Bartholomew J. Bacak

Late-Expiratory Activity: Emergence and Interactions With the Respiratory CPG

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

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

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

Control of breathing by interacting pontine and pulmonary feedback loops.

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

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

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

There are many types of neurons that intrinsically generate rhythmic bursting activity, even when isolated, and these neurons underlie several specific motor behaviors. Rhythmic neurons that drive the inspiratory phase of respiration are located in the medullary pre-Bötzinger Complex (pre-BötC). However, it is not known if their rhythmic bursting is the result of intrinsic mechanisms or synaptic interactions. In many cases, for bursting to occur, the excitability of these neurons needs to be elevated. This excitation is provided in vitro (e.g. in slices), by increasing extracellular potassium concentration (Kout) well beyond physiologic levels. Elevated Kout shifts the reversal potentials for all potassium currents including the potassium component of leakage to higher values. However, how an increase in Kout, and the resultant changes in potassium currents, induce bursting activity, have yet to be established. Moreover, it is not known if the endogenous bursting induced in vitro is representative of neural behavior in vivo. Our modeling study examines the interplay between Kout, excitability, and selected currents, as they relate to endogenous rhythmic bursting. Starting with a Hodgkin-Huxley formalization of a pre-BötC neuron, a potassium ion component was incorporated into the leakage current, and model behaviors were investigated at varying concentrations of Kout. Our simulations show that endogenous bursting activity, evoked in vitro by elevation of Kout, is the result of a specific relationship between the leakage and voltage-dependent, delayed rectifier potassium currents, which may not be observed at physiological levels of extracellular potassium.

Extracellular potassium concentration defines neuronal bursting properties

Many neurons, or populations of neurons, in the brain are capable of producing rhythmic bursting activity. This ability is putatively responsible for rhythmogenic functions like breathing and locomotion. In vivo, rhythms are generated by synaptically interconnected neuronal networks, whereas rhythmic bursting behavior is often induced in vitro by elevating the extracellular potassium concentration (Kout ) [1]. It is known that increasing Kout raises the reversal potentials of potassium and leak currents [2]. However, the complete nature of how these effects underlie bursting activity has yet to be uncovered. A mathematical modeling study was performed to elucidate the interplay between these factors and their roles in a neurons transition from quiescence to rhythmic bursting. A conductance-based model of a neuron from the pre-Botzinger Complex (pre-BotC) was used as a basis [3]. A potassium ion component was incorporated into the leak current, and model behaviors were investigated at varying concentrations of Kout , taking into account its effect on delayed rectifier potassium current responsible for after-spike hyperpolarization. The primary aim of this modeling study was to evaluate the contribution of extracellular potassium ions in the leak and delayed rectifier potassium current, and the subsequent effect of these altered currents on the bursting properties of neurons. Furthermore, the initial model was modified to replicate experimental results and test for conditions of low Kout as seen in vivo. The analysis of our model shows that: (i) in vitro bursting behavior with elevated Kout may occur due to attenuation of the delayed rectifier potassium current and (ii) no oscillations are generated at physiological levels of extracellular potassium. These results indicate that, according to the commonly-accepted models used in our study, neurons that naturally burst in in vitro preparations may not be able to burst in vivo under any circumstances. Accordingly, rhythmic activity in vivo should rely on other mechanisms. For example, Jasinski et al. [4] have shown that the recurrent synaptic excitation in combination with the sodium-potassium exchanger (pump) can result in the robust rhythmic network activity even with all intrinsic bursting mechanisms blocked.