We give a stochastic extension of the Brane Calculus, along the lines of
recent work by Cardelli and Mardare. In this presentation, the semantics of a
Brane process is a measure of the stochastic distribution of possible
derivations. To this end, we first introduce a labelled transition system for
Brane Calculus, proving its adequacy w.r.t. the usual reduction semantics.
Then, brane systems are presented as Markov processes over the measurable space
generated by terms up-to syntactic congruence, and where the measures are
indexed by the actions of this new LTS.
Type theories, logical frameworks and meta-languages form a common foundation
for designing, implementing, and reasoning about formal languages and their
semantics. They are central to the design of modern programming languages,
certified software, and domain specific logics. More generally, they continue
to influence applications in many areas in mathematics, logic and computer
science.
We introduce the BioBeta Framework, a meta-model for both protein-level and
membrane-level interactions of living cells. This formalism aims to provide a
formal setting where to encode, compare and merge models at different
abstraction levels; in particular, higher-level (e.g. membrane) activities can
be given a formal biological justification in terms of low-level (i.e.,
protein) interactions.
We present a bigraphical framework suited for modeling biological systems
both at protein level and at membrane level. We characterize formally bigraphs
corresponding to biologically meaningful systems, and bigraphic rewriting rules
representing biologically admissible interactions. At the protein level, these
bigraphic reactive systems correspond exactly to systems of kappa-calculus.
Membrane-level interactions are represented by just two general rules, whose
application can be triggered by protein-level interactions in a well-de\"ined
and precise way.