The Kolliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnea under resting conditions and the control of active 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.
Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.
Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model burst patterns vary with changes in the conductance of a fast inward current. Using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.
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