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

Unraveling the dynamics of firing patterns for neurons with impairment of sodium channels

Various factors such as mechanical trauma, chemical trauma, local ischemia, and inflammation can impair voltage-gated sodium channels (Nav) in neurons. These impairments lead to a distinctive leftward shift in the activation and inactivation curves of voltage-gated sodium channels. The resulting sodium channel impairments in neurons are known to affect firing patterns, which play a significant role in neuronal activities within the nervous system. However, the underlying dynamic mechanism for the emergence of these firing patterns remains unclear. In this study, we systematically investigated the effects of sodium channel dysfunction on individual neuronal dynamics and firing patterns. By employing codimension-1 bifurcation analysis, we revealed the underlying dynamical mechanism responsible for the generation of different firing patterns. Additionally, through codimension-2 bifurcation analysis, we theoretically determined the distribution of firing patterns on different parameter planes. Our results indicate that the firing patterns of impaired neurons are regulated by multiple parameters, with firing pattern transitions caused by the degree of sodium channel impairment being more diverse than those caused by the ratio of impaired sodium channel and current. Furthermore, we observed that the firing pattern of tonic firing is more likely to be the norm in impaired sodium channel neurons, providing valuable insights into the signaling of impaired neurons. Overall, our findings highlight the intricate relationships among sodium channel impairments, neuronal dynamics, and firing patterns, shedding light on the impact of disruptions in ion concentration gradients on neuronal function.

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.

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.

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.

Role of NaV1.6-mediated persistent sodium current and bursting-pacemaker properties in breathing rhythm generation

Inspiration is the inexorable active phase of breathing. The brainstem pre-Bötzinger complex (preBötC) gives rise to inspiratory neural rhythm, but its underlying cellular and ionic bases remain unclear. The long-standing "pacemaker hypothesis" posits that the persistent Na+ current (INaP) that gives rise to bursting-pacemaker properties in preBötC interneurons is essential for rhythmogenesis. We tested the pacemaker hypothesis by conditionally knocking out and knocking down the Scn8a (Nav1.6 [voltage-gated sodium channel 1.6]) gene in core rhythmogenic preBötC neurons. Deleting Scn8a substantially decreases the INaP and abolishes bursting-pacemaker activity, which slows inspiratory rhythm in vitro and negatively impacts the postnatal development of ventilation. Diminishing Scn8a via genetic interference has no impact on breathing in adult mice. We argue that the Scn8a-mediated INaP is not obligatory but that it influences the development and rhythmic function of the preBötC. The ubiquity of the INaP in respiratory brainstem interneurons could underlie breathing-related behaviors such as neonatal phonation or rhythmogenesis in different physiological conditions.

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.

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.

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

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

Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network

Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.

Dynamic Rhythmogenic Network States Drive Differential Opioid Responses in the In Vitro Respiratory Network

Death from opioid overdose is typically caused by opioid-induced respiratory depression (OIRD). A particularly dangerous characteristic of OIRD is its apparent unpredictability. The respiratory consequences of opioids can be surprisingly inconsistent, even within the same individual. Despite significant clinical implications, most studies have focused on average dose-r esponses rather than individual variation, and there remains little insight into the etiology of this apparent unpredictability. The preBötzinger complex (preBötC) in the ventral medulla is an important site for generating the respiratory rhythm and OIRD. Here, using male and female C57-Bl6 mice in vitro, we demonstrate that the preBötC can assume different network states depending on the excitability of the preBötC and the intrinsic membrane properties of preBötC neurons. These network states predict the functional consequences of opioids in the preBötC, and depending on network state, respiratory rhythmogenesis can be either stabilized or suppressed by opioids. We hypothesize that the dynamic nature of preBötC rhythmogenic properties, required to endow breathing with remarkable flexibility, also plays a key role in the dangerous unpredictability of OIRD.SIGNIFICANCE STATEMENT Opioids can cause unpredictable, life-threatening suppression of breathing. This apparent unpredictability makes clinical management of opioids difficult while also making it challenging to define the underlying mechanisms of OIRD. Here, we find in brainstem slices that the preBötC, an opioid-sensitive subregion of the brainstem, has an optimal configuration of cellular and network properties that results in a maximally stable breathing rhythm. These properties are dynamic, and the state of each individual preBötC network relative to the optimal configuration of the network predicts how vulnerable rhythmogenesis is to the effects of opioids. These insights establish a framework for understanding how endogenous and exogenous modulation of the rhythmogenic state of the preBötC can increase or decrease the risk of OIRD.

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.

The mechanism of non-blocking inhibition of sodium channels revealed by conformation-selective photolabeling

BACKGROUND AND PURPOSE

Sodium channel inhibitors can be used to treat hyperexcitability-related diseases, including epilepsies, pain syndromes, neuromuscular disorders and cardiac arrhythmias. The applicability of these drugs is limited by their nonspecific effect on physiological function. They act mainly by sodium channel block and in addition by modulation of channel kinetics. While channel block inhibits healthy and pathological tissue equally, modulation can preferentially inhibit pathological activity. An ideal drug designed to target the sodium channels of pathological tissue would act predominantly by modulation. Thus far, no such drug has been described.

EXPERIMENTAL APPROACH

Patch-clamp experiments with ultra-fast solution exchange and photolabeling-coupled electrophysiology were applied to describe the unique mechanism of riluzole on Nav1.4 sodium channels. In silico docking experiments were used to study the molecular details of binding.

KEY RESULTS

We present evidence that riluzole acts predominantly by non-blocking modulation. We propose that, being a relatively small molecule, riluzole is able to stay bound to the binding site, but nonetheless stay off the conduction pathway, by residing in one of the fenestrations. We demonstrate how this mechanism can be recognized.

CONCLUSIONS AND IMPLICATIONS

Our results identify riluzole as the prototype of this new class of sodium channel inhibitors. Drugs of this class are expected to selectively prevent hyperexcitability, while having minimal effect on cells firing at a normal rate from a normal resting potential.

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

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

Complex bursting dynamics in an embryonic respiratory neuron model

Pre-Bötzinger complex (pre-BötC) network activity within the mammalian brainstem controls the inspiratory phase of the respiratory rhythm. While bursting in pre-BötC neurons during the postnatal period has been extensively studied, less is known regarding inspiratory pacemaker neuron behavior at embryonic stages. Recent data in mouse embryo brainstem slices have revealed the existence of a variety of bursting activity patterns depending on distinct combinations of burst-generating I_NaP and I_CAN conductances. In this work, we consider a model of an isolated embryonic pre-BötC neuron featuring two distinct bursting mechanisms. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to uncover mechanisms underlying several different types of intrinsic bursting dynamics observed experimentally including several forms of plateau bursts, bursts involving depolarization block, and various combinations of these patterns. Our analysis also yields predictions about how changes in the balance of the two bursting mechanisms contribute to alterations in an inspiratory pacemaker neuron activity during prenatal development.