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.
This project centered on the use of mathematical and computational methods to investigate mechanisms by which networks of neurons generate rhythmic activity linked with respiration and motor behaviors. It led to significant advances in our understanding of how intrinsic properties of neurons combine with interactions between neurons to shape neuronal network outputs, to the development of state-of-the-art computational models representing a variety of specific neuronal networks as well as others related to more general neural systems, to a large number of contributions to the research literature, and to the training and advancement of one postdoctoral researcher and several graduate and undergraduate students. Intellectual Merit: Work on this project produced many advances in knowledge. In the area of respiration, our contributions ranged from novel model development and analysis relating to small networks of neurons in a circuit critical for inspiration, to groundbreaking explorations of larger network models of this circuit constrained by experimental data, to the development of a closed-loop respiratory network model involving neural rhythm generation and driving of physiological components that in turn provide chemo- and mechanosensory feedback to the neurons. Mathematical work in this area advanced methods for analyzing solution behavior, and bifurcations between solutions, in networks with multiple slow variables and with heterogeneity in the properties of network components. In the area of motor rhythms, we developed and applied mathematical methods to study a closed loop model spanning from neural rhythm generation to muscle and force-related feedback in locomotion, obtaining new results on what components of this loop contribute to step cycle changes with changes in walking speed, which may also be relevant to restoring rhythm generation after spinal cord injury. We identified conditions allowing single motor rhythm generation networks to multitask, producing multiple different rhythms selected by non-rhythmic inputs, and to coordinate the timings of multiple muscle groups. We contributed a wide variety of state-of-the-art computational models to the research community, including models for respiratory neurons and networks, for neurons in the subthalamic nucleus of the basal ganglia, for multifunctional rhythm generator networks, for stochastic aspects of short term depression of neuronal communication, for the recruitment of nerve fibers by neural interface stimulation devices, and for reduced representations of rhythmic dynamics that may be useful for efficient network simulations. We have used and developed mathematical and computational methods to attain additional significant advances in theoretical neuroscience, including results on (1) how irregular or chaotic activity, a fundamental neural state found widely in the brain under many conditions, can arise in purely inhibitory networks failing to satisfy the balance conditions previously believed to be required to achieve such behavior, (2) how stochastic effects associated with short term depression in neural transmission can significantly impact synaptic information and signal transfer, with possible implications for attempts to alter pathological neural signaling through neural stimulation, and (3) how adjoint methods and the theory of averaging yield a way to analyze synchronization in neurons coupled indirectly through a slowly evolving external medium such as a shared ion supply, with possible implications for network events such as epileptic seizures. Broader Impact: One postdoctoral researcher and three graduate students were directly funded by this award and were provided with research mentorshop, with opportunities to present their work through publication and conference presentation, and with additional guidance related to professional development. The postdoc is now a tenure-track faculty member at a historically minority-serving institution where he will have the chance to inspire members of underrepresented groups to become involved in STEM careers. Two of the graduate students are women and the third has an auditory disability, such that the award has directly impacted diversity of trainees in this area; one of the women completed her doctoral dissertation and is now a postdoc at Mathematical Biosciences Institute. Six undergraduate students were given opportunities to participate in the supported research projects, including a female student who is now in a Mathematics Ph.D. program with an NSF Graduate Fellowship and several others who are pursuing Ph.D. degrees in STEM areas. The trainees on this award were able to contribute to the Mathematical Biology group within the Department of Mathematics at Pitt, enhancing our training infrastructure. Furthermore, the award support helped foster interdisciplinary collaborations, in many cases involving trainees, with researchers in neuroscience and computational neuroscience at Pitt and several other institutions around the world. On a broader scope, over 20 papers associated with this award were published in peer-reviewed literature, reaching a interdisciplinary audience, and the results of the supported research were disseminated via a large number of talks at universities and research meetings. Finally, several of the research findings of this project are broadly relevant to synchronization of oscillating systems and to the design of nerve stimulation devices and therapies.
