Abstract: The substantial conformational homogeneity of DNA double helix has recently allowed a good progress in the knowledge of the molecular mechanisms which control the functional organization of the genome as well as in the prediction of some biologically relevant structural properties. We developed an analytical method to study the effects of the sequence on modeling the three-dimensional superstructure of DNA based on the theoretically evaluated slight conformational perturbations of the different dinucleotide steps along the sequence. Such a model is capable of predicting in striking agreement with the experimental data: the atomic force microscopy visualization of relevant DNA tracts and in particular the dynamics of a pBR322 plasmide after the mechanical cut of the cycle; the gel electrophoresis anomalies of a very large pull of DNA tracts; the thermodynamic constants of the sequence dependent circularization reactions of many DNAs ranging from 100 to 100000 bp and the sequence dependent writhing transitions from relaxed to supercoiled circular forms also in the presence of DNA binding proteins; and finally, the nucleosome positions and the corresponding thermodynamic stability of more than 50 DNA tracts whose the nucleosome competitive reconstitution experimental data are available. The thermodynamic properties were obtained using an original statistical mechanic approach based on the first order elasticity which allows an analytical solution in Fourier space.

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Abstract: As the microarray technology is emerging as a widely used tool to investigate gene expression and function, laboratories over the world have produced and are producing a huge amount of data, which demand advanced and specialized computational tools to process them. Clustering methods have been successfully applied to such data to reorganize the data and extract biological information from them. But the classical clustering methods [1] such as k-means and hierarchical clustering have some intrinsic limits such as the linear, pair-wise nature of the similarity metrics (which fail to highlight non-linear substructures of the data) and the univocal assignment of each gene to one cluster (which may fail to highlight cluster-to-cluster relationships) [2]. Here we introduce a novel method for clustering microarray data, named Fuzzy Map Clustering (FMC), which may partly overcome these limits. Basically, the clustering process of FMC starts from identification of an initial set of clusters by calculating the “density” around each data point (object), that is, the average proximity of its K nearest other objects (K neighbours) and choosing the ones that have the highest density among all their K neighbors. K can be a fixed number of choice or the number of neighbors within a distance threshold. Then, each object in the dataset is assigned a fuzzy membership to all the defined clusters (a vector containing a percentage of membership to all the clusters). Membership is assigned so that similar objects have similar fuzzy membership vectors. Membership assignment is optimized by measuring how the fuzzy membership vector of one object can be approximated by the vectors of its neighbors. Finally, a process based on the merging of adjacent clusters and fuzzy membership reassignment is reiterated until the number of clusters is reduced to a fixed one decided by the operator. Our computational experiments have shown that FMC can correctly reveal the true cluster structure of the dataset if such structure exists, even if the clusters contained in the dataset have arbitrary shape. And perhaps the basic idea underlying FMC points out a new way to develop novel clustering methods with good mathematical foundation.

Abstract: The increasing pace at which DNA microarray-based genomic expression profiles are generated and published poses the issue of efficient and reliable comparison between datasets obtained by different laboratories and on different microarray platforms. Statistical analysis of microarray data is in continuous evolution, and several procedures have been described for detection and weighing of systematic and random errors coming from the highly parallel -but poorly replicated- microarray expression data. However, data obtained from different microarray platforms may be of substantially different nature. This is particularly evident when comparing two commonly used platforms, spotted cDNA microarrays and High-Density Oligonucleotide (HDO) microarrays of the Affymetrix type. cDNA microarrays yield a reproducible ratio between two signals, deriving respectively from the reference and from the sample. Conversely, absolute signals tend to vary across microarrays. Therefore, cDNA microarray data have to be analyzed with statistics handling repeated measurements or paired data, such as paired T-test. In the case of HDO microarrays, an absolute signal level is obtained from each single mRNA sample. As a consequence, non-paired statistics have to be applied to this type of data. Given the intrinsic differences between cDNA microarrays, data analysis procedures have generally been developed on one of the two platforms and only in some cases adapted to the other, however without a specific focus on systematic comparison and validation across platforms. It is still unclear whether data obtained in the two systems can be treated, compared and eventually merged under a common analysis framework. We addressed these issues by generating expression profiles from the same RNAs with both microarray platforms and by developing an analysis procedure in which inter-platform differences in data treatment are reduced to the minimum essential. We then developed a novel statistical test specifically designed to handle multiple comparisons against the same reference condition (eg many points of stimulation against one unstimulated control). In the Multiple Comparison (MulCom) test, regulated genes are identified by a ‘tunable’ statistic test weighing expression change in each stimulation point against replicate variability calculated across the whole set of stimulation points.