Complex Biological Systems Group
Faculty: Professors Doiron, Ermentrout, Rubin, Swigon, and Troy
Adjunct Faculty: Chow
The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena. Areas of interest include neuroscience, movement disorders, immunology, cellular function, and genetic regulation. The groups uses a wide array of approaches, from applied mathematics and nonlinear analysis, including computer simulations, bifurcation theory, perturbation methods, and mathematical model building, to rigorous analysis.
Dr. Ermentrout is interested in the applications of nonlinear dynamics to biological problems. His main focus is in the area of mathematical neuroscience, where he tries to understand the patterns of activity in networks of neurons. Dr. Ermentrout models recurrent activity, waves, and oscillations in a variety of neural systems, including olfaction (sense of smell), rat whisker barrels, cortical slices, and working memory. He is also interested in problems from physiology, immunology, and cell biology, all of which he has modeled with students and postdocs.
Dr. Rubin works on both theoretical and applied problems coming from neuroscience, as well as on inflammation and related medical issues, in collaboration with students, postdocs, and medical school faculty. In the neuroscience area, Dr. Rubin's research focuses on transitions in activity patterns in respiratory pacemaker networks, tremor and deep brain stimulation for movement disorders such as Parkinson's disease, spike-timing dependent synaptic plasticity, and traveling waves in neuronal media. Many of his projects fall into the general theme of spatio-temporal pattern formation in coupled cell networks.
Dr. Swigon works in molecular biology, with a focus on quantification of the relation between the sequence, mechanical properties, and biological function of intracellular components. He has developed micromechanical models of DNA and protein elasticity that combine atomic-scale and continuum mechanics approaches with recent advances in computational chemistry and employ information obtained by x-ray crystallography, single-molecule manipulation, and other experimental techniques.