Mixed-mode oscillations and population bursting in the pre-Bötzinger complex

Understanding perspectives for mixed mode oscillations of the fractional neural network approaches to the analysis of neurophysiological data from the perspective of the observability of complex networks

Using discrete fractional calculus, a wide variety of physiological phenomena with various time scales have been productively investigated. In order to comprehend the intricate dynamics and activity of neuronal processing, we investigate the behavior of a slow-fast FitzHugh-Rinzel (FH-R) simulation neuron that is driven by physiological considerations via the Caputo fractional difference scheme. Taking into account the discrete fractional commensurate and incommensurate mechanisms, we speculate on the numerical representations of various excitabilities and persistent activation reactions brought about by the administered stimulation. Furthermore, the outcomes concentrate on the variability of several time scales, encompassing mixed-mode oscillations and mixed-mode bursting oscillations formed by the canard occurrence. It is confirmed that the fast-analyzing component, which was isolated within this framework with the slow-fast evaluation process, is bistable, and the criterion for bistability is added as well. The architecture appears to be bistable based on this. The pertinent factors for examining time evolution, Poincaré maps, the bifurcation configuration of the system and chaos illustrations involve the inserted power stimulation using commensurate and incommensurate fractional-order values. We investigate the canards adjacent to the folded platforms using the folded node hypothesis. Additionally, we are employing mixed-mode oscillations to illustrate the homoclinic bifurcation and the resulting chaotic trajectory. Also, we determine our research results by computing the Lyapunov spectra as an expression of time in conjunction with the dominating factor ℑ to demonstrate the chaotic behavior in a particular domain. Besides that, we estimate intricacy employing the sample entropy (Sp-En) approach andC 0 complexity. The emergence of chaos within the hypothesized discrete fractional FH-R system is verified using the 0 - 1 criterion. Ultimately, we examine the prospective implications of mixed-mode oscillations in neuroscience and draw the inference that our observed outcomes could potentially be of great relevance. As a result, the predicted intricacy decreases while applying it to non-horizontal significant models. Finally, the simulation's characteristic phases, canards and mixed model oscillations are achieved statistically with the assistance of varying fractional orders.

Inspiratory and sigh breathing rhythms depend on distinct cellular signalling mechanisms in the preBötzinger complex

Breathing behaviour involves the generation of normal breaths (eupnoea) on a timescale of seconds and sigh breaths on the order of minutes. Both rhythms emerge in tandem from a single brainstem site, but whether and how a single cell population can generate two disparate rhythms remains unclear. We posit that recurrent synaptic excitation in concert with synaptic depression and cellular refractoriness gives rise to the eupnoea rhythm, whereas an intracellular calcium oscillation that is slower by orders of magnitude gives rise to the sigh rhythm. A mathematical model capturing these dynamics simultaneously generates eupnoea and sigh rhythms with disparate frequencies, which can be separately regulated by physiological parameters. We experimentally validated key model predictions regarding intracellular calcium signalling. All vertebrate brains feature a network oscillator that drives the breathing pump for regular respiration. However, in air-breathing mammals with compliant lungs susceptible to collapse, the breathing rhythmogenic network may have refashioned ubiquitous intracellular signalling systems to produce a second slower rhythm (for sighs) that prevents atelectasis without impeding eupnoea. KEY POINTS: A simplified activity-based model of the preBötC generates inspiratory and sigh rhythms from a single neuron population. Inspiration is attributable to a canonical excitatory network oscillator mechanism. Sigh emerges from intracellular calcium signalling. The model predicts that perturbations of calcium uptake and release across the endoplasmic reticulum counterintuitively accelerate and decelerate sigh rhythmicity, respectively, which was experimentally validated. Vertebrate evolution may have adapted existing intracellular signalling mechanisms to produce slow oscillations needed to optimize pulmonary function in mammals.

Understanding and countering opioid-induced respiratory depression

Respiratory depression is the proximal cause of death in opioid overdose, yet the mechanisms underlying this potentially fatal outcome are not well understood. The goal of this review is to provide a comprehensive understanding of the pharmacological mechanisms of opioid-induced respiratory depression, which could lead to improved therapeutic options to counter opioid overdose, as well as other detrimental effects of opioids on breathing. The development of tolerance in the respiratory system is also discussed, as are differences in the degree of respiratory depression caused by various opioid agonists. Finally, potential future therapeutic agents aimed at reversing or avoiding opioid-induced respiratory depression through non-opioid receptor targets are in development and could provide certain advantages over naloxone. By providing an overview of mechanisms and effects of opioids in the respiratory network, this review will benefit future research on countering opioid-induced respiratory depression. LINKED ARTICLES: This article is part of a themed issue on Advances in Opioid Pharmacology at the Time of the Opioid Epidemic. To view the other articles in this section visit http://onlinelibrary.wiley.com/doi/10.1111/bph.v180.7/issuetoc.

Microcircuit Synchronization and Heavy-Tailed Synaptic Weight Distribution Augment preBötzinger Complex Bursting Dynamics

The preBötzinger Complex (preBötC) encodes inspiratory time as rhythmic bursts of activity underlying each breath. Spike synchronization throughout a sparsely connected preBötC microcircuit initiates bursts that ultimately drive the inspiratory motor patterns. Using minimal microcircuit models to explore burst initiation dynamics, we examined the variability in probability and latency to burst following exogenous stimulation of a small subset of neurons, mimicking experiments. Among various physiologically plausible graphs of 1000 excitatory neurons constructed using experimentally determined synaptic and connectivity parameters, directed Erdős-Rényi graphs with a broad (lognormal) distribution of synaptic weights best captured the experimentally observed dynamics. preBötC synchronization leading to bursts was regulated by the efferent connectivity of spiking neurons that are optimally tuned to amplify modest preinspiratory activity through input convergence. Using graph-theoretic and machine learning-based analyses, we found that input convergence of efferent connectivity at the next-nearest neighbor order was a strong predictor of incipient synchronization. Our analyses revealed a crucial role of synaptic heterogeneity in imparting exceptionally robust yet flexible preBötC attractor dynamics. Given the pervasiveness of lognormally distributed synaptic strengths throughout the nervous system, we postulate that these mechanisms represent a ubiquitous template for temporal processing and decision-making computational motifs.SIGNIFICANCE STATEMENT Mammalian breathing is robust, virtually continuous throughout life, yet is inherently labile: to adapt to rapid metabolic shifts (e.g., fleeing a predator or chasing prey); for airway reflexes; and to enable nonventilatory behaviors (e.g., vocalization, breathholding, laughing). Canonical theoretical frameworks-based on pacemakers and intrinsic bursting-cannot account for the observed robustness and flexibility of the preBötzinger Complex rhythm. Experiments reveal that network synchronization is the key to initiate inspiratory bursts in each breathing cycle. We investigated preBötC synchronization dynamics using network models constructed with experimentally determined neuronal and synaptic parameters. We discovered that a fat-tailed (non-Gaussian) synaptic weight distribution-a manifestation of synaptic heterogeneity-augments neuronal synchronization and attractor dynamics in this vital rhythmogenic network, contributing to its extraordinary reliability and responsiveness.

Breathing Rhythm and Pattern and Their Influence on Emotion

Breathing is a vital rhythmic motor behavior with a surprisingly broad influence on the brain and body. The apparent simplicity of breathing belies a complex neural control system, the breathing central pattern generator (bCPG), that exhibits diverse operational modes to regulate gas exchange and coordinate breathing with an array of behaviors. In this review, we focus on selected advances in our understanding of the bCPG. At the core of the bCPG is the preBötzinger complex (preBötC), which drives inspiratory rhythm via an unexpectedly sophisticated emergent mechanism. Synchronization dynamics underlying preBötC rhythmogenesis imbue the system with robustness and lability. These dynamics are modulated by inputs from throughout the brain and generate rhythmic, patterned activity that is widely distributed. The connectivity and an emerging literature support a link between breathing, emotion, and cognition that is becoming experimentally tractable. These advances bring great potential for elucidating function and dysfunction in breathing and other mammalian neural circuits.

Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration

In this work, we consider a mathematical model describing spontaneous calcium signaling in astrocytes. Based on biologically relevant principles, this model simulates experimentally observed calcium oscillations and can predict the emergence of complicated dynamics. Using analytical and numerical analysis, various attracting sets were found and investigated. Employing bifurcation theory analysis, we examined steady state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors. We found that astrocytes possess a variety of complex dynamical modes, including chaos and multistability, that can further provide different modulations of neuronal circuits, enhancing their plasticity and flexibility.

Putting the theory into 'burstlet theory' with a biophysical model of burstlets and bursts in the respiratory preBötzinger complex

Inspiratory breathing rhythms arise from synchronized neuronal activity in a bilaterally distributed brainstem structure known as the preBötzinger complex (preBötC). In in vitro slice preparations containing the preBötC, extracellular potassium must be elevated above physiological levels (to 7-9 mM) to observe regular rhythmic respiratory motor output in the hypoglossal nerve to which the preBötC projects. Reexamination of how extracellular K+ affects preBötC neuronal activity has revealed that low-amplitude oscillations persist at physiological levels. These oscillatory events are subthreshold from the standpoint of transmission to motor output and are dubbed burstlets. Burstlets arise from synchronized neural activity in a rhythmogenic neuronal subpopulation within the preBötC that in some instances may fail to recruit the larger network events, or bursts, required to generate motor output. The fraction of subthreshold preBötC oscillatory events (burstlet fraction) decreases sigmoidally with increasing extracellular potassium. These observations underlie the burstlet theory of respiratory rhythm generation. Experimental and computational studies have suggested that recruitment of the non-rhythmogenic component of the preBötC population requires intracellular Ca2+ dynamics and activation of a calcium-activated nonselective cationic current. In this computational study, we show how intracellular calcium dynamics driven by synaptically triggered Ca2+ influx as well as Ca2+ release/uptake by the endoplasmic reticulum in conjunction with a calcium-activated nonselective cationic current can reproduce and offer an explanation for many of the key properties associated with the burstlet theory of respiratory rhythm generation. Altogether, our modeling work provides a mechanistic basis that can unify a wide range of experimental findings on rhythm generation and motor output recruitment in the preBötC.

Astrocytic modulation of central pattern generating motor circuits

Central pattern generators (CPGs) generate the rhythmic and coordinated neural features necessary for the proper conduction of complex behaviors. In particular, CPGs are crucial for complex motor behaviors such as locomotion, mastication, respiration, and vocal production. While the importance of these networks in modulating behavior is evident, the mechanisms driving these CPGs are still not fully understood. On the other hand, accumulating evidence suggests that astrocytes have a significant role in regulating the function of some of these CPGs. Here, we review the location, function, and role of astrocytes in locomotion, respiration, and mastication CPGs and propose that, similarly, astrocytes may also play a significant role in the vocalization CPG.

Respiratory rhythm and pattern generation: Brainstem cellular and circuit mechanisms

Breathing movements in mammals are driven by rhythmic neural activity automatically generated within spatially and functionally organized brainstem neural circuits comprising the respiratory central pattern generator (CPG). This chapter reviews up-to-date experimental information and theoretical studies of the cellular and circuit mechanisms of respiratory rhythm and pattern generation operating within critical components of this CPG in the lower brainstem. Over the past several decades, there have been substantial advances in delineating the spatial architecture of essential medullary regions and their regional cellular and circuit properties required to understand rhythm and pattern generation mechanisms. A fundamental concept is that the circuits in these regions have rhythm-generating capabilities at multiple cellular and circuit organization levels. The regional cellular properties, circuit organization, and control mechanisms allow flexible expression of neural activity patterns for a repertoire of respiratory behaviors under various physiologic conditions that are dictated by requirements for homeostatic regulation and behavioral integration. Many mechanistic insights have been provided by computational modeling studies driven by experimental results and have advanced understanding in the field. These conceptual and theoretical developments are discussed.

Amplitude-modulated spiking as a novel route to bursting: Coupling-induced mixed-mode oscillations by symmetry breaking

Mixed-mode oscillations consisting of alternating small- and large-amplitude oscillations are increasingly well understood and are often caused by folded singularities, canard orbits, or singular Hopf bifurcations. We show that coupling between identical nonlinear oscillators can cause mixed-mode oscillations because of symmetry breaking. This behavior is illustrated for diffusively coupled FitzHugh-Nagumo oscillators with negative coupling constant, and we show that it is caused by a singular Hopf bifurcation related to a folded saddle-node (FSN) singularity. Inspired by earlier work on models of pancreatic beta-cells [Sherman, Bull. Math. Biol. 56, 811 (1994)], we then identify a new type of bursting dynamics due to diffusive coupling of cells firing action potentials when isolated. In the presence of coupling, small-amplitude oscillations in the action potential height precede transitions to square-wave bursting. Confirming the hypothesis from the earlier work that this behavior is related to a pitchfork-of-limit-cycles bifurcation in the fast subsystem, we find that it is caused by symmetry breaking. Moreover, we show that it is organized by a FSN in the averaged system, which causes a singular Hopf bifurcation. Such behavior is related to the recently studied dynamics caused by the so-called torus canards.

Dynamics of ramping bursts in a respiratory neuron model

Intensive computational and theoretical work has led to the development of multiple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC) of the mammalian brainstem. Nonetheless, these previous models have not captured the pre-inspiratory ramping aspects of these neurons' activity patterns, in which relatively slow tonic spiking gradually progresses to faster spiking and a full-blown burst, with a corresponding gradual development of an underlying plateau potential. In this work, we show that the incorporation of the dynamics of the extracellular potassium ion concentration into an existing model for pre-BötC neuron bursting, along with some parameter adjustments, suffices to induce this ramping behavior. Using fast-slow decomposition, we show that this activity can be considered as a form of parabolic bursting, but with burst termination at a homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate the parameter-dependence of these solutions and show that the proposed model yields a greater dynamic range of burst frequencies, durations, and duty cycles than those produced by other models in the literature.

Dual mechanisms of opioid-induced respiratory depression in the inspiratory rhythm-generating network

The analgesic utility of opioid-based drugs is limited by the life-threatening risk of respiratory depression. Opioid-induced respiratory depression (OIRD), mediated by the μ-opioid receptor (MOR), is characterized by a pronounced decrease in the frequency and regularity of the inspiratory rhythm, which originates from the medullary preBötzinger Complex (preBötC). To unravel the cellular- and network-level consequences of MOR activation in the preBötC, MOR-expressing neurons were optogenetically identified and manipulated in transgenic mice in vitro and in vivo. Based on these results, a model of OIRD was developed in silico. We conclude that hyperpolarization of MOR-expressing preBötC neurons alone does not phenocopy OIRD. Instead, the effects of MOR activation are twofold: (1) pre-inspiratory spiking is reduced and (2) excitatory synaptic transmission is suppressed, thereby disrupting network-driven rhythmogenesis. These dual mechanisms of opioid action act synergistically to make the normally robust inspiratory rhythm-generating network particularly prone to collapse when challenged with exogenous opioids.

Period-doubling route to mixed-mode chaos

Mixed-mode oscillations (MMOs) are a complex dynamical behavior in which each cycle of oscillation consists of one or more large amplitude spikes followed by one or more small amplitude peaks. MMOs typically undergo period-adding bifurcations under parameter variation. We demonstrate here, in a set of three identical, linearly coupled van der Pol oscillators, a scenario in which MMOs exhibit a period-doubling sequence to chaos that preserves the MMO structure, as well as period-adding bifurcations. We characterize the chaotic nature of the MMOs and attribute their existence to a master-slave-like forcing of the inner oscillator by the outer two with a sufficient phase difference between them. Simulations of a single nonautonomous oscillator forced by two sine functions support this interpretation and suggest that the MMO period-doubling scenario may be more general.

The Refractory Period Matters: Unifying Mechanisms of Macroscopic Brain Waves

The relationship between complex brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize maximum caliber, a dynamical inference principle, to build a minimal yet general model of the collective (mean field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a single type of neuron, by which many of these complex oscillatory patterns may emerge. Our model predicts that the refractory period of neurons, which has often been neglected, is essential for these behaviors.

Configuration and dynamics of dominant inspiratory multineuronal activity patterns during eupnea and gasping generation in vitro

The pre-Bötzinger complex (preBötC), located within the ventral respiratory column, produces inspiratory bursts in varying degrees of synchronization/amplitude. This wide range of population burst patterns reflects the flexibility of the preBötC neurons, which is expressed in variations in the onset/offset times of their activations and their activity during the population bursts, with respiratory neurons exhibiting a large cycle-to-cycle timing jitter both at the population activity onset and at the population activity peak, suggesting that respiratory neurons are stochastically activated before and during the inspiratory bursts. However, it is still unknown whether this stochasticity is maintained while evaluating the coactivity of respiratory neuronal ensembles. Moreover, the preBötC topology also remains unknown. In this study, by simultaneously recording tens of preBötC neurons and using coactivation analysis during the inspiratory periods, we found that the preBötC has a scale-free configuration (mixture of not many highly connected nodes, hubs, with abundant poorly connected elements) exhibiting the rich-club phenomenon (hubs more likely interconnected with each other). PreBötC neurons also produce multineuronal activity patterns (MAPs) that are highly stable and change during the hypoxia-induced reconfiguration. Moreover, preBötC contains a coactivating core network shared by all its MAPs. Finally, we found a distinctive pattern of sequential coactivation of core network neurons at the beginning of the inspiratory periods, indicating that, when evaluated at the multicellular level, the coactivation of respiratory neurons seems not to be stochastic.NEW & NOTEWORTHY By means of multielectrode recordings of preBötC neurons, we evaluated their configuration in normoxia and hypoxia, finding that the preBötC exhibits a scale-free configuration with a rich-club phenomenon. preBötC neurons produce multineuronal activity patterns that are highly stable but change during hypoxia. The preBötC contains a coactivating core network that exhibit a distinctive pattern of coactivation at the beginning of inspirations. These results reveal some network basis of inspiratory rhythm generation and its reconfiguration during hypoxia.

Neural Interactions in Developing Rhythmogenic Spinal Networks: Insights From Computational Modeling

The mechanisms involved in generation of rhythmic locomotor activity in the mammalian spinal cord remain poorly understood. These mechanisms supposedly rely on both intrinsic properties of constituting neurons and interactions between them. A subset of Shox2 neurons was suggested to contribute to generation of spinal locomotor activity, but the possible cellular basis for rhythmic bursting in these neurons remains unknown. Ha and Dougherty (2018) recently revealed the presence of bidirectional electrical coupling between Shox2 neurons in neonatal spinal cords, which can be critically involved in neuronal synchronization and generation of populational bursting. Gap junctional connections found between functionally-related Shox2 interneurons decrease with age, possibly being replaced by increasing interactions through chemical synapses. Here, we developed a computational model of a heterogeneous population of neurons sparsely connected by electrical or/and chemical synapses and investigated the dependence of frequency of populational bursting on the type and strength of neuronal interconnections. The model proposes a mechanistic explanation that can account for the emergence of a synchronized rhythmic activity in the neuronal population and provides insights into the possible role of gap junctional coupling between Shox2 neurons in the spinal mechanisms for locomotor rhythm generation.

Neural mass modeling of slow-fast dynamics of seizure initiation and abortion

Epilepsy is a dynamic and complex neurological disease affecting about 1% of the worldwide population, among which 30% of the patients are drug-resistant. Epilepsy is characterized by recurrent episodes of paroxysmal neural discharges (the so-called seizures), which manifest themselves through a large-amplitude rhythmic activity observed in depth-EEG recordings, in particular in local field potentials (LFPs). The signature characterizing the transition to seizures involves complex oscillatory patterns, which could serve as a marker to prevent seizure initiation by triggering appropriate therapeutic neurostimulation methods. To investigate such protocols, neurophysiological lumped-parameter models at the mesoscopic scale, namely neural mass models, are powerful tools that not only mimic the LFP signals but also give insights on the neural mechanisms related to different stages of seizures. Here, we analyze the multiple time-scale dynamics of a neural mass model and explain the underlying structure of the complex oscillations observed before seizure initiation. We investigate population-specific effects of the stimulation and the dependence of stimulation parameters on synaptic timescales. In particular, we show that intermediate stimulation frequencies (>20 Hz) can abort seizures if the timescale difference is pronounced. Those results have the potential in the design of therapeutic brain stimulation protocols based on the neurophysiological properties of tissue.

Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling

In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

Canard-induced complex oscillations in an excitatory network

In Neuroscience, mathematical modelling involving multiple spatial and temporal scales can unveil complex oscillatory activity such as excitable responses to an input current, subthreshold oscillations, spiking or bursting. While the number of slow and fast variables and the geometry of the system determine the type of the complex oscillations, canard structures define boundaries between them. In this study, we use geometric singular perturbation theory to identify and characterise boundaries between different dynamical regimes in multiple-timescale firing rate models of the developing spinal cord. These rate models are either three or four dimensional with state variables chosen within an overall group of two slow and two fast variables. The fast subsystem corresponds to a recurrent excitatory network with fast activity-dependent synaptic depression, and the slow variables represent the cell firing threshold and slow activity-dependent synaptic depression, respectively. We start by demonstrating canard-induced bursting and mixed-mode oscillations in two different three-dimensional rate models. Then, in the full four-dimensional model we show that a canard-mediated slow passage creates dynamics that combine these complex oscillations and give rise to mixed-mode bursting oscillations (MMBOs). We unveil complicated isolas along which MMBOs exist in parameter space. The profile of solutions along each isola undergoes canard-mediated transitions between the sub-threshold regime and the bursting regime; these explosive transitions change the number of oscillations in each regime. Finally, we relate the MMBO dynamics to experimental recordings and discuss their effects on the silent phases of bursting patterns as well as their potential role in creating subthreshold fluctuations that are often interpreted as noise. The mathematical framework used in this paper is relevant for modelling multiple timescale dynamics in excitable systems.

Robustness of respiratory rhythm generation across dynamic regimes

A central issue in the study of the neural generation of respiratory rhythms is the role of the intrinsic pacemaking capabilities that some respiratory neurons exhibit. The debate on this issue has occurred in parallel to investigations of interactions among respiratory network neurons and how these contribute to respiratory behavior. In this computational study, we demonstrate how these two issues are inextricably linked. We use simulations and dynamical systems analysis to show that once a conditional respiratory pacemaker, which can be tuned across oscillatory and non-oscillatory dynamic regimes in isolation, is embedded into a respiratory network, its dynamics become masked: the network exhibits similar dynamical properties regardless of the conditional pacemaker node's tuning, and that node's outputs are dominated by network influences. Furthermore, the outputs of the respiratory central pattern generator as a whole are invariant to these changes of dynamical properties, which ensures flexible and robust performance over a wide dynamic range.

Reduced computational modelling of Kölliker-Fuse contributions to breathing patterns in Rett syndrome

KEY POINTS

Reduced computational models are used to test effects of loss of inhibition to the Kölliker-Fuse nucleus (KFn). Three reduced computational models that simulate eupnoeic and vagotomized respiratory rhythms are considered. All models exhibit the emergence of respiratory perturbations associated with Rett syndrome as inhibition to the KFn is diminished. Simulations suggest that application of 5-HT_1A agonists can mitigate the respiratory pathology. The three models can be distinguished and tested based on their predictions about connections and dynamics within the respiratory circuit and about effects of perturbations on certain respiratory neuron populations.

ABSTRACT

Rett syndrome (RTT) is a developmental disorder that can lead to respiratory disturbances featuring prolonged apnoeas of variable durations. Determining the mechanisms underlying these effects at the level of respiratory neural circuits would have significant implications for treatment efforts and would also enhance our understanding of respiratory rhythm generation and control. While experimental studies have suggested possible factors contributing to the respiratory patterns of RTT, we take a novel computational approach to the investigation of RTT, which allows for direct manipulation of selected system parameters and testing of specific hypotheses. Specifically, we present three reduced computational models, developed using an established framework, all of which successfully simulate respiratory outputs across eupnoeic and vagotomized conditions. All three models show that loss of inhibition to the Kölliker-Fuse nucleus reproduces the key respiratory alterations associated with RTT and, as suggested experimentally, that effects of 5-HT_1A agonists on the respiratory neural circuit suffice to alleviate this respiratory pathology. Each of the models makes distinct predictions regarding the neuronal populations and interactions underlying these effects, suggesting natural directions for future experimental testing.

Biophysical mechanisms in the mammalian respiratory oscillator re-examined with a new data-driven computational model

An autorhythmic population of excitatory neurons in the brainstem pre-Bötzinger complex is a critical component of the mammalian respiratory oscillator. Two intrinsic neuronal biophysical mechanisms—a persistent sodium current (INaP) and a calcium-activated non-selective cationic current (ICAN)—were proposed to individually or in combination generate cellular- and circuit-level oscillations, but their roles are debated without resolution. We re-examined these roles in a model of a synaptically connected population of excitatory neurons with ICAN and INaP. This model robustly reproduces experimental data showing that rhythm generation can be independent of ICAN activation, which determines population activity amplitude. This occurs when ICAN is primarily activated by neuronal calcium fluxes driven by synaptic mechanisms. Rhythm depends critically on INaP in a subpopulation forming the rhythmogenic kernel. The model explains how the rhythm and amplitude of respiratory oscillations involve distinct biophysical mechanisms.

Carotid Bodies and the Integrated Cardiorespiratory Response to Hypoxia

Advances in our understanding of brain mechanisms for the hypoxic ventilatory response, coordinated changes in blood pressure, and the long-term consequences of chronic intermittent hypoxia as in sleep apnea, such as hypertension and heart failure, are giving impetus to the search for therapies to "erase" dysfunctional memories distributed in the carotid bodies and central nervous system. We review current network models, open questions, sex differences, and implications for translational research.

Kinetic properties of persistent Na+ current orchestrate oscillatory bursting in respiratory neurons

The rhythmic pattern of breathing depends on the pre-Bötzinger complex (preBötC) in the brainstem, a vital circuit that contains a population of neurons with intrinsic oscillatory bursting behavior. Here, we investigate the specific kinetic properties that enable voltage-gated sodium channels to establish oscillatory bursting in preBötC inspiratory neurons, which exhibit an unusually large persistent Na⁺ current (I_NaP). We first characterize the kinetics of I_NaP in neonatal rat brainstem slices in vitro, using whole-cell patch-clamp and computational modeling, and then test the contribution of I_NaP to rhythmic bursting in live neurons, using the dynamic clamp technique. We provide evidence that subthreshold activation, persistence at suprathreshold potentials, slow inactivation, and slow recovery from inactivation are kinetic features of I_NaP that regulate all aspects of intrinsic rhythmic bursting in preBötC neurons. The slow and cumulative inactivation of I_NaP during the burst active phase controls burst duration and termination, while the slow recovery from inactivation controls the duration of the interburst interval. To demonstrate this mechanism, we develop a Markov state model of I_NaP that explains a comprehensive set of voltage clamp data. By adding or subtracting a computer-generated I_NaP from a live neuron via dynamic clamp, we are able to convert nonbursters into intrinsic bursters, and vice versa. As a control, we test a model with inactivation features removed. Adding noninactivating I_NaP into nonbursters results in a pattern of random transitions between sustained firing and quiescence. The relative amplitude of I_NaP is the key factor that separates intrinsic bursters from nonbursters and can change the fraction of intrinsic bursters in the preBötC. I_NaP could thus be an important target for regulating network rhythmogenic properties.

The Dynamic Basis of Respiratory Rhythm Generation: One Breath at a Time

Rhythmicity is a universal timing mechanism in the brain, and the rhythmogenic mechanisms are generally dynamic. This is illustrated for the neuronal control of breathing, a behavior that occurs as a one-, two-, or three-phase rhythm. Each breath is assembled stochastically, and increasing evidence suggests that each phase can be generated independently by a dedicated excitatory microcircuit. Within each microcircuit, rhythmicity emerges through three entangled mechanisms: ( a) glutamatergic transmission, which is amplified by ( b) intrinsic bursting and opposed by ( c) concurrent inhibition. This rhythmogenic triangle is dynamically tuned by neuromodulators and other network interactions. The ability of coupled oscillators to reconfigure and recombine may allow breathing to remain robust yet plastic enough to conform to nonventilatory behaviors such as vocalization, swallowing, and coughing. Lessons learned from the respiratory network may translate to other highly dynamic and integrated rhythmic systems, if approached one breath at a time.

Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons

Neural networks generate a variety of rhythmic activity patterns, often involving different timescales. One example arises in the respiratory network in the pre-Bötzinger complex of the mammalian brainstem, which can generate the eupneic rhythm associated with normal respiration as well as recurrent low-frequency, large-amplitude bursts associated with sighing. Two competing hypotheses have been proposed to explain sigh generation: the recruitment of a neuronal population distinct from the eupneic rhythm-generating subpopulation or the reconfiguration of activity within a single population. Here, we consider two recent computational models, one of which represents each of the hypotheses. We use methods of dynamical systems theory, such as fast-slow decomposition, averaging, and bifurcation analysis, to understand the multiple-timescale mechanisms underlying sigh generation in each model. In the course of our analysis, we discover that a third timescale is required to generate sighs in both models. Furthermore, we identify the similarities of the underlying mechanisms in the two models and the aspects in which they differ.