Dynamics of Rhythm Generation in Respiration and Beyond

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A variety of rhythmic movements fundamental to mammalian interactions with the environment emerge from activity in networks of neurons. For example, experiments have revealed the existence of a neuronal rhythm-generating system in the mammalian brainstem that maintains a stable respiratory rhythm and another in the mammalian spinal cord that drives limbed locomotion, both subject to feedback control. This research project will lead to new insights, and generate new predictions, about how the intrinsic properties of neurons, the characteristics of their interactions, and the features of feedback signals contribute to the generation and modulation of these and other neuronal rhythms. Particular issues that will be investigated are the roles of specific ionic currents and the specific patterns of connections between respiratory neurons in generating synchronized bursting, or alternation of activity between silent and active periods, and in switching between different phases of respiration; the effectiveness of particular feedback control targets and signals in regulating respiratory neuron activity under changing environmental or metabolic demands; the relative contributions of rhythmic neuronal activity and of mechanical constraints and feedback signals to asymmetries in locomotor gait phase durations seen in response to changes in top-down drive; and possible mechanisms that can yield recovery of locomotor rhythms if loss of top-down drive associated with spinal cord injury occurs. Results in these areas will be achieved through the mathematical analysis of neuronal network models constrained by experimental data. The models will consist of coupled systems of nonlinear ordinary differential equations, with different model components often evolving at disparate rates. Techniques of fast/slow decomposition and geometric singular perturbation theory, bifurcation analysis, averaging, map derivation, and direct simulation will all be applied to develop new insights and predictions about the dynamics of respiratory and locomotor rhythms as well as general principles of neuronal rhythmogenesis.Respiration and locomotion are among the many rhythmic neuro-mechanical processes that can be maintained without direct voluntary inputs. Significant research efforts have advanced our understanding of the mechanisms through which respiratory and locomotor rhythms are produced and altered in response to changing environmental and metabolic conditions, yet many aspects of this rhythm generation and feedback regulation remain unknown. This research project will address several such open questions using the development of mathematical models constrained by experimental data as well as computer simulations and mathematical analysis of these models. In the context of respiration, this research will consider coordination of activity patterns of key rhythmically active brainstem neurons that drive muscle movements associated with respiration as well as the interaction of these neurons with feedback controls that adjust network activity to handle changing demands. These steps will be performed in collaboration with two neuroscience labs, providing direct access to experimental data and testing of model predictions. In the setting of limbed locomotion, this project will focus on a model that combines a neuronal rhythm generation system and a mechanical limb that it drives, which sends feedback signals, related to muscle actions, back to the rhythm generator. The research in this area will include analysis of how the interactions of these neuronal and mechanical components generate the properties of limbed locomotion as well as of mechanisms that can yield recovery of locomotor rhythms if damage associated with spinal cord injury occurs, which may help guide the development of therapeutic interventions currently under investigation to restore locomotion in individuals with such injuries.