We believe that advancing our understanding of biology and medicine in the 21st century requires both mathematical and experimental research, ideally performed closely together. This is similar to how physics progressed historically. However, one major difference is that biology is more complex and inherently multiscale. To understand a cell, it is not sufficient to understand all molecular components. Different physics can influence the state of a cell. For example, cytoskeletal forces can deform molecules such as Talin which then actives pathways. Or the geometry of cells determines intracellular transport of diffusing molecules and therefore also affects intracellular pathways.

How can we obtain a holistic understanding of the cell, or of whole tissues or organisms, that account for such crosstalk between molecules and physical properties? Traditionally, mathematics was mostly employed for theories or models of single physical problems, e.g. differential equations for the equations of motion in physics or for chemical reaction systems. We develop data-driven mathematical models to study the interplay of qualitatively different features, e.g. mechanical and molecular features, often using machine learning to extract the required information from data.