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Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that rarely can be solved in closed-form, but that can instead be used to reason on the system dynamics. In this context, one of the possible approaches is to perform numerical simulations, which may require a high computational effort. In particular, in order to investigate some dynamical properties, such as robustness or global sensitivity, many simulations have to be performed by varying the initial concentration of chemical species. Results: In order to reduce the computational effort required when many simulations are needed to assess a property, we exploit a new notion of monotonicity of the output of the system (the concentration of a target chemical species at the steady-state) with respect to the input (the initial concentration of another chemical species). To assess such monotonicity behavior, we propose a new graphical approach that allows us to state sufficient conditions for ensuring that the monotonicity property holds. Our sufficient conditions allow us to efficiently verify the monotonicity property by exploring a graph constructed on the basis of the reactions involved in the network. Once established, our monotonicity property allows us to drastically reduce the number of simulations required to assess some dynamical properties of the CRN.

Robustness is an observable property for which a chemical reaction network (CRN) can maintain its functionalities despite the influence of different perturbations. In general, to verify whether a network is robust, it is necessary to consider all the possible parameter configurations. This is a process that can entail a massive computational effort. In the work of Rizk et al., the authors propose a definition of robustness in linear temporal logic (LTL) through which, on the basis of multiple numerical timed traces obtained by considering different parameter configurations, they verify the robustness of a reaction network. In this paper, we focus on a notion of initial concentration robustness ($\alpha$-robustness), which is related to the influence of the perturbation of the initial concentration of one species (i.e., the input) on the concentration of another species (i.e., the output) at the steady state. We characterize this notion of robustness in the framework proposed by Rizk et al., and we show that, for monotonic reaction networks, this allows us to drastically reduce the number of traces necessary to verify robustness of the CRN.

We present model predictions for the Zr isotopic ratios produced by slow neutron captures in C-rich asymptotic giant branch (AGB) stars of masses 1.25 to 4 Msun and metallicities Z=0.01 to 0.03, and compare them to data from single meteoritic stardust silicon carbide (SiC) and high-density graphite grains that condensed in the outflows of these stars. We compare predictions produced using the Zr neutron-capture cross section from Bao et al. (2000) and from n_TOF experiments at CERN, and present a new evaluation for the neutron-capture cross section of the unstable isotope 95Zr, the branching point leading to the production of 96Zr. The new cross sections generally presents an improved match with the observational data, except for the 92Zr/94Zr ratios, which are on average still substantially higher than predicted. The 96Zr/94Zr ratios can be explained using our range of initial stellar masses, with the most 96Zr-depleted grains originating from AGB stars of masses 1.8 - 3 Msun, and the others from either lower or higher masses. The 90,91Zr/94Zr variations measured in the grains are well reproduced by the range of stellar metallicities considered here, which is the same needed to cover the Si composition of the grains produced by the chemical evolution of the Galaxy. The 92Zr/94Zr versus 29Si/28Si positive correlation observed in the available data suggests that stellar metallicity rather than rotation plays the major role in covering the 90,91,92Zr/94Zr spread., Comment: 35 pages, 5 figures, Accepted for publication on The Astrophysical Journal

Reactions forming a pathway can be rewritten by making explicit the different molecular components involved in them. A molecular component represents a biological entity (e.g. a protein) in all its states (free, bound, degraded, etc.). In this paper we show the application of a component identification algorithm to a number of real-world models to experimentally validate the approach. Components identification allows subpathways to be computed to better understand the pathway functioning., Comment: In Proceedings Wivace 2013, arXiv:1309.7122

Modular verification is a technique used to face the state explosion problem often encountered in the verification of properties of complex systems such as concurrent interactive systems. The modular approach is based on the observation that properties of interest often concern a rather small portion of the system. As a consequence, reduced models can be constructed which approximate the overall system behaviour thus allowing more efficient verification. Biochemical pathways can be seen as complex concurrent interactive systems. Consequently, verification of their properties is often computationally very expensive and could take advantage of the modular approach. In this paper we report preliminary results on the development of a modular verification framework for biochemical pathways. We view biochemical pathways as concurrent systems of reactions competing for molecular resources. A modular verification technique could be based on reduced models containing only reactions involving molecular resources of interest. For a proper description of the system behaviour we argue that it is essential to consider a suitable notion of fairness, which is a well-established notion in concurrency theory but novel in the field of pathway modelling. We propose a modelling approach that includes fairness and we identify the assumptions under which verification of properties can be done in a modular way. We prove the correctness of the approach and demonstrate it on the model of the EGF receptor-induced MAP kinase cascade by Schoeberl et al., Comment: In Proceedings MeCBIC 2012, arXiv:1211.3476

Testing equivalence was originally defined by De Nicola and Hennessy in a process algebraic setting (CCS) with the aim of defining an equivalence relation between processes being less discriminating than bisimulation and with a natural interpretation in the practice of system development. Finite characterizations of the defined preorders and relations led to the possibility of verification by comparing an implementation with a specification in a setting where systems were seen as black boxes with input and output capabilities, thus neglecting internal undetectable behaviours. In this paper, we start defining a porting of the well-established testing theory into membrane computing, in order to investigate possible benefits in terms of inherited analysis/verification techniques and interesting biological applications. P Algebra, a process algebra for describing P Systems, is used as a natural candidate for the porting since it enjoys the desirable property of being compositional and comes with other observational equivalences already defined and studied., Comment: Presented at MeCBIC 2011

The article proposes a model for the configuration management of open systems. The model aims at validation of configurations against given specifications. An extension of decision graphs is proposed to express specifications. The proposed model can be used by software developers to validate their own configurations across different versions of the components, or to validate configurations that include components by third parties. The model can also be used by end-users to validate compatibility among different configurations of the same application. The proposed model is first discussed in some application scenarios and then formally defined. Moreover, a type discipline is given to formally define validation of a configuration against a system specification, Comment: 13 pages

We propose a variant of the CCS process algebra with new features aiming at allowing multiscale modelling of biological systems. In the usual semantics of process algebras for modelling biological systems actions are instantaneous. When different scale levels of biological systems are considered in a single model, one should take into account that actions at a level may take much more time than actions at a lower level. Moreover, it might happen that while a component is involved in one long lasting high level action, it is involved also in several faster lower level actions. Hence, we propose a process algebra with operations and with a semantics aimed at dealing with these aspects of multiscale modelling. We study behavioural equivalences for such an algebra and give some examples., Comment: In Proceedings MeCBIC 2010, arXiv:1011.0051

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:1008.3147

This volume contains the papers presented at the first International Workshop on Applications of Membrane Computing, Concurrency and Agent-based Modelling in Population Biology (AMCA-POP 2010) held in Jena, Germany on August 25th, 2010 as a satellite event of the 11th Conference on Membrane Computing (CMC11). The aim of the workshop is to investigate whether formal modelling and analysis techniques could be applied with profit to systems of interest for population biology and ecology. The considered modelling notations include membrane systems, Petri nets, agent-based notations, process calculi, automata-based notations, rewriting systems and cellular automata. Such notations enable the application of analysis techniques such as simulation, model checking, abstract interpretation and type systems to study systems of interest in disciplines such as population biology, ecosystem science, epidemiology, genetics, sustainability science, evolution and other disciplines in which population dynamics and interactions with the environment are studied. Papers contain results and experiences in the modelling and analysis of systems of interest in these fields.

We present the MIM calculus, a modeling formalism with a strong biological basis, which provides biologically-meaningful operators for representing the interaction capabilities of molecular species. The operators of the calculus are inspired by the reaction symbols used in Molecular Interaction Maps (MIMs), a diagrammatic notation used by biologists. Models of the calculus can be easily derived from MIM diagrams, for which an unambiguous and executable interpretation is thus obtained. We give a formal definition of the syntax and semantics of the MIM calculus, and we study properties of the formalism. A case study is also presented to show the use of the calculus for modeling biomolecular networks., Comment: 15 pages; 8 figures; To be published on EPTCS, proceedings of MeCBIC 2009

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. In the literature, delay stochastic simulation algorithms have been proposed. These algorithms follow a "delay as duration" approach, namely they are based on an interpretation of a delay as the elapsing time between the start and the termination of a chemical reaction. This interpretation is not suitable for some classes of biological systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We show on a DDE model of tumor growth that the delay as duration approach for stochastic simulation is not precise, and we propose a simulation algorithm based on a ``purely delayed'' interpretation of delays which provides better results on the considered model.