Abstract
Lymphocytes roll along the walls of vessels to survey the endothelial surface for chemotactic inflammatory signals, which stimulate the lymphocytes to stop rolling and migrate through the endothelium and its supporting basement membrane. Recent studies about the inflammatory process of the brain leading to the multiple sclerosis, have revealed that 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. These interactions are both concurrent and parallel, and consequently their modelling need to be specified in a language able to represent concurrency and parallelism. Process calculi (or process algebras) are a diverse family of related languages developed by in computer science for formally modelling concurrent systems. Here, we propose the use of the biochemical stochastic π-calculus. This 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 to quantitatively describe the rates and the times at which the reactions occur. We use here 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 and the adhesion probability of the cell as function of interaction time. The results of the model reproduce, within the estimated experimental errors, the functional behavior of the data obtained from laboratory measurements.
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Notes
- 1.
Major developments in the 1990s included experiments that provided direct measurements of kinetic rates, lifetimes and detachment force of adhesive interactions.
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Lecca, P. (2012). A Process-Algebra Model of the Cell Mechanics of Autoreactive Lymphocytes Recruitment. In: Natal Jorge, R., Tavares, J., Pinotti Barbosa, M., Slade, A. (eds) Technologies for Medical Sciences. Lecture Notes in Computational Vision and Biomechanics, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4068-6_15
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