We introduce a formal language, the C-calculus, for modelling low-level interaction inside and among cells, the basic building blocks of all known life. We focus on two main actors of cells, proteins and membranes. Proteins are represented as clusters of domains sharing a common hidden name; domain-domain bonds are also represented via name-sharing. Compartments are formed by formal membranes. We treat also channels between membranes allowing transport of proteins, allowing us to capture an observable intermediate state in cell fusion or division, regulated by diffusion. We illustrate the calculus by giving two example models. We exemplify the basic constituents of the calculus, by developing a model of simple cross-membrane signalling via a G-protein coupled receptor protein. We continue by developing a model illustrating part of the endocytic pathway - the formation of clathrin-coated cytoplasmic vesicles, through budding from the plasma membrane (the cell-wall).
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