Biological detection of low radiation doses by combining results of two microarray analysis methods.

The accurate determination of the biological effects of low doses of pollutants is a major public health challenge. DNA microarrays are a powerful tool for investigating small intracellular changes. However, the inherent low reliability of this technique, the small number of replicates and the lack of suitable statistical methods for the analysis of such a large number of attributes (genes) impair accurate data interpretation. To overcome this problem, we combined results of two independent analysis methods (ANOVA and RELIEF). We applied this analysis protocol to compare gene expression patterns in Saccharomyces cerevisiae growing in the absence and continuous presence of varying low doses of radiation. Global distribution analysis highlights the importance of mitochondrial membrane functions in the response. We demonstrate that microarrays detect cellular changes induced by irradiation at doses that are 1000-fold lower than the minimal dose associated with mutagenic effects.

Pairwise sequence alignment using a PROSITE pattern-derived similarity score.

Existing methods for alignments are based on edition costs computed additionally position by position, according to a fixed substitution matrix: a substitution always has the same weight regardless of the position. Nevertheless the biologist favours a similarity according to his knowledge of the structure or the function of the sequences considered. In the particular case of proteins, we present a method consisting in integrating other information, such as patterns of the PROSITE databank, in the classical dynamic programming algorithm. The method consists in making an alignment by dynamic programming taking a decision not only letter by letter as in the Smith & Waterman algorithm but also by giving a reward when aligning patterns.

Sequence alignment: an approximation law for the Z-value with applications to databank scanning.

The Z-value is an attempt to estimate the statistical significance of a Smith and Waterman dynamic programming alignment score (H-score) through the use of a Monte-Carlo procedure. In this paper, we give an approximation for the Z-value law deduced from the Poisson clumping heuristic developed by Waterman and Vingron (Stat. Sci. 9 (1994) 367) in the case of independent and identically distributed sequences comparison. As for non-gapped alignment scores, our approximation is of Gumbel type but with parameters that are sequence independent. This result makes clear the related experimental results mentioned by Comet et al. (Comput. Chem. 23 (1999) 317). Using 'quasi-real' sequences (i.e. randomly shuffled sequences of the same length and amino acid composition as the real ones) we investigate the relevance of our approximation result. Since the Monte-Carlo approach we use generates a bias for the Gumbel decay parameter estimation, a correction procedure is proposed. Applications to real sequences are considered and we show how our results can be used to detect the potential biological relationships between real sequences.

Significance of Z-value statistics of Smith-Waterman scores for protein alignments.

The Z-value is an attempt to estimate the statistical significance of a Smith-Waterman dynamic alignment score (SW-score) through the use of a Monte-Carlo process. It partly reduces the bias induced by the composition and length of the sequences. This paper is not a theoretical study on the distribution of SW-scores and Z-values. Rather, it presents a statistical analysis of Z-values on large datasets of protein sequences, leading to a law of probability that the experimental Z-values follow. First, we determine the relationships between the computed Z-value, an estimation of its variance and the number of randomizations in the Monte-Carlo process. Then, we illustrate that Z-values are less correlated to sequence lengths than SW-scores. Then we show that pairwise alignments, performed on 'quasi-real' sequences (i.e., randomly shuffled sequences of the same length and amino acid composition as the real ones) lead to Z-value distributions that statistically fit the extreme value distribution, more precisely the Gumbel distribution (global EVD, Extreme Value Distribution). However, for real protein sequences, we observe an over-representation of high Z-values. We determine first a cutoff value which separates these overestimated Z-values from those which follow the global EVD. We then show that the interesting part of the tail of distribution of Z-values can be approximated by another EVD (i.e., an EVD which differs from the global EVD) or by a Pareto law. This has been confirmed for all proteins analysed so far, whether extracted from individual genomes, or from the ensemble of five complete microbial genomes comprising altogether 16956 protein sequences.