Stochastic Modeling and Analysis of Pathway Regulation and Dynamics

To effectively understand and treat complex diseases such as cancer, mathematical and statistical modeling is essential if one wants to represent and characterize the interactions among the different regulatory components that govern the underlying decision making process. Like in any other complex decision making networks, the regulatory power is not evenly distributed among its individual members, but rather concentrated in a few high power "commanders". In biology, such commanders are usually called masters or canalizing genes. Characterizing and detecting such genes are thus highly valuable for the treatment of cancer. Chapter II is devoted to this task, where we present a Bayesian framework to model pathway interactions and then study the behavior of master genes and canalizing genes. We also propose a hypothesis testing procedure to detect a "cut" in pathways, which is useful for discerning drugs' therapeutic effect. In Chapter III, we shift our focus to the understanding of the mechanisms of action (MOA) of cancer drugs. For a new drug, the correct understanding of its MOA is a key step for its application to cancer treatments. Using the Green Fluorescent Protein technology, researchers have been able to track various reporter genes from the same cell population for an extended period of time. Such dynamic gene expression data forms the basis for drug similarity comparisons. In Chapter III, we design an algorithm that can identify mechanistic similarities in drug responses, which leads to the characterization of their respective MOAs. Finally, in the course of drug MOA study, we observe that cells in a hypothetical homogeneous population do not respond to drug treatments in a uniform and synchronous way. Instead, each cell makes a large shift in its gene expression level independently and asynchronously from the others. Hence, to systematically study such behavior, we propose a mathematical model that describes the gene expression dynamics for a population of cells after drug treatments. The application of this model to dose response data proviodes us new insights of the dosing effects. Furthermore, the model is capable of generating useful hypotheses for future experimental design

Estimation and Detection of Multivariate Gene Regulatory Relationships

The Coefficient of Determination (CoD) plays an important role in Genomics problems, for instance, in the inference of gene regulatory networks from gene- expression data. However, the inference theory about CoD has not been investigated systematically. In this dissertation, we study the inference of discrete CoD from both frequentist and Bayesian perspectives, with its applications to system identification problems in Genomics. From a frequentist viewpoint, we provide a theoretical framework for CoD estimation by introducing nonparametric CoD estimators and parametric maximum-likelihood (ML) CoD estimators based on static and dynamical Boolean models. Inference algorithms are developed to discover gene regulatory relationships, and numerical examples are provided to validate preferable performance of the ML approach with access to sufficient prior knowledge. To make the applications of the CoD independent of user-selectable thresholds, we describe rigorous multiple testing procedures to investigate significant regulatory relation- ships among genes using the discrete CoD, and to discover canalyzing genes using the intrinsically multivariate prediction (IMP) criterion. We develop practical statistic tools that are open to the scientific community. On the other hand, we propose a Bayesian framework for the inference of the CoD across a parametrized family of joint distributions between target and predictors. Examples of applications of the Bayesian approach are provided against those of nonparametric and parametric approaches by using synthetic data. We have found that, with applications to system identification problems in Genomics, both parametric and Bayesian CoD estimation approaches outperform the nonparametric approaches. Hence, we conclude that parametric and Bayesian estimation approaches are preferred when we have partial knowledge about gene regulation. On the other hand, we have shown that the two proposed statistical testing frameworks can detect well-known gene regulation and canalyzing genes like p53 and DUSP1 from real data sets, respectively. This indicates that our methodology could serve as a promising tool for the detection of potential gene regulatory relationships and canalyzing genes. In one word, this dissertation is intended to serve as foundation for a detailed study of applications of CoD estimation in Genomics and related fields

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

The role of visual adaptation in cichlid fish speciation

D. Shane Wright (1) , Ole Seehausen (2), Ton G.G. Groothuis (1), Martine E. Maan (1) (1) University of Groningen; GELIFES; EGDB(2) Department of Fish Ecology & Evolution, EAWAG Centre for Ecology, Evolution and Biogeochemistry, Kastanienbaum AND Institute of Ecology and Evolution, Aquatic Ecology, University of Bern.In less than 15,000 years, Lake Victoria cichlid fishes have radiated into as many as 500 different species. Ecological and sexual sel ection are thought to contribute to this ongoing speciation process, but genetic differentiation remains low. However, recent work in visual pigment genes, opsins, has shown more diversity. Unlike neighboring Lakes Malawi and Tanganyika, Lake Victoria is highly turbid, resulting in a long wavelength shift in the light spectrum with increasing depth, providing an environmental gradient for exploring divergent coevolution in sensory systems and colour signals via sensory drive. Pundamilia pundamila and Pundamilia nyererei are two sympatric species found at rocky islands across southern portions of Lake Victoria, differing in male colouration and the depth they reside. Previous work has shown species differentiation in colour discrimination, corresponding to divergent female preferences for conspecific male colouration. A mechanistic link between colour vision and preference would provide a rapid route to reproductive isolation between divergently adapting populations. This link is tested by experimental manip ulation of colour vision - raising both species and their hybrids under light conditions mimicking shallow and deep habitats. We quantify the expression of retinal opsins and test behaviours important for speciation: mate choice, habitat preference, and fo raging performance

Investigating the evolution of sex-specific phenotypes

This thesis uses theoretical models to investigate a diverse set of questions that revolve around the evolution sex-specific phenotypes. Chapter 1 studies the evolution of sex-determining mechanisms. It investigates the evolutionary change in the coding sequences of sex determining genes associated with the recruitment of a top regulatory gene in Drosophila. We find that this recruitment coincided with changes in the evolution of all the genes of the sex determining pathway. We discuss how these changes are tied with the genes' molecular functions, and highlight the limits of inference from DNA sequence change only. Chapter 2 investigates the genomic distribution of sexually antagonistic alleles. Our study predicts that the interplay of sexually antagonistic selection and genetic drift leads to the accumulation of sexually antagonistic alleles on the X in XY species and, on the autosomes in ZW species, especially when sexual competition is strong among males. Chapter 3 studies the evolution and consequences of sex-specific reproductive variance by constructing a population genetic model that is based on an explicit representation of sexual reproduction. In particular, we derive the probability of fixation for mutations affecting male and female reproductive traits in different ways and find that sex-specific reproductive variance may have profound consequences for the evolution of sex-specific phenotypes. Finally, chapter 4 adapts this latter model to investigate the evolution of developmental instability in the presence of female choice. Developmental instability can be selected for by female choice. But it can have very dire consequences for other aspects of the phenotype, notably in female fecundity and offspring survival. We discuss the effects of reproductive variance on whether these detrimental effects are capable of preventing developmental instability. Overall, this thesis highlights how not only sex-specific selection, but also sex-specific variance in gene transmission contribute to variation in sex-specific phenotypes