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.

Background: To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems.Results: We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets.Conclusion: The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without anya prioriinformation. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.

One major task in molecular biology is to understand the dependency among genes to model gene regulatory networks. Pearson’s correlation is the most common method used to measure dependence between gene expression signals, but it works well only when data are linearly associated. For other types of association, such as non-linear or non-functional relationships, methods based on the concepts of rank correlation and information theory-based measures are more adequate than the Pearson’s correlation, but are less used in applications, most probably because of a lack of clear guidelines for their use. This work seeks to summarize the main methods (Pearson’s, Spearman’s and Kendall’s correlations; distance correlation; Hoeffding’s D measure; Heller–Heller–Gorfine measure; mutual information and maximal information coefficient) used to identify dependency between random variables, especially gene expression data, and also to evaluate the strengths and limitations of each method. Systematic Monte Carlo simulation analyses ranging from sample size, local dependence and linear/non-linear and also non-functional relationships are shown. Moreover, comparisons in actual gene expression data are carried out. Finally, we provide a suggestive list of methods that can be used for each type of data set.

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a “fingerprint”. Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the “uncertainty” of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

The cerebral cortex and the cerebellum are spatially remote areas that are connected by complex circuits that link both primary and associative areas. Previous studies have revealed abnormalities in \textcolor{red}{autism spectrum disorder} (ASD); however, it is not clear whether cortico-cerebellar connectivity is differentially manifested in the disorder. To explore this issue, we investigated differences in intrinsic cortico-cerebellar functional connectivity between individuals with \textcolor{red}{typical development} (TD) and those with ASD. To this end, we used functional magnetic resonance imaging (fMRI) of 708 subjects under a resting state protocol provided by the ABIDE I Consortium. We found that people with ASD had diminished functional connectivity between the cerebellum and the following cortical regions: (i) right fusiform gyrus, (ii) right postcentral gyrus, (iii) right superior temporal gyrus, (iv) right middle temporal gyrus, and (v) left middle temporal gyrus. All of these regions are involved in many cognitive systems that contribute to commonly affected functions in ASD. For right fusiform gyrus, right superior temporal gyrus, and left middle temporal gyrus, we reproduced the results in an independent cohort composed of 585 subjects of the ABIDE II Consortium. Our results points toward a consistent atypical cortico-cerebellar connectivity in ASD.

A common approach for time series gene expression data analysis includes the clustering of genes with similar expression patterns throughout time. Clustered gene expression profiles point to the joint contribution of groups of genes to a particular cellular process. However, since genes belong to intricate networks, other features, besides comparable expression patterns, should provide additional information for the identification of functionally similar genes.