Paolo Milazzo

The calculus of looping sequences

We describe the Calculus of Looping Sequences (CLS) which is suitable for modeling microbiological systems and their evolution. We present two extensions, CLS with links (LCLS) and Stochastic CLS. LCLS simplifies the description of protein interaction at a lower level of abstraction, namely at the domain level. Stochastic CLS allows us to describe quantitative aspects of the modeled systems, such as the frequency of chemical reactions. As examples of application to real biological systems, we show the simulation of the activity of the lactose operon in E.coli and the quorum sensing process in P.aeruginosa, both described with Stochastic CLS.

Spatial P systems

We present Spatial P systems, a variant of P systems which embodies the concept of space and position inside a membrane. Objects in membranes are associated with positions. Rules specify, in the usual way, the objects which are consumed and the ones which are produced; in addition, they can specify the positions of the produced objects. Objects belong to two different sets: the set of ordinary objects and the set of mutually exclusive objects. Every position inside a membrane can accommodate an arbitrary number of ordinary objects, but at most one mutually exclusive object. We prove that Spatial P systems are universal even if only non-cooperating rules are allowed. We also show how Spatial P systems can be used to model the evolution of populations in presence of geographical separations.

Stochastic Calculus of Looping Sequences for the Modelling and Simulation of Cellular Pathways

The paper presents the Stochastic Calculus of Looping Sequences (SCLS) suitable to describe microbiological systems, such as cellular pathways, and their evolution. Systems are represented by terms. The terms of the calculus are constructed by basic constituent elements and operators of sequencing, looping, containment and parallel composition. The looping operator allows tying up the ends of a sequence, thus creating a circular sequence which can represent a membrane. The evolution of a term is modelled by a set of rewrite rules enriched with stochastic rates representing the speed of the activities described by the rules, and can be simulated automatically. As applications, we give SCLS representations of the regulation process of the lactose operon in Escherichia coli and of the quorum sensing in Pseudomonas aeruginosa . A prototype simulator (SCLSm) has been implemented in F# and used to run the experiments. A public version of the tool is available at the url: http://www.di.unipi.it/~milazzo/biosims/ .

Bisimulations in calculi modelling membranes

Bisimulations are well-established behavioural equivalences that are widely used to study properties of computer science systems. Bisimulations assume the behaviour of systems to be described as labelled transition systems, and properties of a system can be verified by assessing its bisimilarity with a system one knows to enjoy those properties.In this paper we show how semantics based on labelled transition systems and bisimulations can be defined for two formalisms for the description of biological systems, both capable of describing membrane interactions. These two formalisms are the Calculus of Looping Sequences (CLS) and Brane Calculi, and since they stem from two different approaches (rewrite systems and process calculi) bisimulation appears to be a good candidate as a general verification method.We introduce CLS and define a labelled semantics and bisimulations for which we prove some congruence results. We show how bisimulations can be used to verify properties by way of two examples: the description of the regulation of lactose degradation in Escherichia coli and the description of the EGF signalling pathway. We recall the PEP calculus (the simplest of Brane Calculi) and its translation into CLS, we define a labelled semantics and some bisimulation congruences for PEP processes, and we prove that bisimilar PEP processes are translated into bisimilar CLS terms.

Bisimulation congruences in the calculus of looping sequences

The Calculus of Looping Sequences (CLS) is a calculus suitable to describe biological systems and their evolution. CLS terms are constructed by starting from basic constituents and composing them by means of operators of concatenation, looping, containment and parallel composition. CLS terms can be transformed by applying rewrite rules. We give a labeled transition semantics for CLS by using, as labels, contexts in which rules can be applied. We define bisimulation relations that are congruences with respect to the operators on terms, and we show an application of CLS to the modeling of a biological system and we use bisimulations to reason about properties of the described system.

Compositional semantics and behavioral equivalences for P Systems

The aim of the paper is to give a compositional semantics in the style of the Structural Operational Semantics (SOS) and to study behavioral equivalence notions for P Systems. Firstly, we consider P Systems with maximal parallelism and without priorities. We define a process algebra, called P Algebra, whose terms model membranes, we equip the algebra with a Labeled Transition System (LTS) obtained through SOS transition rules, and we study how some equivalence notions defined over the LTS model apply in our case. Then, we consider P Systems with priorities and extend the introduced framework to deal with them. We prove that our compositional semantics reflects correctly maximal parallelism and priorities.

Spatial Calculus of Looping Sequences

The Calculus of Looping Sequences (CLS) enables the description of biological systems and of their evolution. This paper presents the Spatial CLS, an extension of CLS that allows the description of the position of biological elements, and of the space they take up in a 2D/3D space. The elements may move autonomously during the passage of time, and may interact when constraints on their positions are satisfied. The space occupied by each element is modeled as a hard sphere, hence space conflicts may arise during system evolution. These conflicts are resolved by an appropriate algorithm, which rearranges the position of the elements by assuming that they push each other when they are too close. Moreover, rewrite rules are endowed with a parameter describing their reaction rate. The aim of Spatial CLS is to enable a more accurate description of those biological processes whose behaviour depends on the exact position of the elements. As example applications of the calculus, we present a model of cell proliferation, and a model of the quorum sensing process in Pseudomonas aeruginosa.

Tumour suppression by immune system through stochastic oscillations

The well-known Kirschner-Panetta model for tumour-immune System interplay [Kirschner, D., Panetta, J.C., 1998. Modelling immunotherapy of the tumour-immune interaction. J. Math. Biol. 37 (3), 235-252] reproduces a number of features of this essential interaction, but it excludes the possibility of tumour suppression by the immune system in the absence of therapy. Here we present a hybrid-stochastic version of that model. In this new framework, we show that in reality the model is also able to reproduce the suppression, through stochastic extinction after the first spike of an oscillation.

Design and verification of long-running transactions in a timed framework

Long-running transactions consist of tasks which may be executed sequentially and in parallel, may contain subtasks, and may require to be completed before a deadline. These transactions are not atomic and, in case of executions which cannot be completed, a compensation mechanism must be provided. In this paper we develop a model of Communicating Hierarchical Timed Automata suitable to describe the mentioned aspects in a framework where also time is taken into account. We develop the patterns for composing long-running transactions sequentially, in parallel or by nesting. The correct compensation of a composed long-running transaction is preserved by these composition patterns. The automaton-theoretic approach allows the verification of properties by model checking. As a case study, we model and analyse an example of e-commerce application described in terms of long-running transactions.

Extending the calculus of looping sequences to model protein interaction at the domain level

In previous papers we introduced a formalism, called Calculus of Looping Sequences (CLS), for describing biological systems and their evolution. CLS is based on term rewriting. Terms can be constructed by composing symbols of a given alphabet in sequences, which could be closed (looping) and contain other terms. In this paper we extend CLS to represent protein interaction at the domain level. Such an extension, called Calculus of Linked Looping Sequences (LCLS), is obtained by labeling alphabet symbols used in terms. Two symbols with the same label are considered to be linked. We introduce a type system to express a concept of well-formedness of LCLS terms, we give an operational semantics of the new calculus, and we show the application of LCLS to the description of a biological system.