Gene Co-Expression in Breast Cancer: A Matter of Distance.

Gene regulatory and signaling phenomena are known to be relevant players underlying the establishment of cellular phenotypes. It is also known that such regulatory programs are disrupted in cancer, leading to the onset and development of malignant phenotypes. Gene co-expression matrices have allowed us to compare and analyze complex phenotypes such as breast cancer (BrCa) and their control counterparts. Global co-expression patterns have revealed, for instance, that the highest gene-gene co-expression interactions often occur between genes from the same chromosome (cis-), meanwhile inter-chromosome (trans-) interactions are scarce and have lower correlation values. Furthermore, strength of cis- correlations have been shown to decay with the chromosome distance of gene couples. Despite this loss of long-distance co-expression has been clearly identified, it has been observed only in a small fraction of the whole co-expression landscape, namely the most significant interactions. For that reason, an approach that takes into account the whole interaction set results appealing. In this work, we developed a hybrid method to analyze whole-chromosome Pearson correlation matrices for the four BrCa subtypes (Luminal A, Luminal B, HER2+ and Basal), as well as adjacent normal breast tissue derived matrices. We implemented a systematic method for clustering gene couples, by using eigenvalue spectral decomposition and the k-medoids algorithm, allowing us to determine a number of clusters without removing any interaction. With this method we compared, for each chromosome in the five phenotypes: a) Whether or not the gene-gene co-expression decays with the distance in the breast cancer subtypes b) the chromosome location of cis- clusters of gene couples, and c) whether or not the loss of long-distance co-expression is observed in the whole range of interactions. We found that in the correlation matrix for the control phenotype, positive and negative Pearson correlations deviate from a random null model independently of the distance between couples. Conversely, for all BrCa subtypes, in all chromosomes, positive correlations decay with distance, and negative correlations do not differ from the null model. We also found that BrCa clusters are distance-dependent, meanwhile for the control phenotype, chromosome location does not determine the clustering. To our knowledge, this is the first time that a dependence on distance is reported for gene clusters in breast cancer. Since this method uses the whole cis- interaction geneset, combination with other -omics approaches may provide further evidence to understand in a more integrative fashion, the mechanisms that disrupt gene regulation in cancer.

Multiple scaling behaviour and nonlinear traits in music scores.

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis (DFA). We find different fluctuation profiles that correspond to distinct autocorrelation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear autocorrelations by estimating the DFA of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.

Irregular Liesegang-type patterns in gas phase revisited. I. Experimental setup, data processing, and test of the spacing law.

Since the early work on Liesegang rings in gels, they have been a reference point for the study of pattern formation in chemical physics. Here we present a variant of the Liesegang experiment in gas phase, where ammonia and hydrochloric acid react within a glass tube producing a precipitate, which deposits along the tube wall producing a spatial pattern. With this apparently simple experiment a wide range of rich phenomenon can be observed due to the presence of convective flows and irregular dynamics reminiscent of turbulent behavior, for which precise measurements are scarce. In this first part of our work, we describe in detail the experimental setup, the method of data acquisition, the image processing, and the procedure used to obtain an intensity profile, which is representative of the amount of precipitate deposited at the tube walls. Special attention is devoted to the techniques rendering a data series reliable for statistical studies and model building, which may contribute to a characterization and understanding of the pattern formation phenomenon under consideration. As a first step in this direction, based on our data, we are able to show that the observed band pattern follows, with slight deviations, the spacing law encountered in common Liesegang rings, despite that the experimental conditions are very different. A further statistical correlation analysis of the data constitutes Paper II of this research.

A refined potential for hydroxylamine clusters and the liquid phase.

A detailed study including ab initio calculations and classic Monte-Carlo simulations of hydroxylamine in the gas and liquid phases is presented. A classical interaction potential for hydroxylamine, which includes polarizability, many-body effects, and intramolecular relaxation, was constructed. The results of the simulation were compared to the available experimental data in order to validate the model. We conclude that liquid hydroxylamine has a multitude of hydrogen bonds leading to a large density where the existence of cis conformers and clusters of these conformers is possible. This explains the occurrence of the classical [R. Nast and I. Z. Foppl, Z. Anorg. Allg. Chem. 263, 310 (1950)] scheme for the molecule's decomposition at room temperature and its large exothermicity and instability.