Modeling the effects of extracellular potassium on bursting properties in pre-Bötzinger complex neurons

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 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.

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.

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.

Muscarinic Modulation of Morphologically Identified Glycinergic Neurons in the Mouse PreBötzinger Complex

The cholinergic system plays an essential role in central respiratory control, but the underlying mechanisms remain elusive. We used whole-cell recordings in brainstem slices from juvenile mice expressing enhanced green fluorescent protein (EGFP) under the control of the glycine transporter type 2 (GlyT₂) promoter, to examine muscarinic modulation of morphologically identified glycinergic neurons in the preBötzinger complex (preBötC), an area critical for central inspiratory rhythm generation. Biocytin-filled reconstruction of glycinergic neurons revealed that the majority of them had few primary dendrites and had axons arborized within their own dendritic field. Few glycinergic neurons had axon collaterals extended towards the premotor/motor areas or ran towards the contralateral preBötC, and had more primary dendrites and more compact dendritic trees. Spontaneously active glycinergic neurons fired regular spikes, or less frequently in a "burst-like" pattern at physiological potassium concentration. Muscarine suppressed firing in the majority of regular spiking neurons via M₂ receptor activation while enhancing the remaining neurons through M₁ receptors. Interestingly, rhythmic bursting was augmented by muscarine in a small group of glycinergic neurons. In contrast to its heterogeneous modulation of glycinergic neuronal excitability, muscarine generally depressed inhibitory and excitatory synaptic inputs onto both glycinergic and non-glycinergic preBötC neurons, with a stronger effect on inhibitory input. Notably, presynaptic muscarinic attenuation of excitatory synaptic input was dependent on M₁ receptors in glycinergic neurons and on M₂ receptors in non-glycinergic neurons. Additional field potential recordings of excitatory synaptic potentials in the M₂ receptor knockout mice indicate that glycinergic and non-glycinergic neurons contribute equally to the general suppression by muscarine of excitatory activity in preBötC circuits. In conclusion, our data show that preBötC glycinergic neurons are morphologically heterogeneous, and differ in the properties of synaptic transmission and muscarinic modulation in comparison to non-glycinergic neurons. The dominant and cell-type-specific muscarinic inhibition of synaptic neurotransmission and spiking may contribute to central respiratory disturbances in high cholinergic states.

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.

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.