Selective recruitment of cortical neurons by electrical stimulation.

Despite its critical importance in experimental and clinical neuroscience, at present there is no systematic method to predict which neural elements will be activated by a given stimulation regime. Here we develop a novel approach to model the effect of cortical stimulation on spiking probability of neurons in a volume of tissue, by applying an analytical estimate of stimulation-induced activation of different cell types across cortical layers. We utilize the morphology and properties of axonal arborization profiles obtained from publicly available anatomical reconstructions of the twelve main categories of neocortical neurons to derive the dependence of activation probability on cell type, layer and distance from the source. We then propagate this activity through the local network incorporating connectivity, synaptic and cellular properties. Our work predicts that (a) intracranial cortical stimulation induces selective activation across cell types and layers; (b) superficial anodal stimulation is more effective than cathodal at cell activation; (c) cortical surface stimulation focally activates layer I axons, and (d) there is an optimal stimulation intensity capable of eliciting cell activation lasting beyond the end of stimulation. We conclude that selective effects of cortical electrical stimulation across cell types and cortical layers are largely driven by their different axonal arborization and myelination profiles.

Differential roles of sleep spindles and sleep slow oscillations in memory consolidation.

Sleep plays an important role in the consolidation of recent memories. However, the cellular and synaptic mechanisms of consolidation during sleep remain poorly understood. In this study, using a realistic computational model of the thalamocortical network, we tested the role of Non-Rapid Eye Movement (NREM) sleep in memory consolidation. We found that sleep spindles (the hallmark of N2 stage sleep) and slow oscillations (the hallmark of N3 stage sleep) both promote replay of the spike sequences learned in the awake state and replay was localized at the trained network locations. Memory performance improved after a period of NREM sleep but not after the same time period in awake. When multiple memories were trained, the local nature of the spike sequence replay during spindles allowed replay of the distinct memory traces independently, while slow oscillations promoted competition that could prevent replay of the weak memories in a presence of the stronger memory traces. This could lead to extinction of the weak memories unless when sleep spindles (N2 sleep) preceded slow oscillations (N3 sleep), as observed during the natural sleep cycle. Our study presents a mechanistic explanation for the role of sleep rhythms in memory consolidation and proposes a testable hypothesis how the natural structure of sleep stages provides an optimal environment to consolidate memories.

Computational model of brain-stem circuit for state-dependent control of hypoglossal motoneurons.

In patients with obstructive sleep apnea (OSA), the pharyngeal muscles become relaxed during sleep, which leads to a partial or complete closure of upper airway. Experimental studies suggest that withdrawal of noradrenergic and serotonergic drives importantly contributes to depression of hypoglossal motoneurons and, therefore, may contribute to OSA pathophysiology; however, specific cellular and synaptic mechanisms remain unknown. In this new study, we developed a biophysical network model to test the hypothesis that, to explain experimental observations, the neuronal network for monoaminergic control of excitability of hypoglossal motoneurons needs to include excitatory and inhibitory perihypoglossal interneurons that mediate noradrenergic and serotonergic drives to hypoglossal motoneurons. In the model, the state-dependent activation of the hypoglossal motoneurons was in qualitative agreement with in vivo data during simulated rapid eye movement (REM) and non-REM sleep. The model was applied to test the mechanisms of action of noradrenergic and serotonergic drugs during REM sleep as observed in vivo. We conclude that the proposed minimal neuronal circuit is sufficient to explain in vivo data and supports the hypothesis that perihypoglossal interneurons may mediate state-dependent monoaminergic drive to hypoglossal motoneurons. The population of the hypothesized perihypoglossal interneurons may serve as novel targets for pharmacological treatment of OSA. NEW & NOTEWORTHY In vivo studies suggest that during rapid eye movement sleep, withdrawal of noradrenergic and serotonergic drives critically contributes to depression of hypoglossal motoneurons (HMs), which innervate the tongue muscles. By means of a biophysical model, which is consistent with a broad range of empirical data, we demonstrate that the neuronal network controlling the excitability of HMs needs to include excitatory and inhibitory interneurons that mediate noradrenergic and serotonergic drives to HMs.

New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics.

During slow-wave sleep, brain electrical activity is dominated by the slow (< 1 Hz) electroencephalogram (EEG) oscillations characterized by the periodic transitions between active (or Up) and silent (or Down) states in the membrane voltage of the cortical and thalamic neurons. Sleep slow oscillation is believed to play critical role in consolidation of recent memories. Past computational studies, based on the Hodgkin-Huxley type neuronal models, revealed possible intracellular and network mechanisms of the neuronal activity during sleep, however, they failed to explore the large-scale cortical network dynamics depending on collective behavior in the large populations of neurons. In this new study, we developed a novel class of reduced discrete time spiking neuron models for large-scale network simulations of wake and sleep dynamics. In addition to the spiking mechanism, the new model implemented nonlinearities capturing effects of the leak current, the Ca2+ dependent K+ current and the persistent Na+ current that were found to be critical for transitions between Up and Down states of the slow oscillation. We applied the new model to study large-scale two-dimensional cortical network activity during slow-wave sleep. Our study explained traveling wave dynamics and characteristic synchronization properties of transitions between Up and Down states of the slow oscillation as observed in vivo in recordings from cats. We further predict a critical role of synaptic noise and slow adaptive currents for spike sequence replay as found during sleep related memory consolidation.

Linking dynamics of the inhibitory network to the input structure.

Networks of inhibitory interneurons are found in many distinct classes of biological systems. Inhibitory interneurons govern the dynamics of principal cells and are likely to be critically involved in the coding of information. In this theoretical study, we describe the dynamics of a generic inhibitory network in terms of low-dimensional, simplified rate models. We study the relationship between the structure of external input applied to the network and the patterns of activity arising in response to that stimulation. We found that even a minimal inhibitory network can generate a great diversity of spatio-temporal patterning including complex bursting regimes with non-trivial ratios of burst firing. Despite the complexity of these dynamics, the network's response patterns can be predicted from the rankings of the magnitudes of external inputs to the inhibitory neurons. This type of invariant dynamics is robust to noise and stable in densely connected networks with strong inhibitory coupling. Our study predicts that the response dynamics generated by an inhibitory network may provide critical insights about the temporal structure of the sensory input it receives.

Dynamics of multifrequency oscillator communities.

We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The simplest situation of three resonantly interacting groups is analyzed in detail. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations and present examples where the interaction between communities leads to their synchrony or to a partially asynchronous state or to a chaotic dynamics of order parameters.

Multiplicity of singular synchronous states in the Kuramoto model of coupled oscillators.

We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.

Intercommunity resonances in multifrequency ensembles of coupled oscillators.

We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to the resonance 2:1 is considered in detail. We construct uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross coupling across the frequencies can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross coupling is accompanied by a huge multiplicity of distinct synchronous solutions, which is directly related to a multibranch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy phase locking and lead to chaos of mean fields.

Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.

We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.

Effects of nonresonant interaction in ensembles of phase oscillators.

We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via nonoscillating collective variables like the amplitudes of the order parameters defined for each group. We treat the phase dynamics of the groups using the Ott-Antonsen ansatz and reduce it to a system of coupled equations for the order parameters. We describe different regimes of cosynchrony in the groups. For a large number of groups, heteroclinic cycles, corresponding to a sequential synchronous activity of groups and chaotic states where the order parameters oscillate irregularly, are possible.