Reaction Constraints for the Pi-Calculus - A Language for the Stochastic and Spatial Modeling of Cell-Biological Processes
For cell-biological processes, it is the complex interaction of their biochemical components, affected by both stochastic and spatial considerations, that create the overall picture. Formal modeling provides a method to overcome the limits of experimental observation in the wet-lab by moving to the abstract world of the computer. The limits of the abstract world again depend on the expressiveness of the modeling language used to formally describe the system under study. In this thesis, reaction constraints for the pi-calculus are proposed as a language for the stochastic and spatial modeling of cell-biological processes. The goal is to develop a language with sufficient expressive power to model dynamic cell structures, like fusing compartments. To this end, reaction constraints are augmented with two language constructs: priority and a global imperative store, yielding two different modeling languages, including non-deterministic and stochastic semantics. By several modeling examples, e.g. of Euglena's phototaxis, and extensive expressiveness studies, e.g. an encoding of the spatial modeling language BioAmbients, including a prove of its correctness, the usefulness of reaction constraints, priority, and a global imperative store for the modeling of cell-biological processes is shown. Thereby, besides dynamic cell structures, different modeling styles, e.g. individual-based vs. population-based modeling, and different abstraction levels, as e.g. provided by reaction kinetics following the law of Mass action or the Michaelis-Menten theory, are considered.