A Model Predicting Rolling Cells Percentage in Inflamed Brain Venules

We present a stochastic model of the lymphocytes recruitment in inflamed brain microvessels. The framework used is based on stochastic process algebras for mobile systems. The automatic tool used in the simulation is the biochemical stochastic \(\pi \)-calculus. Lymphocytes roll along the walls of vessels to survey the endothelial surface for chemotactic signals, which stimulate the lymphocytes to stop rolling and migrate through the endothelium and its supporting basement membrane. In particular the lymphocytes extravasation is a critical event in the pathogenesis of multiple sclerosis, an autoimmune serious disease of the central nervous system. Recent studies have revealed that the process leading to lymphocytes extravasation is a sequence of dynamical states (contact with endothelium, rolling and firm adhesion), mediated by partially overlapped interactions of different adhesion molecules and activation factors. The biochemical stochastic \(\pi \)-calculus is an efficient tool for describing the concurrency of the different interactions driving the phases of lymphocytes recruitment. It models a biochemical systems as a set of concurrent processes selected according to a suitable probability distribution in order to quantitatively describe the rates and the times at which the reactions occur. We used this tool to model and simulate the molecular mechanisms involved in encephalitogenic lymphocytes recruitment. In particular, we show that the model predicts the percentage of lymphocytes involved in the rolling process on the endothelium of vessels of different diameters. The results of the model reproduce, within the estimated experimental errors, the functional exponential behavior of the data obtained from laboratory measurements.