The BioAmbients calculus is a process algebra suitable for representing compartmentalization, molecular localization and movements between compartments. In this paper we enrich this calculus with a static type system classifying each ambient with group types specifying the kind of compartments in which the ambient can stay. The type system ensures that, in a well-typed process, ambients cannot be nested in a way that violates the type hierarchy. Exploiting the information given by the group types, we also extend the operational semantics of BioAmbients with rules signalling errors that may derive from undesired ambients' moves (i.e. merging incompatible tissues). Thus, the signal of errors can help the modeller to detect and locate unwanted situations that may arise in a biological system, and give practical hints on how to avoid the undesired behaviour.
Deep Dive into Types for BioAmbients.
The BioAmbients calculus is a process algebra suitable for representing compartmentalization, molecular localization and movements between compartments. In this paper we enrich this calculus with a static type system classifying each ambient with group types specifying the kind of compartments in which the ambient can stay. The type system ensures that, in a well-typed process, ambients cannot be nested in a way that violates the type hierarchy. Exploiting the information given by the group types, we also extend the operational semantics of BioAmbients with rules signalling errors that may derive from undesired ambients’ moves (i.e. merging incompatible tissues). Thus, the signal of errors can help the modeller to detect and locate unwanted situations that may arise in a biological system, and give practical hints on how to avoid the undesired behaviour.
BioAmbients [23] is a variant of the Ambient Calculus [11], in which compartments are described as a hierarchy of boundary ambients. This hierarchy can be modified by suitable operations that have an immediate biological interpretation; for example, the interactions between compounds that reside in the cytosol and in the nucleus of a cell could be modelled via parent-child communications. Thus, BioAmbients is quite suitable for the representation of various aspects of molecular localization and compartmentalization, such as the movement of molecules between compartments, the dynamic rearrangement that occurs between cellular compartments, and the interaction between the molecules in a compartmentalized context.
A stochastic semantics for BioAmbients is given in [8], and an abstract machine for this semantics is developed in [20]. In [17] BioAmbients is extended with an operator modelling chain-like biomolecular structures and applied within a DNA transcription example. In [21] a technique for pathway analysis is defined in terms of static control flow analysis. The authors then apply their technique to model and investigate an endocytic pathway that facilitates the process of receptor mediated endocytosis.
In this paper we extend the BioAmbients calculus with a static type system that classifies each ambient with a group type G specifying the kind of compartments in which the ambient can stay [10]. In other words, a group type G describes the properties of all the ambients and processes of that group. Group types are defined as pairs (S, C), where S and C are sets of group types. Intuitively, given G =(S, C), S denotes the set of ambient groups where ambients of type G can stay, while C is the set of ambient groups that can be crossed by ambients of type G. On the one hand, the set S can be used to list all the elements that are allowed within a compartment (complementary, all the elements which are not allowed, i.e. repelled). On the other hand, the set C lists all the elements that can cross an ambient, thus modelling permeability properties of a compartment.
Starting from group types as bases, we define a type system ensuring that, in a well-typed process, ambients cannot be nested in a way that violates the group hierarchy. Then, we extend the operational semantics of BioAmbients, exploiting the information given by the group types, with rules rising warnings and signalling errors that may derive from undesired compartment interactions. For example, while correctness of the enter/accept capabilities (that are used to move a compartment to the inside of another compartment) can be checked statically, the merge capability (which merges two compartments into one) and the exit/expel capabilities (which are used to move a compartment from the inside to the outside of another compartment) could cause the movement of an ambient of type G within an ambient of type G ′ which does not accept it. In these cases, for example when incompatible tissues come in contact, an error signal is raised dynamically and the execution of the system is blocked. The modeller can exploit these signals as helpful debugging information in order to detect and locate the unwanted situations that may arise in a biological system. Intuitively, they give practical hints on how to avoid the undesired behaviour.
In the last few years there has been a growing interest on the use of type disciplines to enforce biological properties. In [3] a type system has been defined to ensure the wellformedness of links between protein sites within the Linked Calculus of Looping Sequences (see [4]). In [16] three type systems are defined for the Biochemical Abstract Machine, BIOCHAM (see [1]). The first one is used to infer the functions of proteins in a reaction model, the second one to infer activation and inhibition effects of proteins, and the last one to infer the topology of compartments. In [15] we have defined a type system for the Calculus of Looping Sequences (see [6]) to guarantee the soundness of reduction rules with respect to the requirement of certain elements, and the repellency of others. Finally, in [14] we have proposed a type system for the Stochastic Calculus of Looping sequences (see [5]) that allows for a quantitative analysis and models how the presence of catalysers (or inibitors) can modify the speed of reactions.
The remainder of the paper is organised as follows. In Section 2 we recall the original BioAmbients’ syntax. In Section 3 we define our type system and in Section 4 we give our typed operational semantics. In Section 5 me formulate two motivating examples, namely we use our type system to analyse blood transfusions (rising errors in the case incompatible blood types get mixed) and spore protection against bacteriophage viruses. Finally, in Section 6 we draw our conclusions.
In this section we recall the BioAmbients calculus. Ambients represent bounded mobile entities that can be nested forming hierarchies. They p
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