We present non-iterative methods for graph embedding in flat and curved manifold and acriterion to assess the quality of the embedding for the purpose of determining what is the optimal latent geometry of a graph. To date, graph embedding procedures have been used in data dimension reduction problems for the purpose of simpler and more efficient data analysis, but little has been done to use them as a tool for the estimation of the latent geometry. The latent geometry of a graph is important since it explains graph organizational structure and dynamics. Advancing the state of the art in this direction is of particular importance for the study of biological networks, since these networks exhibit a high degree of organizational complexity that is difficult to identify with standard analyses of node centrality measures.

We present a mathematical model of the dynamics of a biological network represented as a spring system with n degrees of freedom. The study is inspired by the recent abstraction of a biological network as a system composed of masses (nodes) connected by springs (the arcs between nodes). As a consequence of the mutual interactions between the nodes and/or of stresses deriving from the environmental conditions in which the physical network is immersed, the nodes vibrate around their equilibrium positions. The elastic constant that measures the strength of an ideal spring connecting the vibrating nodes cannot be straightforwardly gauged experimentally, and almost never in the case of large networks whose dynamics has several degrees of freedom. In this study, we show how elastic constants are related to the topology of the network and how they can be derived from the equations of the dynamics at equilibrium. The innovative results of the study are (i) the definition of stiffness vectorial entities as basis of the nullspace of the network incidence matrix, (ii) the introduction of the spring stiffness as an indicator of information propagation between nodes.

The choice of the state space representation of a system can turn into a prominent advantage or burden in any endeavour to mathematically model dynamical systems since it entails the analytical tractability of the related modelling formalism and the efficiency of the numerical computation. The Reaction-Based Model (RBM) of the state space, which is presented in this article, is a novel formalization of the kinetics of a system of interacting molecules. According to our representation, the state$S_\mu$of a system of$M$reactions and$N$molecular species, is identified with the occurrence of the reaction$R_\mu$($\mu = 1, \dots, M$). The transition between any two states$S_\mu$and$S_\nu$is modelled as a first-order reaction$S_\mu \rightarrow S_\nu$and described by mass action-like equation for the partial time derivative of the variables$P(S_\mu, t)$and$P(S_\nu, t)$, which denote the probabilities that the system lies in the two states, respectively. The rate equations for the state probabilities are coupled with those for the abundance of molecular species. Altogether, the rate equations along with the specification of the initial conditions define the Cauchy problem whose solution describes the time-evolution of the system. The RBM has been applied to a typical severely stiff biological case study. The numerical solutions of the system's dynamics turned out to be computationally more efficient and in agreement with the results of the stochastic and hybrid stochastic/deterministic simulation algorithms.

Presents corrections to author information for the above named paper.

Identifiability is a fundamental precondition for model identification and concerns the possibility to determine unique parameters sets using a certain model structure and the experimental observations for the model input-output. In this article we show how to a priori assess the identifiability of model parameters analysing the properties of the likelihood function. More precisely, a model is identifiable if the likelihood function shows a unique absolute minimum beyond the confidence intervals. The study of the likelihood function cannot avoid accompanying the likelihood estimates with the assessment of the confidence intervals, which reflect the variability in experimental data. We then show the results of this approach in cases of biotechnological relevance where the identifiability has been previously assessed.

Statistical hierarchical modelling is a powerful strategy to model complicated processes by a sequence of relatively simple models placed in a hierarchy. A hierarchical model includes the specification of the conditional probability density functions of response variables given candidate predictor variables, along with the specification of the probability density function of each single variable. We developed a statistical hierarchical model of the probability that a bacterial spore germinates, and used this model to predict the number of germinant spores as function of number of bacterial cells, nutrients concentration and amount of germination activation agents.

Molecular interrogation of a biological sample through DNA sequencing, RNA and microRNA profiling, proteomics and other assays, has the potential to provide a systems level approach to predicting treatment response and disease progression, and to developing precision therapies. Large publicly funded projects have generated extensive and freely available multi-assay data resources; however, bioinformatic and statistical methods for the analysis of such experiments are still nascent. We review multi-assay genomic data resources in the areas of clinical oncology, pharmacogenomics and other perturbation experiments, population genomics and regulatory genomics and other areas, and tools for data acquisition. Finally, we review bioinformatic tools that are explicitly geared toward integrative genomic data visualization and analysis. This review provides starting points for accessing publicly available data and tools to support development of needed integrative methods.

Transcript levels do not faithfully predict protein levels, due to post-transcriptional regulation of gene expression mediated by RNA binding proteins (RBPs) and non-coding RNAs. We developed a multivariate linear regression model integrating RBP levels and predicted RBP-mRNA regulatory interactions from matched transcript and protein datasets. RBPs significantly improved the accuracy in predicting protein abundance of a portion of the total modeled mRNAs in three panels of tissues and cells and for different methods employed in the detection of mRNA and protein. The presence of upstream translation initiation sites (uTISs) at the mRNA 5' untranslated regions was strongly associated with improvement in predictive accuracy. On the basis of these observations, we propose that the recently discovered widespread uTISs in the human genome can be a previously unappreciated substrate of translational control mediated by RBPs.

Cancer results from dysregulation of multiple steps of gene expression programs. We review how transcriptome profiling has been widely explored for cancer classification and biomarker discovery but resulted in limited clinical impact. Therefore, we discuss alternative and complementary omics approaches.

SUMMARY: The Atlas of UTR Regulatory Activity (AURA) is a manually curated and comprehensive catalog of human mRNA untranslated regions (UTRs) and UTR regulatory annotations. Through its intuitive web interface, it provides full access to a wealth of information on UTRs that integrates phylogenetic conservation, RNA sequence and structure data, single nucleotide variation, gene expression and gene functional descriptions from literature and specialized databases. AVAILABILITY: http://aura.science.unitn.it CONTACT: [email protected]; [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Transcription Factors (TFs) and microRNAs (miRNAs) are key players for gene expression regulation in higher eukaryotes. In the last years, a large amount of bioinformatic studies were devoted to the elucidation of transcriptional and post-transcriptional (mostly miRNA-mediated) regulatory interactions, but little is known about the interplay between them. DESCRIPTION: Here we describe a dynamic web-accessible database, CircuitsDB, supporting a genome-wide transcriptional and post-transcriptional regulatory network integration, for the human and mouse genomes, based on a bioinformatic sequence-analysis approach. In particular, CircuitsDB is currently focused on the study of mixed miRNA/TF Feed-Forward regulatory Loops (FFLs), i.e. elementary circuits in which a master TF regulates an miRNA and together with it a set of Joint Target protein-coding genes. The database was constructed using an ab-initio oligo analysis procedure for the identification of the transcriptional and post-transcriptional interactions. Several external sources of information were then pooled together to obtain the functional annotation of the proposed interactions. Results for human and mouse genomes are presented in an integrated web tool, that allows users to explore the circuits, investigate their sequence and functional properties and thus suggest possible biological experiments. CONCLUSIONS: We present CircuitsDB, a web-server devoted to the study of human and mouse mixed miRNA/TF Feed-Forward regulatory circuits, freely available at: http://biocluster.di.unito.it/circuits/

BACKGROUND: Common fragile sites (cfs) are specific regions in the human genome that are particularly prone to genomic instability under conditions of replicative stress. Several investigations support the view that common fragile sites play a role in carcinogenesis. We discuss a genome-wide approach based on graph theory and Gene Ontology vocabulary for the functional characterization of common fragile sites and for the identification of genes that contribute to tumour cell biology. RESULTS: Common fragile sites were assembled in a network based on a simple measure of correlation among common fragile site patterns of expression. By applying robust measurements to capture in quantitative terms the non triviality of the network, we identified several topological features clearly indicating departure from the Erdos-Renyi random graph model. The most important outcome was the presence of an unexpected large connected component far below the percolation threshold. Most of the best characterized common fragile sites belonged to this connected component. By filtering this connected component with Gene Ontology, statistically significant shared functional features were detected. Common fragile sites were found to be enriched for genes associated to the immune response and to mechanisms involved in tumour progression such as extracellular space remodeling and angiogenesis. Moreover we showed how the internal organization of the graph in communities and even in very simple subgraphs can be a starting point for the identification of new factors of instability at common fragile sites. CONCLUSION: We developed a computational method addressing the fundamental issue of studying the functional content of common fragile sites. Our analysis integrated two different approaches. First, data on common fragile site expression were analyzed in a complex networks framework. Second, outcomes of the network statistical description served as sources for the functional annotation of genes at common fragile sites by means of the Gene Ontology vocabulary. Our results support the hypothesis that fragile sites serve a function; we propose that fragility is linked to a coordinated regulation of fragile genes expression.