Brane Calculi Research Articles

Membrane automata for modeling biomolecular processes

Bioinspired computation models and mechanisms are widely used in various applications, both in theoretical and practical level. Membrane Computing, a branch of Natural Computing, is constantly producing interesting results the last 15 years. In this work we attempt to describe a mitochondrial fusion process based on membrane automata in a novel way. We combine these computation machines with notions from brane calculus and we depict the procedure of the production of specific proteins that are essential for a successful fusion. We also discuss possible extensions of our methodology stating direction for future works and thoughts.

Formalizing Modularization and Data Hiding in Synthetic Biology

Biological systems employ compartmentalization and other co-localization strategies in order to orchestrate a multitude of biochemical processes by simultaneously enabling “data hiding” and modularization. This article presents recent research that embraces compartmentalization and co-location as an organizational programmatic principle in synthetic biological and biomimetic systems. In these systems, artificial vesicles and synthetic minimal cells are envisioned as nanoscale reactors for programmable biochemical synthesis and as chassis for molecular information processing. We present P systems, brane calculi, and the recently developed chemtainer calculus as formal frameworks providing data hiding and modularization and thus enabling the representation of highly complicated hierarchically organized compartmentalized reaction systems. We demonstrate how compartmentalization can greatly reduce the complexity required to implement computational functionality, and how addressable compartments permit the scaling-up of programmable chemical synthesis.

Mitochondrial fusion through membrane automata.

Studies have shown that malfunctions in mitochondrial processes can be blamed for diseases. However, the mechanism behind these operations is yet not sufficiently clear. In this work we present a novel approach to describe a biomolecular model for mitochondrial fusion using notions from the membrane computing. We use a case study defined in BioAmbient calculus and we show how to translate it in terms of a P automata variant. We combine brane calculi with (mem)brane automata to produce a new scheme capable of describing simple, realistic models. We propose the further use of similar methods and the test of other biomolecular models with the same behaviour.

English

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.

An Analysis for Causal Properties of Membrane Interactions

We present here an analysis, based on Abstract Interpretation [P. Cousot and R. Cousot. Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In Proc. Fourth ACM Symp. Principles of Programming Languages (POPLʼ77), pp. 238–252, 1977.], obtained by defining a finite computable approximation of the causal semantics proposed in [N. Busi. Towards a Causal Semantics for Brane Calculi. In What is it About Government that Americans Dislike, pp. 1945–1965, University Press, 2007.] for the Mate/Bud/Drip (MBD) Brane Calculus [L. Cardelli. Brane calculi - interactions of biological membranes. In Proc. of Computational Methods in Systems Biology (CMSBʼ04), LNCS 3082, pp. 257–280, 2005.]. The causal semantics in [N. Busi. Towards a Causal Semantics for Brane Calculi. In What is it About Government that Americans Dislike, pp. 1945–1965, University Press, 2007.] is able to address different kinds of causal dependencies: structural, synchronisation and the so-called environment causality. Our analysis, being a safe (over)-approximation of such causal semantics, besides modelling all possible evolutions of the system, can be used to formally prove causal properties among membrane interactions.

Implementing the Stochastics Brane Calculus in a Generic Stochastic Abstract Machine

In this paper, we deal with the problem of implementing an abstract machine for a stochastic version of the Brane Calculus. Instead of defining an ad hoc abstract machine, we consider the generic stochastic abstract machine introduced by Lakin, Paulev\'e and Phillips. The nested structure of membranes is flattened into a set of species where the hierarchical structure is represented by means of names. In order to reduce the overhead introduced by this encoding, we modify the machine by adding a copy-on-write optimization strategy. We prove that this implementation is adequate with respect to the stochastic structural operational semantics recently given for the Brane Calculus. These techniques can be ported also to other stochastic calculi dealing with nested structures.

Measurable stochastics for Brane Calculus

The main aim of this work is to give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare (2010) [12]. In this approach, the semantics of a process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a compositional, finitely branching labelled transition system for Brane Calculus; interestingly, the associated strong bisimulation is a congruence. Then, we give a stochastic semantics to Brane systems by defining them 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. Finally, we provide an SOS presentation of this stochastic semantics, which is compositional and syntax-driven, and moreover the induced rate bisimilarity is a congruence.

Mutual mobile membranes with objects on surface

In this paper we study systems of mutual mobile membranes with objects on surface using pino/exo/phago rules. Their rules are applicable whenever there is a mutual agreement between membranes expressed by appropriate objects and co-objects on their surfaces. We investigate the computational power of these systems, and also relate them to brane calculi by encoding the PEP fragment of brane calculus into the systems of mutual mobile membranes with objects on surface.

Editorial: Computing with biomolecules

This special issue contains extended full versions of selected papers presented at the International Workshop on Computing with Biomolecules held on August 27, 2008, in Vienna, Austria, in conjunction with the 7th International Conference on Unconventional Computation, UC 2008. The topic of the workshop, and of this journal issue, lies within molecular and cellular computing, with special emphasis on membrane computing. The articles represent different approaches and cover a wide variety of research topics in these rapidly developing scientific areas, ranging from models of properties of DNA to different variants of P systems, i.e., membrane systems. Additionally, one paper belonging to the general area of biocomputing was submitted specifically for this special journal issue. All contributions were thoroughly refereed and revised, according to the usual standards of Natural Computing Below we provide a summary of each of the seven papers featured in the special issue. The articles are listed in alphabetical order according to the first author. In the first paper, Bogdan Aman and Gabriel Ciobanu consider a new class of membrane systems (P systems), characterized by mutual mobile membranes with objects on the surface. The rules of this class are inspired by the pino, exo and phago operations. The authors investigate the computational power of this class of P systems and establish universality results already with a small number of membranes. In the last section the model is compared with brane calculi. Mark Daley, Ian McQuillan, James M. McQuillan and Kalpana Mahalingam study formal-language-theoretic models for transposable genetic elements. The aim of their work is to improve our understanding of mathematical modeling of transpositions. The genetic transpositions are abstracted as operations on words and languages and the authors investigate the computational power of applying different types of transpositions iteratively.

How many trimers? Modeling influenza virus fusion yields a minimum aggregate size of six trimers, three of which are fusogenic

Conflicting reports in leading journals have indicated the minimum number of influenza hemagglutinin (HA) trimers required for fusion to be between one and eight. Interestingly, the data in these reports are either almost identical, or can be transformed to be directly comparable. Different statistical or phenomenological models, however, were used to analyze these data, resulting in the varied interpretations. In an attempt to resolve this contradiction, we use PABM, a brane calculus we recently introduced, enabling an algorithmic systems biology approach that allows the problem to be modeled in a manner following a biological logic. Since a scalable PABM executor is still under development, we sufficiently simplified the fusion model and analyzed it using the model checker, PRISM. We validated the model against older HA-expressing cell-to-cell fusion data using the same parameters with the exception of three, namely HA and sialic acid (SA) surface densities and the aggregation rate, which were expected to be different as a result of the difference in the experimental setup. Results are consistent with the interpretation that a minimum aggregate size of six HA trimers, of which three undergo a conformational change to become fusogenic, is required for fusion. Of these three, two are free, while one is bound. Finally, we determined the effects of varying the SA surface density and showed that only a limited range of densities permit fusion. Our results demonstrate the potential of modeling in providing more precise interpretations of data.

Measurable Stochastics for Brane Calculus

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. Finally, we provide a SOS presentation of this stochastic semantics, which is compositional and syntax-driven.

A Translation of Beta-binders in a Prioritized Pi-calculus

A translation of Beta-binders in [email protected] is presented. Beta-binders is a bio-inspired formalism that allows the modelling of processes wrapped into boundaries. No notion of enclosing compartment can instead be found in [email protected], a dialect of the pi-calculus where actions are associated with a priority value driving their execution and where channel names can have a composite structure. As recently shown, [email protected] is a suitable language for encoding both Bio-Ambients and Brane Calculi, two of the most well-known formalisms for modelling biological scenarios. The translation provided here, which comes together with results about the operational correspondence of Beta-binders processes and their encodings, goes in the direction of assessing [email protected] as a platform for investigating the relative expressive power of various bio-inspired languages.

Control Flow Analysis for Brane Calculi

We introduce a Control Flow Analysis for Brane Calculi. This verification technique allows properties regarding the behaviour of biological systems to be checked. This is an approximate technique that focusses on the static specification of a system, rather than on its dynamics, striving for effectiveness. Examples illustrate the approach.

Undecidability of Model Checking in Brane Logic

The Brane Calculus is a calculus intended to model the structure and the dynamics of biological membranes. In order to express properties of systems in this calculus, in previous work we have introduced a temporal-spatial logic called Brane Logic. A natural question of great practical importance is if model checking of this logic is decidable, that is, if it is possible to check automatically whether a given system satisfies a given formula. We have already shown that model checking is decidable for replication-free systems and guarantee-free formulas. In this paper, we show that admitting replication in systems, or any guarantee constructor in formulas (and quantifiers), leads model checking to be undecidable. Moreover, we give also a correspondence result between membranes and systems, showing that any system can be obtained by a canonical one where all information are contained on a membrane enclosing an empty compartment.

Membrane computing with transport and embedded proteins

In this paper, we look at the expressive power of P systems with proteins embedded on the membranes. The rules governing the evolution of the embedded proteins are inspired from brane calculi. We use some basic operations of brane calculi, namely, exo, endo, bud, mate, pino, wrap in the formalism of membrane computing. We also use rules allowing the movement of proteins, to pass through membranes and attach to and detach from the membranes. Combining the two kinds of operations, namely, brane calculi operations as well as protein movement operations, we have obtained some universality results of P systems. We have also identified some decidable sub-classes of P systems by restricting the use of the protein movement rules.

A simple calculus for proteins and cells

The use of process calculi to represent biological systems has led to the design of different formalisms such as brane calculi and κ -calculus. Both have proved to be useful to model different types of biological systems. As an attempt to unify the formalisms, we introduce the bio κ - calculus, a simple calculus for describing proteins and cells, in which bonds are represented by means of shared names and interactions are modelled at the domain level. In bio κ -calculus, protein–protein interactions have to be at most binary and cell interactions have to fit with sort constraints. In this contribution we define the semantics of bio κ -calculus, analyse its properties, discuss the expressivity of the calculus by modelling two significant examples–a signalling pathway and a virus infection–and study an implementation in Milner’s π -calculus.

Membrane computing and brane calculi. Old, new, and future bridges

After a short discussion about similarities and dissimilarities of membrane computing and brane calculi, insisting mainly on some recent ideas of bridging the two areas of research, one recalls some details concerning certain classes of P systems based on brane calculi operations. Several open problems are formulated in this context.

Membrane systems with proteins embedded in membranes

Membrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells. We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors). If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors. We also consider a number of decision problems concerning reachability of configurations and boundness.

(Mem)brane automata

We introduce the notion of a P automaton with marked membranes, a P p p automaton for short, which is an accepting variant of P systems. The concept is motivated by the theory of P systems, brane calculi, and the traditional concept of automata. In P systems with marked membranes, bio-molecules (proteins) are allowed to move through the membranes and to attach onto or to de-attach from the membranes. The membrane system evolves according to rules which are defined over multisets of proteins and describe the above actions. In addition to these features, the P automaton with marked membranes is able to consume inputs from its environment, i.e. multisets of proteins, which might influence the behaviour of the system. The result of the computation is the set of multiset sequences consumed by the skin membrane, supposing that the P p p automaton started functioning in the initial configuration and entered a final configuration at halting. We show that any recursively enumerable language can be obtained as the language accepted by a P p p automaton modulo a simple computable mapping.

Expressiveness Issues in Brane Calculi: A Survey

Brane calculi are a family of biologically inspired process calculi proposed in [L. Cardelli. Brane Calculi - Interactions of biological membranes. In Proc. Computational Methods in System Biology 2004 (CMSB 2004), LNCS 3082, Springer, 2005] for modeling the interactions of dynamically nested membranes. In [L. Cardelli. Brane Calculi - Interactions of biological membranes. In Proc. Computational Methods in System Biology 2004 (CMSB 2004), LNCS 3082, Springer, 2005] a basic calculus for membranes interactions – called Phago/Exo/Pino (PEP) – is proposed, whose primitives are inspired by endocytosis and exocytosis. An alternative basic calculus – called Mate/Bud/Drip (MBD) and inspired by membrane fusion and fission – is also outlined and shown to be encodable in Phago/Exo/Pino in [L. Cardelli. Brane Calculi - Interactions of biological membranes. In Proc. Computational Methods in System Biology 2004 (CMSB 2004), LNCS 3082, Springer, 2005]. In this paper we survey some results on the comparison of the expressivity of the PEP and the MBD calculi, w.r.t. their ability to act as computational devices.