Background

Many methods are available for the analysis of expression data from microarrays [1–3]. Most software falls into one of two categories: programs which generate a list of significantly differentially regulated genes and programs which perform an analysis based on such a significant genes list (SGL). The first category includes statistical methods (e.g. SAM [4]) and pattern-grouping methods (e.g. Cluster [5]), the end result of either type of analysis being a list of genes which appear to be significantly differentially regulated. The second category of software includes a variety of approaches which search for relationships between the members of the SGL, such as methods which identify common regulatory motifs [6] or establish significance based on genetic position [7].

In browsing a SGL, lexical trends are frequently observed as genes involved in similar metabolic functions are often coordinately regulated. Identification of such lexical trends is critical for the generation of hypotheses for further experimentation, but the large size of a typical microarray dataset makes objective evaluation by eye difficult, if not impossible. Additionally, the genetic content of the organism, the style of the genome annotation, the features selected for representation on the microarray, and experimental design all contain biases which are ultimately reflected in the SGL, which further confounds objective analysis. A number of publications have addressed some of these issues by designing lexical analyses based on functional classifications [8], Medline MeSH terms [9], or Medline titles and abstracts [10–12] that are associated with the genes in a SGL. Each of these approaches draw upon external information to overlay biological relationships onto the expression data, and the significance of these relationships can then be analyzed using standard statistical tools.

The described methods have all been used to identify previously undetected relationships of possible biological significance in published microarray datasets. However, each approach has drawbacks that limit their use as a generalized analysis tool for the average microarray user. Methods based on functional classifications require that the genes be categorized prior to the analysis. This is often not performed by the sequencing group and too laborious to be practical for most microarray end users. Medline-based methods cannot include genes with putative functions in their analyses, as there is no associated literature for such genes. As over 50% of the genes in most genomes are still of putative function, abstract-based approaches exclude a large proportion of the expression data from the analysis. All of the described approaches are also confounded by ambiguity and variability in the annotations used by different researchers (e.g. genes with multiple names). Most importantly, these methods require a significant degree of computer savvy to set up and execute, which makes use impractical for many microarray users. We developed a program, LACK, which performs a simple but flexible lexical analysis of microarray data that circumvents many of the described problems.

Results and Discussion

Observed Frequency of Search Terms in the SGL

The software requires three input files. The first file contains the SGL. This is usually the output of a clustering or statistical analysis which has been conducted to identify differentially regulated genes. The second file is the full, unanalyzed dataset. This dataset should be identical to the dataset used for the SGL generation to avoid introduction of any bias from the pre-analysis steps (array design, hybridization, feature identification, data filtering, etc.). The third file is a user-specified set of search terms to be used for the lexical analysis.

The software first tallies the number of genes in the SGL containing any of the search terms. The gene is counted as a match if any of the search terms are found within the annotation. The total tally of matches within the SGL represents the observed frequency of the search terms in the analyzed data. The software then identifies the frequencies at which the search terms would be found at random in datasets of identical size to the SGL. Two approaches for generating and analyzing the random datasets are available: binomial and Poisson. The choice is dependent on the size of the datasets being used due to computational limitations (described below).

Binomial Statistics

The default statistical method employed is the binomial distribution to model the data. For each member of the test sample, the binary criterion (contains a search term / does not contain any search terms) is applied. Furthermore, the population from which the test sample (SGL) is chosen is already known (the full dataset), so the precise frequencies of genes containing a search term (p = number of genes containing a match / number of genes) or not containing any of the search terms (q = 1 - p) can be calculated. For a given population, we can calculate the probability of the observed number of matches (or fewer) in the SGL (k) occurring in a random sample of size N by the cumulative binomial probability function:

By using the binomial calculation, there is no need for random sampling, which has the advantages of higher precision in the p-values and reduced computation time. The probability of obtaining j matches, P(j), is calculated for every value of j which generates P(j) = 0.00001 and provided in the output in order to generate enough values for plotting both tails of a histogram.

Poisson Analysis

Because microarray datasets are often very large, the factorial computations in the binomial coefficient can easily exceed the capabilities of modern desktop computers. We therefore provide an option to perform Poisson statistics, which does not require very large integers. Random samples (RSs) that are identical in size to the SGL are repeatedly chosen from the full dataset with replacement, and the number of genes containing any of the search terms is tallied for each RS. The cumulative Poisson probability is calculated for the observed number of matches in the analyzed dataset as compared to the distribution of matches in the RSs:

where k is the number of matches in the SGL and μ is the mean number of matches for all RSs.

We have observed that 100 RSs are generally sufficient to accurately mimic the p-values generated by binomial analysis (Table 1). However, using 1000 RSs requires only slightly more computational time, which is easily outweighed by the benefit of a more accurate p-value. It is also noteworthy that for more significant numbers of matches, there is less variation in the p-values. Therefore, we recommend performing multiple trials when using Poisson statistics, especially in cases where the p-value borders on the selected significance threshold.

Table 1 Variation in cumulative Poisson probabilities in response to number of random samples and SGL matches
Full size table

Additionally, in Poisson output mode, a raw output option can be selected that includes the tally data in the output file for analysis by other statistical methods.

Validation of LACK

We have successfully used LACK to generate and test hypotheses generated from our microarray data. Using our Salmonella enterica serovar Typhimurium LT2 microarray [13], we observed that members of Salmonella Pathogenicity Island 2 (SPI-2) [14, 15] appeared 8 times in the top 256 genes significantly upregulated by the ferrous iron chelator dipyridyl. Because there are 34 genes predicted to be within SPI-2 [14, 15], it seemed possible that this number of matches might appear at random. We constructed a list of the 34 genes in SPI-2 and performed LACK analysis on the dataset. The binomial distribution of the calculated expected frequency of matches and the probability values show that the overrepresentation of SPI-2 in the dataset is unlikely to be random (Figure 1). We have confirmed that SPI-2 is indeed induced by dipyridyl treatment using a SPI-2 promoter (ssaG) fused to GFP (data not shown). During the course of this work, an independent report also confirmed that SPI-2 is indeed upregulated in response to cation starvation [16].

Figure 1
figure 1

Binomial distribution of SPI-2 genes in a dataset The total filtered dataset consisted on 4290 unique elements. An SGL of 256 genes was generated using SAM and analyzed for 34 members of SPI-2. The arrow indicates the number of matches in the SGL, with P(x > 8) = 0.004. The binomial analysis required 5 seconds; Poisson analysis of the same datasets required 7 seconds. A 21,450 element dataset created by replicating the 4290 element dataset 5 times required 8 seconds for binomial analysis. The files used for this analysis are available at the LACK website or as supplementary data.

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Conclusions

We have demonstrated one example of how we have employed LACK for statistical analysis of lexical trends. In analyzing our microarray data, we realized that few simple tools are available for assessing significance of observed trends. While there are a number of other lexical analysis methods available, they employ different goals (i.e. de novo identification of lexical trends) than LACK (significance analysis of specific lexical trends). The primary advantages of LACK over other lexical analysis methods for the typical microarray user are the simplicity of use and the flexibility in searchable concepts. The inputs are text files that are generated as part of a typical microarray analysis, and the output is provided as tab-delimited text; no external information is required apart from the microarray annotation. The inherent flexibility in user-specified search terms makes LACK potentially useful for many microarray users who are interested in determining whether or not specific trends are significant in their data, rather than performing a global search of all possible trends. In addition, this flexibility makes lexical analysis possible for datasets that are difficult to analyze by other lexical methods due to inconsistencies in annotation nomenclature, as the user can specify terms to encompass multiple naming conventions.

It is important to note that with this flexibility comes an additional point at which bias can be introduced: careless selection of search terms can lead to false determination of significance. For example, search terms should not be chosen only from the SGL itself, but rather from the full dataset. To demonstrate such an inappropriate example, we selected a search list based on metabolites found in the top 20 genes of the SGL described above. While there is no clear relationship between the search list terms (glucosamine, methionine sulfoxide, citrate, 2-aminoethylphosphonate, ethanolamine, UDP-glucose, cysteine), LACK indicates a high level of significance in these terms being over-represented in the SGL (p < 0.0005), illustrating the danger of choosing terms directly from the SGL.

One possible approach that avoids this problem is to select a wordlist prior to generation of the SGL. This has the obvious limitation that it cannot be implemented for exploratory microarray experiments, only for specific hypothesis testing. Another approach is to generate the word list in a blinded fashion; for example, a researcher who did not generate the SGL could select search terms from the full dataset. We have also made a tool available, ALACK (automated LACK), which selects single search terms which are over-represented in the SGL in an automated, unbiased fashion (although multiple search terms are not supported in ALACK). While the benefits of LACK far outweigh the potential abuses, it is clear that care must be taken to avoid over-interpretation of significance.

Analysis of the significance of trends in expression data is critical for the generation of further hypotheses, as variation in the arrays and in annotations can confound visual assessment of significance. We have described a method for assessing the statistical significance of lexical trends in microarray data. Our approach is similar to, but distinct from, other lexical analysis methods [3, 8–11], in that our method does not incorporate external information. Rather, LACK is designed to analyze the SGL generated from another analysis within the context of the microarray from which the data was generated. We expect that LACK can serve as a useful adjunct to other microarray analysis methods, including other global lexical trend identification methods.

Methods

LACK Programming

LACK was written and tested using ActiveState Perl Build 631 on an Athlon 1.4 GHz system running Windows 2000 Pro. The graphical user interface uses Perl/Tk. The source has also been successfully tested on RedHat Linux 7.3.

Microarray Experiments

Our Salmonella enterica serovar Typhimurium microarray is described elsewhere [13]. Typhimurium SL1344 was grown in unagitated cultures of 100 ml M9 minimal medium in 125 ml Erlenmeyer flasks to an OD600 of 0.2. The culture was divided in half and transferred to 50 ml Erlenmeyer flasks. 2,2'-dipyridyl was added to 500 μM to one of the half cultures. Aliquots (10 ml) were removed at 10 min, 30 min, and 60 min post-addition and directly added to 1/10 volume of 95% ethanol / 5% phenol stop-solution. RNA was prepared by a modified Qiagen RNeasy prep protocol http://falkow.stanford.edu and hybridized using standard reverse transcription and cDNA-labeling procedures http://www.microarrays.org.