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

A novel mechanism for ramping bursts based on slow negative feedback in model respiratory neurons

Recordings from pre-Bötzinger complex neurons responsible for the inspiratory phase of the respiratory rhythm reveal a ramping burst pattern, starting around the time that the transition from expiration to inspiration begins, in which the spike rate gradually rises until a transition into a high-frequency burst occurs. The spike rate increase along the burst is accompanied by a gradual depolarization of the plateau potential that underlies the spikes. These effects may be functionally important for inducing the onset of inspiration and hence maintaining effective respiration; however, most mathematical models for inspiratory bursting do not capture this activity pattern. Here, we study how the modulation of spike height and afterhyperpolarization via the slow inactivation of an inward current can support various activity patterns including ramping bursts. We use dynamical systems methods designed for multiple timescale systems, such as bifurcation analysis based on timescale decomposition and averaging over fast oscillations, to generate an understanding of and predictions about the specific dynamic effects that lead to ramping bursts. We also analyze how transitions between ramping and other activity patterns may occur with parameter changes, which could be associated with experimental manipulations, environmental conditions, and/or development.

Interdependence of cellular and network properties in respiratory rhythm generation

How breathing is generated by the preBötzinger complex (preBötC) remains divided between two ideological frameworks, and a persistent sodium current (INaP) lies at the heart of this debate. Although INaP is widely expressed, the pacemaker hypothesis considers it essential because it endows a small subset of neurons with intrinsic bursting or "pacemaker" activity. In contrast, burstlet theory considers INaP dispensable because rhythm emerges from "preinspiratory" spiking activity driven by feed-forward network interactions. Using computational modeling, we find that small changes in spike shape can dissociate INaP from intrinsic bursting. Consistent with many experimental benchmarks, conditional effects on spike shape during simulated changes in oxygenation, development, extracellular potassium, and temperature alter the prevalence of intrinsic bursting and preinspiratory spiking without altering the role of INaP. Our results support a unifying hypothesis where INaP and excitatory network interactions, but not intrinsic bursting or preinspiratory spiking, are critical interdependent features of preBötC rhythmogenesis.

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.

Modeling Effects of Variable preBötzinger Complex Network Topology and Cellular Properties on Opioid-Induced Respiratory Depression and Recovery

The preBötzinger complex (preBötC), located in the medulla, is the essential rhythm-generating neural network for breathing. The actions of opioids on this network impair its ability to generate robust, rhythmic output, contributing to life-threatening opioid-induced respiratory depression (OIRD). The occurrence of OIRD varies across individuals and internal and external states, increasing the risk of opioid use, yet the mechanisms of this variability are largely unknown. In this study, we utilize a computational model of the preBötC to perform several in silico experiments exploring how differences in network topology and the intrinsic properties of preBötC neurons influence the sensitivity of the network rhythm to opioids. We find that rhythms produced by preBötC networks in silico exhibit variable responses to simulated opioids, similar to the preBötC network in vitro. This variability is primarily due to random differences in network topology and can be manipulated by imposed changes in network connectivity and intrinsic neuronal properties. Our results identify features of the preBötC network that may regulate its susceptibility to opioids.

Exploring the role of the Kölliker-Fuse nucleus in breathing variability by mathematical modelling

The Kölliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnoea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apnoeas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupnoeic as well as RTT-like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT-like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late-expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing. KEY POINTS: The Kölliker-Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation. Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modelling to explore different dynamical regimes of KF activity and their compatibility with experimental observations. By analysing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT-like respiratory patterns and proposes potential KF local circuit organizations. Two models are presented that simulate both normal breathing and RTT-like breathing patterns. These models provide testable hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.

Interdependence of cellular and network properties in respiratory rhythmogenesis

How breathing is generated by the preBötzinger Complex (preBötC) remains divided between two ideological frameworks, and the persistent sodium current (INaP) lies at the heart of this debate. Although INaP is widely expressed, the pacemaker hypothesis considers it essential because it endows a small subset of neurons with intrinsic bursting or "pacemaker" activity. In contrast, burstlet theory considers INaP dispensable because rhythm emerges from "pre-inspiratory" spiking activity driven by feed-forward network interactions. Using computational modeling, we discover that changes in spike shape can dissociate INaP from intrinsic bursting. Consistent with many experimental benchmarks, conditional effects on spike shape during simulated changes in oxygenation, development, extracellular potassium, and temperature alter the prevalence of intrinsic bursting and pre-inspiratory spiking without altering the role of INaP. Our results support a unifying hypothesis where INaP and excitatory network interactions, but not intrinsic bursting or pre-inspiratory spiking, are critical interdependent features of preBötC rhythmogenesis.

Inhibitory subpopulations in preBötzinger Complex play distinct roles in modulating inspiratory rhythm and pattern

Inhibitory neurons embedded within mammalian neural circuits shape breathing, walking, chewing, and other rhythmic motor behaviors. At the core of the neural circuit controlling breathing is the preBötzinger Complex (preBötC), a nucleus in the ventrolateral medulla necessary for generation of inspiratory rhythm. In the preBötC, a recurrently connected network of glutamatergic Dbx1-derived (Dbx1 + ) neurons generates rhythmic inspiratory drive. Functionally and anatomically intercalated among Dbx1 + preBötC neurons are GABAergic (GAD1/2 + ) and glycinergic (GlyT2 + ) neurons, whose roles in breathing remain unclear. To elucidate the inhibitory microcircuits within preBötC, we first characterized the spatial distribution of molecularly-defined inhibitory preBötC subpopulations in double reporter mice expressing either the red fluorescent protein tdTomato or EGFP in GlyT2 + , GAD1 + , or GAD2 + neurons. We found that, in postnatal mice, the majority of inhibitory preBötC neurons expressed a combination of GlyT2 and GAD2 while a much smaller subpopulation also expressed GAD1. To determine the functional role of these subpopulations, we used holographic photostimulation, a patterned illumination technique with high spatiotemporal resolution, in rhythmically active medullary slices from neonatal Dbx1 tdTomato ;GlyT2 EGFP and Dbx1 tdTomato ;GAD1 EGFP double reporter mice. Stimulation of 4 or 8 preBötC GlyT2 + neurons during endogenous rhythm prolonged the interburst interval in a phase-dependent manner and increased the latency to burst initiation when bursts were evoked by stimulation of Dbx1 + neurons. In contrast, stimulation of 4 or 8 preBötC GAD1 + neurons did not affect interburst interval or latency to burst initiation. Instead, photoactivation of GAD1 + neurons during the inspiratory burst prolonged endogenous and evoked burst duration and decreased evoked burst amplitude. We conclude that the majority of preBötC inhibitory neurons express both GlyT2 and GAD2 and modulate breathing rhythm by delaying burst initiation while a smaller GAD1 + subpopulation shapes inspiratory patterning by altering burst duration and amplitude.

The role of Kölliker-Fuse nucleus in breathing variability

The Kölliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apneas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupneic as well as RTT-like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT-like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late-expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing.

Key points

The Kölliker-Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation. Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modeling to explore different dynamical regimes of KF activity and their compatibility with experimental observations. By analyzing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT-like respiratory patterns and proposes potential KF local circuit organizations. Two models are presented that simulate both normal breathing and RTT-like breathing patterns. These models provide plausible hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.

Synchronization of inspiratory burst onset along the ventral respiratory column in the neonate mouse is mediated by electrotonic coupling

Breathing is a singularly robust behavior, yet this motor pattern is continuously modulated at slow and fast timescales to maintain blood-gas homeostasis, while intercalating orofacial behaviors. This functional multiplexing goes beyond the rhythmogenic function that is typically ascribed to medullary respiration-modulated networks and may explain lack of progress in identifying the mechanism and constituents of the respiratory rhythm generator. By recording optically along the ventral respiratory column in medulla, we found convergent evidence that rhythmogenic function is distributed over a dispersed and heterogeneous network that is synchronized by electrotonic coupling across a neuronal syncytium. First, high-speed recordings revealed that inspiratory onset occurred synchronously along the column and did not emanate from a rhythmogenic core. Second, following synaptic isolation, synchronized stationary rhythmic activity was detected along the column. This activity was attenuated following gap junction blockade and was silenced by tetrodotoxin. The layering of syncytial and synaptic coupling complicates identification of rhythmogenic mechanism, while enabling functional multiplexing.

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.

Predictions and experimental tests of a new biophysical model of the mammalian respiratory oscillator

Previously our computational modeling studies (Phillips et al., 2019) proposed that neuronal persistent sodium current (INaP) and calcium-activated non-selective cation current (ICAN) are key biophysical factors that, respectively, generate inspiratory rhythm and burst pattern in the mammalian preBötzinger complex (preBötC) respiratory oscillator isolated in vitro. Here, we experimentally tested and confirmed three predictions of the model from new simulations concerning the roles of INaP and ICAN: (1) INaP and ICAN blockade have opposite effects on the relationship between network excitability and preBötC rhythmic activity; (2) INaP is essential for preBötC rhythmogenesis; and (3) ICAN is essential for generating the amplitude of rhythmic output but not rhythm generation. These predictions were confirmed via optogenetic manipulations of preBötC network excitability during graded INaP or ICAN blockade by pharmacological manipulations in slices in vitro containing the rhythmically active preBötC from the medulla oblongata of neonatal mice. Our results support and advance the hypothesis that INaP and ICAN mechanistically underlie rhythm and inspiratory burst pattern generation, respectively, in the isolated preBötC.

Inspiratory rhythm generation is stabilized by Ih

Cellular and network properties must be capable of generating rhythmic activity that is both flexible and stable. This is particularly important for breathing, a rhythmic behavior that dynamically adapts to environmental, behavioral, and metabolic changes from the first to the last breath. The pre-Bötzinger complex (preBötC), located within the ventral medulla, is responsible for producing rhythmic inspiration. Its cellular properties must be tunable, flexible as well as stabilizing. Here, we explore the role of the hyperpolarization-activated, nonselective cation current (I_h) for stabilizing PreBötC activity during opioid exposure and reduced excitatory synaptic transmission. Introducing I_h into an in silico preBötC network predicts that loss of this depolarizing current should significantly slow the inspiratory rhythm. By contrast, in vitro and in vivo experiments revealed that the loss of I_h minimally affected breathing frequency, but destabilized rhythmogenesis through the generation of incompletely synchronized bursts (burstlets). Associated with the loss of I_h was an increased susceptibility of breathing to opioid-induced respiratory depression or weakened excitatory synaptic interactions, a paradoxical depolarization at the cellular level, and the suppression of tonic spiking. Tonic spiking activity is generated by nonrhythmic excitatory and inhibitory preBötC neurons, of which a large percentage express I_h. Together, our results suggest that I_h is important for maintaining tonic spiking, stabilizing inspiratory rhythmogenesis, and protecting breathing against perturbations or changes in network state.NEW & NOTEWORTHY The I_h current plays multiple roles within the preBötC. This current is important for promoting intrinsic tonic spiking activity in excitatory and inhibitory neurons and for preserving rhythmic function during conditions that dampen network excitability, such as in the context of opioid-induced respiratory depression. We therefore propose that the I_h current expands the dynamic range of rhythmogenesis, buffers the preBötC against network perturbations, and stabilizes rhythmogenesis by preventing the generation of unsynchronized bursts.