An Intermediate Language for the Simulation of Biological Systems

Abstract

We propose String MultiSet Rewriting (SMSR) as an intermediate language for simulation of biomolecular systems. Higher level formalisms for biological systems description can be translated into SMSR and SMSR descriptions can be simulated by adapting an existing simulator. In this paper we show the translation of one of these formalisms, CLS+, into SMSR, and we prove correctness and completeness of the translation.

An intermediate language for the stochastic simulation of biological systems

“…The formalism sSMSR extends sMSR with strings, rather than individual alphabet symbols, as multiset elements, and with richer rewrite rules. The formalism sSMSR is also the stochastic extension of the String MultiSet Rewriting formalism presented in [2].…”

An encoding of the $$\lambda $$-calculus in the String MultiSet Rewriting calculus

“…Translating higher-level systems to this calculus turned out to be difficult, however. Hence, the calculus of String MultiSet Rewriting (SMSR) was developed [4], which proved to be an appropriate intermediate solution: its main invention is the maximal matching operator, which facilitates the representation of higher-level languages. The underlying idea of that calculus is that, by grabbing the tree-like structures of terms of a formal system, a multiset of strings can describe the index paths from root to leaves in a given term and, consequently, substitutions with terms are encoded as replacement of a whole multiset of strings having a common prefix with another multiset in a single step.…”

“…In this paper, we introduce first the SMSR system following [4]. Then, we show how to represent λ-terms with multisets and define the multiset rewriting rule corresponding to β-reduction.…”

Regulated Multiset Rewriting Systems

“…Multiset rewriting systems (MRSs) [15] provide a modelling formalism suitable in particular for describing biological systems [1,2]. MRS can be considered as a low-level formalism, describing how multisets of elements can be modified by applying rewriting rules representing biological processes.…”