This project will advance the creation and support of a community of scholars, from undergraduate to faculty, working at the interfaces among dynamical systems and biological applications. The three main areas of focus are: 1. Analysis of systems with multiple length and time scales, including applications to pattern formation; 2. Mathematical neuroscience, including analytical methods for working with small networks and reduction of dimension techniques; 3. Gene regulatory networks, including the development of RNA switches, transcriptional bursting and programmable cells. These areas have major applications to issues concerning health and medicine. The project will build on the previous research and training experience of the Center for BioDynamics, co-directed by the Principal Investigator and one of the other senior faculty members. Trainees will be pre- and post-doctoral students who will take part in a wide variety of formal and informal activities, including special seminars, working groups, mini-symposia, laboratory work, journal clubs and social events, which will enable them to acquire the multiple scientific cultures needed to work in a trans-disciplinary manner. The pre-doctoral students will be from the departments of Mathematics or Biomedical Engineering; the postdoctoral associates will be drawn from a wide range of backgrounds, with a focus on applied math. In addition to their research activities, trainees will obtain experience teaching at different levels. Math department faculty and trainees will be involved in the construction of new interdisciplinary curricula for undergraduates in other departments, including Biology; the faculty will mentor the trainees in teaching the new curricula.
Projects Outcome Report Enhancing the Mathematical Sciences Workforce in the 21st Century (EMSW21): BioDynamics at Boston University Grant Abbreviation: RTG - DMS 0602204 09/01/06-08/31/12 The central aim of this grant was to advance the development of a research and training community in biodynamics. This included the training of graduate students and postdoctoral associates to work at the interfaces of dynamical systems and biologically relevant applications, and the production of new research at these boundaries. The RTG built on a previous NSF support for create a community of scholars that would jointly mentor students and postdocs interested in problems involving nonlinear dynamics and biology; the RTG, like its predecessors, was integrated across departments and across levels of achievement. The grant supported a total of 21 graduate students and 11 postdocs over its five-year period. The faculty members were: Nancy Kopell (Math; PI) - rhythms of the nervous system; geometrical analysis using multiple scales. James Collins (Biomed. Eng.; co-PI) - gene regulation, dynamics of gene regulatory networks. Tasso Kaper (Math; co-PI) - multi-scale dynamical systems, applications to fluids and neuroscience. Gene Wayne (Math; co-PI) - infinite-dimensional dynamical systems, applications to fluids. John White (Biomed.Eng; co-PI) - slice physiology, hippocampal formation, computational neuroscience, hybrid networks of in silico and real cells. Tim Gardner (Biomed. Eng.; training faculty) - gene regulation, dynamics of regulatory networks. Eric Kolacyzk (Math and Stats; training faculty, new CBD member) - statistics of multi-scale models, methods for network analysis, interference of gene regulatory networks. Kamal Sen (Biomed Eng; training faculty) - dynamics of nervous system, auditory system. This core group collaborated with many other scientists. These trainees worked in three main areas: pattern formation, neuroscience and systems biology. The topics in each of these were: Nonlinear Dynamics and Pattern Formation: Coherent structures in partial differential equations, including localized structures, front solutions, solitons in partial differential equations; Other infinite dimensional dynamical systems; Multiple scales; Asympototics of ordinary and partial differential equations; Pattern formation in drosophila; Torus canards. Neuroscience: Interactions of neural rhythms; Auditory, olfactory, and gustatory coding; Pathological neural activity; Low dimensional attracting dynamics in networks; Epileptiform activity; Cellular Mechanisms of Excitability; and Hippocampal Coding; Basal ganglia modeling; Dynamics of anesthesia; Data analysis and statistics of neural firing, including methods of spike sorting. Synthetic Biology and Systems Biology: Modeling and machine learning; Gene networks and genomics; Metabolic engineering; Microbial systems biology. In addition to the direct support of the trainees, the RTG had large effects on the formation of scientific community within Boston University, especially in the areas of neuroscience and systems biology. In the first few years, the RTG was part of the Center for BioDynamics (CBD), a larger group of BU faculty with similar training and research aims. In its last year, this RTG group has affiliated its activities with the new Center for Computational Neuroscience and Neural Technology (CompNet) and an emerging initiative in systems Neuroscience, both at BU. The early support for the CBD led to seed money for the creation of a new training program, Program in Mathematical and Computational Neuroscience (PMCN), financed by the Burroughs Wellcome Fund. Currently, the organization and infrastructure created for the RTG and CompNet has enabled the formation of a larger enterprise, the Cognitive Rhythms Collaborative (CRC), a NSF-sponsored "discovery network" of over thirty labs in the greater Boston area interested in the relation of brain dynamics to cognition (cogrhythms.bu.edu). The PI of the RTG was instrumental in the creation of the other training and research programs.
