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Mining microarray data to identify transcription factors expressed in naïve resting but not activated T lymphocytes

Genes & Immunity volume 5, pages 16–25 (2004)Cite this article

Abstract

Transcriptional repressors controlling the expression of cytokine genes have been implicated in a variety of physiological and pathological phenomena. An unknown repressor that binds to the distal NFAT element of the interleukin-2 (IL-2) gene promoter in naive T-helper lymphocytes has been implicated in autoimmune phenomena and has emerged as a potentially important factor controlling the latency of HIV-1. The aim of this paper was the identification of this repressor. We resorted to public microarray databases looking for DNA-binding proteins that are present in naïve resting T cells but are downregulated when the cells are activated. A Bayesian data mining statistical analysis uncovered 25 candidate factors. Of the 25, NFAT4 and the oncogene ets-2 bind to the common motif AAGGAG found in the HIV-1 LTR and IL-2 probes. Ets-2 binding site contains the three G's that have been shown to be important for binding of the unknown factor; hence, we considered it the likeliest candidate. Electrophoretic mobility shift assays confirmed cross-reactivity between the unknown repressor and anti-ets-2 antibodies, and cotransfection experiments demonstrated the direct involvement of Ets-2 in silencing the IL-2 promoter. Designing experiments for transcription factor analysis using microarrays and Bayesian statistical methodologies provides a novel way toward elucidation of gene control networks.

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Author information

Authors and Affiliations

  1. Laboratory of Hematology & Transfusion Medicine, University of Patras, Patras, Greece

    C Argyropoulos, M Theodoropoulou, P Adamopoulos & A Mouzaki

  2. Laboratory of Medical Physics, University of Patras, Patras, Greece

    C Argyropoulos & G C Nikiforidis

  3. Laboratory of Microbiology, University of Patras,, Patras, Greece

    S Boubali & F Paliogianni

  4. Laboratory of Biological Chemistry, Medical School, University of Patras, Patras, Greece

    T N Georgakopoulos & A G Papavassiliou

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  1. C Argyropoulos
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  2. G C Nikiforidis
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  3. M Theodoropoulou
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  4. P Adamopoulos
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Correspondence to A Mouzaki.

Appendix

Appendix

The Bayesian interpretation of probability and the Behrens–Fisher problem

Traditionally, probability is identified with the long-run relative frequency of occurrence of an event, either in a sequence of repeated experiments or in an ensemble of ‘identical’ systems. This view of probability is known as the ‘frequentist’ view; it is also called the ‘classical,’ ‘orthodox’ or ‘sampling theory’ view. It is the basis for many of the textbook statistical procedures currently in use. Bayesian probability theory (BPT) is founded on a much more general definition of probability. In BPT, probability is regarded as a real-number-valued measure of the plausibility of a proposition when incomplete knowledge does not allow us to establish its truth or falsehood with certainty. The measure is taken on a scale where 1 represents certainty of the truth of the proposition and 0 represents certainty of its falsehood. In the Bayesian framework probability theory is just common sense reduced to numbers, and probability represents the observer's belief that a certain event is true.51

The tool for updating one's beliefs about the plausibility of a hypothesis (H) given available data (E) and background information (ie context I) is given by Bayes theorem

The left-hand term, π(H∣E, I), is called the posterior probability, and it gives the probability of the hypothesis H after considering the effect of evidence E in context I. The P(H∣I) term is just the prior probability of H given I alone, that is, the belief in H before the evidence E is considered. The term P(E∣H,I) is called the likelihood, and it gives the probability of the evidence assuming the hypothesis H and background information I are true. The denominator is independent of H, and can be regarded as a normalizing or scaling constant. The information I is a conjunction of (at least) all of the other statements (background knowledge) relevant to determining P(H∣I) and P(E∣I). For notational reasons and when the context is understood, I is dropped from the expressions.

The posterior distribution is the fundamental object of Bayesian analysis and contains the relevant information needed to reason further about a hypothesis.

Turning to our example of gene downregulation, we calculate the two posterior probabilities (which sum to one, since they represent mutually exclusive events): π(H0∣E,I) (probability that a gene is downregulated given microarray measurements) and π(H1∣E,I) (probability that a gene is not downregulated given microarray measurements).

The ratio of the two posterior probabilities gives the posterior odds (ie how more likely is the null hypothesis vs the alternative) and is called the POR. A ratio for exmaple of 20 implies that the null hypothesis is 20 times more likely than the alternative one. A POR threshold essentially defines a region separating downregulated from upregulated and ‘no-change’ genes in a probabilistic manner. This follows from the simple probability calculus relation:

If the events of up- and downregulation are defined in terms of a symmetric arbitrary cutoff (C) for the difference δ, the equation above is written as

or

Substituting the definition of POR we obtain:

The calculation of the relevant posterior probabilities in the present situation is known as the two means or the BF problem. The latter, which represents the most common problem in applied statistics,32 is concerned with the determination of hypothesis tests for comparing the means of two normally distributed populations. The original BF solution (known as the BF Distribution) is an exact solution that can be derived when one adopts a Bayesian perspective; in the frequentist viewpoint one is left with approximations, notably the Welch–Satterwaite test,52 which would be inadequate for small sample sizes.33

To find out the posterior probability of downregulation from the available data, one needs to calculate the right tail region of the BF distribution. In the analysis of the current data set, the prior used is the so-called reference prior,53 which considers all possible values of θ1, θ2, (mean expression levels for a single gene in the resting and activated state) and σ1, σ2 (dispersions of expression ratios) equally likely. The choice of this prior is motivated by the following:

  1. 1

    it is the option that would have the least impact on the final results,53 letting the data ‘speak for themselves,’

  2. 2

    lack of background data to guide the specification of informative priors for EST probes,

  3. 3

    a convenient default option due to the number of comparisons made(>10 000 in our case).

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Argyropoulos, C., Nikiforidis, G., Theodoropoulou, M. et al. Mining microarray data to identify transcription factors expressed in naïve resting but not activated T lymphocytes. Genes Immun 5, 16–25 (2004). https://doi.org/10.1038/sj.gene.6364034

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