Lev B. Klebanov

Synergistic response to oncogenic mutations defines gene class critical to cancer phenotype

Understanding the molecular underpinnings of cancer is of critical importance to the development of targeted intervention strategies. Identification of such targets, however, is notoriously difficult and unpredictable. Malignant cell transformation requires the cooperation of a few oncogenic mutations that cause substantial reorganization of many cell features and induce complex changes in gene expression patterns. Genes critical to this multifaceted cellular phenotype have therefore only been identified after signalling pathway analysis or on an ad hoc basis. Our observations that cell transformation by cooperating oncogenic lesions depends on synergistic modulation of downstream signalling circuitry suggest that malignant transformation is a highly cooperative process, involving synergy at multiple levels of regulation, including gene expression. Here we show that a large proportion of genes controlled synergistically by loss-of-function p53 and Ras activation are critical to the malignant state of murine and human colon cells. Notably, 14 out of 24 ‘cooperation response genes’ were found to contribute to tumour formation in gene perturbation experiments. In contrast, only 1 in 14 perturbations of the genes responding in a non-synergistic manner had a similar effect. Synergistic control of gene expression by oncogenic mutations thus emerges as an underlying key to malignancy, and provides an attractive rationale for identifying intervention targets in gene networks downstream of oncogenic gain- and loss-of-function mutations.

The effects of normalization on the correlation structure of microarray data.

BackgroundStochastic dependence between gene expression levels in microarray data is of critical importance for the methods of statistical inference that resort to pooling test-statistics across genes. It is frequently assumed that dependence between genes (or tests) is suffciently weak to justify the proposed methods of testing for differentially expressed genes. A potential impact of between-gene correlations on the performance of such methods has yet to be explored.ResultsThe paper presents a systematic study of correlation between the t-statistics associated with different genes. We report the effects of four different normalization methods using a large set of microarray data on childhood leukemia in addition to several sets of simulated data. Our findings help decipher the correlation structure of microarray data before and after the application of normalization procedures.ConclusionA long-range correlation in microarray data manifests itself in thousands of genes that are heavily correlated with a given gene in terms of the associated t-statistics. By using normalization methods it is possible to significantly reduce correlation between the t-statistics computed for different genes. Normalization procedures affect both the true correlation, stemming from gene interactions, and the spurious correlation induced by random noise. When analyzing real world biological data sets, normalization procedures are unable to completely remove correlation between the test statistics. The long-range correlation structure also persists in normalized data.

How high is the level of technical noise in microarray data

BackgroundMicroarray gene expression data are commonly perceived as being extremely noisy because of many imperfections inherent in the current technology. A recent study conducted by the MicroArray Quality Control (MAQC) Consortium and published in Nature Biotechnology provides a unique opportunity to probe into the true level of technical noise in such data.ResultsIn the present report, the MAQC study is reanalyzed in order to quantitatively assess measurement errors inherent in high-density oligonucleotide array technology (Affymetrix platform). The level of noise is directly estimated from technical replicates of gene expression measurements in the absence of biological variability. For each probe set, the magnitude of random fluctuations across technical replicates is characterized by the standard deviation of the corresponding log-expression signal. The resultant standard deviations appear to be uniformly small and symmetrically distributed across probe sets. The observed noise level does not cause any tangible bias in estimated pair-wise correlation coefficients, the latter being particularly prone to its presence in microarray data.ConclusionThe reported analysis strongly suggests that, contrary to popular belief, the random fluctuations of gene expression signals caused by technical noise are quite low and the effect of such fluctuations on the results of statistical inference from Affymetrix GeneChip microarray data is negligibly small.ReviewersThe paper was reviewed by A. Mushegian, K. Jordan, and E. Koonin.

Correlation Between Gene Expression Levels and Limitations of the Empirical Bayes Methodology for Finding Differentially Expressed Genes

Stochastic dependence between gene expression levels in microarray data is of critical importance for the methods of statistical inference that resort to pooling test statistics across genes. The empirical Bayes methodology in the nonparametric and parametric formulations, as well as closely related methods employing a two-component mixture model, represent typical examples. It is frequently assumed that dependence between gene expressions (or associated test statistics) is sufficiently weak to justify the application of such methods for selecting differentially expressed genes. By applying resampling techniques to simulated and real biological data sets, we have studied a potential impact of the correlation between gene expression levels on the statistical inference based on the empirical Bayes methodology. We report evidence from these analyses that this impact may be quite strong, leading to a high variance of the number of differentially expressed genes. This study also pinpoints specific components of the empirical Bayes method where the reported effect manifests itself.

Detecting intergene correlation changes in microarray analysis: a new approach to gene selection

BackgroundMicroarray technology is commonly used as a simple screening tool with a focus on selecting genes that exhibit extremely large differential expressions between different phenotypes. It lacks the ability to select genes that change their relationships with other genes in different biological conditions (differentially correlated genes). We intend to enrich the above procedure by proposing a nonparametric selection procedure that selects differentially correlated genes.ResultsUsing both simulations and resampling techniques, we found that our procedure correctly detected genes that were not differentially expressed but differentially correlated. We also applied our procedure to a set of biological data and found some potentially important genes that were not selected by the traditional method.Discussion and ConclusionMicroarray technology yields multidimensional information on the function of the whole genome. Rather than treating intergene correlation as a nuisance to the traditional gene selection procedures which are essentially univariate, our method utilizes the rich information contained in the correlation as a new selection criterion. It can provide additional useful candidate genes for the biologists.

A stochastic model of radiation carcinogenesis: latent time distributions and their properties

A stochastic model of radiation carcinogenesis is proposed that has much in common with the ideas suggested by M. Pike as early as 1966. The model allows us to obtain a parametric family of substochastic-type distributions for the time of tumor latency that provides a description of the rate of tumor development and the number of affected individuals. With this model it is possible to interpret data on tumor incidence in terms of promotion and progression processes. The basic model is developed for a prolonged irradiation at a constant dose rate and includes short-term irradiation as a special case. A limiting form of the latent time distribution for short-term irradiation at high doses is obtained. This distribution arises in the extreme value theory within the random minima framework. An estimate for the rate of convergence to a limiting distribution is given. Based on the proposed latent time distributions, long-term predictions of carcinogenic risk do not call for information about irradiation dose. As shown by computer simulation studies and real data analysis, the parametric estimation of carcinogenic risk appears to be robust to the loss of statistical information caused by the right-hand censoring of time-to-tumor observations. It seems likely that this property, although revealed by means of a purely empirical procedure, may be useful in selecting a model for the practical purpose of risk prediction.

Multivariate search for differentially expressed gene combinations

BackgroundTo identify differentially expressed genes, it is standard practice to test a two-sample hypothesis for each gene with a proper adjustment for multiple testing. Such tests are essentially univariate and disregard the multidimensional structure of microarray data. A more general two-sample hypothesis is formulated in terms of the joint distribution of any sub-vector of expression signals.ResultsBy building on an earlier proposed multivariate test statistic, we propose a new algorithm for identifying differentially expressed gene combinations. The algorithm includes an improved random search procedure designed to generate candidate gene combinations of a given size. Cross-validation is used to provide replication stability of the search procedure. A permutation two-sample test is used for significance testing. We design a multiple testing procedure to control the family-wise error rate (FWER) when selecting significant combinations of genes that result from a successive selection procedure. A target set of genes is composed of all significant combinations selected via random search.ConclusionsA new algorithm has been developed to identify differentially expressed gene combinations. The performance of the proposed search-and-testing procedure has been evaluated by computer simulations and analysis of replicated Affymetrix gene array data on age-related changes in gene expression in the inner ear of CBA mice.

The Methods of Distances in the Theory of Probability and Statistics

Main directions in the theory of probability metrics.- Probability distances and probability metrics: Definitions.- Primary, simple and compound probability distances, and minimal and maximal distances and norms.- A structural classification of probability distances.-Monge-Kantorovich mass transference problem, minimal distances and minimal norms.- Quantitative relationships between minimal distances and minimal norms.- K-Minimal metrics.- Relations between minimal and maximal distances.- Moment problems related to the theory of probability metrics: Relations between compound and primary distances.- Moment distances.- Uniformity in weak and vague convergence.- Glivenko-Cantelli theorem and Bernstein-Kantorovich invariance principle.- Stability of queueing systems.-Optimal quality usage.- Ideal metrics with respect to summation scheme for i.i.d. random variables.- Ideal metrics and rate of convergence in the CLT for random motions.- Applications of ideal metrics for sums of i.i.d. random variables to the problems of stability and approximation in risk theory.- How close are the individual and collective models in risk theory?- Ideal metric with respect to maxima scheme of i.i.d. random elements.- Ideal metrics and stability of characterizations of probability distributions.- Positive and negative de nite kernels and their properties.- Negative definite kernels and metrics: Recovering measures from potential.- Statistical estimates obtained by the minimal distances method.- Some statistical tests based on N-distances.- Distances defined by zonoids.- N-distance tests of uniformity on the hypersphere.-

A MULTIVARIATE EXTENSION OF THE GENE SET ENRICHMENT ANALYSIS

A test-statistic typically employed in the gene set enrichment analysis (GSEA) prevents this method from being genuinely multivariate. In particular, this statistic is insensitive to changes in the correlation structure of the gene sets of interest. The present paper considers the utility of an alternative test-statistic in designing the confirmatory component of the GSEA. This statistic is based on a pertinent distance between joint distributions of expression levels of genes included in the set of interest. The null distribution of the proposed test-statistic, known as the multivariate N-statistic, is obtained by permuting group labels. Our simulation studies and analysis of biological data confirm the conjecture that the N-statistic is a much better choice for multivariate significance testing within the framework of the GSEA. We also discuss some other aspects of the GSEA paradigm and suggest new avenues for future research.

Utility of correlation measures in analysis of gene expression.

SummaryThe role of the correlation structure of gene expression data are two-fold: It is a source of complications and useful information at the same time. Ignoring the strong stochastic dependence between gene expression levels in statistical methodologies for microarray data analysis may deteriorate their performance. However, there is a host of valuable information in the correlation structure that deserves a closer look. A proper use of correlation measures can remedy deficiencies of currently practiced methods that are focused too heavily on strong effects in terms of differential expression of genes. The present paper discusses the utility of correlation measures in microarray data analysis and gene regulatory network reconstruction, along with various pitfalls in both research areas that have been uncovered in methodological studies. These issues have broad applicability to all genomic studies examining the biology, diagnosis, and treatment of neurological disorders.