The Calculus of Looping Sequences for Modeling Biological Membranes

Abstract

We survey the formalism Calculus of Looping Sequences (CLS) and a number of its variants from the point of view of their use for describing biological membranes. The formalism CLS is based on term rewriting and allows describing biomolecular systems. A first variant of CLS, called Stochastic CLS, extends the formalism with stochastic time, another variant, called LCLS (CLS with links), allows describing proteins interaction at the domain level. A third variant is introduced for easier description of biological membranes. This extension can be encoded into CLS as well as other formalisms capable of membrane description such as Brane Calculi and P Systems. Such encodings allow verifying and simulating descriptions in Brane Calculi and P Systems by means of verifiers and simulators developed for CLS.

An Intermediate Language for the Simulation of Biological Systems

“…In this section we recall the Calculus of Looping Sequences (CLS) in one of its variants, CLS+ [11,2]. CLS+ is essentially based on term rewriting, hence a CLS+ model consists of a term and a set of rewrite rules.…”

“…The idea is that a term can be seen as a tree, a tree can be seen as a set of strings representing all paths from root to leaves and the replacement of a subtree becomes the replacement of a set of strings having a common prefix. As an example we show how a formalism based on term rewriting, CLS+ [11,2] can be translated into SMSR, proving translation correctness and completeness.…”

An intermediate language for the stochastic simulation of biological systems

“…In order to show that sSMSR can be suitably used as an intermediate language, we define the encoding into sSMSR of two formalisms which are representative of the two mentioned classes, namely Stochastic CLS and the Stochastic π -calculus. The former, an extension of CLS [4,5], has been shown to be suitable for describing various kinds of biological phenomena and it has been chosen also because the rewriting mechanism on which it is based makes the translation into sSMSR easy to understand. The latter has been widely used for the description of biological systems and many other formalisms are defined as extensions of the Stochastic π-calculus.…”

Implementing the Stochastics Brane Calculus in a Generic Stochastic Abstract Machine

“…A fundamental issue in Systems Biology is modelling the membrane interaction machinery. Several models have been proposed in the literature [11,14,3]; among them, the Brane Calculus [4] has been arisen as a good model focusing on abstract membrane interactions, still being sound with respect to biological constraints (e.g. bitonality).…”