This special focus is jointly sponsored by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), the Biological, Mathematical, and Physical Sciences Interfaces Institute for Quantitative Biology (BioMaPS), and the Rutgers Center for Molecular Biophysics and Biophysical Chemistry (MB Center).
Multi-scale activity is a universal characteristic of biological processes. In particular, novel dynamics emerge from arrangements of components and events across different scales of distance and time that are intertwined to translate biomolecular events into recognizable phenotypes. While a quantitative understanding and predictive mathematical modeling of these complexities on the level of organisms is acknowledged to be a very long-range goal, there are opportunities for more modest but still fundamental steps. Pertinent to the modeling challenge is the notion of time. The multi-scale aspect of biology guarantees that the regulatory biological processes occur at different locations, times, and rates. Nevertheless, these processes achieve remarkable temporal and quantitative coordination. The observations suggest that accounting for - and adapting to - time delay is central to biological complexity and robustness.
Two key advances - one in biology and one in mathematics - suggest that there is an immediate opportunity for progress in this arena. In biology, new experimental tools that allow for reliable, comprehensive and serial assessments of the states and processes of gene regulatory networks have become widely available. In mathematics, new theoretical developments suggest the possibility to develop a theory of the global dynamics of nonlinear systems with multiple or variable delays.
The immediate goal of this workshop is to begin a dialogue between mathematicians with expertise in the dynamics of delay differential equations and control theory, and biologists with expertise in the mechanisms in signal transduction/gene regulatory networks. For the biologists the potential benefit will be new models within which to understand, test, and control gene regulation. For the mathematicians the potential benefit will be a concrete set of problems around which the development of this new theory can be focused.