The Discovery of Initial Fluxes of Metabolic P Systems

A central issue in systems biology is the study of efficient methods to infer fluxes of biological reactions starting from experimental data. Among the different techniques proposed in the last years, in the theory of Metabolic P systems Log-Gain principles have been introduced, which prove to be helpful for deducing biological fluxes from temporal series of observed dynamics. However, crucial tasks remain to be performed for a complete suitable application of these principles. In particular the algebraic systems introduced by the Log-Gain principles require the knowledge of the initial fluxes associated with a set of biochemical reactions. In this paper we propose an algorithm for estimating initial fluxes, which is tested in two case studies

On Modeling Signal Transduction Networks

Signal transduction networks are very complex processes employed by the living cell to suitably react to environmental stimuli. Qualitative and quantitative computational models play an increasingly important role in the representation of these networks and in the search of new insights about these phenomena. In this work we analyze some graph-based models used to discover qualitative properties of such networks. In turn, we show that MP systems can naturally extend these graph-based models by adding some qualitative elements. The case study of integrins activation during the lymphocyte recruitment, a crucial phenomenon in inflammatory processes, is described, and a first MP graph for this network is designed. Finally, we discuss some open problems related to the qualitative modeling of signaling networks

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

The Intra Venous Glucose Tolerance Test (IVGTT) is an experimental pro- cedure in which a challenge bolus of glucose is administered intra-venously and plasma glucose and insulin concentrations are then frequently sampled. An open problem is to construct a model representing simultaneously the entire control system. In the last three decades, several models appeared in the literature. One of the mostly used one is known as the minimal model, which has been challenged by the dynamical model. However, both the models have not escape from criticisms and drawbacks. In this paper we apply Metabolic P systems theory for developing new physiologically based models of the glucose-insulin system which can be applied to the Intra Venous Glucose Tolerance Test. We considered ten data-sets obtained from literature and for each of them we found an MP model which ts the data and explains the regulations of the dynamics. Finally, further analysis are planned in order to de ne common patterns which explain, in general, the action of the glucose-insulin control system

Linking Bistable Dynamics to Metabolic P Systems

Bistability, or more generally multistability, is an important recurring theme in biological systems. In particular, the discovery of bistability in signal pathways of genetic networks, prompts strong interest in understanding both the design and function of these networks. Therefore, modelling these systems is crucial to understand their behaviors, and also to analyze and identify characteristics that would otherwise be di cult to realize. Although di erent classes of models have been used to study bistable dynamics, there is a lag in the development of models for bistable systems starting from experimental data. This is due to the lack of detailed knowledge of biochemical reactions and kinetic rates. In this work, we propose a procedure to develop, starting from observed dynamics, Metabolic P models for multistable processes. As a case study, a mathematical model of the Schl ogel's dynamics, which represents an example of a chemical reaction system that exhibits bistability, is inferred starting from observed stochastic bistable dynamics. Since, recent experiments indicate that noise plays an important role in the switching of bistable systems, the success of this work suggests that this approach is a very promising one for studying dynamics and role of noise in biological systems, such as, for example, genetic regulatory networks

Deterministic and stochastic P systems for modelling cellular processes

This paper presents two approaches based on metabolic and stochastic P systems, together with their associated analysis methods, for modelling biological sys- tems and illustrates their use through two case studies.Kingdom's Engineering and Physical Sciences Research Council EP/ E017215/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/D019613/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/F01855X/

an algorithm for initial fluxes of metabolic p systems

A central issue in systems biology is the study of efficient methods inferring fluxes of biological reactions by starting from experimental data. Among the different techniques proposed in the last years, the theory of Metabolic P systems, which is based on the Log-Gain principle, proved to be helpful for deducing biologi- cal fluxes from temporal series of observed dynamics. According to this approach, the algebraic systems provided by the Log-Gain principle determine the reaction fluxes underlying a system dynamics when initial fluxes are known. Here we propose a heuristic algorithm for estimating the initial fluxes, that is tested in two case studies

An Algorithm for Initial Fluxes of Metabolic P Systems

A central issue in systems biology is the study of efficient methods inferring fluxes of biological reactions by starting from experimental data. Among the different techniques proposed in the last years, the theory of Metabolic P systems, which is based on the Log-Gain principle, proved to be helpful for deducing biologi- cal fluxes from temporal series of observed dynamics. According to this approach, the algebraic systems provided by the Log-Gain principle determine the reaction fluxes underlying a system dynamics when initial fluxes are known. Here we propose a heuristic algorithm for estimating the initial fluxes, that is tested in two case studies

Algorithms and Software for Biological MP Modeling by Statistical and Optimization Techniques

I sistemi biologici sono gruppi di entit\ue0 biologiche (es. molecole ed organismi), che interagiscono producendo specifiche dinamiche. Questi sistemi sono solitamente caratterizzati da una elevata complessit\ue0 perch\ue8 coinvolgono un elevato numero di componenti con molte interconnessioni. La comprensione dei meccanismi che governano i sistemi biologici e la previsione dei loro comportamenti in condizioni normali e patologiche \ue8 una sfida cruciale della biologia dei sistemi (in inglese detta systems biology), un'area di ricerca al confine tra biologia, medicina, matematica ed informatica. In questa tesi i P sistemi metabolici, detti brevemente sistemi MP, sono stati utilizzati come modello discreto per l'analisi di dinamiche biologiche. Essi sono una classe deterministica dei P sistemi classici, che utilizzano regole di riscrittura per rappresentare le reazioni chimiche e "funzioni di regolazioni di flusso" per regolare la reattivit\ue0 di ciascuna reazione rispetto alla quantita' di sostanze presenti istantaneamente nel sistema. Dopo un excursus sulla letteratura relativa ad alcuni modelli convenzionali (come le equazioni differenziali ed i modelli stocastici proposti da Gillespie) e non-convenzionali (come i P sistemi ed i P sistemi metabolici), saranno presentati i risultati della mia ricerca. Essi riguardano tre argomenti principali: i) l'equivalenza tra sistemi MP e reti di Petri ibride funzionali, ii) le prospettive statistiche e di ottimizzazione nella generazione di sistemi MP a partire da dati sperimentali, iii) lo sviluppo di un laboratorio virtuale chiamato MetaPlab, un software Java basato sui sistemi MP. L'equivalenza tra i sistemi MP e le reti di Petri ibride funzionali \ue8 stata dimostrata per mezzo di due teoremi ed alcuni esperimenti al computer per il caso di studio del meccanismo regolativo del gene operone lac nella pathway glicolitica. Il secondo argomento di ricerca concerne nuovi approcci per la sintesi delle funzioni di regolazione di flusso. La regressione stepwise e le reti neurali sono state impiegate come approssimatori di funzioni, mentre algoritmi di ottimizzazione classici ed evolutivi (es. backpropagation, algoritmi genetici, particle swarm optimization ed algoritmi memetici) sono stati impiegati per l'addestramento dei modelli. Una completo workflow per l'analisi dei dati sperimentali \ue8 stato presentato. Esso gestisce ed indirizza l'intero processo di sintesi delle funzioni di regolazione, dalla preparazione dei dati alla selezione delle variabili, fino alla generazione dei modelli ed alla loro validazione. Le metodologie proposte sono state testate con successo tramite esperimenti al computer sui casi di studio dell'oscillatore mitotico negli embrioni anfibi e del non photochemical quenching (NPQ). L'ultimo tema di ricerca \ue8 infine piu' applicativo e riguarda la progettazione e lo sviluppo di una architettura Java basata su plugin e di una serie di plugin che consentono di automatizzare varie fasi del processo di modellazione con sistemi MP, come la simulazione di dinamiche, la determinazione dei flussi e la generazione delle funzioni di regolazione.Biological systems are groups of biological entities, (e.g., molecules and organisms), that interact together producing specific dynamics. These systems are usually characterized by a high complexity, since they involve a large number of components having many interconnections. Understanding biological system mechanisms, and predicting their behaviors in normal and pathological conditions is a crucial challenge in systems biology, which is a central research area on the border among biology, medicine, mathematics and computer science. In this thesis metabolic P systems, also called MP systems, have been employed as discrete modeling framework for the analysis of biological system dynamics. They are a deterministic class of P systems employing rewriting rules to represent chemical reactions and "flux regulation functions" to tune reactions reactivity according to the amount of substances present in the system. After an excursus on the literature about some conventional (i.e., differential equations, Gillespie's models) and unconventional (i.e., P systems and metabolic P systems) modeling frameworks, the results of my research are presented. They concern three research topics: i) equivalences between MP systems and hybrid functional Petri nets, ii) statistical and optimization perspectives in the generation of MP models from experimental data, iii) development of the virtual laboratory MetaPlab, a Java software based on MP systems. The equivalence between MP systems and hybrid functional Petri nets is proved by two theorems and some in silico experiments for the case study of the lac operon gene regulatory mechanism and glycolytic pathway. The second topic concerns new approaches to the synthesis of flux regulation functions. Stepwise linear regression and neural networks are employed as function approximators, and classical/evolutionary optimization algorithms (e.g., backpropagation, genetic algorithms, particle swarm optimization, memetic algorithms) as learning techniques. A complete pipeline for data analysis is also presented, which addresses the entire process of flux regulation function synthesis, from data preparation to feature selection, model generation and statistical validation. The proposed methodologies have been successfully tested by means of in silico experiments on the mitotic oscillator in early amphibian embryos and the non photochemical quenching (NPQ). The last research topic is more applicative, and pertains the design and development of a Java plugin architecture and several plugins which enable to automatize many tasks related to MP modeling, such as, dynamics computation, flux discovery, and regulation function synthesis