To respond to diverse and frequently changing environmental conditions, yeast cells must precisely mediate the synthesis and function of the proteins in the cell. This is controlled in part by the overall genomic expression program that results from the combined action of different regulatory factors, each of which responds to specific extra- and intra-cellular signals. Many of these regulators act under specific conditions, and together they govern the expression of overlapping sets of genes. Individual genes, in turn, are regulated by multiple, condition-specific systems that result in each gene being coexpressed with different groups of genes under different situations.
Although examples of this type of regulation have been observed on an individual gene basis, our results suggest that the condition-specific regulation of overlapping sets of yeast genes is a prevalent theme in the regulation of yeast gene expression. A large fraction of yeast genes is expressed in patterns that are similar to different groups of genes in response to different subsets of the experiments (Table ). Furthermore, a substantial number of these genes contain multiple transcription factor binding sites in their promoters (Figure , and see [14
]), consistent with the idea that they are conditionally regulated by multiple, independent regulatory systems. The condition-specific regulation of gene expression has also been implicated in higher organisms [63
] and probably has a significant role in regulating genomic expression. This is in contrast to the regulatory logic of prokaryotes, in which the expression of defined sets of genes in operons is a predominant feature of regulation. Thus, the conditional regulation of overlapping groups of genes may represent a regulatory theme that is particularly important in eukaryotes.
The prevalence of conditional gene coexpression poses a challenge for the analysis of gene-expression data, because many genes will have expression patterns that are similar to multiple, distinct gene groups. Fuzzy k-means clustering is well suited to identifying conditionally coexpressed genes for a number of reasons. First and foremost, the method can present overlapping clusters, revealing distinct features of each gene's function and regulation. The resulting implications can be used to assign refined hypothetical functions to uncharacterized gene products on the basis of the known functions encoded by the genes in each cluster. In addition, this information can suggest additional cellular roles of well studied proteins (see [14
]). The overlapping clusters identified by fuzzy k-means clustering also present more comprehensive groups of conditionally coregulated genes. This is especially important for the successful identification of regulatory motifs common to the promoters of similarly expressed genes, because motif-finding algorithms are often hindered by small sample sets. More than two-thirds of the gene clusters we identified are not enriched for known regulatory elements, highlighting the potential for discovering novel sequences involved in gene-expression regulation. We expect that fuzzy k-means clustering will advance that discovery, as illustrated by our ability to identify new sequences conserved in the promoters of clustered genes.
Another benefit of the fuzzy k-means algorithm is that it identifies continuous clusters of genes. This allows each cluster to be expanded or collapsed to view genes of varying similarity in expression. While the genes of highest membership in a given cluster are often tightly correlated in terms of biochemical function and regulation, expanding the cluster can identify genes that are similarly expressed in only subsets of the experimental conditions. The resulting gene relationships can suggest details about the cellular roles served by the encoded gene products and the regulatory systems that govern the genes' expression in response to the relevant conditions. Thus, the results of fuzzy k-means clustering are naturally suited for biologists to use in an intuitive and physiologically meaningful way.
The unique features of fuzzy k-means clustering have allowed us to uncover complex similarities in yeast gene-expression patterns, identify putative transcription factor binding sites present in the genes' promoters, and elucidate the environmental conditions that trigger changes in gene expression. Integrating these details can indicate the cellular signals and regulatory systems that govern the expression of specific sets of genes in yeast (Figure ). For example, the fuzzy clustering of genes involved in methionine biosynthesis with other amino-acid biosynthetic genes and with genes involved in nitrogen utilization lead to the identification of multiple transcription factor binding sites in the genes' promoters. Together, these details reflect the alternative regulatory systems that are known to govern the expression of the methionine biosynthesis genes. Although they are induced by one regulatory system (Cbf1p-Met31/32p) according to the demand for the pathway's products, they are induced by an alternative system (Gcn4p) in response to a general signal of amino-acid starvation [34
], and they are probably also regulated by a third mechanism (GATA factors) in response to the available nitrogen source. Combining this information with similar indications for other sets of genes gives a summary of the details discussed in this study and suggests a model for the organization of the regulatory system that controls gene expression in yeast (Figure ). The overlapping nature of the sets of coregulated genes supports the ability of the cell to customize the emergent genomic expression program to the particular needs of the cell, while minimizing the number of regulators required to produce each genomic expression program.
Figure 9 Integration of gene expression, regulatory sequences, and environmental responsiveness. Schematics illustrating the hypotheses presented in this paper regarding the regulation of expression of genes that respond to (a) amino-acid and nitrogen source limitation (more ...)
The fuzzy k-means algorithm used here was chosen for its conceptual and algorithmic simplicity. There are many alternative algorithms that might accomplish the same ends. For example, Ihmels et al.
] have applied a heuristic algorithm to the analysis of yeast gene-expression data to identify overlapping sets of genes whose expression is similar to known gene-expression patterns. This method produced interesting results and identified genes that were similarly expressed to known transcription factor targets. A key difference between these algorithms is that fuzzy k-means clustering requires no a priori
information about the dataset. Thus, each method may be suitable for a different biological question, namely identifying genes whose expression is similar to known or expected gene expression patterns versus an unbiased, de novo
exploration of the gene-expression dataset.
Despite the advantages of fuzzy k-means clustering discussed above, the method also has a number of limitations. Most notably, the assignment of genes to the clusters requires a user-defined membership cutoff. While this allows complete flexibility in data exploration, selecting meaningful cutoffs is a challenge. Choice of cutoff can be guided by a number of criteria, including the coherence of the selected gene-expression patterns, the functional relationships of the characterized genes selected, or the statistical enrichment of sequences in the selected genes' promoters. We have attempted to alleviate the challenge of selecting cutoffs by providing visualization software specifically designed for the fuzzy clustering results, allowing the gene expression data to be inspected directly and dynamically.
Although the fuzzy k-means clustering method successfully identified nearly 90% of the known clusters in the dataset, it routinely failed to identify a small number of groups that were identified by hierarchical clustering. The inability of the method to find the expression patterns representing these groups seemed to be dependent on the overall properties of the dataset, rather than the absence of an appropriate eigen vector used to initiate the process, as the program was unable to identify these patterns even when the process was initiated by seeding the centroids with the unidentified patterns (data not shown). We have accounted for this limitation by allowing any number of expression patterns to be added to the final list of identified cluster centroids, thereby revealing genes that are similarly expressed to the pattern in question.
Despite these limitations, the unique advantages of fuzzy k-means clustering make the technique a valuable tool for gene-expression analysis. We believe that fuzzy k-means clustering will be a useful complement to other computational methods commonly used to analyze gene-expression data. Whereas algorithms that present discrete gene clusters provide a straightforward method of initial data exploration, the flexibility of fuzzy k-means clustering can be used to reveal more complex correlations between gene-expression patterns, promoting refined hypotheses of the role and regulation of gene-expression changes.