Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription

Abstract

We describe an integrative data-driven mathematical framework that formulates any number of genome-scale molecular biological data sets in terms of one chosen set of data samples, or of profiles extracted mathematically from data samples, designated the ''basis'' set. By using pseudoinverse projection, the molecular biological profiles of the data samples are least-squares-approximated as superpositions of the basis profiles. Reconstruction of the data in the basis simulates experimental observation of only the cellular states manifest in the data that correspond to those of the basis. Classification of the data samples according to their reconstruction in the basis, rather than their overall measured profiles, maps the cellular states of the data onto those of the basis and gives a global picture of the correlations and possibly also causal coordination of these two sets of states. We illustrate this framework with an integration of yeast genome-scale proteins' DNA-binding data with cell cycle mRNA expression time course data. Novel correlation between DNA replication initiation and RNA transcription during the yeast cell cycle, which might be due to a previously unknown mechanism of regulation, is predicted. singular value decomposition ͉ generalized singular value decomposition ͉ DNA microarrays ͉ yeast Saccharomyces cerevisiae cell cycle R ecent advances in high-throughput technologies enable monitoring molecular biological signals, e.g., mRNA expression levels and proteins' DNA-binding occupancy levels, that correspond to activities of cellular systems, e.g., DNA replication, RNA transcription, and proteins' DNA-binding on a genomic scale. Integrative analysis of these global signals promises to give new insights into cellular mechanisms of regulation, i.e., global causal coordination of cellular activities. Integrative analysis of different types of large-scale molecular biological data requires mathematical tools that are able to formulate any number of large-scale data sets in terms of a common frame of reference, while reducing the complexity of the data to make them comprehensible (1, 2). These tools should provide data-driven models or mathematical frameworks for the description of the data, where the variables, i.e., the patterns that they uncover in the data, and operations, i.e., data reconstruction and classification in subspaces spanned by these patterns, may represent some biological reality.Recently we showed that singular value decomposition (SVD) (3, 4) and generalized SVD (GSVD) (5) provide such data-driven frameworks for genome-scale molecular biological data. For example, the variables of SVD, ''eigengenes'' and corresponding ''eigenarrays,'' in the analyses of yeast Saccharomyces cerevisiae cell cycle time course mRNA expression data (6), and those of GSVD, ''genelets'' and corresponding ''arraylets,'' in the comparative analysis of yeast and human (7) cell cycle time course mRNA expression data, were shown to correlate with observed genome-scale effects of known cell cycle regulators and...

Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening

“…Integrating genome-scale proteins' DNA-binding data with cell cycle mRNA expression time course data from yeast, using pseudoinverse projection, we predicted a previously unknown correlation between DNA replication initiation and RNA transcription, which might be due to an undiscovered mechanism of regulation (21). Now we reveal a previously unknown physical principle by modeling DNA microarray data.…”

Pattern discovery and cancer gene identification in integrated cancer genomic data

“…The method was recently used in a landmark study to predict novel breast cancer subtypes with distinct clinical outcomes (9), and it was found that the joint clustering of copy number and gene expression profiles resolved the considerable heterogeneity of the expression-only subgroups. Other approaches on data integration that have emerged in recent years include generalized data decomposition methods (10,11) and nonparametric Bayesian models (12). However, two major challenges have not yet been fully addressed.…”

Discovery of principles of nature from mathematical modeling of DNA microarray data

“…One study found a chromosome-wide pattern of correlation between DNA binding of cohesin, a protein that holds together sister chromatids, and convergent transcription of genes, suggesting a mechanism for the relocation of cohesion during DNA replication (26). Another study discovered a genome-wide pattern of correlation between the activation of replication origins and minima or even shutdown of the transcription of adjacent genes during the cell-cycle stage G 1 , by using pseudoinverse projection to map DNA-binding of replication initiation proteins onto the SVD-and GSVDreconstructed phase-spaces of yeast cell-cycle mRNA expression (6). This pattern might be explained by a previously unknown mechanism of regulation, which is in agreement with current understanding of replication initiation (27) and is supported by recent experimental results (28).…”

“…The operations, such as data classification and reconstruction in subspaces of selected patterns, might simulate experimental observation of the correlations and possibly also causal coordination of these activities. Such models were recently created from DNA microarray data by using singular value decomposition (SVD) (4) and generalized SVD (GSVD) (5), and their ability to predict previously unknown biological as well as physical principles was demonstrated (6,7).…”