Dietmar Oelz

Biological systems integrate a multitude of processes on various spatial and temporal scales. The output of biological processes is typically robust to a range of random perturbations. Mathematics is an outstanding tool to investigate such cooperative mechanisms on the molecular level which can hardly be assessed experimentally.

Building on a sound applied mathematics and partial differential equations (PDE) background, the area of my research is to identify and describe biological processes by formulating mathematical models, to evaluate them using numerical simulation and mathematical analysis and to validate such models against experimental data.

A ubiquitous example for a highly complex biological system are cells. They use cytoskeletons composed of long fibers on the micron length scale to sustain their shape mechanically. Molecular processes on the nanoscale which change the structure of these fibers as well as force generation by motor proteins promote remodeling of cell shape, cell migration and intracellular transport. This is the basis for vital processes such as muscle contraction, cell division, immune system response, wound healing and embryogenesis, and it plays a crucial role in pathological processes such as tumor metastasis and neurodegenerative deseases.

The central question of my research is: how do proteins on the nanoscale and larger protein complexes on the micronscale cooperate in living cells to promote cell movement, shape changes, force generation and intra- cellular transport? This type of research contributes to the development of new techniques in bioengineering and of new therapeutic approaches in clinical fields such as oncology and immunology.

One important aspect of biological mechanisms is insensitivity to random perturbations. Hence mathe- matical models on the microscopic level are necessarily stochastic and I employ mathematical analysis and numerical simulation such as Brownian Dynamics to analyze the sensitivity of models and to identify robust characteristics of a systems output. Especially the smallness of the molecular length scales interferes with experimental imaging techniques to assess these biological processes in vivo. For this reason an essential aspect of my research is to use asymptotic analysis to derive and justify macroscopic coarse-grained models based on thoroughly formulated microscopic models. In general this process yields partial differential equations such as reaction-drift-diffusion models and fluid dynamics models. I analyze these models, which often exhibit amazingly rich mathematical properties, analytically and by numerical simulation in order to relate the experimentally measurable macroscopic features to the microscopic dynamics of interest.