Spatial Calculus of Looping Sequences

The Calculus of Looping Sequences (CLS) enables the description of biological systems and of their evolution. This paper presents the Spatial CLS, an extension of CLS that allows the description of the position of biological elements, and of the space they take up in a 2D/3D space. The elements may move autonomously during the passage of time, and may interact when constraints on their positions are satisfied. The space occupied by each element is modeled as a hard sphere, hence space conflicts may arise during system evolution. These conflicts are resolved by an appropriate algorithm, which rearranges the position of the elements by assuming that they push each other when they are too close. Moreover, rewrite rules are endowed with a parameter describing their reaction rate. The aim of Spatial CLS is to enable a more accurate description of those biological processes whose behaviour depends on the exact position of the elements. As example applications of the calculus, we present a model of cell proliferation, and a model of the quorum sensing process in Pseudomonas aeruginosa.