External Control in Process Algebra for Systems Biology

A critical aspect in the modeling of biological systems is the description view point. On the one hand, the Stochastic \u3c0-calculus formalism provides an intuitive and compact representation from an internal perspective. On the other hand, other proposed languages such as Hybrid Automata and Stochastic Concurrent Constraint Programming introduce in the system description an external control and provide more structured models. This work aims at bridging the above discussed gap. In particular, we propose a different approach for the encoding of biological systems in Stochastic \u3c0-calculus in the direction of introducing an external control and comparing different formalisms. We show the effectiveness of our method on some examples

AI and OR in management of operations: history and trends

The last decade has seen a considerable growth in the use of Artificial Intelligence (AI) for operations management with the aim of finding solutions to problems that are increasing in complexity and scale. This paper begins by setting the context for the survey through a historical perspective of OR and AI. An extensive survey of applications of AI techniques for operations management, covering a total of over 1200 papers published from 1995 to 2004 is then presented. The survey utilizes Elsevier's ScienceDirect database as a source. Hence, the survey may not cover all the relevant journals but includes a sufficiently wide range of publications to make it representative of the research in the field. The papers are categorized into four areas of operations management: (a) design, (b) scheduling, (c) process planning and control and (d) quality, maintenance and fault diagnosis. Each of the four areas is categorized in terms of the AI techniques used: genetic algorithms, case-based reasoning, knowledge-based systems, fuzzy logic and hybrid techniques. The trends over the last decade are identified, discussed with respect to expected trends and directions for future work suggested

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

BlenX-based compositional modeling of complex reaction mechanisms

Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of the biological networks calls for conceptual tools that manage the combinatorial explosion of the set of possible interactions. A suitable conceptual tool to attack complexity is compositionality, already successfully used in the process algebra field to model computer systems. We rely on the BlenX programming language, originated by the beta-binders process calculus, to specify and simulate high-level descriptions of biological circuits. The Gillespie's stochastic framework of BlenX requires the decomposition of phenomenological functions into basic elementary reactions. Systematic unpacking of complex reaction mechanisms into BlenX templates is shown in this study. The estimation/derivation of missing parameters and the challenges emerging from compositional model building in stochastic process algebras are discussed. A biological example on circadian clock is presented as a case study of BlenX compositionality