NMDA-induced burst firing in a model subthalamic nucleus neuron

Slow negative feedback enhances robustness of square-wave bursting

Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.

Structure, Function, and Pharmacology of Glutamate Receptor Ion Channels

Many physiologic effects of l-glutamate, the major excitatory neurotransmitter in the mammalian central nervous system, are mediated via signaling by ionotropic glutamate receptors (iGluRs). These ligand-gated ion channels are critical to brain function and are centrally implicated in numerous psychiatric and neurologic disorders. There are different classes of iGluRs with a variety of receptor subtypes in each class that play distinct roles in neuronal functions. The diversity in iGluR subtypes, with their unique functional properties and physiologic roles, has motivated a large number of studies. Our understanding of receptor subtypes has advanced considerably since the first iGluR subunit gene was cloned in 1989, and the research focus has expanded to encompass facets of biology that have been recently discovered and to exploit experimental paradigms made possible by technological advances. Here, we review insights from more than 3 decades of iGluR studies with an emphasis on the progress that has occurred in the past decade. We cover structure, function, pharmacology, roles in neurophysiology, and therapeutic implications for all classes of receptors assembled from the subunits encoded by the 18 ionotropic glutamate receptor genes. SIGNIFICANCE STATEMENT: Glutamate receptors play important roles in virtually all aspects of brain function and are either involved in mediating some clinical features of neurological disease or represent a therapeutic target for treatment. Therefore, understanding the structure, function, and pharmacology of this class of receptors will advance our understanding of many aspects of brain function at molecular, cellular, and system levels and provide new opportunities to treat patients.

Robust switches in thalamic network activity require a timescale separation between sodium and T-type calcium channel activations

Switches in brain states, synaptic plasticity and neuromodulation are fundamental processes in our brain that take place concomitantly across several spatial and timescales. All these processes target neuron intrinsic properties and connectivity to achieve specific physiological goals, raising the question of how they can operate without interfering with each other. Here, we highlight the central importance of a timescale separation in the activation of sodium and T-type calcium channels to sustain robust switches in brain states in thalamic neurons that are compatible with synaptic plasticity and neuromodulation. We quantify the role of this timescale separation by comparing the robustness of rhythms of six published conductance-based models at the cellular, circuit and network levels. We show that robust rhythm generation requires a T-type calcium channel activation whose kinetics are situated between sodium channel activation and T-type calcium channel inactivation in all models despite their quantitative differences.

Our brain is constantly processing information either from the environment to quickly react to incoming events or learning from experience to shape our memory. These brain states translate a collective activity of neurons interconnected via synaptic connections. Here, we focus on the thalamic network showing a transition from an active to an oscillatory mode at the population level, reverberating a switch from tonic to bursting mode at the cellular level. We are questioning how these activity fluctuations can be robustly modeled despite synaptic plasticity affecting the network configuration and the presence of neuromodulators affecting neuron intrinsic properties. To do so, we investigate six conductance-based models and their ability to reproduce activity switches at the cellular, circuit and population levels. We highlight that the robustness requires the timescale separation between the fast activation of sodium channels compared to the slow activation of T-type calcium channels. Our results show that this kinetics difference is not a computational detail but rather makes a model suitable and robust to study the interaction between switches in brain states, synaptic plasticity and neuromodulation.

Switchable slow cellular conductances determine robustness and tunability of network states

Neuronal information processing is regulated by fast and localized fluctuations of brain states. Brain states reliably switch between distinct spatiotemporal signatures at a network scale even though they are composed of heterogeneous and variable rhythms at a cellular scale. We investigated the mechanisms of this network control in a conductance-based population model that reliably switches between active and oscillatory mean-fields. Robust control of the mean-field properties relies critically on a switchable negative intrinsic conductance at the cellular level. This conductance endows circuits with a shared cellular positive feedback that can switch population rhythms on and off at a cellular resolution. The switch is largely independent from other intrinsic neuronal properties, network size and synaptic connectivity. It is therefore compatible with the temporal variability and spatial heterogeneity induced by slower regulatory functions such as neuromodulation, synaptic plasticity and homeostasis. Strikingly, the required cellular mechanism is available in all cell types that possess T-type calcium channels but unavailable in computational models that neglect the slow kinetics of their activation.

Brain information processing involves electrophysiological signals at multiple temporal and spatial timescales, from the single neuron level to whole brain areas. A fast and local control of these signals by neurochemicals called neuromodulators is essential in complex tasks such as movement initiation and attentional focus. The neuromodulators act at the cellular scale to control signals that propagate at potentially much larger scales. The present paper highlights the critical role of a cellular switch of excitability for the fast and localized control of cellular and network states. By turning ON and OFF the cellular switch, neuromodulators can robustly switch large populations between distinct network states. We stress the importance of controlling the switch at a cellular level and independently of the connectivity to allow for tunable spatiotemporal signatures of the network states.

Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically rely on currents that provide slow positive feedback to the membrane potential. Such currents have the ability to make the total conductance of the circuit negative in a timescale that is termed "slow" because it is intermediate between the fast timescale of the spike upstroke and the ultraslow timescale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale. NEW & NOTEWORTHY Nervous system functions rely on the modulation of neuronal activity between different rhythmic patterns. The mechanisms of this modulation are still poorly understood. Using computational modeling, we show the critical role of currents that provide slow negative conductance, distinct from the fast negative conductance necessary for spike generation. The significance of the slow negative conductance for neuromodulation is often overlooked, leading to computational models that are rigid and fragile.

Computational models of basal ganglia dysfunction: the dynamics is in the details

The development, simulation, and analysis of mathematical models offer helpful tools for integrating experimental findings and exploring or suggesting possible explanatory mechanisms. As models relating to basal ganglia dysfunction have proliferated, however, there has not always been consistency among their findings. This work points out several ways in which biological details, relating to ionic currents and synaptic pathways, can influence the dynamics of models of the basal ganglia under parkinsonian conditions and hence may be important for inclusion in models. It also suggests some additional useful directions for future modeling studies relating to basal ganglia dysfunction.

Basal ganglia activity patterns in parkinsonism and computational modeling of their downstream effects

The availability of suitable animal models and the opportunity to record electrophysiologic data in movement disorder patients undergoing neurosurgical procedures has allowed researchers to investigate parkinsonism-related changes in neuronal firing patterns in the basal ganglia and associated areas of the thalamus and cortex. These studies have shown that parkinsonism is associated with increased activity in the basal ganglia output nuclei, along with increases in burst discharges, oscillatory firing and synchronous firing patterns throughout the basal ganglia. Computational approaches have the potential to play an important role in the interpretation of these data. Such efforts can provide a formalized view of neuronal interactions in the network of connections between the basal ganglia, thalamus, and cortex, allow for the exploration of possible contributions of particular network components to parkinsonism, and potentially result in new conceptual frameworks and hypotheses that can be subjected to biological testing. It has proven very difficult, however, to integrate the wealth of the experimental findings into coherent models of the disease. In this review, we provide an overview of the abnormalities in neuronal activity that have been associated with parkinsonism. Subsequently, we discuss some particular efforts to model the pathophysiologic mechanisms that may link abnormal basal ganglia activity to the cardinal parkinsonian motor signs and may help to explain the mechanisms underlying the therapeutic efficacy of deep brain stimulation for Parkinson's disease. We emphasize the logical structure of these computational studies, making clear the assumptions from which they proceed and the consequences and predictions that follow from these assumptions.