Evaluating different methods of microarray data normalization

Abstract Background With the development of DNA hybridization microarray technologies, nowadays it is possible to simultaneously assess the expression levels of thousands to tens of thousands of genes. Quantitative comparison of microarrays uncovers distinct patterns of gene expression, which define different cellular phenotypes or cellular responses to drugs. Due to technical biases, normalization of the intensity levels is a pre-requisite to performing further statistical analyses. Therefore, choosing a suitable approach for normalization can be critical, deserving judicious consideration. Results Here, we considered three commonly used normalization approaches, namely: Loess, Splines and Wavelets, and two non-parametric regression methods, which have yet to be used for normalization, namely, the Kernel smoothing and Support Vector Regression. The results obtained were compared using artificial microarray data and benchmark studies. The results indicate that the Support Vector Regression is the most robust to outliers and that Kernel is the worst normalization technique, while no practical differences were observed between Loess, Splines and Wavelets. Conclusion In face of our results, the Support Vector Regression is favored for microarray normalization due to its superiority when compared to the other methods for its robustness in estimating the normalization curve.

BayGO: Bayesian analysis of ontology term enrichment in microarray data

Abstract Background The search for enriched (aka over-represented or enhanced) ontology terms in a list of genes obtained from microarray experiments is becoming a standard procedure for a system-level analysis. This procedure tries to summarize the information focussing on classification designs such as Gene Ontology, KEGG pathways, and so on, instead of focussing on individual genes. Although it is well known in statistics that association and significance are distinct concepts, only the former approach has been used to deal with the ontology term enrichment problem. Results BayGO implements a Bayesian approach to search for enriched terms from microarray data. The R source-code is freely available at http://blasto.iq.usp.br/~tkoide/BayGO in three versions: Linux, which can be easily incorporated into pre-existent pipelines; Windows, to be controlled interactively; and as a web-tool. The software was validated using a bacterial heat shock response dataset, since this stress triggers known system-level responses. Conclusion The Bayesian model accounts for the fact that, eventually, not all the genes from a given category are observable in microarray data due to low intensity signal, quality filters, genes that were not spotted and so on. Moreover, BayGO allows one to measure the statistical association between generic ontology terms and differential expression, instead of working only with the common significance analysis.

Dietary restriction abrogates antibody production induced by a DNA vaccine encoding the mycobacterial 65 kDa heat shock protein

Abstract Background Protein-calorie malnutrition (PCM) is the most common type of malnutrition. PCM leads to immunodeficiency and consequent increased susceptibility to infectious agents. In addition, responses to prophylactic vaccines depend on nutritional status. This study aims to evaluate the ability of undernourished mice to mount an immune response to a genetic vaccine (pVAXhsp65) against tuberculosis, containing the gene coding for the heat shock protein 65 from mycobacteria. Methods Young adult female BALB/c mice were fed ad libitum or with 80% of the amount of food consumed by a normal diet group. We initially characterized a mice model of dietary restriction by determining body and spleen weights, hematological parameters and histopathological changes in lymphoid organs. The ability of splenic cells to produce IFN-gamma and IL-4 upon in vitro stimulation with LPS or S. aureus and the serum titer of specific IgG1 and IgG2a anti-hsp65 antibodies after intramuscular immunization with pVAXhsp65 was then tested. Results Dietary restriction significantly decreased body and spleen weights and also the total lymphocyte count in blood. This restriction also determined a striking atrophy in lymphoid organs as spleen, thymus and lymphoid tissue associated with the small intestine. Specific antibodies were not detected in mice submitted to dietary restriction whereas the well nourished animals produced significant levels of both, IgG1 and IgG2a anti-hsp65. Conclusion 20% restriction in food intake deeply compromised humoral immunity induced by a genetic vaccine, alerting, therefore, for the relevance of the nutritional condition in vaccination programs based on these kinds of constructs.

New insights about host response to smallpox using microarray data

Abstract Background Smallpox is a lethal disease that was endemic in many parts of the world until eradicated by massive immunization. Due to its lethality, there are serious concerns about its use as a bioweapon. Here we analyze publicly available microarray data to further understand survival of smallpox infected macaques, using systems biology approaches. Our goal is to improve the knowledge about the progression of this disease. Results We used KEGG pathways annotations to define groups of genes (or modules), and subsequently compared them to macaque survival times. This technique provided additional insights about the host response to this disease, such as increased expression of the cytokines and ECM receptors in the individuals with higher survival times. These results could indicate that these gene groups could influence an effective response from the host to smallpox. Conclusion Macaques with higher survival times clearly express some specific pathways previously unidentified using regular gene-by-gene approaches. Our work also shows how third party analysis of public datasets can be important to support new hypotheses to relevant biological problems.

Development and validation of a Xanthomonas axonopodis pv. citri DNA microarray platform (XACarray) generated from the shotgun libraries previously used in the sequencing of this bacterial genome

Abstract Background From shotgun libraries used for the genomic sequencing of the phytopathogenic bacterium Xanthomonas axonopodis pv. citri (XAC), clones that were representative of the largest possible number of coding sequences (CDSs) were selected to create a DNA microarray platform on glass slides (XACarray). The creation of the XACarray allowed for the establishment of a tool that is capable of providing data for the analysis of global genome expression in this organism. Findings The inserts from the selected clones were amplified by PCR with the universal oligonucleotide primers M13R and M13F. The obtained products were purified and fixed in duplicate on glass slides specific for use in DNA microarrays. The number of spots on the microarray totaled 6,144 and included 768 positive controls and 624 negative controls per slide. Validation of the platform was performed through hybridization of total DNA probes from XAC labeled with different fluorophores, Cy3 and Cy5. In this validation assay, 86% of all PCR products fixed on the glass slides were confirmed to present a hybridization signal greater than twice the standard deviation of the deviation of the global median signal-to-noise ration. Conclusions Our validation of the XACArray platform using DNA-DNA hybridization revealed that it can be used to evaluate the expression of 2,365 individual CDSs from all major functional categories, which corresponds to 52.7% of the annotated CDSs of the XAC genome. As a proof of concept, we used this platform in a previously work to verify the absence of genomic regions that could not be detected by sequencing in related strains of Xanthomonas.

Analysis of ripening-related gene expression in papaya using an Arabidopsis-based microarray

Abstract Background Papaya (Carica papaya L.) is a commercially important crop that produces climacteric fruits with a soft and sweet pulp that contain a wide range of health promoting phytochemicals. Despite its importance, little is known about transcriptional modifications during papaya fruit ripening and their control. In this study we report the analysis of ripe papaya transcriptome by using a cross-species (XSpecies) microarray technique based on the phylogenetic proximity between papaya and Arabidopsis thaliana. Results Papaya transcriptome analyses resulted in the identification of 414 ripening-related genes with some having their expression validated by qPCR. The transcription profile was compared with that from ripening tomato and grape. There were many similarities between papaya and tomato especially with respect to the expression of genes encoding proteins involved in primary metabolism, regulation of transcription, biotic and abiotic stress and cell wall metabolism. XSpecies microarray data indicated that transcription factors (TFs) of the MADS-box, NAC and AP2/ERF gene families were involved in the control of papaya ripening and revealed that cell wall-related gene expression in papaya had similarities to the expression profiles seen in Arabidopsis during hypocotyl development. Conclusion The cross-species array experiment identified a ripening-related set of genes in papaya allowing the comparison of transcription control between papaya and other fruit bearing taxa during the ripening process.

IgG Antibody responses in mice coinfected with Toxocara canis and other helminths or protozoan parasites

The immune response expressed by IgG antibodies in BALB/c mice experimentally infected with Toxocara canis, was studied with the aim of verifying the possible in vivo cross-reactivity between antigens of T. canis and other parasites (Ascaris suum, Taenia crassiceps, Schistosoma mansoni, Strongyloides venezuelensis and Toxoplasma gondii). Experiments included three groups of mice: one infected only by T. canis, another with one of the other species of parasites and a third concomitantly infected with T. canis and the other species in question. Animals were bled by orbital plexus at 23, 38 and 70 days post infection (p.i.). Sera were analyzed for anti-Toxocara antibodies by ELISA and Immunoblotting, using excretion-secretion antigens (ES), obtained from culture of third-stage larvae of T. canis. For all experiments a control group comprised by ten non-infected mice was used. Only in the case of A. suum infection, in these experimental conditions, the occurrence of cross-reactivity with T. canis was observed. However, in the case of co-infection of T. canis - S. mansoni, T. canis - S. venezuelensis and T. canis - T. crassiceps the production of anti-Toxocara antibodies was found at levels significantly lower than those found in mice infected with T. canis only. Co-infection with S. mansoni or S. venezuelensis showed lower mortality rates compared to what occurred in the animals with single infections. Results obtained in mice infected with T. canis and T. gondii showed significant differences between the mean levels of the optical densities of animals infected with T. canis and concomitantly infected with the protozoan only in the 23rd day p.i.

Antibody levels to hantavirus in inhabitants of western Santa Catarina State, Brazil

Hantavirus cardiopulmonary syndrome (HCPS) is an infectious disease caused by hantaviruses of the family Bunyaviridae, and is transmitted by aerosols of excreta of infected rodents. The aim of the present study was to determine antibody levels to hantavirus in the population that lives at frontier of Brazil and Argentina. Participated of the study 405 individuals living in the municipalities of Bandeirante, Santa Helena, Princesa and Tunapolis, state of Santa Catarina, Brazil. IgG antibodies to hantavirus were analyzed in sera by an ELISA that uses a recombinant N protein of Araraquara hantavirus as antigen. The results were also confirmed by immunofluorescent test. Eight individuals showed antibodies to hantavirus (1.97% positivity), with serum titers ranging from 100 to 800. Six seropositives were males, older than 30 years and farmers. Our results reinforce previous data on hantavirus circulation and human infections in the southern border of Brazil with Argentina.

The relationship between lymphatic vascular density and vascular endothelial growth factor A (VEGF-A) expression with clinical-pathological features and survival in pancreatic adenocarcinomas

Abstract: Background Pancreatic cancer is a rare tumor with an extremely low survival rate. Its known risk factors include the chronic use of tobacco and excessive alcohol consumption and the presence of chronic inflammatory diseases, such as pancreatitis and type 2 diabetes. Angiogenesis and lymphangiogenesis, which have been the focus of recent research, are considered prognostic factors for cancer development. Knowing the angiogenic and lymphangiogenic profiles of a tumor may provide new insights for designing treatments according to the different properties of the tumor. The aim of this study was to evaluate the density of blood and lymphatic vessels, and the expression of VEGF-A, in pancreatic adenocarcinomas, as well as the relationship between blood and lymphatic vascular density and the prognostically important clinical-pathological features of pancreatic tumors. Methods Paraffin blocks containing tumor samples from 100 patients who were diagnosed with pancreatic cancer between 1990 and 2010 were used to construct a tissue microarray. VEGF expression was assessed in these samples by immunohistochemistry. To assess the lymphatic and vascular properties of the tumors, 63 cases that contained sufficient material were sectioned routinely. The sections were then stained with the D2-40 antibody to identify the lymphatic vessels and with a CD34 antibody to identify the blood vessels. The vessels were counted individually with the Leica Application Suite v4 program. All statistical analyses were performed using SPSS 18.0 (Chicago, IL, USA) software, and p values ≤ 0.05 were considered significant. Results In the Cox regression analysis, advanced age (p=0.03) and a history of type 2 diabetes (p=0.014) or chronic pancreatitis (p=0.02) were shown to be prognostic factors for pancreatic cancer. Blood vessel density (BVD) had no relationship with clinical-pathological features or death. Lymphatic vessel density (LVD) was inversely correlated with death (p=0.002), and by Kaplan-Meyer survival analysis, we found a significant association between low LVD (p=0.021), VEGF expression (p=0.023) and low patient survival. Conclusions Pancreatic carcinogenesis is related to a history of chronic inflammatory processes, such as type 2 diabetes and chronic pancreatitis. In pancreatic cancer development, lymphangiogenesis can be considered an early event that enables the dissemination of metastases. VEGF expression and low LVD can be considered as poor prognostic factors as tumors with this profile are fast growing and highly aggressive. Virtual slides. The virtual slide(s) for this article can be found here: http://www.diagnosticpathology.diagnomx.eu/vs/5113892881028514

Natural antibody response to Plasmodium falciparum merozoite antigens MSP5, MSP9 and EBA175 is associated to clinical protection in the Brazilian Amazon

BACKGROUND: Antibodies have an essential role in the acquired immune response against blood stage P. falciparum infection. Although several antigens have been identified as important antibody targets, it is still elusive which antigens have to be recognized for clinical protection. Herein, we analyzed antibodies from plasmas from symptomatic or asymptomatic individuals living in the same geographic area in the Western Amazon, measuring their recognition of multiple merozoite antigens. METHODS: Specific fragments of genes encoding merozoite proteins AMA1 and members of MSP and EBL families from circulating P. falciparum field isolates present in asymptomatic and symptomatic patients were amplified by PCR. After cloning and expression of different versions of the antigens as recombinant GST-fusion peptides, we tested the reactivity of patients' plasmas by ELISA and the presence of IgG subclasses in the most reactive plasmas. RESULTS: 11 out of 24 recombinant antigens were recognized by plasmas from either symptomatic or asymptomatic infections. Antibodies to MSP9 (X2(DF=1) = 9.26/p = 0.0047) and MSP5 (X2(DF=1) = 8.29/p = 0.0069) were more prevalent in asymptomatic individuals whereas the opposite was observed for MSP1 block 2-MAD20 (X2(DF=1) = 6.41/p = 0.0206, Fisher's exact test). Plasmas from asymptomatic individuals reacted more intensely against MSP4 (U = 210.5, p < 0.03), MSP5 (U = 212, p < 0.004), MSP9 (U = 189.5, p < 0.002) and EBA175 (U = 197, p < 0.014, Mann-Whitney's U test). IgG1 and IgG3 were predominant for all antigens, but some patients also presented with IgG2 and IgG4. The recognition of MSP5 (OR = 0.112, IC95% = 0.021-0.585) and MSP9 (OR = 0.125, IC95% = 0.030-0.529, cross tab analysis) predicted 8.9 and 8 times less chances, respectively, to present symptoms. Higher antibody levels against MSP5 and EBA175 were associated by odds ratios of 9.4 (IC95% = 1.29-69.25) and 5.7 (IC95% = 1.12-29.62, logistic regression), respectively, with an asymptomatic status. CONCLUSIONS: Merozoite antigens were targets of cytophilic antibodies and antibodies against MSP5, MSP9 and EBA175 were independently associated with decreased symptoms.

Anti-Leishmania infantum IgG Antibody Avidity in Visceral Leishmaniasis

IgG avidity tests are used to discriminate acute from chronic infections. There are few reports on the IgG avidity profile of patients with visceral leishmaniasis (VL). This study investigated the anti-Leishmania IgG avidity in patients with classic VL (n = 10), patients showing clinical cure after treatment (n = 18), and asymptomatic subjects with at least one positive Leishmania test (n = 20). All subjects were from areas in Brazil where VL is endemic. Serum samples were collected from each subject on two different occasions. IgG avidity was evaluated by Western blotting. The proportion of high-avidity antibodies was higher in all samples from patients with classic VL. In contrast, low-avidity antibodies predominated in subjects with a history of VL, including 13 cases (72.2%) in the first assessment and 14 (77.8%) in the second. Fifteen (75%) of the asymptomatic subjects presented a predominance of low-avidity antibodies in the first assessment, and the frequency of high-avidity antibodies increased over time in seven subjects (35%) of this group. Antibodies against the 14- and/or 16-kDa antigen fraction were detected in the first assessment in all patients with classic VL, in 10 (55.5%) treated patients, and in 10 (50%) asymptomatic subjects. These were high-avidity antibodies in most cases. In the asymptomatic group, an increase in IgG avidity against the 14- and/or 16-kDa antigen fraction was observed in three cases (15%). The results indicate distinct responses in infected and asymptomatic subjects, probably associated with the length of time after infection. In this respect, IgG avidity tests represent a new approach to better characterize asymptomatic VL.

Antibody responses in Plasmodium falciparum malaria and their relation to protection against the disease

Protective immunity against Plasmodium falciparum may be obtained after repeated exposure to infection. Several studies indicate that immunity against the blood stages of the P. Falciparum infection is mainly antibody mediated. Protective antibodies may act either on their own, mediate antibody-dependent phagocytosis and/or cell-mediated neutralization of parasites. This thesis describes several aspects of humoral immune responses to P. falciparum infection in individuals of different age groups, different genetic background and with different degrees of malaria exposure. Several target antigens for antibody-mediated inhibition of parasite growth or invasion have been identified. One such antigen is Pf332, which appears on the surface of parasitized erythrocytes at late trophozoite and schizont stage. This surface exposure makes the antigen a possible target for opsonizing antibodies. We optimized an in vitro assay for studying cellmediated parasite neutralization in the presence of Pf332-reactive antibodies. Our data demonstrate that, Pf332 specific antibodies are able to inhibit parasite growth on their own and in cooperation with human monocytes. The P. falciparum parasites have evolved several mechanisms to evade the host neutralizing immune responses. In this thesis, we show that freshly isolated P. falciparum parasites from children living in a malaria endemic area of Burkina Faso were less sensitive for growth inhibition in vitro by autologous immunoglobulins (Ig) compared with heterologous ones. Analyses of two consecutive isolates taken 14 days apart, with regard to genotypes and sensitivity to growth inhibition in vitro, did not give any clear-cut indications on possible mechanisms leading to a reduced inhibitory activity in autologous parasite/antibody combinations. The frequent presence of persisting parasite clones in asymptomatic children indicates that the parasite possesses as yet undefined mechanisms to evade neutralizing immune responses. Transmission reducing measures such insecticide treated nets (ITNs) have been shown to be effective in reducing morbidity and mortality from malaria. However, concerns have been raised that ITNs usage could affect the acquisition of malaria immunity. We studied the effect of the use of insecticide treated curtains (ITC) on anti-malarial immune responses of children living in villages with ITC since birth. The use of ITC did neither affect the levels of parasite neutralizing immune responses nor the multiplicity of infection. These results indicate that the use of ITC does not interfere with the acquisition of anti-malarial immunity in children living in a malaria hyperendemic area. There is substantial evidence that the African Fulani tribe is markedly less susceptible to malaria infection compared to other sympatrically living ethnic tribes. We investigated the isotypic humoral responses against P. falciparum asexual blood stages in different ethnic groups living in sympatry in two countries exhibiting different malaria transmission intensities, Burkina Faso and Mali. We observed higher levels of the total malaria-specific-IgG and its cytophilic subclasses in individuals of the Fulani tribe as compared to non-Fulani individuals. Fulani individuals also showed higher levels of antibodies to measles antigen, indicating that the intertribal differences are not specific for malaria and might reflect a generally activated immune system in the Fulani.

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.