Modelization and Simulation of Nano Devices in nano κ Calculus

Abstract

Abstract. We develop a process calculus -the nanoκ calculus -for modeling, analyzing and validating the properties of molecular devices. The nanoκ calculus is equipped with a simple stochastic models. We then study the modelization and simulation of the behaviour of a molecular shuttle, a basic nano device currently used for building more complex systems.

The κ-Lattice: Decidability Boundaries for Qualitative Analysis in Biological Languages

“…The general shape of reactions is defined in the next definition. Following [19], we extend the definition of [3] with exchange reactions, thus the calculus is an extension of the κ-calculus.…”

“…Our analysis also takes into account a different axis. In [19] a new reaction rule has been introduced, called exchange. According to this reaction, the interaction between two molecules may flip a bond from one to the other.…”

Expressivity in the κ Family

“…Some years later, a new formalism -the nanoκ calculus -similar to κ and mκ, was introduced for modelling nano-technologies [2]. This calculus has binary interactions (as mκ) but no multiedge is admitted (as in κ).…”

On the Computational Power of Biochemistry

“…Between an association event involving two molecules and their subsequent dissociation, the two molecules can still freely interact with other molecules or among themselves. In other more expressive formalisms, see for instance the so-called exchange reactions in [5], it is possible to specify events that change the internal state of one molecule only if it is complexed with another one having a particular state.…”

“…Notations have emerged from biology that use such an idea to describe large biochemical systems [9,8]. Many formalized and computerized approaches are currently being developed, including: practical tools, where molecules are drawn as boxes with connecting lines [6]; graph-rewriting and term-rewriting systems where a molecular complex is represented as a graph or term, and a reaction is a graph or term rewrite [7,5]; coding techniques in process algebra, where complexation can be expressed via some advanced features [16]; and finally, specialized process algebras where molecular interfaces and complexation are taken as primitive [15,4]. All these approaches aim to find a descriptive framework that goes beyond simple chemical reactions, and that can be used to represent common biochemical situations finitely and modularly.…”