A Mechanism of Co-Existence of Bursting and Silent Regimes of Activities of a Neuron

The co-existence of bursting activity and silence is a common property of various neuronal models. We describe a novel mechanism explaining the co-existence of and the transition between these two regimes. It is based on the specific homoclinic and Andronov-Hopf bifurcations of the hyper- and depolarized steady states that determine the co-existence domain in the parameter space of the leech heart interneuron models: canonical and simplified. We found that a sub-critical Andronov-Hopf bifurcation of the hyperpolarized steady state gives rise to small amplitude sub-threshold oscillations terminating through the secondary homoclinic bifurcation. Near the corresponding boundary the system can exhibit long transition from bursting oscillations into silence, as well as the bi-stability where the observed regime is determined by the initial state of the neuron. The mechanism found is shown to be generic for the simplified 4D and the original 14D leech heart interneuron models

Six Types of Multistability in a Neuronal Model Based on Slow Calcium Current

Background: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified. Methodology/Principal Findings: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate. Conclusions: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability

Layered Chaos in Mean-field and Quantum Many-body Dynamics

We investigate the dimension of the phase space attractor of a quantum chaotic many-body ratchet in the mean-field limit. Specifically, we explore a driven Bose-Einstein condensate in three distinct dynamical regimes - Rabi oscillations, chaos, and self-trapping regime, and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free non-interacting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of a local density in each of the dynamical regimes, has an attractor characterized with a higher fractal dimension, $D_{R}=2.59\pm0.01$, $D_{C}=3.93\pm0.04$, and $D_{S}=3.05\pm0.05$, as compared to the global measure of current, $D_{R}=2.07\pm0.02$, $D_{C}=2.96\pm0.05$, and $D_{S}=2.30\pm0.02$. We find that the many-body case converges to mean-field limit with strong sub-unity power laws in particle number $N$, namely $N^{\alpha}$ with $\alpha_{R}={0.28\pm0.01}$, $\alpha_{C}={0.34\pm0.067}$ and $\alpha_{S}={0.90\pm0.24}$ for each of the dynamical regimes mentioned above. The deviation between local and global measurement of the attractor's dimension corresponds to an increase towards high condensate depletion which remains constant for long time scales in both Rabi and chaotic regimes. The depletion is found to scale polynomially with particle number as $N^{\beta}$ with $\beta_{R}={0.51\pm0.004}$ and $\beta_{C}={0.18\pm0.004}$ for the two regimes. Thus, we find a strong deviation from the mean-field results, especially in the chaotic regime of the quantum ratchet. The ratchet also reveals quantum revivals in the Rabi and self-trapped regimes but not in the chaotic regime. Based on the obtained results we outline pathways for the identification and characterization of the emergent phenomena in driven many-body systems

CELLULAR AND CIRCUIT PROPERTIES OF SLOW OSCILLATIONS IN THE THALAMIC RETICULAR NUCLEUS

During sleep, neurons in the thalamic reticular nucleus (TRN) generate distinct types of oscillatory activity. While the reciprocal synaptic circuits between TRN and sensory thalamic nuclei underlie the generation of sleep spindles, the mechanisms regulating slow (\u3c1 \u3eHz) forms of thalamic oscillations are poorly understood. Under in vitro conditions, in the absence of synaptic inputs, TRN neurons can generate slow oscillations in a cell-intrinsic manner. Activation of postsynaptic Group 1 metabotropic glutamate receptors (mGluR) leads to long-lasting plateau potentials thought to be mediated by both T-type calcium currents and calcium-activated nonselective cation currents (ICAN). However, the identity of ICAN and the possible contribution of thalamic circuits to slow rhythmic activity remain unclear. Using intracellular recordings of neurons in thalamic slices derived from adult male and female mice, I recorded slow forms of rhythmic activity in TRN neurons. Slow oscillations were driven by fast glutamatergic inputs from thalamic relay neurons, but did not require postsynaptic mGluR activation. For a significant minority of TRN neurons (33%), synaptic inputs or brief depolarizing current steps led to plateau potentials and persistent firing (PF), and in turn, resulted in persistent synaptic inhibition in postsynaptic relay neurons of the ventrobasal thalamus (VB). Pharmacological approaches indicated that plateau potentials were triggered by calcium influx through T-type calcium channels and mediated by calcium and voltage-dependent transient receptor potential melastatin 4 (TRPM4) channels. Taken together, my results suggest that thalamic circuits can generate slow oscillatory activity, mediated by an interplay of TRN-VB synaptic circuits that generate rhythmicity and TRN cell-intrinsic mechanisms that control PF and oscillation frequency

Dendritic spikes induce ripples in parvalbumin interneurons during hippocampal sharp waves.

Sharp-wave ripples are transient oscillatory events in the hippocampus that are associated with the reactivation of neuronal ensembles within specific circuits during memory formation. Fast-spiking, parvalbumin-expressing interneurons (FS-PV INs) are thought to provide fast integration in these oscillatory circuits by suppressing regenerative activity in their dendrites. Here, using fast 3D two-photon imaging and a caged glutamate, we challenge this classical view by demonstrating that FS-PV IN dendrites can generate propagating Ca(2+) spikes during sharp-wave ripples. The spikes originate from dendritic hot spots and are mediated dominantly by L-type Ca(2+) channels. Notably, Ca(2+) spikes were associated with intrinsically generated membrane potential oscillations. These oscillations required the activation of voltage-gated Na(+) channels, had the same frequency as the field potential oscillations associated with sharp-wave ripples, and controlled the phase of action potentials. Furthermore, our results demonstrate that the smallest functional unit that can generate ripple-frequency oscillations is a segment of a dendrite

Gravitational waves from single neutron stars: an advanced detector era survey

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.Comment: 39 pages, 12 figures, 2 tables. Chapter of the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action 1304. Minor corrections to match published versio

Global neural rhythm control by local neuromodulation

Neural oscillations are a ubiquitous form of neural activity seen across scales and modalities. These neural rhythms correlate with diverse cognitive functions and brain states. One mechanism for changing the oscillatory dynamics of large neuronal populations is through neuromodulator activity. An intriguing phenomenon explored here is when local neuromodulation of a distinct neuron type within a single brain nucleus exerts a powerful influence on global cortical rhythms. One approach to investigate the impact of local circuits on global rhythms is through optogenetic techniques. My first project involves the statistical analysis of electrophysiological recordings of an optogenetically-mediated Parkinsonian phenotype. Empirical studies demonstrate that Parkinsonian motor deficits correlate with the emergence of exaggerated beta frequency (15-30 Hz) oscillations throughout the cortico-basal ganglia-thalamic network. However, the mechanism of these aberrant oscillatory dynamics is not well understood. A previous modeling study predicted that cholinergic neuromodulation of medium spiny neurons in the striatum of the basal ganglia may mediate the pathologic beta rhythm. Here, this hypothesis was tested using selective optogenetic stimulation of striatal cholinergic interneurons in normal mice; stimulation robustly and reversibly amplified beta oscillations and Parkinsonian motor symptoms. The modulation of global rhythms by local networks was further studied using computational modeling in the context of intrathalamic neuromodulation. While intrathalamic vasoactive intestinal peptide (VIP) is known to cause long-lasting excitation in vitro, its in vivo dynamical effects have not been reported. Here, biophysical computational models were used to elucidate the impact of VIP on thalamocortical dynamics during sleep and propofol general anesthesia. The modeling results suggest that VIP can form robust sleep spindle oscillations and control aspects of sleep architecture through a novel homeostatic mechanism. This homeostatic mechanism would be inhibited by general anesthesia, representing a new mechanism contributing to anesthetic-induced loss of consciousness. While the previous two projects differed in their use of empirical versus theoretical methods, a challenge common to both domains is the difficulty in visualizing and analyzing large multi-dimensional datasets. A tool to mitigate these issues is introduced here: GIMBL-Vis is a Graphical Interactive Multi-dimensional extensiBLe Visualization toolbox for Matlab. This toolbox simplifies the process of exploring multi-dimensional data in Matlab by providing a graphical interface for visualization and analysis. Furthermore, it provides an extensible open platform for distributed development by the community

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

Mechanisms of Multistability in Neuronal Models

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center. We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents\u27 parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-Bӧtzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described