Multiple rhythmic states in a model of the respiratory central pattern generator

Respiratory rhythm generation in vivo

The cellular and circuit mechanisms generating the rhythm of breathing in mammals have been under intense investigation for decades. Here, we try to integrate the key discoveries into an updated description of the basic neural processes generating respiratory rhythm under in vivo conditions.

The cellular building blocks of breathing

Respiratory brainstem neurons fulfill critical roles in controlling breathing: they generate the activity patterns for breathing and contribute to various sensory responses including changes in O2 and CO2. These complex sensorimotor tasks depend on the dynamic interplay between numerous cellular building blocks that consist of voltage-, calcium-, and ATP-dependent ionic conductances, various ionotropic and metabotropic synaptic mechanisms, as well as neuromodulators acting on G-protein coupled receptors and second messenger systems. As described in this review, the sensorimotor responses of the respiratory network emerge through the state-dependent integration of all these building blocks. There is no known respiratory function that involves only a small number of intrinsic, synaptic, or modulatory properties. Because of the complex integration of numerous intrinsic, synaptic, and modulatory mechanisms, the respiratory network is capable of continuously adapting to changes in the external and internal environment, which makes breathing one of the most integrated behaviors. Not surprisingly, inspiration is critical not only in the control of ventilation, but also in the context of "inspiring behaviors" such as arousal of the mind and even creativity. Far-reaching implications apply also to the underlying network mechanisms, as lessons learned from the respiratory network apply to network functions in general.

Resuscitation and auto resuscitation by airway reflexes in animals

Various diseases often result in decompensation requiring resuscitation. In infants moderate hypoxia evokes a compensatory augmented breath - sigh and more severe hypoxia results in a solitary gasp. Progressive asphyxia provokes gasping respiration saving the healthy infant - autoresuscitation by gasping. A neonate with sudden infant death syndrome, however, usually will not survive. Our systematic research in animals indicated that airway reflexes have similar resuscitation potential as gasping respiration. Nasopharyngeal stimulation in cats and most mammals evokes the aspiration reflex, characterized by spasmodic inspiration followed by passive expiration. On the contrary, expiration reflex from the larynx, or cough reflex from the pharynx and lower airways manifest by a forced expiration, which in cough is preceded by deep inspiration. These reflexes of distinct character activate the brainstem rhythm generators for inspiration and expiration strongly, but differently. They secondarily modulate the control mechanisms of various vital functions of the organism. During severe asphyxia the progressive respiratory insufficiency may induce a life-threatening cardio-respiratory failure. The sniff- and gasp-like aspiration reflex and similar spasmodic inspirations, accompanied by strong sympatho-adrenergic activation, can interrupt a severe asphyxia and reverse the developing dangerous cardiovascular and vasomotor dysfunctions, threatening with imminent loss of consciousness and death. During progressive asphyxia the reversal of gradually developing bradycardia and excessive hypotension by airway reflexes starts with reflex tachycardia and vasoconstriction, resulting in prompt hypertensive reaction, followed by renewal of cortical activity and gradual normalization of breathing. A combination of the aspiration reflex supporting venous return and the expiration or cough reflex increasing the cerebral perfusion by strong expirations, provides a powerful resuscitation and autoresuscitation potential, proved in animal experiments. They represent a simple but unique model tested in animal experiments.

Structural-functional properties of identified excitatory and inhibitory interneurons within pre-Botzinger complex respiratory microcircuits

We comparatively analyzed cellular and circuit properties of identified rhythmic excitatory and inhibitory interneurons within respiratory microcircuits of the neonatal rodent pre-Bötzinger complex (pre-BötC), the structure generating inspiratory rhythm in the brainstem. We combined high-resolution structural-functional imaging, molecular assays for neurotransmitter phenotype identification in conjunction with electrophysiological property phenotyping, and morphological reconstruction of interneurons in neonatal rat and mouse slices in vitro. This approach revealed previously undifferentiated structural-functional features that distinguish excitatory and inhibitory interneuronal populations. We identified distinct subpopulations of pre-BötC glutamatergic, glycinergic, GABAergic, and glycine-GABA coexpressing interneurons. Most commissural pre-BötC inspiratory interneurons were glutamatergic, with a substantial subset exhibiting intrinsic oscillatory bursting properties. Commissural excitatory interneurons projected with nearly planar trajectories to the contralateral pre-BötC, many also with axon collaterals to areas containing inspiratory hypoglossal (XII) premotoneurons and motoneurons. Inhibitory neurons as characterized in the present study did not exhibit intrinsic oscillatory bursting properties, but were electrophysiologically distinguished by more pronounced spike frequency adaptation properties. Axons of many inhibitory neurons projected ipsilaterally also to regions containing inspiratory XII premotoneurons and motoneurons, whereas a minority of inhibitory neurons had commissural axonal projections. Dendrites of both excitatory and inhibitory interneurons were arborized asymmetrically, primarily in the coronal plane. The dendritic fields of inhibitory neurons were more spatially compact than those of excitatory interneurons. Our results are consistent with the concepts of a compartmental circuit organization, a bilaterally coupled excitatory rhythmogenic kernel, and a role of pre-BötC inhibitory neurons in shaping inspiratory pattern as well as coordinating inspiratory and expiratory activity.

Control of breathing by interacting pontine and pulmonary feedback loops

The medullary respiratory network generates respiratory rhythm via sequential phase switching, which in turn is controlled by multiple feedbacks including those from the pons and nucleus tractus solitarii; the latter mediates pulmonary afferent feedback to the medullary circuits. It is hypothesized that both pontine and pulmonary feedback pathways operate via activation of medullary respiratory neurons that are critically involved in phase switching. Moreover, the pontine and pulmonary control loops interact, so that pulmonary afferents control the gain of pontine influence of the respiratory pattern. We used an established computational model of the respiratory network (Smith et al., 2007) and extended it by incorporating pontine circuits and pulmonary feedback. In the extended model, the pontine neurons receive phasic excitatory activation from, and provide feedback to, medullary respiratory neurons responsible for the onset and termination of inspiration. The model was used to study the effects of: (1) "vagotomy" (removal of pulmonary feedback), (2) suppression of pontine activity attenuating pontine feedback, and (3) these perturbations applied together on the respiratory pattern and durations of inspiration (T(I)) and expiration (T(E)). In our model: (a) the simulated vagotomy resulted in increases of both T(I) and T(E), (b) the suppression of pontine-medullary interactions led to the prolongation of T(I) at relatively constant, but variable T(E), and (c) these perturbations applied together resulted in "apneusis," characterized by a significantly prolonged T(I). The results of modeling were compared with, and provided a reasonable explanation for, multiple experimental data. The characteristic changes in T(I) and T(E) demonstrated with the model may represent characteristic changes in the balance between the pontine and pulmonary feedback control mechanisms that may reflect specific cardio-respiratory disorders and diseases.

Spontaneous autoresuscitation in a model of respiratory control

We introduce a closed-loop model of respiratory control incorporating a conductance-based central pattern generator (CPG), low-pass filtering of CPG output by the respiratory musculature, gas exchange in the lung, metabolic oxygen demand, and chemosensation. The CPG incorporates Butera, Rinzel and Smith (BRS)'s (1999) conditional pacemaker model. BRS model cells can support quiescent, bursting, or beating activity depending on the level of excitatory drive; we identify these activity modes with apnea (cessation of breathing), eupnea (normal breathing), and tachypnea (excessively rapid breathing). We demonstrate the coexistence of two dynamically stable behaviors in the closed-loop model, corresponding respectively to eupnea and tachypnea. The latter state represents a novel failure mode within a respiratory control model. In addition, the closed-loop system exhibits a form of autoresuscitation: conductances intrinsic to the BRS model buffer the CPG against brief episodes of hypoxia, steering the system away from catastrophic collapse as can occur with tachypnea.

Brainstem respiratory networks: building blocks and microcircuits

Breathing movements in mammals are driven by rhythmic neural activity generated within spatially and functionally organized brainstem neural circuits comprising the respiratory central pattern generator (CPG). This rhythmic activity provides homeostatic regulation of gases in blood and tissues and integrates breathing with other motor acts. We review new insights into the spatial-functional organization of key neural microcircuits of this CPG from recent multidisciplinary experimental and computational studies. The emerging view is that the microcircuit organization within the CPG allows the generation of multiple rhythmic breathing patterns and adaptive switching between them, depending on physiological or pathophysiological conditions. These insights open the possibility for site- and mechanism-specific interventions to treat various disorders of the neural control of breathing.

Understanding the rhythm of breathing: so near, yet so far

Breathing is an essential behavior that presents a unique opportunity to understand how the nervous system functions normally, how it balances inherent robustness with a highly regulated lability, how it adapts to both rapidly and slowly changing conditions, and how particular dysfunctions result in disease. We focus on recent advancements related to two essential sites for respiratory rhythmogenesis: (a) the preBötzinger Complex (preBötC) as the site for the generation of inspiratory rhythm and (b) the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) as the site for the generation of active expiration.

Patterns of inspiratory phase-dependent activity in the in vitro respiratory network

Mechanistic descriptions of rhythmogenic neural networks have often relied on ball-and-stick diagrams, which define interactions between functional classes of cells assumed to be reasonably homogenous. Application of this formalism to networks underlying respiratory rhythm generation in mammals has produced increasingly intricate models that have generated significant insight, but the underlying assumption that individual cells within these network fall into distinct functional classes has not been rigorously tested. In the present study we used multiunit extracellular recording in the in vitro pre-Bötzinger complex to identify and characterize the rhythmic activity of 951 cells. Inspiratory phase-dependent activity was estimated for all cells, and the data set as a whole was analyzed with principal component analysis, nonlinear dimensionality reduction, and hierarchical clustering techniques. None of these techniques revealed categorically distinct functional cell classes, indicating instead that the behavior of these cells within the network falls along several continua of spiking behavior.

Computational models and emergent properties of respiratory neural networks

Computational models of the neural control system for breathing in mammals provide a theoretical and computational framework bringing together experimental data obtained from different animal preparations under various experimental conditions. Many of these models were developed in parallel and iteratively with experimental studies and provided predictions guiding new experiments. This data-driven modeling approach has advanced our understanding of respiratory network architecture and neural mechanisms underlying generation of the respiratory rhythm and pattern, including their functional reorganization under different physiological conditions. Models reviewed here vary in neurobiological details and computational complexity and span multiple spatiotemporal scales of respiratory control mechanisms. Recent models describe interacting populations of respiratory neurons spatially distributed within the Bötzinger and pre-Bötzinger complexes and rostral ventrolateral medulla that contain core circuits of the respiratory central pattern generator (CPG). Network interactions within these circuits along with intrinsic rhythmogenic properties of neurons form a hierarchy of multiple rhythm generation mechanisms. The functional expression of these mechanisms is controlled by input drives from other brainstem components,including the retrotrapezoid nucleus and pons, which regulate the dynamic behavior of the core circuitry. The emerging view is that the brainstem respiratory network has rhythmogenic capabilities at multiple levels of circuit organization. This allows flexible, state-dependent expression of different neural pattern-generation mechanisms under various physiological conditions,enabling a wide repertoire of respiratory behaviors. Some models consider control of the respiratory CPG by pulmonary feedback and network reconfiguration during defensive behaviors such as cough. Future directions in modeling of the respiratory CPG are considered.

Irregular Breathing in Mice following Genetic Ablation of V2a Neurons

Neural networks called central pattern generators (CPGs) generate repetitive motor behaviors such as locomotion and breathing. Glutamatergic neurons are required for the generation and inhibitory neurons for the patterning of the motor activity associated with repetitive motor behaviors. In the mouse, glutamatergic V2a neurons coordinate the activity of left and right leg CPGs in the spinal cord enabling mice to generate an alternating gait. Here, we investigate the role of V2a neurons in the neural control of breathing, an essential repetitive motor behavior. We find that, following the ablation of V2a neurons, newborn mice breathe at a lower frequency. Recordings of respiratory activity in brainstem-spinal cord and respiratory slice preparations demonstrate that mice lacking V2a neurons are deficient in central respiratory rhythm generation. The absence of V2a neurons in the respiratory slice preparation can be compensated for by bath application of neurochemicals known to accelerate the breathing rhythm. In this slice preparation, V2a neurons exhibit a tonic firing pattern. The existence of direct connections between V2a neurons in the medial reticular formation and neurons of the pre-Bötzinger complex indicates that V2a neurons play a direct role in the function of the respiratory CPG in newborn mice. Thus, neurons of the embryonic V2a lineage appear to have been recruited to neural networks that control breathing and locomotion, two prominent CPG-driven, repetitive motor behaviors.

Pre-Bötzinger complex receives glutamatergic innervation from galaninergic and other retrotrapezoid nucleus neurons

The retrotrapezoid nucleus (RTN) contains CO(2) -responsive neurons that regulate breathing frequency and amplitude. These neurons (RTN-Phox2b neurons) contain the transcription factor Phox2b, vesicular glutamate transporter 2 (VGLUT2) mRNA, and a subset contains preprogalanin mRNA. We wished to determine whether the terminals of RTN-Phox2b neurons contain galanin and VGLUT2 proteins, to identify the specific projections of the galaninergic subset, to test whether RTN-Phox2b neurons contact neurons in the pre-Bötzinger complex, and to identify the ultrastructure of these synapses. The axonal projections of RTN-Phox2b neurons were traced by using biotinylated dextran amine (BDA), and many BDA-ir boutons were found to contain galanin immunoreactivity. RTN galaninergic neurons had ipsilateral projections that were identical with those of this nucleus at large: the ventral respiratory column, the caudolateral nucleus of the solitary tract, and the pontine Kölliker-Fuse, intertrigeminal region, and lateral parabrachial nucleus. For ultrastructural studies, RTN-Phox2b neurons (galaninergic and others) were transfected with a lentiviral vector that expresses mCherry almost exclusively in Phox2b-ir neurons. After spinal cord injections of a catecholamine neuron-selective toxin, there was a depletion of C1 neurons in the RTN area; thus it was determined that the mCherry-positive terminals located in the pre-Bötzinger complex originated almost exclusively from the RTN-Phox2b (non-C1) neurons. These terminals were generally VGLUT2-immunoreactive and formed numerous close appositions with neurokinin-1 receptor-ir pre-Bötzinger complex neurons. Their boutons (n = 48) formed asymmetric synapses filled with small clear vesicles. In summary, RTN-Phox2b neurons, including the galaninergic subset, selectively innervate the respiratory pattern generator plus a portion of the dorsolateral pons. RTN-Phox2b neurons establish classic excitatory glutamatergic synapses with pre-Bötzinger complex neurons presumed to generate the respiratory rhythm.

Explicit maps to predict activation order in multiphase rhythms of a coupled cell network

We present a novel extension of fast-slow analysis of clustered solutions to coupled networks of three cells, allowing for heterogeneity in the cells' intrinsic dynamics. In the model on which we focus, each cell is described by a pair of first-order differential equations, which are based on recent reduced neuronal network models for respiratory rhythmogenesis. Within each pair of equations, one dependent variable evolves on a fast time scale and one on a slow scale. The cells are coupled with inhibitory synapses that turn on and off on the fast time scale. In this context, we analyze solutions in which cells take turns activating, allowing any activation order, including multiple activations of two of the cells between successive activations of the third. Our analysis proceeds via the derivation of a set of explicit maps between the pairs of slow variables corresponding to the non-active cells on each cycle. We show how these maps can be used to determine the order in which cells will activate for a given initial condition and how evaluation of these maps on a few key curves in their domains can be used to constrain the possible activation orders that will be observed in network solutions. Moreover, under a small set of additional simplifying assumptions, we collapse the collection of maps into a single 2D map that can be computed explicitly. From this unified map, we analytically obtain boundary curves between all regions of initial conditions producing different activation patterns.

Interaction between telencephalic signals and respiratory dynamics in songbirds

The mechanisms by which telencephalic areas affect motor activities are largely unknown. They could either take over motor control from downstream motor circuits or interact with the intrinsic dynamics of these circuits. Both models have been proposed for telencephalic control of respiration during learned vocal behavior in birds. The interactive model postulates that simple signals from the telencephalic song control areas are sufficient to drive the nonlinear respiratory network into producing complex temporal sequences. We tested this basic assumption by electrically stimulating telencephalic song control areas and analyzing the resulting respiratory patterns in zebra finches and in canaries. We found strong evidence for interaction between the rhythm of stimulation and the intrinsic respiratory rhythm, including naturally emerging subharmonic behavior and integration of lateralized telencephalic input. The evidence for clear interaction in our experimental paradigm suggests that telencephalic vocal control also uses a similar mechanism. Furthermore, species differences in the response of the respiratory system to stimulation show parallels to differences in the respiratory patterns of song, suggesting that the interactive production of respiratory rhythms is manifested in species-specific specialization of the involved circuitry.

Small is beautiful: models of small neuronal networks

Modeling has contributed a great deal to our understanding of how individual neurons and neuronal networks function. In this review, we focus on models of the small neuronal networks of invertebrates, especially rhythmically active CPG networks. Models have elucidated many aspects of these networks, from identifying key interacting membrane properties to pointing out gaps in our understanding, for example missing neurons. Even the complex CPGs of vertebrates, such as those that underlie respiration, have been reduced to small network models to great effect. Modeling of these networks spans from simplified models, which are amenable to mathematical analyses, to very complicated biophysical models. Some researchers have now adopted a population approach, where they generate and analyze many related models that differ in a few to several judiciously chosen free parameters; often these parameters show variability across animals and thus justify the approach. Models of small neuronal networks will continue to expand and refine our understanding of how neuronal networks in all animals program motor output, process sensory information and learn.

Phox2b-expressing neurons of the parafacial region regulate breathing rate, inspiration, and expiration in conscious rats

The retrotrapezoid nucleus contains Phox2b-expressing glutamatergic neurons (RTN-Phox2b neurons) that regulate breathing in a CO₂-dependent manner. Here we use channelrhodopsin-based optogenetics to explore how these neurons control breathing in conscious and anesthetized adult rats. Respiratory entrainment (pacing) of breathing frequency (fR) was produced over 57% (anesthetized) and 28% (conscious) of the natural frequency range by burst activation of RTN-Phox2b neurons (3-8 × 0.5-20 ms pulses at 20 Hz). In conscious rats, pacing under normocapnic conditions increased tidal volume (V(T)) and each inspiration was preceded by active expiration, denoting abdominal muscle contraction. During long-term pacing V(T) returned to prestimulation levels, suggesting that central chemoreceptors such as RTN-Phox2b neurons regulate V(T) partly independently of their effect on fR. Randomly applied light trains reset the respiratory rhythm and shortened the expiratory phase when the stimulus coincided with late-inspiration or early-expiration. Importantly, continuous (20 Hz) photostimulation of the RTN-Phox2b neurons and a saturating CO₂ concentration produced similar effects on breathing that were much larger than those elicited by phasic RTN stimulation. In sum, consistent with their anatomical projections, RTN-Phox2b neurons regulate lung ventilation by controlling breathing frequency, inspiration, and active expiration. Adult RTN-Phox2b neurons can entrain the respiratory rhythm if their discharge is artificially synchronized, but continuous activation of these neurons is much more effective at increasing lung ventilation. These results suggest that RTN-Phox2b neurons are no longer rhythmogenic in adulthood and that their average discharge rate may be far more important than their discharge pattern in driving lung ventilation.

Drive latencies in hypoglossal motoneurons indicate developmental change in the brainstem respiratory network

The respiratory rhythm originates and diverges from the brainstem to drive thousands of motoneurons that are responsible for control of the diaphragm, intercostals and upper airway. These motoneurons are known to have a wide range of phase relationships, even within a single motoneuron pool. The proposed source of this rhythm, the preBötzinger complex (preBötC), responds to an array of developmental changes in the first days post-birth, specifically at postnatal day 3 (P3). We hypothesize that such developmental changes in the preBötC have a direct effect on motoneuron phase relationships and should be detectable around age P3. To test our hypothesis, we obtained single- and dual-voltage-clamp recordings of hypoglossal motoneurons in an in vitro slice preparation. We introduce a novel approach to analyzing the phase relationships between motoneurons by using cross-correlation analysis to determine the drive latencies. This analysis reveals that the distribution of drive latencies undergoes a significant change at or before age P3. We use a computational model of the in vitro slice to demonstrate the observed phase differences and hypothesize that network heterogeneity alone may not be sufficient to explain them. Through simulations, we show the effects on the preBötC of different network characteristics such as clustering and common inputs.

Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

The preBötzinger complex (preBötC) is a heterogeneous neuronal network within the mammalian brainstem that has been experimentally found to generate robust, synchronous bursts that drive the inspiratory phase of the respiratory rhythm. The persistent sodium (NaP) current is observed in every preBötC neuron, and significant modeling effort has characterized its contribution to square-wave bursting in the preBötC. Recent experimental work demonstrated that neurons within the preBötC are endowed with a calcium-activated nonspecific cationic (CAN) current that is activated by a signaling cascade initiated by glutamate. In a preBötC model, the CAN current was shown to promote robust bursts that experience depolarization block (DB bursts). We consider a self-coupled model neuron, which we represent as a single compartment based on our experimental finding of electrotonic compactness, under variation of g (NaP), the conductance of the NaP current, and g (CAN), the conductance of the CAN current. Varying these two conductances yields a spectrum of activity patterns, including quiescence, tonic activity, square-wave bursting, DB bursting, and a novel mixture of square-wave and DB bursts, which match well with activity that we observe in experimental preparations. We elucidate the mechanisms underlying these dynamics, as well as the transitions between these regimes and the occurrence of bistability, by applying the mathematical tools of bifurcation analysis and slow-fast decomposition. Based on the prevalence of NaP and CAN currents, we expect that the generalizable framework for modeling their interactions that we present may be relevant to the rhythmicity of other brain areas beyond the preBötC as well.

Control of vocal and respiratory patterns in birdsong: dissection of forebrain and brainstem mechanisms using temperature

Learned motor behaviors require descending forebrain control to be coordinated with midbrain and brainstem motor systems. In songbirds, such as the zebra finch, regular breathing is controlled by brainstem centers, but when the adult songbird begins to sing, its breathing becomes tightly coordinated with forebrain-controlled vocalizations. The periods of silence (gaps) between song syllables are typically filled with brief breaths, allowing the bird to sing uninterrupted for many seconds. While substantial progress has been made in identifying the brain areas and pathways involved in vocal and respiratory control, it is not understood how respiratory and vocal control is coordinated by forebrain motor circuits. Here we combine a recently developed technique for localized brain cooling, together with recordings of thoracic air sac pressure, to examine the role of cortical premotor nucleus HVC (proper name) in respiratory-vocal coordination. We found that HVC cooling, in addition to slowing all song timescales as previously reported, also increased the duration of expiratory pulses (EPs) and inspiratory pulses (IPs). Expiratory pulses, like song syllables, were stretched uniformly by HVC cooling, but most inspiratory pulses exhibited non-uniform stretch of pressure waveform such that the majority of stretch occurred late in the IP. Indeed, some IPs appeared to change duration by the earlier or later truncation of an underlying inspiratory event. These findings are consistent with the idea that during singing the temporal structure of EPs is under the direct control of forebrain circuits, whereas that of IPs can be strongly influenced by circuits downstream of HVC, likely in the brainstem. An analysis of the temporal jitter of respiratory and vocal structure suggests that IPs may be initiated by HVC at the end of each syllable and terminated by HVC immediately before the onset of the next syllable.

Computational modelling of 5-HT receptor-mediated reorganization of the brainstem respiratory network

Brainstem respiratory neurons express the glycine α(3) receptor (Glyα(3) R), which is a target of modulation by several serotonin (5-HT) receptor agonists. Application of the 5-HT(1A) receptor (5-HT(1A) R) agonist 8-OH-DPAT was shown (i) to depress cellular cAMP, leading to dephosphorylation of Glyα(3) R and augmentation of postsynaptic inhibition of neurons expressing Glyα(3) R (Manzke et al., 2010) and (ii) to hyperpolarize respiratory neurons through 5-HT-activated potassium channels. These processes counteract opioid-induced depression and restore breathing from apnoeas often accompanying pharmacotherapy of pain. The effect is postulated to rely on the enhanced Glyα(3) R-mediated inhibition of inhibitory neurons causing disinhibition of their target neurons. To evaluate this proposal and investigate the neural mechanisms involved, an established computational model of the brainstem respiratory network (Smith et al., 2007), was extended by (i) incorporating distinct subpopulations of inhibitory neurons (glycinergic and GABAergic) and their synaptic interconnections within the Bötzinger and pre-Bötzinger complexes and (ii) assigning the 5-HT(1A) R-Glyα(3) R complex to some of these inhibitory neuron types in the network. The modified model was used to simulate the effects of 8-OH-DPAT on the respiratory pattern and was able to realistically reproduce a number of experimentally observed responses, including the shift in the onset of post-inspiratory activity to inspiration and conversion of the eupnoeic three-phase rhythmic pattern into a two-phase pattern lacking the post-inspiratory phase. The model shows how 5-HT(1A) R activation can produce a disinhibition of inspiratory neurons, leading to the recovery of respiratory rhythm from opioid-induced apnoeas.

Sequentially firing neurons confer flexible timing in neural pattern generators

Neuronal networks exhibit a variety of complex spatiotemporal patterns that include sequential activity, synchrony, and wavelike dynamics. Inhibition is the primary means through which such patterns are implemented. This behavior is dependent on both the intrinsic dynamics of the individual neurons as well as the connectivity patterns. Many neural circuits consist of networks of smaller subcircuits (motifs) that are coupled together to form the larger system. In this paper, we consider a particularly simple motif, comprising purely inhibitory interactions, which generates sequential periodic dynamics. We first describe the dynamics of the single motif both for general balanced coupling (all cells receive the same number and strength of inputs) and then for a specific class of balanced networks: circulant systems. We couple these motifs together to form larger networks. We use the theory of weak coupling to derive phase models which, themselves, have a certain structure and symmetry. We show that this structure endows the coupled system with the ability to produce arbitrary timing relationships between symmetrically coupled motifs and that the phase relationships are robust over a wide range of frequencies. The theory is applicable to many other systems in biology and physics.

The interaction of intrinsic dynamics and network topology in determining network burst synchrony

The pre-Bötzinger complex (pre-BötC), within the mammalian respiratory brainstem, represents an ideal system for investigating the synchronization properties of complex neuronal circuits via the interaction of cell-type heterogeneity and network connectivity. In isolation, individual respiratory neurons from the pre-BötC may be tonically active, rhythmically bursting, or quiescent. Despite this intrinsic heterogeneity, coupled networks of pre-BötC neurons en bloc engage in synchronized bursting that can drive inspiratory motor neuron activation. The region's connection topology has been recently characterized and features dense clusters of cells with occasional connections between clusters. We investigate how the dynamics of individual neurons (quiescent/bursting/tonic) and the betweenness centrality of neurons' positions within the network connectivity graph interact to govern network burst synchrony, by simulating heterogeneous networks of computational model pre-BötC neurons. Furthermore, we compare the prevalence and synchrony of bursting across networks constructed with a variety of connection topologies, analyzing the same collection of heterogeneous neurons in small-world, scale-free, random, and regularly structured networks. We find that several measures of network burst synchronization are determined by interactions of network topology with the intrinsic dynamics of neurons at central network positions and by the strengths of synaptic connections between neurons. Surprisingly, despite the functional role of synchronized bursting within the pre-BötC, we find that synchronized network bursting is generally weakest when we use its specific connection topology, which leads to synchrony within clusters but poor coordination across clusters. Overall, our results highlight the relevance of interactions between topology and intrinsic dynamics in shaping the activity of networks and the concerted effects of connectivity patterns and dynamic heterogeneities.

Interacting oscillations in neural control of breathing: modeling and qualitative analysis

In mammalian respiration, late-expiratory (late-E, or pre-inspiratory) oscillations emerge in abdominal motor output with increasing metabolic demands (e.g., during hypercapnia, hypoxia, etc.). These oscillations originate in the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) and couple with the respiratory oscillations generated by the interacting neural populations of the Bötzinger (BötC) and pre-Bötzinger (pre-BötC) complexes, representing the kernel of the respiratory central pattern generator. Recently, we analyzed experimental data on the generation of late-E oscillations and proposed a large-scale computational model that simulates the possible interactions between the BötC/pre-BötC and RTN/pFRG oscillations under different conditions. Here we describe a reduced model that maintains the essential features and architecture of the large-scale model, but relies on simplified activity-based descriptions of neural populations. This simplification allowed us to use methods of dynamical systems theory, such as fast-slow decomposition, bifurcation analysis, and phase plane analysis, to elucidate the mechanisms and dynamics of synchronization between the RTN/pFRG and BötC/pre-BötC oscillations. Three physiologically relevant behaviors have been analyzed: emergence and quantal acceleration of late-E oscillations during hypercapnia, transformation of the late-E activity into a biphasic-E activity during hypercapnic hypoxia, and quantal slowing of BötC/pre-BötC oscillations with the reduction of pre-BötC excitability. Each behavior is elicited by gradual changes in excitatory drives or other model parameters, reflecting specific changes in metabolic and/or physiological conditions. Our results provide important theoretical insights into interactions between RTN/pFRG and BötC/pre-BötC oscillations and the role of these interactions in the control of breathing under different metabolic conditions.

Late-expiratory activity: emergence and interactions with the respiratory CpG

The respiratory rhythm and motor pattern are hypothesized to be generated by a brain stem respiratory network with a rhythmogenic core consisting of neural populations interacting within and between the pre-Bötzinger (pre-BötC) and Bötzinger (BötC) complexes and controlled by drives from other brain stem compartments. Our previous large-scale computational model reproduced the behavior of this network under many different conditions but did not consider neural oscillations that were proposed to emerge within the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) and drive preinspiratory (or late-expiratory, late-E) discharges in the abdominal motor output. Here we extend the analysis of our previously published data and consider new data on the generation of abdominal late-E activity as the basis for extending our computational model. The extended model incorporates an additional late-E population in RTN/pFRG, representing a source of late-E oscillatory activity. In the proposed model, under normal metabolic conditions, this RTN/pFRG oscillator is inhibited by BötC/pre-BötC circuits, and the late-E oscillations can be released by either hypercapnia-evoked activation of RTN/pFRG or by hypoxia-dependent suppression of RTN/pFRG inhibition by BötC/pre-BötC. The proposed interactions between BötC/pre-BötC and RTN/pFRG allow the model to reproduce several experimentally observed behaviors, including quantal acceleration of abdominal late-E oscillations with progressive hypercapnia and quantal slowing of phrenic activity with progressive suppression of pre-BötC excitability, as well as to predict a release of late-E oscillations by disinhibition of RTN/pFRG under normal conditions. The extended model proposes mechanistic explanations for the emergence of RTN/pFRG oscillations and their interaction with the brain stem respiratory network.

Respiratory responses induced by blockades of GABA and glycine receptors within the Bötzinger complex and the pre-Bötzinger complex of the rabbit

The respiratory role of GABA(A), GABA(B) and glycine receptors within the Bötzinger complex (BötC) and the pre-Bötzinger complex (preBötC) was investigated in alpha-chloralose-urethane anesthetized, vagotomized, paralysed and artificially ventilated rabbits by using bilateral microinjections (30-50 nl) of GABA and glycine receptor agonists and antagonists. GABA(A) receptor blockade by bicuculline (5mM) or gabazine (2mM) within the BötC induced strong depression of respiratory activity up to apnea. The latter was reversed by hypercapnia. Glycine receptor blockade by strychnine (5mM) within the BötC decreased the frequency and amplitude of phrenic bursts. Bicuculline microinjections into the preBötC caused decreases in respiratory frequency and the appearance of two alternating different levels of peak phrenic activity. Strychnine microinjections into the preBötC increased respiratory frequency and decreased peak phrenic amplitude. GABA(A), but not glycine receptor antagonism within the preBötC restored respiratory rhythmicity during apnea due to bicuculline or gabazine applied to the BötC. GABA(B) receptor blockade by CGP-35348 (50mM) within the BötC and the preBötC did not affect baseline respiratory activity, though microinjections of the GABA(B) receptor agonist baclofen (1mM) into the same regions altered respiratory activity. The results show that only GABA(A) and glycine receptors within the BötC and the preBötC mediate a potent control on both the intensity and frequency of inspiratory activity during eupneic breathing. This study is the first to provide evidence that these inhibitory receptors have a respiratory function within the BötC.

Site-specific effects on respiratory rhythm and pattern of ibotenic acid injections in the pontine respiratory group of goats

To probe further the contributions of the rostral pons to eupneic respiratory rhythm and pattern, we tested the hypothesis that ibotenic acid (IA) injections in the pontine respiratory group (PRG) would disrupt eupneic respiratory rhythm and pattern in a site- and state-specific manner. In 15 goats, cannulas were bilaterally implanted into the rostral pontine tegmental nuclei (RPTN; n = 3), the lateral (LPBN; n = 4) or medial parabrachial nuclei (MPBN; n = 4), or the Kölliker-Fuse nucleus (KFN; n = 4). After recovery from surgery, 1- and 10-microl injections (1 wk apart) of IA were made bilaterally through the implanted cannulas during the day. Over the first 5 h after the injections, there were site-specific ventilatory effects, with increased (P < 0.05) breathing frequency in RPTN-injected goats, increased (P < 0.05) pulmonary ventilation (Vi) in LPBN-injected goats, no effect (P < 0.05) in MPBN-injected goats, and a biphasic Vi response (P < 0.05) in KFN-injected goats. This biphasic response consisted of a hyperpnea for 30 min, followed by a prolonged hypopnea and hypoventilation with marked apneas, apneusis-like breathing patterns, and/or shifts in the temporal relationships between inspiratory flow and diaphragm activity. In the awake state, 10-15 h after the 1-microl injections, the number of apneas was greater (P < 0.05) than during other studies at night. However, there were no incidences of terminal apneas. Breathing rhythm and pattern were normal 22 h after the injections. Subsequent histological analysis revealed that for goats with cannulas implanted into the KFN, there were nearly 50% fewer neurons (P < 0.05) in all three PRG subnuclei than in control goats. We conclude that in awake goats, 1) IA injections into the PRG have site-specific effects on breathing, and 2) the KFN contributes to eupneic respiratory pattern generation.

Control of breathing: two types of delays studied in an integrated model of the respiratory system

We use a recently developed mathematical model that integrates a reduced representation of the brainstem respiratory neural controller together with peripheral gas exchange and transport to study numerically the dynamic response of the respiratory system to several physiological stimuli. We compare between the system responses with two major sources of delay: circulatory transport vs. neural feedback dynamics, and we show that the dynamics of the neural feedback processes dictates the dynamic response to hypoxia and hypercapnia. The source of the circulatory delay (blood velocity vs. distance from the lungs to chemoreceptors) was found to be important. Our model predicts that periodic breathing is associated with the ventilatory "afterdischarge" (slow recovery of ventilation) after a brief perturbation of CO(2). We also predict that there could be two possible mechanisms for the appearance of periodic breathing and that circulatory delay is not a necessary condition for this to occur in certain cases.

Synaptically activated burst-generating conductances may underlie a group-pacemaker mechanism for respiratory rhythm generation in mammals

Breathing, chewing, and walking are critical life-sustaining behaviors in mammals that consist essentially of simple rhythmic movements. Breathing movements in particular involve the diaphragm, thorax, and airways but emanate from a network in the lower brain stem. This network can be studied in reduced preparations in vitro and using simplified mathematical models that make testable predictions. An iterative approach that employs both in vitro and in silico models argues against canonical mechanisms for respiratory rhythm in neonatal rodents that involve reciprocal inhibition and pacemaker properties. We present an alternative model in which emergent network properties play a rhythmogenic role. Specifically, we show evidence that synaptically activated burst-generating conductances-which are only available in the context of network activity-engender robust periodic bursts in respiratory neurons. Because the cellular burst-generating mechanism is linked to network synaptic drive we dub this type of system a group pacemaker.

Structural and functional architecture of respiratory networks in the mammalian brainstem

Neural circuits controlling breathing in mammals are organized within serially arrayed and functionally interacting brainstem compartments extending from the pons to the lower medulla. The core circuit components that constitute the neural machinery for generating respiratory rhythm and shaping inspiratory and expiratory motor patterns are distributed among three adjacent structural compartments in the ventrolateral medulla: the Bötzinger complex (BötC), pre-Bötzinger complex (pre-BötC) and rostral ventral respiratory group (rVRG). The respiratory rhythm and inspiratory-expiratory patterns emerge from dynamic interactions between: (i) excitatory neuron populations in the pre-BötC and rVRG active during inspiration that form inspiratory motor output; (ii) inhibitory neuron populations in the pre-BötC that provide inspiratory inhibition within the network; and (iii) inhibitory populations in the BötC active during expiration that generate expiratory inhibition. Network interactions within these compartments along with intrinsic rhythmogenic properties of pre-BötC neurons form a hierarchy of multiple oscillatory mechanisms. The functional expression of these mechanisms is controlled by multiple drives from more rostral brainstem components, including the retrotrapezoid nucleus and pons, which regulate the dynamic behaviour of the core circuitry. The emerging view is that the brainstem respiratory network has rhythmogenic capabilities at multiple hierarchical levels, which allows flexible, state-dependent expression of different rhythmogenic mechanisms under different physiological and metabolic conditions and enables a wide repertoire of respiratory behaviours.

A mathematical model of the sleep/wake cycle

We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous "flip-flop" conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip-flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip-flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip-flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics.