A model of technical variation of microarray signals.

We describe a mathematical model of signal from single-channel direct hybridization microarray platforms. The model establishes a linear relationship between microarray signals and their standard deviations from a minimum set of assumptions. We use the model to precisely define important microarray quality characteristics: resolved fold change and dynamic range. The definitions lead to closed form expressions relating these characteristics to physical parameters of the microarray experiment in the case when both specific and nonspecific binding of target to probe are governed by the Langmuir hybridization isotherm. The predictions of the model are in close agreement to data obtained from spike-in experiments. Given the generality of the model, the introduced definitions of dynamic range and resolved concentration fold-change can be used to conduct cross-platform comparisons and to guide improvement of the microarray platform.

A new estimator of significance of correlation in time series data.

Many expression array experiments monitor gene activity as an organism goes through some biological process. It is desirable to find genes with similar expression patterns in the resulting time series data. We propose a new simulation approach that assesses the statistical significance of similarity scores between expression patterns. The simulation takes into account the dependence between columns of data.

Distribution and abundance of microsatellites in the yeast genome can Be explained by a balance between slippage events and point mutations.

We fit a Markov chain model of microsatellite evolution introduced by Kruglyak et al. to data on all di-, tri-, and tetranucleotide repeats in the yeast genome. Our results suggest that many features of the distribution of abundance and length of microsatellites can be explained by this simple model, which incorporates a competition between slippage events and base pair substitutions, with no need to invoke selection or constraints on the lengths. Our results provide some new information on slippage rates for individual repeat motifs, which suggest that AT-rich trinucleotide repeats have higher slippage rates. As our model predicts, we found that many repeats were adjacent to shorter repeats of the same motif. However, we also found a significant tendency of microsatellites of different motifs to cluster.

Exploring expression data: identification and analysis of coexpressed genes.

Analysis procedures are needed to extract useful information from the large amount of gene expression data that is becoming available. This work describes a set of analytical tools and their application to yeast cell cycle data. The components of our approach are (1) a similarity measure that reduces the number of false positives, (2) a new clustering algorithm designed specifically for grouping gene expression patterns, and (3) an interactive graphical cluster analysis tool that allows user feedback and validation. We use the clusters generated by our algorithm to summarize genome-wide expression and to initiate supervised clustering of genes into biologically meaningful groups.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations.

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Multistage sequencing by hybridization.

The sequencing of DNA is an important and difficult problem. Many interesting algorithms combine various technologies in an attempt to sequence long regions of DNA. One such algorithm is sequencing by hybridization (SBH). We briefly review SBH and mention the drawbacks that prevent it from being used in practice. We then present a theoretical algorithm that uniquely determines a sequence of length n through hybridization experiments that require the examination of only O(n2log(n)) subsequences. The key idea is to double subsequence length in each iteration of the algorithm. There are various problems associated with transforming the theoretical algorithm into a practical biological procedure. However, the general strategy of increasing subsequence length may be used to develop algorithms that are feasible given the current state of technology. Combining this strategy with a computer processing phase leads to a novel method of extending the resolving power of standard SBH techniques.