Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

New approaches to open problems in gene expression microarray data

In the past decade, the advent of efficient genome sequencing tools and high-throughput experimental biotechnology has lead to enormous progress in the life science. Among the most important innovations is the microarray tecnology. It allows to quantify the expression for thousands of genes simultaneously by measurin the hybridization from a tissue of interest to probes on a small glass or plastic slide. The characteristics of these data include a fair amount of random noise, a predictor dimension in the thousand, and a sample noise in the dozens. One of the most exciting areas to which microarray technology has been applied is the challenge of deciphering complex disease such as cancer. In these studies, samples are taken from two or more groups of individuals with heterogeneous phenotypes, pathologies, or clinical outcomes. these samples are hybridized to microarrays in an effort to find a small number of genes which are strongly correlated with the group of individuals. Eventhough today methods to analyse the data are welle developed and close to reach a standard organization (through the effort of preposed International project like Microarray Gene Expression Data -MGED- Society [1]) it is not unfrequant to stumble in a clinician's question that do not have a compelling statistical method that could permit to answer it.The contribution of this dissertation in deciphering disease regards the development of new approaches aiming at handle open problems posed by clinicians in handle specific experimental designs. In Chapter 1 starting from a biological necessary introduction, we revise the microarray tecnologies and all the important steps that involve an experiment from the production of the array, to the quality controls ending with preprocessing steps that will be used into the data analysis in the rest of the dissertation. While in Chapter 2 a critical review of standard analysis methods are provided stressing most of problems that In Chapter 3 is introduced a method to adress the issue of unbalanced design of miacroarray experiments. In microarray experiments, experimental design is a crucial starting-point for obtaining reasonable results. In a two-class problem, an equal or similar number of samples it should be collected between the two classes. However in some cases, e.g. rare pathologies, the approach to be taken is less evident. We propose to address this issue by applying a modified version of SAM [2]. MultiSAM consists in a reiterated application of a SAM analysis, comparing the less populated class (LPC) with 1,000 random samplings of the same size from the more populated class (MPC) A list of the differentially expressed genes is generated for each SAM application. After 1,000 reiterations, each single probe given a "score" ranging from 0 to 1,000 based on its recurrence in the 1,000 lists as differentially expressed. The performance of MultiSAM was compared to the performance of SAM and LIMMA [3] over two simulated data sets via beta and exponential distribution. The results of all three algorithms over low- noise data sets seems acceptable However, on a real unbalanced two-channel data set reagardin Chronic Lymphocitic Leukemia, LIMMA finds no significant probe, SAM finds 23 significantly changed probes but cannot separate the two classes, while MultiSAM finds 122 probes with score >300 and separates the data into two clusters by hierarchical clustering. We also report extra-assay validation in terms of differentially expressed genes Although standard algorithms perform well over low-noise simulated data sets, multi-SAM seems to be the only one able to reveal subtle differences in gene expression profiles on real unbalanced data. In Chapter 4 a method to adress similarities evaluation in a three-class prblem by means of Relevance Vector Machine [4] is described. In fact, looking at microarray data in a prognostic and diagnostic clinical framework, not only differences could have a crucial role. In some cases similarities can give useful and, sometimes even more, important information. The goal, given three classes, could be to establish, with a certain level of confidence, if the third one is similar to the first or the second one. In this work we show that Relevance Vector Machine (RVM) [2] could be a possible solutions to the limitation of standard supervised classification. In fact, RVM offers many advantages compared, for example, with his well-known precursor (Support Vector Machine - SVM [3]). Among these advantages, the estimate of posterior probability of class membership represents a key feature to address the similarity issue. This is a highly important, but often overlooked, option of any practical pattern recognition system. We focused on Tumor-Grade-three-class problem, so we have 67 samples of grade I (G1), 54 samples of grade 3 (G3) and 100 samples of grade 2 (G2). The goal is to find a model able to separate G1 from G3, then evaluate the third class G2 as test-set to obtain the probability for samples of G2 to be member of class G1 or class G3. The analysis showed that breast cancer samples of grade II have a molecular profile more similar to breast cancer samples of grade I. Looking at the literature this result have been guessed, but no measure of significance was gived before.

Identification of surface protein complexes of Streptococcus pyogenes through protein microarray technology

A systematic characterization of the composition and structure of the bacterial cell-surface proteome and its complexes can provide an invaluable tool for its comprehensive understanding. The knowledge of protein complexes composition and structure could offer new, more effective targets for a more specific and consequently effective immune response against a complex instead of a single protein. Large-scale protein-protein interaction screens are the first step towards the identification of complexes and their attribution to specific pathways. Currently, several methods exist for identifying protein interactions and protein microarrays provide the most appealing alternative to existing techniques for a high throughput screening of protein-protein interactions in vitro under reasonably straightforward conditions. In this study approximately 100 proteins of Group A Streptococcus (GAS) predicted to be secreted or surface exposed by genomic and proteomic approaches were purified in a His-tagged form and used to generate protein microarrays on nitrocellulose-coated slides. To identify protein-protein interactions each purified protein was then labeled with biotin, hybridized to the microarray and interactions were detected with Cy3-labelled streptavidin. Only reciprocal interactions, i. e. binding of the same two interactors irrespective of which of the two partners is in solid-phase or in solution, were taken as bona fide protein-protein interactions. Using this approach, we have identified 20 interactors of one of the potent toxins secreted by GAS and known as superantigens. Several of these interactors belong to the molecular chaperone or protein folding catalyst families and presumably are involved in the secretion and folding of the superantigen. In addition, a very interesting interaction was found between the superantigen and the substrate binding subunit of a well characterized ABC transporter. This finding opens a new perspective on the current understanding of how superantigens are modified by the bacterial cell in order to become major players in causing disease.

Genomic characterization of the italian wolf (Canis lupus): the genes involved in black coat colour determination and application of microarray technique for snps detection.

This study provides a comprehensive genetic overview on the endangered Italian wolf population. In particular, it focuses on two research lines. On one hand, we focalised on melanism in wolf in order to isolate a mutation related with black coat colour in canids. With several reported black individuals (an exception at European level), the Italian wolf population constituted a challenging research field posing many unanswered questions. As found in North American wolf, we reported that melanism in the Italian population is caused by a different melanocortin pathway component, the K locus, in which a beta-defensin protein acts as an alternative ligand for the Mc1r. This research project was conducted in collaboration with Prof. Gregory Barsh, Department of Genetics and Paediatrics, Stanford University. On the other hand, we performed analysis on a high number of SNPs thanks to a customized Canine microarray useful to integrate or substitute the STR markers for genotyping individuals and detecting wolf-dog hybrids. Thanks to DNA microchip technology, we obtained an impressive amount of genetic data which provides a solid base for future functional genomic studies. This study was undertaken in collaboration with Prof. Robert K. Wayne, Department of Ecology and Evolutionary Biology, University of California, Los Angeles (UCLA).

Exploring host-pathogen interactions through protein microarray. Large-scale protein microarray analysis revealed novel human receptors for the staphylococcal immune evasion protein FLIPr and for the neisserial adhesin NadA

Adhesion, immune evasion and invasion are key determinants during bacterial pathogenesis. Pathogenic bacteria possess a wide variety of surface exposed and secreted proteins which allow them to adhere to tissues, escape the immune system and spread throughout the human body. Therefore, extensive contacts between the human and the bacterial extracellular proteomes take place at the host-pathogen interface at the protein level. Recent researches emphasized the importance of a global and deeper understanding of the molecular mechanisms which underlie bacterial immune evasion and pathogenesis. Through the use of a large-scale, unbiased, protein microarray-based approach and of wide libraries of human and bacterial purified proteins, novel host-pathogen interactions were identified. This approach was first applied to Staphylococcus aureus, cause of a wide variety of diseases ranging from skin infections to endocarditis and sepsis. The screening led to the identification of several novel interactions between the human and the S. aureus extracellular proteomes. The interaction between the S. aureus immune evasion protein FLIPr (formyl-peptide receptor like-1 inhibitory protein) and the human complement component C1q, key players of the offense-defense fighting, was characterized using label-free techniques and functional assays. The same approach was also applied to Neisseria meningitidis, major cause of bacterial meningitis and fulminant sepsis worldwide. The screening led to the identification of several potential human receptors for the neisserial adhesin A (NadA), an important adhesion protein and key determinant of meningococcal interactions with the human host at various stages. The interaction between NadA and human LOX-1 (low-density oxidized lipoprotein receptor) was confirmed using label-free technologies and cell binding experiments in vitro. Taken together, these two examples provided concrete insights into S. aureus and N. meningitidis pathogenesis, and identified protein microarray coupled with appropriate validation methodologies as a powerful large scale tool for host-pathogen interactions studies.