Gene expression Identifying genes from up – down properties of microarray expression series

Motivation: We consider any collection of microarrays that can be ordered to form a progression; for example, as a function of time, severity of disease or dose of a stimulant. By plotting the expression level of each gene as a function of time, or severity, or dose, we form an expression series, or curve, for each gene. While most of these curves will exhibit random fluctuations, some will contain a pattern, and these are the genes that are most likely associated with the quantity used to order them. Results: We introduce a method of identifying the pattern and hence genes in microarray expression curves without knowing what kind of pattern to look for. Key to our approach is the sequence of ups and downs formed by pairs of consecutive data points in each curve. As a benchmark, we blindly identified genes from yeast cell cycles without selecting for periodic or any other anticipated behaviour. Contact: tmf20@cam.ac.uk Supplementary information: The complete versions of Table 2 and Figure 4, as well as other material, can be found at http://www.lps. ens.fr/∼willbran/up-down/ or http://www.tcm. phy.cam.ac.uk/∼tmf20/ up-down/ INTRODUCTION The ability to measure thousands of gene expression levels in parallel using microarrays has provided scientists with a complex, unique fingerprint of a cell or tissue sample (The Chipping Forecast II, 2002). Understanding how this fingerprint changes during physiological or pathological processes is one of the most pressing—and promising—problems in bioinformatics. We introduce a fundamentally new approach, unrelated to clustering, to identifying genes from any collection of expression arrays that can be ordered to form a progression (e.g. time series experiments). We construct for each gene a plot of expression level as a function of progression and identify pairs of consecutive data points as increasing (+) or decreasing (−). By studying this succession of +’s and −’s, we identify the genes that are correlated with the progression without knowing the kind of pattern they might exhibit. As a benchmark, we analysed Cho’s and Spellman’s classic yeast cell cycle expression data (Cho et al., 1998; Spellman et al., 1998). We identified 154 (266) genes which with 95% (90%) probability are correlated with cell cycle. ∗To whom correspondence should be addressed. Because up–down analysis can be used to study gene expression as a function of time or disease progression or any increasing dose of a stimulus (Cho et al., 1998; Spellman et al., 1998; Whitfield et al., 2002; Alazawi et al., 2002), we believe it opens a new program of microarray analysis. We refer to whatever parameter we use to order our microarray progressions as the independent variable. The expression levels of most genes will not be correlated with the independent variable, and the corresponding curves will behave randomly. The small fraction of genes that are correlated will not exhibit random behaviour, but will display some pattern or regularity. Our goal in this paper is to identify these correlated genes by the presence or absence of pattern in their expression curves and to quantify our belief that a given gene is correlated. Our problem is difficult for two reasons. First, because we want to identify regulatory (or regulated) genes without knowing details of their role, we do not know what kind of pattern we are looking for. Therefore we need a test for pattern that makes no assumptions about what it might find. Second, we must be beware of false alarms in the form of random curves exhibiting pattern by chance alone. If we look at enough genes, and hence expression curves, we will find any pattern we might imagine. So whatever our test for pattern is, it must become more stringent as the number of curves examined increases. One of the simplest ways of analysing expression curves is to connect pairs of neighbouring data points with line segments and to label these segments up or down. In this way a set of N + 1 data points can be reduced to its signature σ , a string of +’s and −’s of length N . For example, the data 0.3, 0.8, 0.6 and 0.2 have signature σ = + − −, which we abbreviate by (1,2), that is, the number of +’s followed by the number of −’s, etc. Rather than studying the up–down properties of expression curves of correlated genes explicitly, we ask a simpler question: What are the up–down properties of non-correlated, or random, curves? For small numbers of data points, we list the distribution of signatures in Figure 1 and Table 1. We say that a gene is likely to be correlated with the independent variable if the probability P(σ) of its up–down signature is low enough to be statistically deviant from the expected distribution for random curves. The essence of our approach is the mapping of ordered datasets (curves) to real numbers such that random curves tend to be mapped to higher values and regular or patterned curves to lower numbers. We say a curve has more pattern than another if its algorithmic © The Author 2005. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org 3859