Modeling and Data Analysis in Cellular Biophysics

Abstract: Cellular biophysics deals with the physical aspects of cell biology. This thesis presents a number of studies where mathematical models and data analysis can increase our understanding of this field.During recent years development in experimental methods and mathematical modeling have driven the amount of data and complexity in our understanding of cellular biology to a new level. This development has made it possible to describe cellular systems quantitatively where only qualitative descriptions were previously possible. To deal with the complex data and models that arise in this kind of research a combination of tools from physics and cell biology has to be applied; this constitutes a field we call cellular biophysics. The aim of this doctoral thesis is to develop novel approaches in this field. I present eight studies where quantitative modeling and analysis are involved.The first two studies concern cells interacting with their surrounding environment in the kidney. These cells sense fluid flow and respond with calcium (Ca2+) signals. The interaction between fluid and cells in renal tubular epithelium can be described by biomechanical models. This thesis describes a mathematical model of flow sensing by cilia with focus on the flow frequency response and time delay between the mechanical stress and the Ca2+ signaling response.Intracellular Ca2+ is kept at a very low level compared to the extracellular environment, while several intracellular compartments have higher Ca2+ concentration than the cytoplasm. This makes Ca2+ an efficient messenger for intra­cellular signaling, the process whereby signals are transduced from an extracellular stimulus to an intracellular activity such as gene expression. An important type of Ca2+ signaling is oscillations in intracellular Ca2+ concentration which occur due to the concerted interplay between different transport mechanisms within a cell. A study in this thesis examines ways to explain these mechanisms in terms of a mathematical model. Another study in the thesis reports that erythropoietin can regulate the water permeability of astrocytes and that it alters the pattern of Ca2+ oscillations in astrocytes. In this thesis the analysis of this Ca2+ signaling is described.Simulations described in one of the studies show how different geometries can affect the fluorescence recovery and that geometrically constrained reactions can trap diffusing receptors in dendritic spines. When separate time scales are present in a fluorescence revovery after photobleaching (FRAP) experiment the reaction and diffusion components can be studied separately.Applying single particle tracking methods to the migration trajectories of natural killer cells shows that there is a correlation between the formation of conjugates and transient confinement zones (TCZs) in these trajectories in vitro. TCZs are also present in in vivo experiments where they show strong similarities with the in vitro situation. This approach is a novel concept in data analysis methods for tracking immune cells.