Process Calculi Abstractions for Biology

Several approaches have been proposed to model biological systems by means of the formal techniques and tools available in computer science. To mention just a few of them, some representations are inspired by Petri Nets theory, and some other by stochastic processes. A most recent approach consists in interpreting the living entities as terms of process calculi where the behavior of the represented systems can be inferred by applying syntax-driven rules. A comprehensive picture of the state of the art of the process calculi approach to biological modeling is still missing. This paper goes in the direction of providing such a picture by presenting a comparative survey of the process calculi that have been used and proposed to describe the behavior of living entities. This is the preliminary version of a paper that was published in Algorithmic Bioprocesses. The original publication is available at http://www.springer.com/computer/foundations/book/978-3-540-88868-

A criterion for separating process calculi

We introduce a new criterion, replacement freeness, to discern the relative expressiveness of process calculi. Intuitively, a calculus is strongly replacement free if replacing, within an enclosing context, a process that cannot perform any visible action by an arbitrary process never inhibits the capability of the resulting process to perform a visible action. We prove that there exists no compositional and interaction sensitive encoding of a not strongly replacement free calculus into any strongly replacement free one. We then define a weaker version of replacement freeness, by only considering replacement of closed processes, and prove that, if we additionally require the encoding to preserve name independence, it is not even possible to encode a non replacement free calculus into a weakly replacement free one. As a consequence of our encodability results, we get that many calculi equipped with priority are not replacement free and hence are not encodable into mainstream calculi like CCS and pi-calculus, that instead are strongly replacement free. We also prove that variants of pi-calculus with match among names, pattern matching or polyadic synchronization are only weakly replacement free, hence they are separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

Priorities Without Priorities: Representing Preemption in Psi-Calculi

Psi-calculi is a parametric framework for extensions of the pi-calculus with data terms and arbitrary logics. In this framework there is no direct way to represent action priorities, where an action can execute only if all other enabled actions have lower priority. We here demonstrate that the psi-calculi parameters can be chosen such that the effect of action priorities can be encoded. To accomplish this we define an extension of psi-calculi with action priorities, and show that for every calculus in the extended framework there is a corresponding ordinary psi-calculus, without priorities, and a translation between them that satisfies strong operational correspondence. This is a significantly stronger result than for most encodings between process calculi in the literature. We also formally prove in Nominal Isabelle that the standard congruence and structural laws about strong bisimulation hold in psi-calculi extended with priorities.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

A flat process calculus for nested membrane interactions

The link-calculus has been recently proposed as a process calculus for representing interactions that are open (i.e. that the number of processes may vary), and multiparty (i.e. that may involve more than two processes). Here, we apply the link-calculus for expressing, possibly hierarchical and non dyadic, biological interactions. In particular, we provide a natural encoding of Cardelli's Brane calculus, a compartment-based calculus, introduced to model the behaviour of nested membranes. Notably, the link-calculus is at, but we can model membranes just as special processes taking part in the biological reaction. Moreover, we give evidence that the link-calculus allows one to directly model biological phenomena at the more appropriate level of abstraction

Process algebra modelling styles for biomolecular processes

We investigate how biomolecular processes are modelled in process algebras, focussing on chemical reactions. We consider various modelling styles and how design decisions made in the definition of the process algebra have an impact on how a modelling style can be applied. Our goal is to highlight the often implicit choices that modellers make in choosing a formalism, and illustrate, through the use of examples, how this can affect expressability as well as the type and complexity of the analysis that can be performed

Dynamic Compartments in the Imperative Pi Calculus

International audienceDynamic compartments with mutable configurations and variable volumes are of basic interest for the stochastic modeling of biochemistry in cells. We propose a new language to express dynamic compartments that we call the imperative π-calculus. It is obtained from the attributed π-calculus by adding imperative assignment operations to a global store. Previous approaches to dynamic compartments are improved in flexibility or efficiency. This is illustrated by an appropriate model of osmosis and a correct encoding of BioAmbients

A Flat Process Calculus for Nested Membrane Interactions

The link-calculus has been recently proposed as a process calculus for representing interactions that are open (i.e., that the number of processes may vary), and multiparty (i.e., that may involve more than two processes). Here, we apply the link-calculus for expressing, possibly hierarchical and non dyadic, biological interactions. In particular, we provide a natural encoding of Cardelli's Brane calculus, a compartment-based calculus, introduced to model the behaviour of nested membranes. Notably, the link-calculus is flat, but we can model membranes just as special processes taking part in the biological reaction. Moreover, we give evidence that the link-calculus allows one to directly model biological phenomena at the more appropriate level of abstraction

The Attributed Pi Calculus with Priorities

International audienceWe present the attributed $\pi$-calculus for modeling concurrent systems with interaction constraints depending on the values of attributes of processes. The $\pi$-calculus serves as a constraint language underlying the $\pi$-calculus. Interaction constraints subsume priorities, by which to express global aspects of populations. We present a nondeterministic and a stochastic semantics for the attributed $\pi$-calculus. We show how to encode the $\pi$-calculus with priorities and polyadic synchronization $\pi$@ and thus dynamic compartments, as well as the stochastic $\pi$-calculus with concurrent objects spico. We illustrate the usefulness of the attributed $\pi$-calculus for modeling biological systems at two particular examples: Euglena’s spatial movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda. Furthermore, population-based model is supported beside individual-based modeling. A stochastic simulation algorithm for the attributed $\pi$-calculus is derived from its stochastic semantics. We have implemented a simulator and present experimental results, that confirm the practical relevance of our approach

An Abstract Machine for the Stochastic Bioambient calculus

AbstractThis paper presents an abstract machine for the stochastic bioambient calculus. The abstract machine is proved sound and complete with respect to a novel stochastic semantics, and is also shown to preserve the reduction probabilities of the calculus. The machine is implemented as an extension to an existing simulator for stochastic pi-calculus