Elsevier

Biosystems

Volume 91, Issue 3, March 2008, Pages 489-498
Biosystems

Biological networks in metabolic P systems

https://doi.org/10.1016/j.biosystems.2006.11.009Get rights and content

Abstract

The metabolic P algorithm is a procedure which determines, in a biochemically realistic way, the evolution of P systems representing biological phenomena. A new formulation of this algorithm is given and a graphical formalism is introduced which seems to be very natural in expressing biological networks by means of a two level representation: a basic biochemical level and a second one which regulates the dynamical interaction among the reactions of the first level. After some basic examples, the mitotic oscillator in amphibian embryos is considered as an important case study. Three formulations of this biological network are developed. The first two are directly derived by Goldbeter’s differential equations representation. The last one, entirely deduced by translating the biological description of the phenomenon in our diagrams, exhibits an analogous pattern, but it is conceptually simpler and avoids many details on the kinetic aspects of the reactions.

Introduction

One of the most important problems mathematicians and computer scientists have to cope with, while modelling biological phenomena, is a deep understanding and a clear representation of the phenomena related to intercellular or intracellular information transfer. In fact, in the analysis of the interactions occurring in metabolic or signal pathways, very complex networks are expressed, in their specific mechanisms, by terms like synthesis, production, catalysis, degradation, introduction, expulsion, consumption, influence, activation, inactivation, inhibition and promotion. Many of these concepts have a simple translation in formal terms, but other are very often vague, ambiguous, or strongly depending on the specific contexts in which they are embedded. The graphical notations which are used in the visualizations of these networks Segel and Cohen, 2001, Voit, 2000 have only an intuitive basis and when one attempts to express them in mathematical terms, then many inconsistencies or confuse meanings are easily encountered; moreover, they do not provide information about the dynamics of the network they represent. Therefore, a natural question arises: is it possible to reduce the most important biological regulation mechanisms to some basic relationships which could permit rigorous mathematical translations? In this paper, we present some initial steps along this direction. In fact, a notation for representing some biological networks is here described which is related to the metabolic algorithm Bianco et al., 2006a, Bianco et al., 2006b, Fontana et al., 2006, Manca et al., 2005, an effective method for “computing” biological dynamics we have developed in the framework of P systems Păun, 2000, Păun, 2002. This notation provides not only the basic information of the biochemical reactions, but it also gives the reaction regulation functions which are the core of metabolic algorithm for computing the dynamics of a special class of biologically meaningful P systems. One of the main purposes of Systems Biology, is to understand the dynamic and molecular-level relationships among biological molecules in living systems. For this reason, tools which provide intuitive ways for representing and analyzing the dynamics of complex biological networks seem to be a necessary step in the assessment of a discipline that seeks to find the “hidden” structures underlying molecular data.

Section snippets

The P Metabolic Algorithm

P systems are a computational model based on the compartmentalization of the workspace and on multiset rewriting. These concepts were introduced due to their strong biological motivation; in fact, they are intrinsically related to the basic role that membranes have in biological organisms and in the biochemical basis of any biological reality. In other words, the localization and the concentrations of any biochemical element at each instant determines all the relevant properties which underlie

Metabolic P Graphs

A Metabolic P system of level 0 (with only one membrane), shortly a MP system, is given by a structure M=(T,Q,R,F,q0) where T is an alphabet of types of M; Q are the states of M, functions from T to the set N of natural numbers; R is the set of rules of M which are denoted by αβ with α,β strings over T; F={fr|rR} is the set of reaction maps of M, with fr:QR taking values in the set R of real numbers; and q0Q is the initial state of M.

The evolution of M in time is given by a dynamical

A Case Study: The Mitotic Oscillator in Amphibian Embryos

In this section, we apply our modelling framework to a case study of mitotic oscillator Goldbeter, 1991, Goldbeter, 2004. Mitotic oscillations are a mechanism exploited by nature to regulate the onset of mitosis, that is the process of cell division aimed at producing two identical daughter cells from a single parent cell. More precisely, mitotic oscillations concern the fluctuation in the activation state of a protein produced by cdc2 gene in fission yeasts or by homologs genes in other

Conclusions

In this paper, we continue our investigation regarding the application of P systems to biological phenomena. A new version of Metabolic P Algorithm (MPA) is presented which is strictly related to the graphical formalism of MP graphs, here introduced for providing natural descriptions of biochemical systems. Interestingly enough, MP graphs can also be seen as particular neuron-like membrane systems, according to Păun (2002) and Ciobanu et al. (2006) terminology. The direct application of MPA to

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