MOTIVATION: High throughput technologies are widely employed in modern biomedical research. They yield measurements of a large number of biomolecules in a single experiment. The number of experiments usually is much smaller than the number of measurements in each experiment. The simultaneous measurements of biomolecules provide a basis for a comprehensive, systems view for describing relevant biological processes. Often it is necessary to determine correlations between the data matrices under different conditions or pathways. However, the techniques for analyzing the data with a low number of samples for possible correlations within or between conditions are still in development. Earlier developed correlative measures, such as the RV coefficient, use the trace of the product of data matrices as the most relevant characteristic. However, a recent study has shown that the RV coefficient consistently overestimates the correlations in the case of low sample numbers. To correct for this bias, it was suggested to discard the diagonal elements of the outer products of each data matrix. In this work, a principled approach based on the matrix decomposition generates three trace-independent parts for every matrix. These components are unique, and they are used to determine different aspects of correlations between the original datasets. RESULTS: Simulations show that the decomposition results in the removal of high correlation bias and the dependence on the sample number intrinsic to the RV coefficient. We then use the correlations to analyze a real proteomics dataset. AVAILABILITY AND IMPLEMENTATION: The python code can be downloaded from http://dynamic-proteome.utmb.edu/MatrixCorrelations.aspx. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Eukaryotic DNA replication is elaborately orchestrated to duplicate the genome timely and faithfully. Replication initiates at multiple origins from which replication forks emanate and travel bi-directionally. The complex spatio-temporal regulation of DNA replication remains incompletely understood. To study it, computational models of DNA replication have been developed in S. cerevisiae. However, in spite of the experimental evidence of forks' speed stochasticity, all models assumed that forks' speeds are the same. Here, we present the first model of DNA replication assuming that speeds vary stochastically between forks. Utilizing data from both wild-type and hydroxyurea-treated yeast cells, we show that our model is more accurate than models assuming constant forks' speed and reconstructs dynamics of DNA replication faithfully starting both from population-wide data and data reflecting fork movement in individual cells. Completion of replication in a timely manner is a challenge due to its stochasticity; we propose an empirically derived modification to replication speed based on the distance to the approaching fork, which promotes timely completion of replication. In summary, our work discovers a key role that stochasticity of the forks' speed plays in the dynamics of DNA replication. We show that without including stochasticity of forks' speed it is not possible to accurately reconstruct movement of individual replication forks, measured by DNA combing.