Luca Marchetti

MP Modelling of Glucose-Insulin Interactions in the Intravenous Glucose Tolerance Test

The Intravenous Glucose Tolerance Test is an experimental procedure used to study the glucose-insulin endocrine regulatory system. An open problem is to construct a model representing simultaneously the entire regulative mechanism. In the past three decades, several models have appeared, but they have not escaped criticisms and drawbacks. In this paper, the authors apply the Metabolic P systems theory for developing new physiologically based models of the glucose-insulin system, which can be applied to the IVGTT. Ten datasets obtained from literature were considered and an MP model was found for each, which fits the data and explains the regulations of the dynamics. Finally, each model is analysed to define a common pattern which explains, in general, the action of the glucose-insulin control system. DOI: 10.4018/jncr.2011070102 14 International Journal of Natural Computing Research, 2(3), 13-24, July-September 2011 Copyright

Solving dynamical inverse problems by means of Metabolic P systems

MP (Metabolic P) systems are a class of P systems introduced for modelling metabolic processes. We refer to the dynamical inverse problem as the problem of identifying (discrete) mathematical models exhibiting an observed dynamics. In this paper, we complete the definition of the algorithm LGSS (Log-gain Stoichiometric Stepwise regression) introduced in Manca and Marchetti (2011) for solving a general class of dynamical inverse problems. To this aim, we develop a reformulation of the classical stepwise regression in the context of MP systems. We conclude with a short review of two applications of LGSS for discovering the internal regulation logic of two phenomena relevant in systems biology.

LOG-GAIN STOICHIOMETRIC STEPWISE REGRESSION FOR MP SYSTEMS

MP systems are a class of P systems introduced for modeling metabolic processes. Here a regression method is presented for deducing a MP system exhibiting the dynamics of an observed metabolic system. In the procedure here described the knowledge of the stoichiometry of the system is combined with the log-gain principle of MP systems and is integrated with the Least Square Estimation method and with the stepwise regression approximation.

A methodology based on MP theory for gene expression analysis

In this paper we develop an application of the MP theory to gene expression analysis. After introducing some general concepts about transcriptome analysis and about gene networks, we delineate a methodology for modelling such kind of networks by means of Metabolic P systems. MP systems were initially introduced as models of metabolic processes, but they can be successfully used in each context where we want to infer models of a system from a given set of time series. In the case of gene expression analysis, we found a standard way for translating MP grammars involving gene expressions into corresponding quantitative gene networks. Pre-processing methods of raw time series have been also elaborated in order to achieve a successful MP modelling of the underlying gene network.

Metabolic approximation of real periodical functions

Abstract MP systems are a class of P systems introduced for modeling metabolic processes. Here approximation of real functions is approached by using MP systems. An example is presented which provides a good approximation of sine and cosine functions based on a surprisingly simple MP system. Other interesting oscillators are also presented, and possible extensions of the method are outlined.

Goldbeter's mitotic oscillator entirely modeled by MP systems

MP systems are a class of P systems introduced for modeling metabolic processes. Here we apply an algorithm, we call Log-Gain Stoichiometric Stepwise Regression (LGSS), to Golbeters oscillator. In general, LGSS derives MP models from the time series of observed dynamics. In the case of Golbeters oscillator, we found that by considering different values of the resolution time τ, different analytical forms of regulation maps were appropriate. By means of a suitable MATLAB implementation of LGSS, we automatically generated 700 MP models (τ varying from 10-3 min to 700 ċ 10-3 min with increments of 10-3 min). Many of these models exhibit a good approximation, and have second degree polynomials as regulation maps. These results provide an experimental evidence of LGSS adequacy.

An algebraic formulation of inverse problems in MP dynamics

Metabolic P (MP) grammars are a particular class of multiset rewriting grammars introduced in the MP theory for modelling metabolic processes. In this paper, a new algebraic formulation of inverse problems, based on MP grammars and Kronecker product, is given, for further motivating the correctness of the LGSS (Log-Gain Stoichiometric Stepwise) algorithm, introduced in 2010s for solving inverse problems in the MP framework. At the end of the paper, a section is included that introduces the problem of multicollinearity, which could arise during the execution of LGSS, and that defines an algorithm, based on a hierarchical clustering technique, that solves it in a suitable way.

Psim: a simulator for biomolecular dynamics based on P systems

Metabolic P systems, shortly MP systems, are a special class of P systems, introduced for expressing biological metabolism. Their dynamics is computed by metabolic algorithms which transform populations of objects according to a mass partition principle, based on suitable generalizations of chemical laws. The basic principles of MP systems are discussed and Psim, a simulation tool we developed in this context to discretely compute systems dynamics, is highlighted in its basic features. A concrete example is reported as well including a real simulation experiment by means of Psim.

MP Modelling for Systems Biology: Two Case Studies

Metabolic P systems (MP systems), based on Păun’s P systems, were introduced for modelling metabolic systems by means of suitable multiset rewriting grammars. The initial modelling framework has been widely extended in last years and equipped with a new regression algorithm which derives MP models from the time series of observed dynamics. This has allowed us to dramatically extend the range of possible MP modelling applications from metabolic dynamics to more general kinds of dynamical systems. In this work two applications of MP systems are presented, for discovering the internal regulation logic of two phenomena relevant to systems biology. The first one is a metabolic dynamics related to glucose/insulin interactions during the Intravenous Glucose Tolerance Test. The second one deals with the definition of gene expression networks related to breast cancer under the inhibition of a growth factor.

XML Representation of Metabolic P Systems

Metabolic P systems (MP systems) are a special class of P systems introduced for expressing biological metabolic phenomena. The graphical formalism of MP graphs represents, in a simple and intuitive way, the structure of these systems. However, there are some cases in which they would be better specified by semi-structured textual documents, especially for information exchanging between different computational tools elaborating on different biological aspects. The aim of this paper is to define such a way of exportation from MP graphs to XML documents. It turns out that all properties which guarantee the correctness of MP graphs can be formally described by means of logical formulae on trees, and completely expressed as XML constraints in XSD (XML Schema Definition), a W3C standard for XML validation.