This one-semester program will bring together researchers from mathematics, chemistry, physics, biology, computer science, and engineering to explore new ways to bridge these diverse disciplines, and to facilitate the use of mathematics to solve open problems at the forefront of the molecular biosciences...
Networks and deterministic and stochastic dynamical systems on networks are used as models in many areas of biology. This underscores the importance of developing tools to understand the interplay between network structures and dynamical processes, as well as how network dynamics can be controlled. The dynamics associated with such models are often different from what one might traditionally expect from a large system of equations, and these differences present the opportunity to develop exciting new theories and methods that should facilitate the analysis of specific models.
Within the next few years all fields of mathematical biology will be impacted by large amounts of complex data. Because of this, there are many new mathematical questions to be addressed. Should old simple models be thrown out and should we begin again with newer complex models? Or are there mathematical ways to use the new data to determine parameters in the old models more accurately and thus allow their parameters to be updated automatically in real time as the data stream in. These questions are fundamental to medical practice in acute crises, to the dynamical behavior of cells, to policy decisions about vaccination and epidemic spread, to the effects of climate change on ecological niches, and to our understanding of brain function.
Morphogenesis, the origin of form during the development of an organism, constitutes the processes by which simple cellular arrays are transformed into highly structured and often complex tissues, organs and appendages. The mechanisms of morphogenesis are exceptionally complex and diverse, and are only partially understood. There is a large experimental literature on how various genetic, physiological and morphological perturbations alter morphogenesis, but the interpretation of those results is largely done through verbal, conceptual and diagrammatic models. Although such models have an internal logic they are not quantitatively rigorous and typically do not suggest specific mechanisms other than simple single-level biological processes like transcription or translation. Mathematical modeling has played an important role in developing a deeper understanding of the capacities and limitations of various mechanisms. Problems in morphogenesis have also led to the development of new mathematics such as Turing systems and the development of multiscale modeling approaches.