Giuditta Franco

P Systems for Biological Dynamics

P systems have clear structural analogies with the cell. However, certain difficulties arise when one attempts to represent a biomolecular process using these systems. This chapter suggests some ways to overcome such difficulties and to provide P systems with further functionalities aimed at increasing their versatility in the modeling of biomolecular processes. Concepts from state transition dynamics are taken to put P systems in a general analysis framework for dynamical discrete systems. An explicit notion of environment is proposed to provide P systems with a regulatory and constraining agent, as real biomolecular processes must deal with. The chapter focuses on a new rewriting strategy inspired by biochemistry, in which reactivities play a central role in driving the rules as happens during biochemical reactions. Tests on an algorithm implementing rewriting with reactivities, realized on a simulator called Psim, show the capability of this algorithm to express several processes with precision, particularly those presenting oscillatory phenomena. Finally, an analysis of the process of leukocyte recruitment is also performed using Psim.

A Membrane System for the Leukocyte Selective Recruitment

A formal description is developed for the phenomenon of leukocyte recruitment that plays a critical role in the immune response. Due to its complex nature and capability to rapidly adapt to the attack of infectious agents, the immune system may be considered a typical example of complex adaptive system [9]. Here the leukocyte selective recruitment, crucial in immunity, is modeled as a dynamical system of interactions between leukocytes and endothelial cells, where a special kind of membrane structure turns out to be a very useful tool in the formal analysis of the recruitment process. In our membrane system, besides the traditional rules for communication and transformation of P systems [8], rules are allowed for the expression of receptors, for adhesion between membranes, and for the encapsulation of a membrane inside another membrane.

Data analysis pipeline from laboratory to MP models

A workflow for data analysis is introduced to synthesize flux regulation maps of a Metabolic P system from time series of data observed in laboratory. The procedure is successfully tested on a significant case study, the photosynthetic phenomenon called NPQ, which determines plant accommodation to environmental light. A previously introduced MP model of such a photosynthetic process has been improved, by providing an MP system with a simpler regulative network that reproduces the observed behaviors of the natural system. Two regression techniques were employed to find out the regulation maps, and interesting experimental results came out in the context of their residual analysis for model validation.

A dictionary based informational genome analysis.

BackgroundIn the post-genomic era several methods of computational genomics are emerging to understand how the whole information is structured within genomes. Literature of last five years accounts for several alignment-free methods, arisen as alternative metrics for dissimilarity of biological sequences. Among the others, recent approaches are based on empirical frequencies of DNA k-mers in whole genomes.ResultsAny set of words (factors) occurring in a genome provides a genomic dictionary. About sixty genomes were analyzed by means of informational indexes based on genomic dictionaries, where a systemic view replaces a local sequence analysis. A software prototype applying a methodology here outlined carried out some computations on genomic data. We computed informational indexes, built the genomic dictionaries with different sizes, along with frequency distributions. The software performed three main tasks: computation of informational indexes, storage of these in a database, index analysis and visualization. The validation was done by investigating genomes of various organisms. A systematic analysis of genomic repeats of several lengths, which is of vivid interest in biology (for example to compute excessively represented functional sequences, such as promoters), was discussed, and suggested a method to define synthetic genetic networks.ConclusionsWe introduced a methodology based on dictionaries, and an efficient motif-finding software application for comparative genomics. This approach could be extended along many investigation lines, namely exported in other contexts of computational genomics, as a basis for discrimination of genomic pathologies.

Mitotic oscillators as MP graphs

This paper proposes a model in terms of metabolic P graphs of a few important processes occurring during the biological phase where the choice is made to begin again mitosis or to arrest it. The cellular processes during this phase turn out to be especially interesting in the case of DNA damage, which triggers a specific destruction of Cdc25A phosphatase. It has important implications to understand the role of cell cycle checkpoints and the mechanism(s) guiding the proliferation of UV-resistant tumored cells. The formalism of metabolic P graphs highlights the relevant information of the biological network dynamics, and the individuation of few parameters rules the basic mechanisms of Cdc25A degradation, involving a couple of important mitotic oscillators.

Hybrid Functional Petri Nets as MP systems

In this work we give a formalization of Hybrid Functional Petri Nets, shortly HFPN, an extension of Petri Nets for biopathways modelling, and we compare them with Metabolic P Systems. An introduction to both the formalisms is given, together with highlights about respective similarities and differences. Their equivalence is thus proved by means of a theorem which holds under quite general hypotheses. The case study of the lac operon gene regulatory mechanism in the glycolytic pathway of Escherichia coli is modeled by an MP system which provides the same dynamics of an equivalent HFPN model.

Knee joint injury and repair modeled by membrane systems.

Tissue reparative processes following tissue injury are modeled by a basic membrane system, dealing only with objects, non-active membranes, and non-deterministic evolution rules. At the biological level, tissue repair is regulated by multiple interactions between cells and macromolecules, the latter acting as signals. Such signals modify cell behavior including proliferation, migration, differentiation, and phagocytosis. The signaling components themselves are produced and removed by the resident cell population, and this set of events may provide additional stimuli for altering cell activities. In this paper we have focused on modeling the biology of events following an injury to the knee joint, and have used hyaluronan (a polymer produced by cartilage and synovial cells) as an example for a signaling component in the healing process. The intrinsic non-determinism of the model is a key feature, which allows a mathematical description of the repair responses as well as a possibility for either functional restoration or chronic degeneration, leading to arthritis.

An algorithmic analysis of DNA structure

Bilinearity, complementarity and antiparallelism of the double stranded DNA structure are proved, in a general and abstract setting, as requirements of an efficient duplication algorithm for ‘mobile strings’.

DNA recombination by XPCR

The first step of the Adleman-Lipton extract model in DNA computing is the combinatorial generation of libraries. In this paper a new method is proposed for generating a initial pool, it is a quaternary recombination of strings via application of null context splicing rules. Its implementation, based on a kind of PCR called XPCR, results to be convenient with respect to the standard methods, in terms of efficiency; speed and feasibility. The generation algorithm we propose was tested by a lab experiment here described, since the presence of few sequences is enough for checking the completeness of the library. The simple technology of this approach is interesting in and of itself, and it can have many useful applications in biological contexts.

A relational view of recurrence and attractors in state transition dynamics

The classical dynamics concepts of recurrence and attractor are analysed in the basic mathematical setting of state transition systems, where both time and space are discrete, and no structure is assumed on the state space besides a binary transition relation. This framework proves useful to the dynamical analysis of computations and biomolecular processes. Here a relational formulation of this framework is presented, where the concepts of attractor and recurrence surface in two variants, respectively relating to the two fundamental modalities. A strong link between recurrence and both existence and extent of attractors, in either variant, is established by a novel characterization theorem.