Discovery of principles of nature from mathematical modeling of DNA microarray data.
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Genome↗
Biomedical subjects
Orly Alter
Publications and source records attributed to Orly Alter.
Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening.
We describe the singular value decomposition (SVD) of yeast genome-scale mRNA lengths distribution data measured by DNA microarrays. SVD uncovers in the mRNA abundance levels data matrix of genes x arrays, i.e., electrophoretic gel migration lengths or mRNA lengths, mathematically unique decorrelated and decoupled "eigengenes." The eigengenes are the eigenvectors of the arrays x arrays correlation matrix, with the corresponding series of eigenvalues proportional to the series of the "fractions of eigen abundance." Each fraction of eigen abundance indicates the significance of the corresponding eigengene relative to all others. We show that the eigengenes fit "asymmetric Hermite functions," a generalization of the eigenfunctions of the quantum harmonic oscillator and the integral transform which kernel is a generalized coherent state. The fractions of eigen abundance fit a geometric series as do the eigenvalues of the integral transform which kernel is a generalized coherent state. The "asymmetric generalized coherent state" models the measured data, where the profiles of mRNA abundance levels of most genes as well as the distribution of the peaks of these profiles fit asymmetric Gaussians. We hypothesize that the asymmetry in the distribution of the peaks of the profiles is due to two competing evolutionary forces. We show that the asymmetry in the profiles of the genes might be due to a previously unknown asymmetry in the gel electrophoresis thermal broadening of a moving, rather than a stationary, band of RNA molecules.
Evolution, Molecular↗
Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations.
We describe the use of the matrix eigenvalue decomposition (EVD) and pseudoinverse projection and a tensor higher-order EVD (HOEVD) in reconstructing the pathways that compose a cellular system from genome-scale nondirectional networks of correlations among the genes of the system. The EVD formulates a genes x genes network as a linear superposition of genes x genes decorrelated and decoupled rank-1 subnetworks, which can be associated with functionally independent pathways. The integrative pseudoinverse projection of a network computed from a "data" signal onto a designated "basis" signal approximates the network as a linear superposition of only the subnetworks that are common to both signals and simulates observation of only the pathways that are manifest in both experiments. We define a comparative HOEVD that formulates a series of networks as linear superpositions of decorrelated rank-1 subnetworks and the rank-2 couplings among these subnetworks, which can be associated with independent pathways and the transitions among them common to all networks in the series or exclusive to a subset of the networks. Boolean functions of the discretized subnetworks and couplings highlight differential, i.e., pathway-dependent, relations among genes. We illustrate the EVD, pseudoinverse projection, and HOEVD of genome-scale networks with analyses of yeast DNA microarray data.
Computational Biology↗
Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription.
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.
Cell Cycle↗
Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms.
We describe a comparative mathematical framework for two genome-scale expression data sets. This framework formulates expression as superposition of the effects of regulatory programs, biological processes, and experimental artifacts common to both data sets, as well as those that are exclusive to one data set or the other, by using generalized singular value decomposition. This framework enables comparative reconstruction and classification of the genes and arrays of both data sets. We illustrate this framework with a comparison of yeast and human cell-cycle expression data sets.
Cell Cycle↗
Variation in gene expression patterns in follicular lymphoma and the response to rituximab.
Analysis of the patterns of gene expression in follicular lymphomas from 24 patients suggested that two groups of tumors might be distinguished. All patients, whose biopsies were obtained before any treatment, were treated with rituximab, a monoclonal antibody directed against the B cell antigen, CD20. Gene expression patterns in the tumors that subsequently failed to respond to rituximab appeared more similar to those of normal lymphoid tissues than to gene expression patterns of tumors from rituximab responders. These findings suggest the possibility that the response of follicular lymphoma to rituximab treatment may be predicted from the gene expression pattern of tumors.
Adult↗
Molecular characterisation of soft tissue tumours: a gene expression study.
BACKGROUND: Soft-tissue tumours are derived from mesenchymal cells such as fibroblasts, muscle cells, or adipocytes, but for many such tumours the histogenesis is controversial. We aimed to start molecular characterisation of these rare neoplasms and to do a genome-wide search for new diagnostic markers. METHODS: We analysed gene-expression patterns of 41 soft-tissue tumours with spotted cDNA microarrays. After removal of errors introduced by use of different microarray batches, the expression patterns of 5520 genes that were well defined were used to separate tumours into discrete groups by hierarchical clustering and singular value decomposition. FINDINGS: Synovial sarcomas, gastrointestinal stromal tumours, neural tumours, and a subset of the leiomyosarcomas, showed strikingly distinct gene-expression patterns. Other tumour categories--malignant fibrous histiocytoma, liposarcoma, and the remaining leiomyosarcomas--shared molecular profiles that were not predicted by histological features or immunohistochemistry. Strong expression of known genes, such as KIT in gastrointestinal stromal tumours, was noted within gene sets that distinguished the different sarcomas. However, many uncharacterised genes also contributed to the distinction between tumour types. INTERPRETATION: These results suggest a new method for classification of soft-tissue tumours, which could improve on the method based on histological findings. Large numbers of uncharacterised genes contributed to distinctions between the tumours, and some of these could be useful markers for diagnosis, have prognostic significance, or prove possible targets for treatment.
Gene Expression Profiling↗