On the dynamics of electrically-coupled neurons with inhibitory synapses

Locus Ceruleus Norepinephrine Release: A Central Regulator of CNS Spatio-Temporal Activation?

Norepinephrine (NE) is synthesized in the Locus Coeruleus (LC) of the brainstem, from where it is released by axonal varicosities throughout the brain via volume transmission. A wealth of data from clinics and from animal models indicates that this catecholamine coordinates the activity of the central nervous system (CNS) and of the whole organism by modulating cell function in a vast number of brain areas in a coordinated manner. The ubiquity of NE receptors, the daunting number of cerebral areas regulated by the catecholamine, as well as the variety of cellular effects and of their timescales have contributed so far to defeat the attempts to integrate central adrenergic function into a unitary and coherent framework. Since three main families of NE receptors are represented-in order of decreasing affinity for the catecholamine-by: α2 adrenoceptors (α2Rs, high affinity), α1 adrenoceptors (α1Rs, intermediate affinity), and β adrenoceptors (βRs, low affinity), on a pharmacological basis, and on the ground of recent studies on cellular and systemic central noradrenergic effects, we propose that an increase in LC tonic activity promotes the emergence of four global states covering the whole spectrum of brain activation: (1) sleep: virtual absence of NE, (2) quiet wake: activation of α2Rs, (3) active wake/physiological stress: activation of α2- and α1-Rs, (4) distress: activation of α2-, α1-, and β-Rs. We postulate that excess intensity and/or duration of states (3) and (4) may lead to maladaptive plasticity, causing-in turn-a variety of neuropsychiatric illnesses including depression, schizophrenic psychoses, anxiety disorders, and attention deficit. The interplay between tonic and phasic LC activity identified in the LC in relationship with behavioral response is of critical importance in defining the short- and long-term biological mechanisms associated with the basic states postulated for the CNS. While the model has the potential to explain a large number of experimental and clinical findings, a major challenge will be to adapt this hypothesis to integrate the role of other neurotransmitters released during stress in a centralized fashion, like serotonin, acetylcholine, and histamine, as well as those released in a non-centralized fashion, like purines and cytokines.

Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic β-cells, which in isolation are known to exhibit irregular spiking (Sherman and Rinzel, Biophys J 54:411-425, 1988; Sherman and Rinzel, Biophys J 59:547-559, 1991). At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, building on an earlier analysis of denoising in networks of integrate-and-fire neurons (Medvedev, Neural Comput 21 (11):3057-3078, 2009) and our recent study of spontaneous activity in a closely related model of the Locus Coeruleus network (Medvedev and Zhuravytska, The geometry of spontaneous spiking in neuronal networks, submitted, 2012), we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity (Fiedler, Czech Math J 23(98):298-305, 1973) or small total effective resistance (Bollobas, Modern graph theory, Graduate Texts in Mathematics, vol. 184, Springer, New York, 1998) are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models.

Electrical coupling promotes fidelity of responses in the networks of model neurons

We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.

Predicting synchronous and asynchronous network groupings of hippocampal interneurons coupled with dendritic gap junctions

Direct electrical communication between central nervous system (CNS) neurons including those in the hippocampus is well-established. This form of communication is mediated by gap junctions and it is known that this coupling is important for brain rhythms such as gamma (20-80 Hz) which occur during active behavioural states. It is also known that gap junctions are present at several locations along the dendrites of hippocampal interneurons including parvalbumin-positive basket cell types. Weakly coupled oscillator theory, which uses phase response curves (PRCs), has been used to understand and predict the dynamics of electrically coupled networks. Here we use compartmental models of hippocampal basket cells with different levels of basal and apical spike attenuation together with the theory to show that network output can be broken down into three groupings: synchronous, asynchronous and antiphase-like patterns. Moreover, quantified PRCs can be used as a rule of thumb to determine the occurrence of a particular grouping under weak coupling conditions, which in turn implies that spike delays are critical factors in determining network output. In moving beyond weak coupling to encompass the full physiological regime of coupling strengths with network simulations, we note that it is important to be able to differentiate between these different groupings as it affects how the network responds with modulation. Specifically, an asynchronous grouping provides more dynamic richness as a larger range of phase-locked states can be expressed with strength changes. From a functional viewpoint it may be that modulation of electrically coupled networks are key to controlling cell assemblies that contribute to information coding brain substrates.

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.

Inferring connection proximity in networks of electrically coupled cells by subthreshold frequency response analysis

Electrical synapses continuously transfer signals bi-directionally from one cell to another, directly or indirectly via intermediate cells. Electrical synapses are common in many brain structures such as the inferior olive, the subcoeruleus nucleus and the neocortex, between neurons and between glial cells. In the cortex, interneurons have been shown to be electrically coupled and proposed to participate in large, continuous cortical syncytia, as opposed to smaller spatial domains of electrically coupled cells. However, to explore the significance of these findings it is imperative to map the electrical synaptic microcircuits, in analogy with in vitro studies on monosynaptic and disynaptic chemical coupling. Since "walking" from cell to cell over large distances with a glass pipette is challenging, microinjection of (fluorescent) dyes diffusing through gap-junctions remains so far the only method available to decipher such microcircuits even though technical limitations exist. Based on circuit theory, we derive analytical descriptions of the AC electrical coupling in networks of isopotential cells. We then suggest an operative electrophysiological protocol to distinguish between direct electrical connections and connections involving one or more intermediate cells. This method allows inferring the number of intermediate cells, generalizing the conventional coupling coefficient, which provides limited information. We validate our method through computer simulations, theoretical and numerical methods and electrophysiological paired recordings.