Analysis of previously published sets of DNA microarray gene expression data by singular value decomposition has uncovered underlying patterns or ''characteristic modes'' in their temporal profiles. These patterns contribute unequally to the structure of the expression profiles. Moreover, the essential features of a given set of expression profiles are captured using just a small number of characteristic modes. This leads to the striking conclusion that the transcriptional response of a genome is orchestrated in a few fundamental patterns of gene expression change. These patterns are both simple and robust, dominating the alterations in expression of genes throughout the genome. Moreover, the characteristic modes of gene expression change in response to environmental perturbations are similar in such distant organisms as yeast and human cells. This analysis reveals simple regularities in the seemingly complex transcriptional transitions of diverse cells to new states, and these provide insights into the operation of the underlying genetic networks.T he recent development of DNA microarray technology has enabled the genome-wide measurement of temporal changes in gene expression levels (1, 2). Analysis of the expression patterns obtained with large gene arrays has revealed the existence of groups or ''clusters'' of genes with similar expression patterns (3-6). Not surprisingly, gene clusters often contain genes that encode proteins required for a common function, and, hence, co-clustering has been helpful in identifying the functions of unknown gene products. However, such cluster analyses provide little insight into the relationships among groups of co-regulated genes or the behavior of biological networks as a whole.In this paper, we report the results of subjecting several large published gene expression data sets to singular value decomposition (SVD), a standard and straight-forward analytic procedure. We show that highly complex sets of gene expression profiles can be represented by a small number of ''characteristic modes'' that capture the temporal patterns of gene expression change. These modes are somewhat analogous to the characteristic vibration modes of a tuned violin string. The tone produced by the vibrating string can be entirely specified by the contributions of its characteristic vibration modes. We show here that a gene expression profile, similarly, can be precisely represented by specifying the magnitude and sign of the contribution of each of its characteristic modes. This type of ''spectral'' analysis yields a hierarchical interpretation of the expression data and provides insights into the nature and behavior of genetic networks. MethodsThe mathematical analysis is carried out straightforwardly by using SVD (7). The gene expression data of n genes, each measured at m discrete time points, may be written as an n ϫ m matrix, A. Following the procedures outlined in ref. 6, we have polished the data by requiring that the rows and columns have a zero mean by subtracting the mean values of the raw...
We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.
We present and implement a distance-based clustering of amino acids within the framework of a statistically derived interaction matrix and show that the resulting groups faithfully reproduce, for well-designed sequences, thermodynamic stability in and kinetic accessibility to the native state. A simple interpretation of the groups is obtained by eigenanalysis of the interaction matrix.
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