological properties of fluorescent interneurons from Pvalb-Cre, Sst-Cre, and X98 mice differed. Distinct physiological groups of presubicular interneurons were resolved by unsupervised cluster analysis of parameters describing passive properties, firing patterns and AP shapes. One group consisted of SOM-positive, Martinotti type neurons with a low firing threshold (cluster 1). Fast spiking basket cells, mainly from the Pvalb-Cre line, formed a distinct group (cluster 3). Another group (cluster 2) contained interneurons of intermediate electrical properties and basket-cell like morphologies. These labeled neurons were recorded from both Sst-Cre and Pvalb-Cre animals. Thus, our results reveal a wide variation in anatomical and physiological properties for these interneurons, a real overlap of interneurons immuno-positive for both PV and SOM as well as an off-target recombination in the Sst-Cre line, possibly linked to maternal cre inheritance.

/pdf/diversity-and-overlap-of-parvalbumin-and-somatostatin-5e7q4rgzl4.pdf

Richard B. Miles

Papers

Instantaneous velocity fields and background suppression by filtered Rayleigh scattering

Unitary inhibitory field potentials in the CA3 region of rat hippocampus

Hypersonic‐helium‐flow‐field measurements with the resonant Doppler velocimeter

Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering

Diversity and overlap of parvalbumin and somatostatin expressing interneurons in mouse presubiculum