Mathematical Biology

Abstract

This meeting on Mathematical Biology tied in with the long tradition of these workshops in Oberwolfach and at the same time aimed to account for the fast growing synergy between biology and mathematics of the recent years. The use of new instrumentation and visualization methods at the molecular scale in biological and medical experiments allows for measurements which have not been possible a few years ago. Major questions for theoreticians and experimentalists are how to tackle this vast complexity of biological information and data, and, more important, if underlying principles can be found. Finding these would enable the field to become more predictive. Here is exactly where mathematical modeling, analysis, and simulation can contribute. On the other hand, mathematical biologists and mathematicians are now providing first new models to explain the measurements, and these models are ready for mathematical analysis. The synergy between mathematics and physics, chemistry, engineering, and material sciences, has already proven to greatly advance the respective sciences and mathematics itself. To further deepen the connections between mathematics and biology, a group of experimental biologists, mathematical biologists, and mathematicians – especially many young scientists – met, joining the lively talks and discussions in this workshop. The meeting intentionally focussed on some specific biological topics this time. Among those were cell movement, where results on the dynamics of the cellular cytoskeleton were presented, as well as on chemotaxis and cell adhesion. Questions of pattern and structure formation in cell systems were discussed for self-organizing microorganisms and cancer invasion. The analysis of structured population models in this context is new, but has a long tradition in ecology and epidemiology. Further topics of interest with clear mathematical challenges were transport and molecular motors, the organization of cell membranes, and the process of photo-transduction. Wherever possible, the experimentalists talks were placed in tandem with related presentations on mathematical modeling. Mathematical topics were: reaction-diffusion equations, parabolic and hyperbolic chemotaxis equations, fluid dynamics, variational principles and methods based on the Wasserstein distance, homogenization, singular perturbations, bifurcation analysis, and numerical simulations. Besides the lectures, two discussion groups were organized, one on mathematical results for chemotaxis equations and one on cell motility. A round table discussion on ‘mathematical modeling in biology, aims and scopes’ rounded off the meeting, not to forget the nice concert, organized by some of the participants. We would like to express our sincere thanks to the very dynamic and kind support of the Oberwolfach team before and during the workshop.