Laguerre-Gaussian wave propagation in parabolic media

We report a new set of Laguerre-Gaussian wave-packets that propagate with periodical self-focusing and finite beam width in weakly guiding inhomogeneous media. These wave-packets are solutions to the paraxial form of the wave equation for a medium with parabolic refractive index. The beam width is defined as a solution of the Ermakov equation associated to the harmonic oscillator, so its amplitude is modulated by the strength of the medium inhomogeneity. The conventional Laguerre-Gaussian modes, available for homogenous media, are recovered as a particular case.Comment: 11 pages, 5 figure

Synaptic Transmission and Plasticity in an Active Cortical Network

BACKGROUND: The cerebral cortex is permanently active during both awake and sleep states. This ongoing cortical activity has an impact on synaptic transmission and short-term plasticity. An activity pattern generated by the cortical network is a slow rhythmic activity that alternates up (active) and down (silent) states, a pattern occurring during slow wave sleep, anesthesia and even in vitro. Here we have studied 1) how network activity affects short term synaptic plasticity and, 2) how synaptic transmission varies in up versus down states. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular recordings obtained from cortex in vitro and in vivo were used to record synaptic potentials, while presynaptic activation was achieved either with electrical or natural stimulation. Repetitive activation of layer 4 to layer 2/3 synaptic connections from ferret visual cortex slices displayed synaptic augmentation that was larger and longer lasting in active than in silent slices. Paired-pulse facilitation was also significantly larger in an active network and it persisted for longer intervals (up to 200 ms) than in silent slices. Intracortical synaptic potentials occurring during up states in vitro increased their amplitude while paired-pulse facilitation disappeared. Both intracortical and thalamocortical synaptic potentials were also significantly larger in up than in down states in the cat visual cortex in vivo. These enhanced synaptic potentials did not further facilitate when pairs of stimuli were given, thus paired-pulse facilitation during up states in vivo was virtually absent. Visually induced synaptic responses displayed larger amplitudes when occurring during up versus down states. This was further tested in rat barrel cortex, where a sensory activated synaptic potential was also larger in up states. CONCLUSIONS/SIGNIFICANCE: These results imply that synaptic transmission in an active cortical network is more secure and efficient due to larger amplitude of synaptic potentials and lesser short term plasticity

Activity of cortical and thalamic neurons during the slow (<1 Hz) rhythm in the mouse in vivo

During NREM sleep and under certain types of anaesthesia, the mammalian brain exhibits a distinctive slow (<1 Hz) rhythm. At the cellular level, this rhythm correlates with so-called UP and DOWN membrane potential states. In the neocortex, these UP and DOWN states correspond to periods of intense network activity and widespread neuronal silence, respectively, whereas in thalamocortical (TC) neurons, UP/DOWN states take on a more stereotypical oscillatory form, with UP states commencing with a low-threshold Ca2+ potential (LTCP). Whilst these properties are now well recognised for neurons in cats and rats, whether or not they are also shared by neurons in the mouse is not fully known. To address this issue, we obtained intracellular recordings from neocortical and TC neurons during the slow (<1 Hz) rhythm in anaesthetised mice. We show that UP/DOWN states in this species are broadly similar to those observed in cats and rats, with UP states in neocortical neurons being characterised by a combination of action potential output and intense synaptic activity, whereas UP states in TC neurons always commence with an LTCP. In some neocortical and TC neurons, we observed ‘spikelets’ during UP states, supporting the possible presence of electrical coupling. Lastly, we show that, upon tonic depolarisation, UP/DOWN states in TC neurons are replaced by rhythmic high-threshold bursting at ~5 Hz, as predicted by in vitro studies. Thus, UP/DOWN state generation appears to be an elemental and conserved process in mammals that underlies the slow (<1 Hz) rhythm in several species, including humans

A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols

Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep

Neuron-glial Interactions

Although lagging behind classical computational neuroscience, theoretical and computational approaches are beginning to emerge to characterize different aspects of neuron-glial interactions. This chapter aims to provide essential knowledge on neuron-glial interactions in the mammalian brain, leveraging on computational studies that focus on structure (anatomy) and function (physiology) of such interactions in the healthy brain. Although our understanding of the need of neuron-glial interactions in the brain is still at its infancy, being mostly based on predictions that await for experimental validation, simple general modeling arguments borrowed from control theory are introduced to support the importance of including such interactions in traditional neuron-based modeling paradigms.Junior Leader Fellowship Program by “la Caixa” Banking Foundation (LCF/BQ/LI18/11630006

Abstract concept learning in a simple neural network inspired by the insect brain

The capacity to learn abstract concepts such as 'sameness' and 'difference' is considered a higher-order cognitive function, typically thought to be dependent on top-down neocortical processing. It is therefore surprising that honey bees apparantly have this capacity. Here we report a model of the structures of the honey bee brain that can learn sameness and difference, as well as a range of complex and simple associative learning tasks. Our model is constrained by the known connections and properties of the mushroom body, including the protocerebral tract, and provides a good fit to the learning rates and performances of real bees in all tasks, including learning sameness and difference. The model proposes a novel mechanism for learning the abstract concepts of 'sameness' and 'difference' that is compatible with the insect brain, and is not dependent on top-down or executive control processing

Neuron-Glial Interactions

Although lagging behind classical computational neuroscience, theoretical and computational approaches are beginning to emerge to characterize different aspects of neuron-glial interactions. This chapter aims to provide essential knowledge on neuron-glial interactions in the mammalian brain, leveraging on computational studies that focus on structure (anatomy) and function (physiology) of such interactions in the healthy brain. Although our understanding of the need of neuron-glial interactions in the brain is still at its infancy, being mostly based on predictions that await for experimental validation, simple general modeling arguments borrowed from control theory are introduced to support the importance of including such interactions in traditional neuron-based modeling paradigms.Comment: 43 pages, 2 figures, 1 table. Accepted for publication in the "Encyclopedia of Computational Neuroscience," D. Jaeger and R. Jung eds., Springer-Verlag New York, 2020 (2nd edition