Ecological Modelling with the Calculus of Wrapped Compartments

The Calculus of Wrapped Compartments is a framework based on stochastic multiset rewriting in a compartmentalised setting originally developed for the modelling and analysis of biological interactions. In this paper, we propose to use this calculus for the description of ecological systems and we provide the modelling guidelines to encode within the calculus some of the main interactions leading ecosystems evolution. As a case study, we model the distribution of height of Croton wagneri, a shrub constituting the endemic predominant species of the dry ecosystem in southern Ecuador. In particular, we consider the plant at different altitude gradients (i.e. at different temperature conditions), to study how it adapts under the effects of global climate change.Comment: A preliminary version of this paper has been presented in CMC13 (LNCS 7762, pp 358-377, 2013

Modelling Cell Cycle using Different Levels of Representation

Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform computerised simulations of biological systems, which are called in silico experiments, to attain important insights and predictions about the system behaviour with a considerably lower cost. Computer visualisation is an important part of this approach, since it provides a realistic representation of the system behaviour. We define a formal methodology to model biological systems using different levels of representation: a purely formal representation, which we call molecular level, models the biochemical dynamics of the system; visualisation-oriented representations, which we call visual levels, provide views of the biological system at a higher level of organisation and are equipped with the necessary spatial information to generate the appropriate visualisation. We choose Spatial CLS, a formal language belonging to the class of Calculi of Looping Sequences, as the formalism for modelling all representation levels. We illustrate our approach using the budding yeast cell cycle as a case study

Modelling the Dynamics of an Aedes albopictus Population

We present a methodology for modelling population dynamics with formal means of computer science. This allows unambiguous description of systems and application of analysis tools such as simulators and model checkers. In particular, the dynamics of a population of Aedes albopictus (a species of mosquito) and its modelling with the Stochastic Calculus of Looping Sequences (Stochastic CLS) are considered. The use of Stochastic CLS to model population dynamics requires an extension which allows environmental events (such as changes in the temperature and rainfalls) to be taken into account. A simulator for the constructed model is developed via translation into the specification language Maude, and used to compare the dynamics obtained from the model with real data.Comment: In Proceedings AMCA-POP 2010, arXiv:1008.314

Topological Calculus of Looping Sequences

Il Calculus of Looping Sequences (CLS) permette la descrizione dei sistemi biologici e della loro evoluzione. Nell'ambito del lavoro di tesi e' stata sviluppata una estensione del CLS, chiamata Topological CLS (TCLS), dove ad ogni oggetto del sistema biologico sono associate una precisa posizione e dimensione nello spazio. Gli oggetti possono muoversi autonomamente e l'applicabilita' delle regole di riscrittura, che modellano le reazioni tra gli elementi, puo' essere determinata dalle posizioni degli oggetti coinvolti. Infine, alle regole di riscrittura e' associato un parametro che ne specifica la velocita' di reazione. Il Topological CLS e' stato quindi utilizzato per modellare due esempi di sistemi biologici: il processo di mitosi e il quorum-sensing

Parallel BioScape: A Stochastic and Parallel Language for Mobile and Spatial Interactions

BioScape is a concurrent language motivated by the biological landscapes found at the interface of biology and biomaterials. It has been motivated by the need to model antibacterial surfaces, biofilm formation, and the effect of DNAse in treating and preventing biofilm infections. As its predecessor, SPiM, BioScape has a sequential semantics based on Gillespie's algorithm, and its implementation does not scale beyond 1000 agents. However, in order to model larger and more realistic systems, a semantics that may take advantage of the new multi-core and GPU architectures is needed. This motivates the introduction of parallel semantics, which is the contribution of this paper: Parallel BioScape, an extension with fully parallel semantics.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Formal Modelling and Simulation of Biological Systems with Spatiality

In Systems Biology, spatial modelling allows an accurate description of phenomena whose behaviour is influenced by the spatial arrangement of the elements. In this thesis, we present various modelling formalisms with spatial features, each using a different abstraction level of the real space. From the formalisms with the most abstract notion of space, to the most concrete, we formally define the MIM Calculus with compartments, the Spatial P systems, and the Spatial CLS. Each formalism is suitable for the description of different kinds of systems, which call for the use of different space modelling abstractions. We present models of various real-world systems which benefit from the ability to precisely describe space-dependent behaviours. We define the MIM Calculus, inspired by Molecular Interaction Maps, a graphical notation for bioregulatory networks. The MIM Calculus provides high-level operators with a direct biological meaning, which are used to describe the interaction capabilities of the elements of such systems. Its spatial extension includes the most abstract notion of space, namely it only allows the modelling of compartments. Such a feature allows distinguishing only the abstract position where an element is, identified by the name of the compartment. Subsequently, we propose a spatial extension to the membrane computing formalism P systems. In this case, we follow a more precise approach to spatial modelling, by embedding membranes and objects in a two-dimensional discrete space. Some objects of a Spatial P system can be declared as mutually exclusive objects, with the constraint that each position can accommodate at most one of them. The distinction between ordinary and mutually exclusive objects can be thought of as an abstraction on the size of the objects. We study the computational complexity of the formalism and the problem of efficient simulation of some kinds of models. Finally, we present the Spatial Calculus of Looping Sequences (Spatial CLS), which is an extension of the Calculus of Looping Sequences (CLS), a formalism geared towards the modelling of cellular systems. In this case, models are based on two/three dimensional continuous space, and allow an accurate description of the motion of the elements, and of their size. In particular, Spatial CLS allows the description of the space occupied by elements and membranes, which can change their sizes dynamically as the system evolves. Space conflicts which may occur can be resolved by performing a rearrangement of elements and membranes. As example applications of the calculus we present a model of cell proliferation, and a model of the quorum sensing process in Pseudomonas aeruginosa

Brane Calculi Systems: A Static Preview of their Possible Behaviour

We improve the precision of a previous Control Flow Analysis for Brane Calculi, by adding information on the context and introducing causality information on the membranes. This allows us to prove some biological properties on the behaviour of systems specified in Brane Calculi.Comment: Presented at MeCBIC 201

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014