A physical memristor based Muthuswamy-Chua-Ginoux system.

In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive inductor, a linear passive capacitor, a nonlinear resistor and a thermistor, that is, a nonlinear "locally active" memristor. Thus, the purpose of this work was to use a physical memristor, the thermistor, in a Muthuswamy-Chua chaotic system (circuit) instead of memristor emulators. Such circuit has been modeled by a new three-dimensional autonomous dynamical system exhibiting very particular properties such as the transition from torus breakdown to chaos. Then, mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the so-called route to Shilnikov spiral chaos but gives rise to a "double spiral attractor".

Delayed dynamics in an electronic relaxation oscillator.

We present an experimental investigation of the complex dynamics of a modulated relaxation oscillator implemented by using a unipolar junction transistor (UJT) showing the transition to chaos through torus breakdown. In a previous paper a continuous model was introduced for the same system, explaining chaos based on analogy with a memristor. We propose here a new approach based on a piecewise linear model with delay considering a measured parasitic delay effect. The inclusion of this delay, accounting for memory effects, increases the dimensionality of the model, allowing the transition to chaos as observed in the experiment. The piecewise delayed model shows analogies with a two-dimensional leaky integrate-and-fire model used in neurodynamics.

Phase-locking patterns in a resonate and fire neural model with periodic drive.

In this paper we studied a resonate and fire relaxation oscillator subject to time dependent modulation to investigate phase-locking phenomena occurring in neurophysiological systems. The neural model (denoted LFHN) was obtained by linearization of the FitzHugh-Nagumo neural model near an hyperbolic fixed point and then by introducing an integrate-and-fire mechanism for spike generation. By employing specific tools to study circle maps, we showed that this system exhibits several phase-locking patterns in the presence of periodic perturbations. Moreover, both the amplitude and frequency of the modulation strongly impact its phase-locking properties. In addition, general conditions for the generation of firing activity were also obtained. In addition, it was shown that for moderate noise levels the phase-locking patterns of the LFHN persist. Moreover, in the presence of noise, the rotation number changes smoothly as the stimulation current increases. Then, the statistical properties of the firing map were investigated too. Lastly, the results obtained with the forced LFHN suggest that such neural model could be used to fit specific experimental data on the firing times of neurons.

Dynamical properties of LFPs from mice with unilateral injection of TeNT.

Local field potential (LFP) recordings were performed from the visual cortex (V1) of a focal epilepsy mouse model. Epilepsy was induced by a unilateral injection of the synaptic blocker tetanus neurotoxin (TeNT). LFP signals were simultaneously recorded from V1 of both hemispheres of each animal under acute and chronic conditions (i.e. during and after the period of TeNT action). All data were analysed by using nonlinear time series methods. Suitable values of the lag time and embedding dimension for phase space reconstruction were estimated by employing well-known methods. The results showed that lag times are sensitive to the presence of TeNT. Interestingly, TeNT promoted an increase in the level of linear and nonlinear correlation of LFP signals. The values of the embedding dimension failed to show any dependence on the presence of the neurotoxin. However, a local nonlinear prediction method showed that the presence of TeNT increases the predictability, quantified by the normalized prediction error, of the neural recordings. From a neurophysiological point of view, the above results suggest that TeNT injected in one hemisphere strongly impacts the local electrical activity of the neural populations in the opposite hemisphere. We hypothesize that this could arise from a qualitative and quantitative alteration of the transmission properties of the callosal fibers.

Neuroplastic Changes Following Brain Ischemia and their Contribution to Stroke Recovery: Novel Approaches in Neurorehabilitation.

Ischemic damage to the brain triggers substantial reorganization of spared areas and pathways, which is associated with limited, spontaneous restoration of function. A better understanding of this plastic remodeling is crucial to develop more effective strategies for stroke rehabilitation. In this review article, we discuss advances in the comprehension of post-stroke network reorganization in patients and animal models. We first focus on rodent studies that have shed light on the mechanisms underlying neuronal remodeling in the perilesional area and contralesional hemisphere after motor cortex infarcts. Analysis of electrophysiological data has demonstrated brain-wide alterations in functional connectivity in both hemispheres, well beyond the infarcted area. We then illustrate the potential use of non-invasive brain stimulation (NIBS) techniques to boost recovery. We finally discuss rehabilitative protocols based on robotic devices as a tool to promote endogenous plasticity and functional restoration.

Post-Stroke Longitudinal Alterations of Inter-Hemispheric Correlation and Hemispheric Dominance in Mouse Pre-Motor Cortex.

PURPOSE: Limited restoration of function is known to occur spontaneously after an ischemic injury to the primary motor cortex. Evidence suggests that Pre-Motor Areas (PMAs) may "take over" control of the disrupted functions. However, little is known about functional reorganizations in PMAs. Forelimb movements in mice can be driven by two cortical regions, Caudal and Rostral Forelimb Areas (CFA and RFA), generally accepted as primary motor and pre-motor cortex, respectively. Here, we examined longitudinal changes in functional coupling between the two RFAs following unilateral photothrombotic stroke in CFA (mm from Bregma: +0.5 anterior, +1.25 lateral). METHODS: Local field potentials (LFPs) were recorded from the RFAs of both hemispheres in freely moving injured and naïve mice. Neural signals were acquired at 9, 16 and 23 days after surgery (sub-acute period in stroke animals) through one bipolar electrode per hemisphere placed in the center of RFA, with a ground screw over the occipital bone. LFPs were pre-processed through an efficient method of artifact removal and analysed through: spectral,cross-correlation, mutual information and Granger causality analysis. RESULTS: Spectral analysis demonstrated an early decrease (day 9) in the alpha band power in both the RFAs. In the late sub-acute period (days 16 and 23), inter-hemispheric functional coupling was reduced in ischemic animals, as shown by a decrease in the cross-correlation and mutual information measures. Within the gamma and delta bands, correlation measures were already reduced at day 9. Granger analysis, used as a measure of the symmetry of the inter-hemispheric causal connectivity, showed a less balanced activity in the two RFAs after stroke, with more frequent oscillations of hemispheric dominance. CONCLUSIONS: These results indicate robust electrophysiological changes in PMAs after stroke. Specifically, we found alterations in transcallosal connectivity, with reduced inter-hemispheric functional coupling and a fluctuating dominance pattern. These reorganizations may underlie vicariation of lost functions following stroke.

Anharmonic longitudinal motion of bases and dynamics of nonlinear excitation in DNA.

The dynamics of the transcription bubble in DNA is studied by using a nonlinear model in which torsional and longitudinal conformations of the biomolecule are coupled. In the absence of forcing and dissipation the torsional dynamics is described by a perturbed kink of the Sine-Gordon DNA model, while the longitudinal conformational energy propagate as phonons. It was found that for random initial conditions of the longitudinal conformational field the presence of the kink promotes the creation of phonons propagating along the chain axis. Moreover, the presence of forcing, describing the active role of RNA polymerase, determines in agreement to the experimental data a modulation of the velocity of the transcription bubble. Lastly, it was shown that the presence of dissipation impacts the dynamic of the phonon by reducing the amplitude of the corresponding conformational field. On the contrary, dissipation and forcing modulate the velocity of the transcription bubble alone.

Environmental enrichment strengthens corticocortical interactions and reduces amyloid-ß oligomers in aged mice.

Brain aging is characterized by global changes which are thought to underlie age-related cognitive decline. These include variations in brain activity and the progressive increase in the concentration of soluble amyloid-ß (Aß) oligomers, directly impairing synaptic function and plasticity even in the absence of any neurodegenerative disorder. Considering the high social impact of the decline in brain performance associated to aging, there is an urgent need to better understand how it can be prevented or contrasted. Lifestyle components, such as social interaction, motor exercise and cognitive activity, are thought to modulate brain physiology and its susceptibility to age-related pathologies. However, the precise functional and molecular factors that respond to environmental stimuli and might mediate their protective action again pathological aging still need to be clearly identified. To address this issue, we exploited environmental enrichment (EE), a reliable model for studying the effect of experience on the brain based on the enhancement of cognitive, social and motor experience, in aged wild-type mice. We analyzed the functional consequences of EE on aged brain physiology by performing in vivo local field potential (LFP) recordings with chronic implants. In addition, we also investigated changes induced by EE on molecular markers of neural plasticity and on the levels of soluble Aß oligomers. We report that EE induced profound changes in the activity of the primary visual and auditory cortices and in their functional interaction. At the molecular level, EE enhanced plasticity by an upward shift of the cortical excitation/inhibition balance. In addition, EE reduced brain Aß oligomers and increased synthesis of the Aß-degrading enzyme neprilysin. Our findings strengthen the potential of EE procedures as a non-invasive paradigm for counteracting brain aging processes.

Longitudinal displacements of base pairs in DNA and effects on the dynamics of nonlinear excitations.

A model of the DNA is proposed and studied analytically and numerically. The model is an extension of a well known model and describes the double helix as two chains of pendula (each pendulum representing a base). Each base (or pendulum) can rotate and translate along the helix axis. In the continuum limit the system is described by the perturbed Sine-Gordon equation describing the twist of the bases and by a nonlinear partial differential equation (PDE) describing the longitudinal displacements of the bases. This coupled system of PDEs was studied analytically using different approaches and the corresponding results were tested through numerical simulations. It was found that if the coupling parameters satisfy a well defined relationship, then there exist bounded travelling wave solutions.

Environmental enrichment modulates cortico-cortical interactions in the mouse.

Environmental enrichment (EE) is an experimental protocol based on a complex sensorimotor stimulation that dramatically affects brain development. While it is widely believed that the effects of EE result from the unique combination of different sensory and motor stimuli, it is not known whether and how cortico-cortical interactions are shaped by EE. Since the primary visual cortex (V1) is one of the best characterized targets of EE, we looked for direct cortico-cortical projections impinging on V1, and we identified a direct monosynaptic connection between motor cortex and V1 in the mouse brain. To measure the interactions between these areas under standard and EE rearing conditions, we used simultaneous recordings of local field potentials (LFPs) in awake, freely moving animals. LFP signals were analyzed by using different methods of linear and nonlinear analysis of time series (cross-correlation, mutual information, phase synchronization). We found that EE decreases the level of coupling between the electrical activities of the two cortical regions with respect to the control group. From a functional point of view, our results indicate, for the first time, that an enhanced sensorimotor experience impacts on the brain by affecting the functional crosstalk between different cortical areas.

Evidence for two conductive pathways in P2X receptor: differences in modulation and selectivity.

The P2X(7) receptor (P2X(7)R) is an ATP-gated cation channel whose biophysical properties remain to be unravelled unequivocally. Its activity is modulated by divalent cations and organic messengers such as arachidonic acid (AA). In this study, we analysed the differential modulation of magnesium (Mg(2+)) and AA on P2X(7)R by measuring whole-cell currents and intracellular Ca(2+) ([Ca(2+)](i)) and Na(+) ([Na(+)](i)) dynamics in HEK293 cells stably expressing full-length P2X(7)R and in cells endowed with the P2X(7)R variant lacking the entire C-terminus tail (trP2X(7)R), which is thought to control the pore activation. AA induced a robust potentiation of the P2X(7)R- and trP2X(7)R-mediated [Ca(2+)](i) rise but did not affect the ionic currents in both conditions. Extracellular Mg(2+) reduced the P2X7R- and trP2X(7)R-mediated [Ca(2+)](i) rise in a dose-dependent manner through a competitive mechanism. The modulation of the magnitude of the P2X(7)R-mediated ionic current and [Na(+)](i) rise were strongly dependent on Mg(2+) concentration but occurred in a non-competitive manner. In contrast, in cells expressing the trP2X(7)R, the small ionic currents and [Na(+)](i) signals were totally insensitive to Mg(2+). Collectively, these results support the tenet of a functional structure of P2X(7)R possessing at least two distinct conductive pathways one for Ca(2+) and another for monovalent ions, with the latter which depends on the presence of the receptor C-terminus.

Dynamics of a minimal neural model consisting of an astrocyte, a neuron, and an interneuron.

In this paper, a biophysical neural network model consisting of a pyramidal neuron, an interneuron, and the astrocyte is studied. The corresponding dynamical properties are mainly investigated by using numerical simulations. The results show that the presence of the adenosine triphosphate and of the interneuron impacts the overall neural activity. It is shown that the fluxes of calcium through the cellular membrane strongly affect the modulation of the neural activity arising from the astrocyte.

Temporal information coding properties of a network of inhibitory interneurons.

Inhibitory interneurons are coupled by electrical and inhibitory synapses and exert a powerful control of the discharges of principal cells. In this paper, the transmission properties of excitatory synaptic inputs by a network of interneurons, are studied by using a computational approach. It is shown that both the rise and decay time constants, describing the time course of the excitatory synaptic inputs, have a strong effect on the output jitter of the fired spikes. Similar results were found by changing the values of the other parameters describing the network. Lastly, it is shown that the presence of the electrical coupling between interneurons confers to the network the capability of transmitting, with less temporal spread, the timing information contained in its inputs.

The electrical coupling confers to a network of interneurons the ability of transmitting excitatory inputs with high temporal precision.

The transmission of excitatory inputs by inhibitory networks of different sizes is investigated by means of numerical simulations. The interneurons are coupled by electrical and/or inhibitory synapses and each of them receives an excitatory pulse at a random time. The pulse times are extracted from a Gaussian distribution and each cell model is subject to an independent noisy current. The results described in this paper suggest that the presence of the electrical coupling promotes the transmission of the excitatory synaptic inputs on a time scale of a few milliseconds.

Botulinum neurotoxin E (BoNT/E) reduces CA1 neuron loss and granule cell dispersion, with no effects on chronic seizures, in a mouse model of temporal lobe epilepsy.

Mesial temporal lobe epilepsy (MTLE) is often the result of an early insult that induces a reorganization in hippocampal circuitry leading, after a latent period, to chronic epilepsy. Hippocampal rearrangements during the latent phase include neuronal loss, axonal and dendritic plasticity, neurogenesis, and cell repositioning, but the role of these changes in epilepsy development is unclear. Here we have tested whether administration of the synaptic blocker botulinum neurotoxin E (BoNT/E) interferes with development of spontaneous seizures and histopathological changes following an episode of status epilepticus (SE). SE was induced by unilateral intrahippocampal injection of kainic acid in mice and BoNT/E was delivered to the same hippocampus 3 h later. We found that treatment with BoNT/E prolonged the duration of the latent period but did not block the occurrence of spontaneous seizures. At the histopathological level, BoNT/E reduced loss of CA1 pyramidal neurons and dispersion of dentate granule cells. Downregulation of reelin expression along the hippocampal fissure was also suppressed by BoNT/E treatment. Our findings indicate that administration of BoNT/E after SE inhibits specific morphological changes in hippocampal circuitry but not the development of spontaneous seizures. This indicates a dissociation between certain anatomical modifications and establishment of chronic epilepsy in MTLE.

The synchronization properties of a network of inhibitory interneurons depend on the biophysical model.

The synchronization properties of a pair of coupled fast spiking interneurons are studied by using the theory of weakly coupled oscillators. Four different biophysical models of the single fast spiking interneuron are used and the corresponding results are compared. It is shown that for a pair of identical coupled cells, the synchronization properties are model-dependent. In particular, the firing coherence of the network is strongly affected by the reversal potential, the kinetics of the inhibitory postsynaptic current and the electrical coupling; the activation properties of the sodium and potassium currents play a significant role too.

Calcium signalling in astrocytes and modulation of neural activity.

Starting from the experimental data on ATP evoked calcium responses in astrocytes, a biophysical model describing these phenomena was built. The simulations showed, in agreement with the experimental findings, that the intracellular calcium fluxes mediated by the P2X and P2Y purinoreceptors are responsible for the biphasic ATP evoked calcium response in astrocytes. Then, the modulation effects on the neural dynamics arising from the release of glutamate from astrocyte are also investigated. By using a minimal network model describing a neuron coupled to the astrocyte, we demonstrated that the calcium extrusion rate through the astrocyte membrane is critically involved in the generation of different firing patterns of the neuron.

Stochastic resonance in two simple compare-and-fire models.

Two neural models are analysed and shown to exhibit the stochastic resonance effect. Namely, they respond to an underthreshold sinusoidal signal with an output signal whose signal-to-noise ratio (SNR) firstly increases then decreases as the intensity of noise affecting the system increases. The resonance curves are determined, analytically for the first and simplest model and by a synthetic method for the second one, and the respective resonant behaviours are illustrated and interpreted.

Signal processing properties of fast spiking interneurons.

Fast spiking interneurons receive excitatory synaptic inputs from pyramidal cells and a relevant problem is to understand how these cells readout this information. Here this topic is investigated theoretically by using a biophysical modeling of a pair of coupled fast spiking interneuron models. The model predicts, in agreement with the experimental findings, that these cells are capable of transmitting pre-synaptic signals with high temporal precision and transferring high frequency inputs while preserving their relative timing. Moreover, it is shown that a pair of fast spiking interneurons, coupled through both inhibitory and electrical synapses, behaves as a coincidence detector. Lastly, to understand the mechanisms underlying these phenomena, a theoretical analysis is carried out by using a simpler modeling approach.

Synchronization in a network of fast-spiking interneurons.

Experimental results revealed that in neocortex inhibitory fast-spiking (FS) interneurons interact also by electrical synapses (gap-junctions). They receive sensory information from thalamus and transfer it to principal cells by feedforward inhibition. Moreover, their synchronous discharge enhances their inhibitory control of pyramidal neurons. By using a biophysical model of FS interneurons the synchronization properties of a network of two synaptically coupled units are investigated. In the case they interact only by inhibitory synapses, well defined regions exist in the parameters space described by the strength and duration of the synaptic current, where synchronous regimes occur. Then an empirical protocol is proposed to determine approximately the borders of the synchronization manifold (SM). When electrical synapses are included, the region of synchronous discharge of the two interneurons becomes larger. In both cases, the coherent states are characterized by discharge frequencies in the gamma range. Lastly, the effects of heterogeneity, either obtained by using different stimulation currents or unidirectional inhibitory coupling, are studied.