arXiv subjects

Giulio Caravagna

Publications and source records attributed to Giulio Caravagna.

21 records · Page 2Linked to original sources

arXiv2010

Aspects of multiscale modelling in a process algebra for biological systems

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.

cs.LO↗

arXiv2010

Modeling biological systems with delays in Bio-PEPA

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.

cs.CE↗

arXiv2009

On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems

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.

q-bio.QM↗