Kathleen A. Hoffman

Sensory Feedback and Neuromechanical Locomotion

As a result of the year long immersion program at College Park in A. Cohen's biology lab, I developed a research program in sensory feedback in neuromechanical locomotion in collaboration with an international multidisciplinary group of researchers focused on how the lamprey swim. We are concerned with developing, understanding and analyzing components of lamprey swimming: from nerve conduction along an axon, to muscle contraction and body dynamics to interaction with the fluid environment. Then using those components to make the model lamprey swim. The group is a consortium of researchers from UMCP, Princeton, JHU, Tulane, and St. George's Medical School in London. Based on our ongoing collaboration and yearly meetings, NSF recently awarded us a Research Coordination Network in the Physical and Life Sciences grant (PIs L. Fauci and A. Cohen). The grant is designed to support communication and coordination of our research efforts across disciplinary, organizational, institutional and geographical boundaries. As part of this multi-institution effort, I am chairing the organizing committee (consisting of myself, N. Cowen (JHU) and A. Smits (Princeton)) of the first annual Winter Workshop on Neuromechanical Locomotion at Princeton University, January 2012. The grant will also facilitate travel to conferences, extended visits, and interdisciplinary collaborations for ourselves and our students to interact with other members of the community. The group listed above serves as a steering committee and is tasked with distribution of funds. My focus on this project was to understand sensory input into the central pattern generator, which consists of a group of neurons in the spinal cord that control vertebrate locomotion. This work has been funded by an NSF grant for interdisciplinary work in the mathematical sciences, as well as an REU supplement for my student Geoff Clapp. To date, I have three major contributions to the field of vertebrate locomotion:

  • Analyzing the effects of random connections in the central pattern generator In this work, which appeared in the J. Computational Neuroscience, I showed that random connections between oscillators approach a deterministic limit.
  • Studying entrainment ranges for the phase model The simplest mathematical model of the central pattern generator is a called a phase model, in which each oscillator is modeled by a single variable, called the phase. I developed analytical expressions for the entrainment ranges of the phase model for two different network architectures. The results from the phase model indicate that experimental results on the central pattern generator are not generic for chains of coupled oscillators and imply a non-uniform coupling asymmetry in the connections between oscillators. Additionally, we were able to completely classify loss of entrainment mechanisms. Results of this work appeared in the Journal of Mathematical Biology.
  • Studying entrainment ranges for a neural model I considered a neural model in which each segment of the central pattern generator consists of three classes of neurons (excitatory, lateral inhibitory, and crossed inhibitory). Along with my undergraduate student Geoff Clapp, we have shown that entrainment ranges from this work are similar to those of the phase model. This result suggests that the non-uniform coupling asymmetry that was needed to qualitatively reproduce experimental data is not model specific, but represents a more robust phenomenon among coupled oscillators, thus providing evidence for a possible coupling scheme for the lamprey central pattern generator. This is an example where modeling played an essential role in developing insight into a biological system, since experiments to address these questions are challenging.

Maintained by: Kathleen A. Hoffman (khoffman@math.umbc.edu).