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Formal molecular biology. (English) Zbl 1071.68041
Summary: A language of formal proteins, the $$\kappa$$-calculus, is introduced. Interactions are modeled at the domain level, bonds are represented by means of shared names, and reactions are required to satisfy a causality requirement of monotonicity.
An example of a simplified signalling pathway is introduced to illustrate how standard biological events can be expressed in our protein language. A more comprehensive example, the lactose operon, is also developed, bringing some confidence in the formalism considered as a modeling language.
Then a finer-grained concurrent model, the $$m\kappa$$-calculus, is considered, where interactions have to be at most binary. We show how to embed the coarser-grained language in the latter, a property which we call self-assembly.
Finally we show how the finer-grained language can itself be encoded in $$\pi$$-calculus, a standard foundational language for concurrency theory.

##### MSC:
 68Q45 Formal languages and automata 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) 92C40 Biochemistry, molecular biology
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