Dynamical systems analysis of patterning and robustness of bursts in neuronal models.

Neurons in the brain are known to exhibit diverse bursting patterns. In this work, which combines three projects, we develop and analyze computational models to study various bursting activity displayed by respiratory neurons within the mammalian brainstem. In the first project, we examine minimal mathematical models that exhibit square wave bursting (SW) and analyze the transition of SW to other activity patterns due to parameter modifications. In particular, using these models, we analyze the robustness of SW with respect to the timescale associated with the conductance of a fast inward current. In the next project, we develop models that exhibit the "ramping" bursting pattern observed in the activity traces of neurons within the pre-Botzinger Complex. Furthermore, we propose two mechanisms that help control the amplitude and frequency of spikes within the burst to obtain the desired ramping dynamics. In the final project, we explore the dynamics of Kolliker-Fuse nucleus (KF) which plays a role in the development of breathing abnormalities associated with Rett syndrome (RTT). We present reduced computational models of the respiratory core neurons along with the KF unit that simulate normal as well as RTT-like breathing patterns. These models provide a general framework for understanding KF dynamics and potential network interactions