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

Authors:
Jonathan E. Rubin;Bartholomew J. Bacak;Yaroslav I. Molkov;Natalia A. Shevtsova;Jeffrey C. Smith;Ilya A. Rybak
Affiliations:
Department of Mathematics, University of Pittsburgh, Pittsburgh, USA 15260;Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, USA 19129;Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, USA 19129;Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, USA 19129;Cellular and Systems Neurobiology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, USA 20892;Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, USA 19129
Venue:
Journal of Computational Neuroscience
Year:
2011

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Abstract

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.