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

COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator

Silent hypoxemia, or "happy hypoxia," is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturation ( SaO 2 < 80%) but do not experience discomfort in breathing. The mechanism by which this blunted response to hypoxia occurs is unknown. We have previously shown that a computational model of the respiratory neural network (Diekman et al. in J Neurophysiol 118(4):2194-2215, 2017) can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for the blunted response to hypoxia. Here, we use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. We then vary other parameters in the model and show that oxygen carrying capacity is the most salient factor for producing silent hypoxemia. We call for clinicians to measure hematocrit as a clinical index of altered physiology in response to COVID-19 infection.

Operation regimes of spinal circuits controlling locomotion and role of supraspinal drives and sensory feedback

Locomotion in mammals is directly controlled by the spinal neuronal network, operating under the control of supraspinal signals and somatosensory feedback that interact with each other. However, the functional architecture of the spinal locomotor network, its operation regimes, and the role of supraspinal and sensory feedback in different locomotor behaviors, including at different speeds, remain unclear. We developed a computational model of spinal locomotor circuits receiving supraspinal drives and limb sensory feedback that could reproduce multiple experimental data obtained in intact and spinal-transected cats during tied-belt and split-belt treadmill locomotion. We provide evidence that the spinal locomotor network operates in different regimes depending on locomotor speed. In an intact system, at slow speeds (< 0.4 m/s), the spinal network operates in a non-oscillating state-machine regime and requires sensory feedback or external inputs for phase transitions. Removing sensory feedback related to limb extension prevents locomotor oscillations at slow speeds. With increasing speed and supraspinal drives, the spinal network switches to a flexor-driven oscillatory regime and then to a classical half-center regime. Following spinal transection, the model predicts that the spinal network can only operate in the state-machine regime. Our results suggest that the spinal network operates in different regimes for slow exploratory and fast escape locomotor behaviors, making use of different control mechanisms.

CB 1 Cannabinoid Receptor Agonists Induce Acute Respiratory Depression in Awake Mice

Recreational use of synthetic cannabinoid agonists (i.e., "Spice" compounds) that target the Cannabinoid Type 1 receptor (CB 1 ) can cause respiratory depression in humans. However, Δ 9 -tetrahydrocannabinol (THC), the major psychoactive phytocannabinoid in cannabis, is not traditionally thought to interact with CNS control of respiration, based largely upon sparse labeling of CB1 receptors in the medulla and few reports of clinically significant respiratory depression following cannabis overdose. The respiratory effects of CB 1 agonists have rarely been studied in vivo , suggesting that additional inquiry is required to reconcile the conflict between conventional wisdom and human data. Here we used whole body plethysmography to examine the respiratory effects of the synthetic high efficacy CB 1 agonist CP55,940, and the low efficacy CB 1 agonist Δ 9 -tetrahydrocannabinol in male and female mice. CP55,940 and THC, administered systemically, both robustly suppressed minute ventilation. Both cannabinoids also produced sizable reductions in tidal volume, decreasing both peak inspiratory and expiratory flow - measures of respiratory effort. Similarly, both drugs reduced respiratory frequency, decreasing both inspiratory and expiratory time while markedly increasing expiratory pause, and to a lesser extent, inspiratory pause. Respiratory suppressive effects occurred at lower doses in females than in males, and at many of the same doses shown to produce cardinal behavioral signs of CB 1 activation. We next used RNAscope in situ hybridization to localize CB 1 mRNA to glutamatergic neurons in the medullary pre-Bötzinger Complex, a critical nucleus in controlling respiration. Our results show that, contrary to previous conventional wisdom, CB 1 mRNA is expressed in glutamatergic neurons in a brain region essential for breathing and CB 1 agonists can cause significant respiratory depression.

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.

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.

COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator

Silent hypoxemia, or 'happy hypoxia', is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturation (SaO2 < 80%) but do not experience discomfort in breathing. The mechanism by which this blunted response to hypoxia occurs is unknown. We have previously shown that a computational model (Diekman et al., 2017, J. Neurophysiol) of the respiratory neural network can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for the blunted response to hypoxia. Here, we use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. We then vary other parameters in the model and show that oxygen carrying capacity is the most salient factor for producing silent hypoxemia. We call for clinicians to measure hematocrit as a clinical index of altered physiology in response to COVID-19 infection.

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.

Noise-activated barrier crossing in multiattractor dissipative neural networks

Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. At low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape probability becomes comparable to the intrabasin hopping probability, the lifetime of attractors is given by a detailed balance where the less coherent attractors act as a sink for the more coherent ones. In this regime, the escape probability follows an activation law allowing us to assign pseudoactivation energies to limit cycle attractors. These pseudoenergies introduce a useful metric for evaluating the resilience of biological rhythms to perturbations.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Advancing respiratory-cardiovascular physiology with the working heart-brainstem preparation over 25 years

Twenty‐five years ago, a new physiological preparation called the working heart–brainstem preparation (WHBP) was introduced with the claim it would provide a new platform allowing studies not possible before in cardiovascular, neuroendocrine, autonomic and respiratory research. Herein, we review some of the progress made with the WHBP, some advantages and disadvantages along with potential future applications, and provide photographs and technical drawings of all the customised equipment used for the preparation. Using mice or rats, the WHBP is an in situ experimental model that is perfused via an extracorporeal circuit benefitting from unprecedented surgical access, mechanical stability of the brain for whole cell recording and an uncompromised use of pharmacological agents akin to in vitro approaches. The preparation has revealed novel mechanistic insights into, for example, the generation of distinct respiratory rhythms, the neurogenesis of sympathetic activity, coupling between respiration and the heart and circulation, hypothalamic and spinal control mechanisms, and peripheral and central chemoreceptor mechanisms. Insights have been gleaned into diseases such as hypertension, heart failure and sleep apnoea. Findings from the in situ preparation have been ratified in conscious in vivo animals and when tested have translated to humans. We conclude by discussing potential future applications of the WHBP including two‐photon imaging of peripheral and central nervous systems and adoption of pharmacogenetic tools that will improve our understanding of physiological mechanisms and reveal novel mechanisms that may guide new treatment strategies for cardiorespiratory diseases.

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.

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.

Heartbeats entrain breathing via baroreceptor-mediated modulation of expiratory activity

NEW FINDINGS

  Cardio-ventilatory coupling refers to the onset of inspiration occurring at a preferential latency following the last heartbeat (HB) in expiration. According to the cardiac-trigger hypothesis, the pulse pressure initiates an inspiration via baroreceptor activation. However, the central neural substrate mediating this coupling remains undefined. Using a combination of animal data, human data and mathematical modelling, this study tests the hypothesis that the HB, by way of pulsatile baroreflex activation, controls the initiation of inspiration that occurs through a rapid neural activation loop from the carotid baroreceptors to Bötzinger complex expiratory neurons.

ABSTRACT

Cardio-ventilatory coupling refers to a heartbeat (HB) occurring at a preferred latency prior to the next breath. We hypothesized that the pressure pulse generated by a HB activates baroreceptors that modulate brainstem expiratory neuronal activity and delay the initiation of inspiration. In supine male subjects, we recorded ventilation, electrocardiogram and blood pressure during 20-min epochs of baseline, slow-deep breathing and recovery. In in situ rodent preparations, we recorded brainstem activity in response to pulses of perfusion pressure. We applied a well-established respiratory network model to interpret these data. In humans, the latency between a HB and onset of inspiration was consistent across different breathing patterns. In in situ preparations, a transient pressure pulse during expiration activated a subpopulation of expiratory neurons normally active during post-inspiration, thus delaying the next inspiration. In the model, baroreceptor input to post-inspiratory neurons accounted for the effect. These studies are consistent with baroreflex activation modulating respiration through a pauci-synaptic circuit from baroreceptors to onset of inspiration.

On the Organization of the Locomotor CPG: Insights From Split-Belt Locomotion and Mathematical Modeling

Rhythmic limb movements during locomotion are controlled by central pattern generator (CPG) circuits located in the spinal cord. It is considered that these circuits are composed of individual rhythm generators (RGs) for each limb interacting with each other through multiple commissural and long propriospinal circuits. The organization and operation of each RG are not fully understood, and different competing theories exist about interactions between its flexor and extensor components, as well as about left-right commissural interactions between the RGs. The central idea of circuit organization proposed in this study is that with an increase of excitatory input to each RG (or an increase in locomotor speed) the rhythmogenic mechanism of the RGs changes from "flexor-driven" rhythmicity to a "classical half-center" mechanism. We test this hypothesis using our experimental data on changes in duration of stance and swing phases in the intact and spinal cats walking on the ground or tied-belt treadmills (symmetric conditions) or split-belt treadmills with different left and right belt speeds (asymmetric conditions). We compare these experimental data with the results of mathematical modeling, in which simulated CPG circuits operate in similar symmetric and asymmetric conditions with matching or differing control drives to the left and right RGs. The obtained results support the proposed concept of state-dependent changes in RG operation and specific commissural interactions between the RGs. The performed simulations and mathematical analysis of model operation under different conditions provide new insights into CPG network organization and limb coordination during locomotion.

Morphine in the Setting of Acute Heart Failure: Do the Risks Outweigh the Benefits?

The use of opioids in acute pulmonary oedema is considered standard therapy by many physicians. The immediate relieving effect of morphine on the key symptomatic discomfort associated with acute heart failure, dyspnoea, facilitated the categorisation of morphine as a beneficial treatment in this setting. During the last decade, several retrospective studies raised concerns regarding the safety and efficacy of morphine in the setting of acute heart failure. In this article, the physiological effects of morphine on the cardiovascular and respiratory systems are summarised, as well as the potential clinical benefits and risks associated with morphine therapy. Finally, the reported clinical outcomes and adverse event profiles from recent observational studies are discussed, as well as future perspectives and potential alternatives to morphine in the setting of acute heart failure.

Inhibitory control of active expiration by the Bötzinger complex in rats

KEY POINTS

Contraction of abdominal muscles at the end of expiration during metabolic challenges (such as hypercapnia and hypoxia) improves pulmonary ventilation. The emergence of this active expiratory pattern requires the recruitment of the expiratory oscillator located on the ventral surface of the medulla oblongata. Here we show that an inhibitory circuitry located in the Bötzinger complex is an important source of inhibitory drive to the expiratory oscillator. This circuitry, mediated by GABAergic and glycinergic synapses, provides expiratory inhibition that restrains the expiratory oscillator under resting condition and regulates the formation of abdominal expiratory activity during active expiration. By combining experimental and modelling approaches, we propose the organization and connections within the respiratory network that control the changes in the breathing pattern associated with elevated metabolic demand.

ABSTRACT

The expiratory neurons of the Bötzinger complex (BötC) provide inhibitory inputs to the respiratory network, which, during eupnoea, are critically important for respiratory phase transition and duration control. Here, we investigated how the BötC neurons interact with the expiratory oscillator located in the parafacial respiratory group (pFRG) and control the abdominal activity during active expiration. Using the decerebrated, arterially perfused in situ preparations of juvenile rats, we recorded the activity of expiratory neurons and performed pharmacological manipulations of the BötC and pFRG during hypercapnia or after the exposure to short-term sustained hypoxia - conditions that generate active expiration. The experimental data were integrated in a mathematical model to gain new insights into the inhibitory connectome within the respiratory central pattern generator. Our results indicate that the BötC neurons may establish mutual connections with the pFRG, providing expiratory inhibition during the first stage of expiration and receiving excitatory inputs during late expiration. Moreover, we found that application of GABAergic and glycinergic antagonists in the BötC caused opposing effects on abdominal expiratory activity, suggesting complex inhibitory circuitry within the BötC. Using mathematical modelling, we propose that the BötC network organization and its interactions with the pFRG restrain abdominal activity under resting conditions and contribute to abdominal expiratory pattern formation during active expiration observed during hypercapnia or after the exposure to short-term sustained hypoxia.

Volumetric mapping of the functional neuroanatomy of the respiratory network in the perfused brainstem preparation of rats

KEY POINTS

The functional neuroanatomy of the mammalian respiratory network is far from being understood since experimental tools that measure neural activity across this brainstem-wide circuit are lacking. Here, we use silicon multi-electrode arrays to record respiratory local field potentials (rLFPs) from 196-364 electrode sites within 8-10 mm³ of brainstem tissue in single arterially perfused brainstem preparations with respect to the ongoing respiratory motor pattern of inspiration (I), post-inspiration (PI) and late-expiration (E2). rLFPs peaked specifically at the three respiratory phase transitions, E2-I, I-PI and PI-E2. We show, for the first time, that only the I-PI transition engages a brainstem-wide network, and that rLFPs during the PI-E2 transition identify a hitherto unknown role for the dorsal respiratory group. Volumetric mapping of pontomedullary rLFPs in single preparations could become a reliable tool for assessing the functional neuroanatomy of the respiratory network in health and disease.

ABSTRACT

While it is widely accepted that inspiratory rhythm generation depends on the pre-Bötzinger complex, the functional neuroanatomy of the neural circuits that generate expiration is debated. We hypothesized that the compartmental organization of the brainstem respiratory network is sufficient to generate macroscopic local field potentials (LFPs), and if so, respiratory (r) LFPs could be used to map the functional neuroanatomy of the respiratory network. We developed an approach using silicon multi-electrode arrays to record spontaneous LFPs from hundreds of electrode sites in a volume of brainstem tissue while monitoring the respiratory motor pattern on phrenic and vagal nerves in the perfused brainstem preparation. Our results revealed the expression of rLFPs across the pontomedullary brainstem. rLFPs occurred specifically at the three transitions between respiratory phases: (1) from late expiration (E2) to inspiration (I), (2) from I to post-inspiration (PI), and (3) from PI to E2. Thus, respiratory network activity was maximal at respiratory phase transitions. Spatially, the E2-I, and PI-E2 transitions were anatomically localized to the ventral and dorsal respiratory groups, respectively. In contrast, our data show, for the first time, that the generation of controlled expiration during the post-inspiratory phase engages a distributed neuronal population within ventral, dorsal and pontine network compartments. A group-wise independent component analysis demonstrated that all preparations exhibited rLFPs with a similar temporal structure and thus share a similar functional neuroanatomy. Thus, volumetric mapping of rLFPs could allow for the physiological assessment of global respiratory network organization in health and disease.

Development of the brainstem respiratory circuit

The respiratory circuit is comprised of over a dozen functionally and anatomically segregated brainstem nuclei that work together to control respiratory rhythms. These respiratory rhythms emerge prenatally but only acquire vital importance at birth, which is the first time the respiratory circuit faces the sole responsibility for O₂ /CO₂ homeostasis. Hence, the respiratory circuit has little room for trial-and-error-dependent fine tuning and relies on a detailed genetic blueprint for development. This blueprint is provided by transcription factors that have specific spatiotemporal expression patterns along the rostral-caudal or dorsal-ventral axis of the developing brainstem, in proliferating precursor cells and postmitotic neurons. Studying these transcription factors in mice has provided key insights into the functional segregation of respiratory control and the vital importance of specific respiratory nuclei. Many studies converge on just two respiratory nuclei that each have rhythmogenic properties during the prenatal period: the preBötzinger complex (preBötC) and retrotrapezoid nucleus/parafacial nucleus (RTN/pF). Here, we discuss the transcriptional regulation that guides the development of these nuclei. We also summarize evidence showing that normal preBötC development is necessary for neonatal survival, and that neither the preBötC nor the RTN/pF alone is sufficient to sustain normal postnatal respiratory rhythms. Last, we highlight several studies that use intersectional genetics to assess the necessity of transcription factors only in subregions of their expression domain. These studies independently demonstrate that lack of RTN/pF neurons weakens the respiratory circuit, yet these neurons are not necessary for neonatal survival because developmentally related populations can compensate for abnormal RTN/pF function at birth. This article is categorized under: Nervous System Development > Vertebrates: Regional Development.

Effects of persistent sodium current blockade in respiratory circuits depend on the pharmacological mechanism of action and network dynamics

The mechanism(s) of action of most commonly used pharmacological blockers of voltage-gated ion channels are well understood; however, this knowledge is rarely considered when interpreting experimental data. Effects of blockade are often assumed to be equivalent, regardless of the mechanism of the blocker involved. Using computer simulations, we demonstrate that this assumption may not always be correct. We simulate the blockade of a persistent sodium current (I_NaP), proposed to underlie rhythm generation in pre-Bötzinger complex (pre-BötC) respiratory neurons, via two distinct pharmacological mechanisms: (1) pore obstruction mediated by tetrodotoxin and (2) altered inactivation dynamics mediated by riluzole. The reported effects of experimental application of tetrodotoxin and riluzole in respiratory circuits are diverse and seemingly contradictory and have led to considerable debate within the field as to the specific role of I_NaP in respiratory circuits. The results of our simulations match a wide array of experimental data spanning from the level of isolated pre-BötC neurons to the level of the intact respiratory network and also generate a series of experimentally testable predictions. Specifically, in this study we: (1) provide a mechanistic explanation for seemingly contradictory experimental results from in vitro studies of I_NaP block, (2) show that the effects of I_NaP block in in vitro preparations are not necessarily equivalent to those in more intact preparations, (3) demonstrate and explain why riluzole application may fail to effectively block I_NaP in the intact respiratory network, and (4) derive the prediction that effective block of I_NaP by low concentration tetrodotoxin will stop respiratory rhythm generation in the intact respiratory network. These simulations support a critical role for I_NaP in respiratory rhythmogenesis in vivo and illustrate the importance of considering mechanism when interpreting and simulating data relating to pharmacological blockade.

The application of pharmacological agents that affect transmembrane ionic currents in neurons is a commonly used experimental technique. A simplistic interpretation of experiments involving these agents suggests that antagonist application removes the impacted current and that subsequently observed changes in activity are attributable to the loss of that current’s effects. The more complex reality, however, is that different drugs may have distinct mechanisms of action, some corresponding not to a removal of a current but rather to a changing of its properties. We use computational modeling to explore the implications of the distinct mechanisms associated with two drugs, riluzole and tetrodotoxin, that are often characterized as sodium channel blockers. Through this approach, we offer potential explanations for disparate findings observed in experiments on neural respiratory circuits and show that the experimental results are consistent with a key role for the persistent sodium current in respiratory rhythm generation.

Curated Model Development Using NEUROiD: A Web-Based NEUROmotor Integration and Design Platform

Decades of research on neuromotor circuits and systems has provided valuable information on neuronal control of movement. Computational models of several elements of the neuromotor system have been developed at various scales, from sub-cellular to system. While several small models abound, their structured integration is the key to building larger and more biologically realistic models which can predict the behavior of the system in different scenarios. This effort calls for integration of elements across neuroscience and musculoskeletal biomechanics. There is also a need for development of methods and tools for structured integration that yield larger in silico models demonstrating a set of desired system responses. We take a small step in this direction with the NEUROmotor integration and Design (NEUROiD) platform. NEUROiD helps integrate results from motor systems anatomy, physiology, and biomechanics into an integrated neuromotor system model. Simulation and visualization of the model across multiple scales is supported. Standard electrophysiological operations such as slicing, current injection, recording of membrane potential, and local field potential are part of NEUROiD. The platform allows traceability of model parameters to primary literature. We illustrate the power and utility of NEUROiD by building a simple ankle model and its controlling neural circuitry by curating a set of published components. NEUROiD allows researchers to utilize remote high-performance computers for simulation, while controlling the model using a web browser.

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.

The logic behind neural control of breathing pattern

The respiratory rhythm generator is spectacular in its ability to support a wide range of activities and adapt to changing environmental conditions, yet its operating mechanisms remain elusive. We show how selective control of inspiration and expiration times can be achieved in a new representation of the neural system (called a Boolean network). The new framework enables us to predict the behavior of neural networks based on properties of neurons, not their values. Hence, it reveals the logic behind the neural mechanisms that control the breathing pattern. Our network mimics many features seen in the respiratory network such as the transition from a 3-phase to 2-phase to 1-phase rhythm, providing novel insights and new testable predictions.

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.

Bifurcations of Limit Cycles in a Reduced Model of the Xenopus Tadpole Central Pattern Generator

We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These synchronous episodes are rarely recorded and have no identified behavioural purpose. However, metamorphosing tadpoles require both anti-phase and in-phase oscillations for swimming locomotion. Previous models have shown the ability to generate biologically realistic patterns of synchrony and swimming oscillations in tadpoles, but a mathematical description of how these oscillations appear is still missing. We define a simplified model that incorporates the key operating principles of tadpole locomotion. The model generates the various outputs seen in experimental recordings, including swimming and synchrony. To study the model, we perform detailed one- and two-parameter bifurcation analysis. This reveals the critical boundaries that separate different dynamical regimes and demonstrates the existence of parameter regions of bi-stable swimming and synchrony. We show that swimming is stable in a significantly larger range of parameters, and can be initiated more robustly, than synchrony. Our results can explain the appearance of long-lasting synchrony bouts seen in experiments at the start of a swimming episode.

Loss of Atoh1 from neurons regulating hypoxic and hypercapnic chemoresponses causes neonatal respiratory failure in mice

Atoh1-null mice die at birth from respiratory failure, but the precise cause has remained elusive. Loss of Atoh1 from various components of the respiratory circuitry (e.g. the retrotrapezoid nucleus (RTN)) has so far produced at most 50% neonatal lethality. To identify other Atoh1-lineage neurons that contribute to postnatal survival, we examined parabrachial complex neurons derived from the rostral rhombic lip (rRL) and found that they are activated during respiratory chemochallenges. Atoh1-deletion from the rRL does not affect survival, but causes apneas and respiratory depression during hypoxia, likely due to loss of projections to the preBötzinger Complex and RTN. Atoh1 thus promotes the development of the neural circuits governing hypoxic (rRL) and hypercapnic (RTN) chemoresponses, and combined loss of Atoh1 from these regions causes fully penetrant neonatal lethality. This work underscores the importance of modulating respiratory rhythms in response to chemosensory information during early postnatal life.

Organization of the core respiratory network: Insights from optogenetic and modeling studies

The circuit organization within the mammalian brainstem respiratory network, specifically within and between the pre-Bötzinger (pre-BötC) and Bötzinger (BötC) complexes, and the roles of these circuits in respiratory pattern generation are continuously debated. We address these issues with a combination of optogenetic experiments and modeling studies. We used transgenic mice expressing channelrhodopsin-2 under the VGAT-promoter to investigate perturbations of respiratory circuit activity by site-specific photostimulation of inhibitory neurons within the pre-BötC or BötC. The stimulation effects were dependent on the intensity and phase of the photostimulation. Specifically: (1) Low intensity (≤ 1.0 mW) pulses delivered to the pre-BötC during inspiration did not terminate activity, whereas stronger stimulations (≥ 2.0 mW) terminated inspiration. (2) When the pre-BötC stimulation ended in or was applied during expiration, rebound activation of inspiration occurred after a fixed latency. (3) Relatively weak sustained stimulation (20 Hz, 0.5-2.0 mW) of pre-BötC inhibitory neurons increased respiratory frequency, while a further increase of stimulus intensity (> 3.0 mW) reduced frequency and finally (≥ 5.0 mW) terminated respiratory oscillations. (4) Single pulses (0.2-5.0 s) applied to the BötC inhibited rhythmic activity for the duration of the stimulation. (5) Sustained stimulation (20 Hz, 0.5-3.0 mW) of the BötC reduced respiratory frequency and finally led to apnea. We have revised our computational model of pre-BötC and BötC microcircuits by incorporating an additional population of post-inspiratory inhibitory neurons in the pre-BötC that interacts with other neurons in the network. This model was able to reproduce the above experimental findings as well as previously published results of optogenetic activation of pre-BötC or BötC neurons obtained by other laboratories. The proposed organization of pre-BötC and BötC circuits leads to testable predictions about their specific roles in respiratory pattern generation and provides important insights into key circuit interactions operating within brainstem respiratory networks.

Transient Receptor Potential Channels TRPM4 and TRPC3 Critically Contribute to Respiratory Motor Pattern Formation but not Rhythmogenesis in Rodent Brainstem Circuits

Transient receptor potential channel, TRPM4, the putative molecular substrate for Ca²⁺-activated nonselective cation current (I_CAN), is hypothesized to generate bursting activity of pre-Bötzinger complex (pre-BötC) inspiratory neurons and critically contribute to respiratory rhythmogenesis. Another TRP channel, TRPC3, which mediates Na⁺/Ca²⁺ fluxes, may be involved in regulating Ca²⁺-related signaling, including affecting TRPM4/I_CAN in respiratory pre-BötC neurons. However, TRPM4 and TRPC3 expression in pre-BötC inspiratory neurons and functional roles of these channels remain to be determined. By single-cell multiplex RT-PCR, we show mRNA expression for these channels in pre-BötC inspiratory neurons in rhythmically active medullary in vitro slices from neonatal rats and mice. Functional contributions were analyzed with pharmacological inhibitors of TRPM4 or TRPC3 in vitro as well as in mature rodent arterially perfused in situ brainstem-spinal cord preparations. Perturbations of respiratory circuit activity were also compared with those by a blocker of I_CAN. Pharmacologically attenuating endogenous activation of TRPM4, TRPC3, or I_CANin vitro similarly reduced the amplitude of inspiratory motoneuronal activity without significant perturbations of inspiratory frequency or variability of the rhythm. Amplitude perturbations were correlated with reduced inspiratory glutamatergic pre-BötC neuronal activity, monitored by multicellular dynamic calcium imaging in vitro. In more intact circuits in situ, the reduction of pre-BötC and motoneuronal inspiratory activity amplitude was accompanied by reduced post-inspiratory motoneuronal activity, without disruption of rhythm generation. We conclude that endogenously activated TRPM4, which likely mediates I_CAN, and TRPC3 channels in pre-BötC inspiratory neurons play fundamental roles in respiratory pattern formation but are not critically involved in respiratory rhythm generation.

Mechanisms involved in brain dysfunction in mechanically ventilated critically ill patients: implications and therapeutics

Critical illness may lead to significant long-term neurological morbidity and patients frequently develop neuropsychological disturbances including acute delirium or memory impairment after intensive care unit (ICU) discharge. Mechanical ventilation (MV) is a risk factor to the development of adverse neurocognitive outcomes. Patients undergoing MV for long periods present neurologic impairment with memory and cognitive alteration. Delirium is considered an acute form of brain dysfunction and its prevalence rises in mechanically ventilated patients. Delirium duration is an independent predictor of mortality, ventilation time, ICU length of stay and short- and long-term cognitive impairment in the ICU survivors. Although, neurocognitive sequelae tend to improve after hospital discharge, residual deficits persist even 6 years after ICU stay. ICU-related neurocognitive impairments occurred in many cognitive domains and are particularly pronounced with regard to memory, executive functions, attentional functions, and processing speed. These sequelae have an important impact on patients' lives and ICU survivors often require institutionalization and hospitalization. Experimental studies have served to explore the possible mechanisms or pathways involved in this lung to brain interaction. This communication can be mediated via a complex web of signaling events involving neural, inflammatory, immunologic and neuroendocrine pathways. MV can affect respiratory networks and the application of protective ventilation strategies is mandatory in order to prevent adverse effects. Therefore, strategies focused to minimize lung stretch may improve outcomes, avoiding failure of distal organ, including the brain. Long-term neurocognitive impairments experienced by critically ill survivors may be mitigated by early interventions, combining cognitive and physical therapies. Inpatient rehabilitation interventions in ICU promise to improve outcomes in critically ill patients. The cross-talk between lung and brain, involving specific pathways during critical illness deserves further efforts to evaluate, prevent and improve cognitive alterations after ICU admission, and highlights the crucial importance of tailoring MV to prevent adverse outcomes.

Different roles for inhibition in the rhythm-generating respiratory network

Unraveling the interplay of excitation and inhibition within rhythm-generating networks remains a fundamental issue in neuroscience. We use a biophysical model to investigate the different roles of local and long-range inhibition in the respiratory network, a key component of which is the pre-Bötzinger complex inspiratory microcircuit. Increasing inhibition within the microcircuit results in a limited number of out-of-phase neurons before rhythmicity and synchrony degenerate. Thus unstructured local inhibition is destabilizing and cannot support the generation of more than one rhythm. A two-phase rhythm requires restructuring the network into two microcircuits coupled by long-range inhibition in the manner of a half-center. In this context, inhibition leads to greater stability of the two out-of-phase rhythms. We support our computational results with in vitro recordings from mouse pre-Bötzinger complex. Partial excitation block leads to increased rhythmic variability, but this recovers after blockade of inhibition. Our results support the idea that local inhibition in the pre-Bötzinger complex is present to allow for descending control of synchrony or robustness to adverse conditions like hypoxia. We conclude that the balance of inhibition and excitation determines the stability of rhythmogenesis, but with opposite roles within and between areas. These different inhibitory roles may apply to a variety of rhythmic behaviors that emerge in widespread pattern-generating circuits of the nervous system.NEW & NOTEWORTHY The roles of inhibition within the pre-Bötzinger complex (preBötC) are a matter of debate. Using a combination of modeling and experiment, we demonstrate that inhibition affects synchrony, period variability, and overall frequency of the preBötC and coupled rhythmogenic networks. This work expands our understanding of ubiquitous motor and cognitive oscillatory networks.

Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model

How sensory information influences the dynamics of rhythm generation varies across systems, and general principles for understanding this aspect of motor control are lacking. Determining the origin of respiratory rhythm generation is challenging because the mechanisms in a central circuit considered in isolation may be different from those in the intact organism. We analyze a closed-loop respiratory control model incorporating a central pattern generator (CPG), the Butera-Rinzel-Smith (BRS) model, together with lung mechanics, oxygen handling, and chemosensory components. We show that 1) embedding the BRS model neuron in a control loop creates a bistable system; 2) although closed-loop and open-loop (isolated) CPG systems both support eupnea-like bursting activity, they do so via distinct mechanisms; 3) chemosensory feedback in the closed loop improves robustness to variable metabolic demand; 4) the BRS model conductances provide an autoresuscitation mechanism for recovery from transient interruption of chemosensory feedback; and 5) the in vitro brain stem CPG slice responds to hypoxia with transient bursting that is qualitatively similar to in silico autoresuscitation. Bistability of bursting and tonic spiking in the closed-loop system corresponds to coexistence of eupnea-like breathing, with normal minute ventilation and blood oxygen level and a tachypnea-like state, with pathologically reduced minute ventilation and critically low blood oxygen. Disruption of the normal breathing rhythm, through either imposition of hypoxia or interruption of chemosensory feedback, can push the system from the eupneic state into the tachypneic state. We use geometric singular perturbation theory to analyze the system dynamics at the boundary separating eupnea-like and tachypnea-like outcomes.NEW & NOTEWORTHY A common challenge facing rhythmic biological processes is the adaptive regulation of central pattern generator (CPG) activity in response to sensory feedback. We apply dynamical systems tools to understand several properties of a closed-loop respiratory control model, including the coexistence of normal and pathological breathing, robustness to changes in metabolic demand, spontaneous autoresuscitation in response to hypoxia, and the distinct mechanisms that underlie rhythmogenesis in the intact control circuit vs. the isolated, open-loop CPG.

Computational study on neuronal activities arising in the pre-Bötzinger complex

Experimental investigations have shown that the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem generates the inspiratory phase of respiratory rhythm. Based on a single-compartment model of a pre-BötC inspiratory neuron, we, in this paper, use semi-analytical, numerical as well as fast-slow dynamical methods to investigate the effects of sodium conductance ([Formula: see text]) and potassium conductance ([Formula: see text]) on the firing activities of pre-BötC and try to reveal the dynamical mechanisms behind them. We show how [Formula: see text] and [Formula: see text] affect the bifurcations of the fast-subsystem and how the the firing patterns of pre-BötC transit according to the bifurcations.

Dynamics of in-phase and anti-phase bursting in the coupled pre-Bötzinger complex cells

Activity of neurons in the pre-Bötzinger complex within the mammalian brain stem has an important role in the generation of respiratory rhythms. Previous experimental results have shown that the dynamics of sodium and calcium within each cell may be responsible for various bursting mechanisms. In this paper, we study the bursting dynamics of the two-coupled pre-Bötzinger complex neurons. Using a combination of fast-slow decomposition and two-parameter bifurcation analysis, we explore the possible forms of dynamics that the model network can produce as well the transitions of in-phase and anti-phase bursting respectively.

Robustness, flexibility, and sensitivity in a multifunctional motor control model

Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as "robustness," and the ability of a system to deploy alternative strategies that improve fitness as "flexibility." Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. Here we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes and that the system exhibits bistability between the two. In the "heteroclinic mode," higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the "limit cycle mode," lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment.

Computational models of the neural control of breathing

The ongoing process of breathing underlies the gas exchange essential for mammalian life. Each respiratory cycle ensues from the activity of rhythmic neural circuits in the brainstem, shaped by various modulatory signals, including mechanoreceptor feedback sensitive to lung inflation and chemoreceptor feedback dependent on gas composition in blood and tissues. This paper reviews a variety of computational models designed to reproduce experimental findings related to the neural control of breathing and generate predictions for future experimental testing. The review starts from the description of the core respiratory network in the brainstem, representing the central pattern generator (CPG) responsible for producing rhythmic respiratory activity, and progresses to encompass additional complexities needed to simulate different metabolic challenges, closed-loop feedback control including the lungs, and interactions between the respiratory and autonomic nervous systems. The integrated models considered in this review share a common framework including a distributed CPG core network responsible for generating the baseline three-phase pattern of rhythmic neural activity underlying normal breathing. WIREs Syst Biol Med 2017, 9:e1371. doi: 10.1002/wsbm.1371 For further resources related to this article, please visit the WIREs website.

Kölliker-Fuse nuclei regulate respiratory rhythm variability via a gain-control mechanism

Respiration varies from breath to breath. On the millisecond timescale of spiking, neuronal circuits exhibit variability due to the stochastic properties of ion channels and synapses. Does this fast, microscopic source of variability contribute to the slower, macroscopic variability of the respiratory period? To address this question, we modeled a stochastic oscillator with forcing; then, we tested its predictions experimentally for the respiratory rhythm generated by the in situ perfused preparation during vagal nerve stimulation (VNS). Our simulations identified a relationship among the gain of the input, entrainment strength, and rhythm variability. Specifically, at high gain, the periodic input entrained the oscillator and reduced variability, whereas at low gain, the noise interacted with the input, causing events known as "phase slips", which increased variability on a slow timescale. Experimentally, the in situ preparation behaved like the low-gain model: VNS entrained respiration but exhibited phase slips that increased rhythm variability. Next, we used bilateral muscimol microinjections in discrete respiratory compartments to identify areas involved in VNS gain control. Suppression of activity in the nucleus tractus solitarii occluded both entrainment and amplification of rhythm variability by VNS, confirming that these effects were due to the activation of the Hering-Breuer reflex. Suppressing activity of the Kölliker-Fuse nuclei (KFn) enhanced entrainment and reduced rhythm variability during VNS, consistent with the predictions of the high-gain model. Together, the model and experiments suggest that the KFn regulates respiratory rhythm variability via a gain control mechanism.

Central control of interlimb coordination and speed-dependent gait expression in quadrupeds

KEY POINTS

Quadrupeds express different gaits depending on speed of locomotion. Central pattern generators (one per limb) within the spinal cord generate locomotor oscillations and control limb movements. Neural interactions between these generators define interlimb coordination and gait. We present a computational model of spinal circuits representing four rhythm generators with left-right excitatory and inhibitory commissural and fore-hind inhibitory interactions within the cord. Increasing brainstem drive to all rhythm generators and excitatory commissural interneurons induces an increasing frequency of locomotor oscillations accompanied by speed-dependent gait changes from walk to trot and to gallop and bound. The model closely reproduces and suggests explanations for multiple experimental data, including speed-dependent gait transitions in intact mice and changes in gait expression in mutants lacking certain types of commissural interneurons. The model suggests the possible circuit organization in the spinal cord and proposes predictions that can be tested experimentally.

ABSTRACT

As speed of locomotion is increasing, most quadrupeds, including mice, demonstrate sequential gait transitions from walk to trot and to gallop and bound. The neural mechanisms underlying these transitions are poorly understood. We propose that the speed-dependent expression of different gaits results from speed-dependent changes in the interactions between spinal circuits controlling different limbs and interlimb coordination. As a result, the expression of each gait depends on (1) left-right interactions within the spinal cord mediated by different commissural interneurons (CINs), (2) fore-hind interactions on each side of the spinal cord and (3) brainstem drives to rhythm-generating circuits and CIN pathways. We developed a computational model of spinal circuits consisting of four rhythm generators (RGs) with bilateral left-right interactions mediated by V0 CINs (V0_D and V0_V sub-types) providing left-right alternation, and conditional V3 CINs promoting left-right synchronization. Fore and hind RGs mutually inhibited each other. We demonstrate that linearly increasing excitatory drives to the RGs and V3 CINs can produce a progressive increase in the locomotor speed accompanied by sequential changes of gaits from walk to trot and to gallop and bound. The model closely reproduces and suggests explanations for the speed-dependent gait expression observed in vivo in intact mice and in mutants lacking V0_V or all V0 CINs. Specifically, trot is not expressed after removal of V0_V CINs, and only bound is expressed after removal of all V0 CINs. The model provides important insights into the organization of spinal circuits and neural control of locomotion.

Effects of ion channel noise on neural circuits: an application to the respiratory pattern generator to investigate breathing variability

Neural activity generally displays irregular firing patterns even in circuits with apparently regular outputs, such as motor pattern generators, in which the output frequency fluctuates randomly around a mean value. This "circuit noise" is inherited from the random firing of single neurons, which emerges from stochastic ion channel gating (channel noise), spontaneous neurotransmitter release, and its diffusion and binding to synaptic receptors. Here we demonstrate how to expand conductance-based network models that are originally deterministic to include realistic, physiological noise, focusing on stochastic ion channel gating. We illustrate this procedure with a well-established conductance-based model of the respiratory pattern generator, which allows us to investigate how channel noise affects neural dynamics at the circuit level and, in particular, to understand the relationship between the respiratory pattern and its breath-to-breath variability. We show that as the channel number increases, the duration of inspiration and expiration varies, and so does the coefficient of variation of the breath-to-breath interval, which attains a minimum when the mean duration of expiration slightly exceeds that of inspiration. For small channel numbers, the variability of the expiratory phase dominates over that of the inspiratory phase, and vice versa for large channel numbers. Among the four different cell types in the respiratory pattern generator, pacemaker cells exhibit the highest sensitivity to channel noise. The model shows that suppressing input from the pons leads to longer inspiratory phases, a reduction in breathing frequency, and larger breath-to-breath variability, whereas enhanced input from the raphe nucleus increases breathing frequency without changing its pattern.

NEW & NOTEWORTHY

A major source of noise in neuronal circuits is the "flickering" of ion currents passing through the neurons' membranes (channel noise), which cannot be suppressed experimentally. Computational simulations are therefore the best way to investigate the effects of this physiological noise by manipulating its level at will. We investigate the role of noise in the respiratory pattern generator and show that endogenous, breath-to-breath variability is tightly linked to the respiratory pattern.

Voltage-Dependent Rhythmogenic Property of Respiratory Pre-Bötzinger Complex Glutamatergic, Dbx1-Derived, and Somatostatin-Expressing Neuron Populations Revealed by Graded Optogenetic Inhibition

The rhythm of breathing in mammals, originating within the brainstem pre-Bötzinger complex (pre-BötC), is presumed to be generated by glutamatergic neurons, but this has not been directly demonstrated. Additionally, developmental expression of the transcription factor Dbx1 or expression of the neuropeptide somatostatin (Sst), has been proposed as a marker for the rhythmogenic pre-BötC glutamatergic neurons, but it is unknown whether these other two phenotypically defined neuronal populations are functionally equivalent to glutamatergic neurons with regard to rhythm generation. To address these problems, we comparatively investigated, by optogenetic approaches, the roles of pre-BötC glutamatergic, Dbx1-derived, and Sst-expressing neurons in respiratory rhythm generation in neonatal transgenic mouse medullary slices in vitro and also more intact adult perfused brainstem-spinal cord preparations in situ. We established three different triple-transgenic mouse lines with Cre-driven Archaerhodopsin-3 (Arch) expression selectively in glutamatergic, Dbx1-derived, or Sst-expressing neurons for targeted photoinhibition. In each line, we identified subpopulations of rhythmically active, Arch-expressing pre-BötC inspiratory neurons by whole-cell recordings in medullary slice preparations in vitro, and established that Arch-mediated hyperpolarization of these inspiratory neurons was laser power dependent with equal efficacy. By site- and population-specific graded photoinhibition, we then demonstrated that inspiratory frequency was reduced by each population with the same neuronal voltage-dependent frequency control mechanism in each state of the respiratory network examined. We infer that enough of the rhythmogenic pre-BötC glutamatergic neurons also have the Dbx1 and Sst expression phenotypes, and thus all three phenotypes share the same voltage-dependent frequency control property.

Perturbations of Respiratory Rhythm and Pattern by Disrupting Synaptic Inhibition within Pre-Bötzinger and Bötzinger Complexes

The pre-Bötzinger (pre-BötC) and Bötzinger (BötC) complexes are the brainstem compartments containing interneurons considered to be critically involved in generating respiratory rhythm and motor pattern in mammals.

The pre-Bötzinger (pre-BötC) and Bötzinger (BötC) complexes are the brainstem compartments containing interneurons considered to be critically involved in generating respiratory rhythm and motor pattern in mammals. Current models postulate that both generation of the rhythm and coordination of the inspiratory-expiratory pattern involve inhibitory synaptic interactions within and between these regions. Both regions contain glycinergic and GABAergic neurons, and rhythmically active neurons in these regions receive appropriately coordinated phasic inhibition necessary for generation of the normal three-phase respiratory pattern. However, recent experiments attempting to disrupt glycinergic and GABAergic postsynaptic inhibition in the pre-BötC and BötC in adult rats in vivo have questioned the critical role of synaptic inhibition in these regions, as well as the importance of the BötC, which contradicts previous physiological and pharmacological studies. To further evaluate the roles of synaptic inhibition and the BötC, we bilaterally microinjected the GABA_A receptor antagonist gabazine and glycinergic receptor antagonist strychnine into the pre-BötC or BötC in anesthetized adult rats in vivo and in perfused in situ brainstem–spinal cord preparations from juvenile rats. Muscimol was microinjected to suppress neuronal activity in the pre-BötC or BötC. In both preparations, disrupting inhibition within pre-BötC or BötC caused major site-specific perturbations of the rhythm and disrupted the three-phase motor pattern, in some experiments terminating rhythmic motor output. Suppressing BötC activity also potently disturbed the rhythm and motor pattern. We conclude that inhibitory circuit interactions within and between the pre-BötC and BötC critically regulate rhythmogenesis and are required for normal respiratory motor pattern generation.

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

This study focuses on computational and theoretical investigations of neuronal activity arising in the pre-Bötzinger complex (pre-BötC), a medullary region generating the inspiratory phase of breathing in mammals. A progressive increase of neuronal excitability in medullary slices containing the pre-BötC produces mixed-mode oscillations (MMOs) characterized by large amplitude population bursts alternating with a series of small amplitude bursts. Using two different computational models, we demonstrate that MMOs emerge within a heterogeneous excitatory neural network because of progressive neuronal recruitment and synchronization. The MMO pattern depends on the distributed neuronal excitability, the density and weights of network interconnections, and the cellular properties underlying endogenous bursting. Critically, the latter should provide a reduction of spiking frequency within neuronal bursts with increasing burst frequency and a dependence of the after-burst recovery period on burst amplitude. Our study highlights a novel mechanism by which heterogeneity naturally leads to complex dynamics in rhythmic neuronal populations.

DOI:http://dx.doi.org/10.7554/eLife.13403.001

Each breath we take removes carbon dioxide from the body and exchanges it for oxygen. A structure called the brainstem, which connects the brain with the spinal cord, generates the breathing rhythm and controls its rate. While this process normally occurs automatically, we can also control our breathing voluntarily, such as when singing or speaking.

Within the brainstem, a group of neurons in the area known as the pre-Bötzinger complex is responsible for ensuring that an animal breathes in at regular intervals. Recordings of the electrical activity from slices of brainstem show that pre-Bötzinger neurons display rhythmic activity with characteristic patterns called “mixed-mode oscillations”. These rhythms consist of bursts of strong activity (“large amplitude bursts”), essential for triggering regular breathing, separated by a series of bursts of weak activity (“small amplitude bursts”). However, it is not clear how mixed-mode oscillations arise.

Bacak, Kim et al. now provide insights into this process by developing two computational models of the pre-Bötzinger complex. The first model consists of a diverse population of 100 neurons joined by a relatively small number of weak connections to form a network. The second model is a simplified version of the first, consisting of just three neurons. By manipulating the properties of the simulated networks, and analysing the data mathematically, Bacak, Kim et al. identify the properties of the neurons that allow them to generate mixed-mode oscillations and thus rhythmic breathing.

The models suggest that mixed-mode oscillations result from the synchronization of many neurons with different levels of activity (excitability). Neurons with low excitability have low bursting frequencies, but generate strong activity and recruit other neurons, ultimately producing large amplitude bursts that cause breathing.

Many parts of the nervous system are also made up of networks of neurons with diverse excitability. A challenge for future studies is thus to investigate whether other networks of neurons similar to the pre-Bötzinger complex generate rhythms that control other repetitive actions, such as walking and chewing.

DOI:http://dx.doi.org/10.7554/eLife.13403.002

Conditions for Multi-functionality in a Rhythm Generating Network Inspired by Turtle Scratching

Rhythmic behaviors such as breathing, walking, and scratching are vital to many species. Such behaviors can emerge from groups of neurons, called central pattern generators, in the absence of rhythmic inputs. In vertebrates, the identification of the cells that constitute the central pattern generator for particular rhythmic behaviors is difficult, and often, its existence has only been inferred. For example, under experimental conditions, intact turtles generate several rhythmic scratch motor patterns corresponding to non-rhythmic stimulation of different body regions. These patterns feature alternating phases of motoneuron activation that occur repeatedly, with different patterns distinguished by the relative timing and duration of activity of hip extensor, hip flexor, and knee extensor motoneurons. While the central pattern generator network responsible for these outputs has not been located, there is hope to use motoneuron recordings to deduce its properties. To this end, this work presents a model of a previously proposed central pattern generator network and analyzes its capability to produce two distinct scratch rhythms from a single neuron pool, selected by different combinations of tonic drive parameters but with fixed strengths of connections within the network. We show through simulation that the proposed network can achieve the desired multi-functionality, even though it relies on hip unit generators to recruit appropriately timed knee extensor motoneuron activity, including a delay relative to hip activation in rostral scratch. Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay. This framework is harnessed to consider bistability and to make predictions about the responses of the scratch rhythms to input changes for future experimental testing.

Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics

How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrophysiological recordings, that SF/SD can occur at preBötC synapses on timescales that influence rhythmic population activity. We conclude that nondeterministic neuronal spiking and dynamic synaptic strengths in a randomly connected network are sufficient to give rise to regular respiratory-like rhythmic network activity and lability, which may play an important role in generating the rhythm for breathing and other coordinated motor activities in mammals.

Mechanisms of left-right coordination in mammalian locomotor pattern generation circuits: a mathematical modeling view

The locomotor gait in limbed animals is defined by the left-right leg coordination and locomotor speed. Coordination between left and right neural activities in the spinal cord controlling left and right legs is provided by commissural interneurons (CINs). Several CIN types have been genetically identified, including the excitatory V3 and excitatory and inhibitory V0 types. Recent studies demonstrated that genetic elimination of all V0 CINs caused switching from a normal left-right alternating activity to a left-right synchronized “hopping” pattern. Furthermore, ablation of only the inhibitory V0 CINs (V0_D subtype) resulted in a lack of left-right alternation at low locomotor frequencies and retaining this alternation at high frequencies, whereas selective ablation of the excitatory V0 neurons (V0_V subtype) maintained the left–right alternation at low frequencies and switched to a hopping pattern at high frequencies. To analyze these findings, we developed a simplified mathematical model of neural circuits consisting of four pacemaker neurons representing left and right, flexor and extensor rhythm-generating centers interacting via commissural pathways representing V3, V0_D, and V0_V CINs. The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations. The model demonstrated a typical left-right alternating pattern under control conditions, switching to a hopping activity at any frequency after removing both V0 connections, a synchronized pattern at low frequencies with alternation at high frequencies after removing only V0_D connections, and an alternating pattern at low frequencies with hopping at high frequencies after removing only V0_V connections. We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them. The model reproduced, and suggested explanation for, a series of experimental phenomena and generated predictions available for experimental testing.

Movements of left and right limbs in mammals during locomotion are controlled by distinct rhythm-generating neuronal circuits in the spinal cord. Complex interactions between these circuits provide flexible coordination of limb movements in different gaits. It was shown that interactions between left and right spinal circuits are mediated by commissural interneurons. Genetic ablation of a particular type of these interneurons, called V0, leads to switching from a regular, left-right alternating “walking” activity to a left-right synchronous “hopping” pattern. Moreover, the V0 commissural interneurons have excitatory and inhibitory subtypes that appear to play different roles in the left-right coordination depending on locomotor speed. In this theoretical study, we build a simplified mathematical model of spinal circuits that describes left and right rhythm generators interacting bilaterally via several types of commissural connections. Using this model, we simulate different experimental manipulations, analyze the resultant alternating and synchronous regimes of activity, and propose explanations for the results of experimental studies. We show that although both excitatory and inhibitory V0 commissural pathways support left-right alternation, the resultant locomotor pattern and gait depend on the balance between different commissural interactions, which in turn may depend on the level of neuronal excitation and locomotor speed.

A closed-loop model of the respiratory system: focus on hypercapnia and active expiration

Breathing is a vital process providing the exchange of gases between the lungs and atmosphere. During quiet breathing, pumping air from the lungs is mostly performed by contraction of the diaphragm during inspiration, and muscle contraction during expiration does not play a significant role in ventilation. In contrast, during intense exercise or severe hypercapnia forced or active expiration occurs in which the abdominal “expiratory” muscles become actively involved in breathing. The mechanisms of this transition remain unknown. To study these mechanisms, we developed a computational model of the closed-loop respiratory system that describes the brainstem respiratory network controlling the pulmonary subsystem representing lung biomechanics and gas (O₂ and CO₂) exchange and transport. The lung subsystem provides two types of feedback to the neural subsystem: a mechanical one from pulmonary stretch receptors and a chemical one from central chemoreceptors. The neural component of the model simulates the respiratory network that includes several interacting respiratory neuron types within the Bötzinger and pre-Bötzinger complexes, as well as the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) representing the central chemoreception module targeted by chemical feedback. The RTN/pFRG compartment contains an independent neural generator that is activated at an increased CO₂ level and controls the abdominal motor output. The lung volume is controlled by two pumps, a major one driven by the diaphragm and an additional one activated by abdominal muscles and involved in active expiration. The model represents the first attempt to model the transition from quiet breathing to breathing with active expiration. The model suggests that the closed-loop respiratory control system switches to active expiration via a quantal acceleration of expiratory activity, when increases in breathing rate and phrenic amplitude no longer provide sufficient ventilation. The model can be used for simulation of closed-loop control of breathing under different conditions including respiratory disorders.

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.