Many yeast genes are conditionally coregulated. (a) A Venn diagram representing hypothetical genes that are coregulated by transcription factor A (TF A) in response to condition a, transcription factor B (TF B) in response to condition b, or transcription factor C (TF C) in response to condition c. The regions of overlap in the diagram represent genes that are conditionally coregulated with each respective group of genes (for example, gene 4). (b) Hypothetical gene-expression patterns for four representative genes in groups from (a) show that the expression pattern for gene 4 has similarities to the expression patterns of each of the other genes. For this and other diagrams, gene-expression data are represented in a colorized, tabular format in which each row indicates the relative transcript abundance for a given gene, and each column represents the relative transcript abundance for many genes as measured in one experiment. A red square indicates that a gene was induced in response to the condition listed, a green square indicates that a gene was repressed under those conditions, a black square indicates that there was no detectable change in expression, and a gray square represents missing data. (c) The gene-expression patterns of around 40 of the 70 known Yap1p targets are shown, as the genes appear in the complete, hierarchically clustered dataset. Because these genes were coordinately induced in response to only subsets of the conditions shown here (labeled in red), the entire set of Yap1p targets was assigned to multiple hierarchical clusters, the largest of which are shown here. The remaining Yap1p targets were assigned to other hierarchical clusters and are not shown in this display. The colored triangles above the figure represent the microarray time courses that measured the changes in transcript abundance in response to zinc or phosphate limitation (Zn Pho), treatment with methylmethane sulfonate (MMS), ionizing radiation (IR), heat shock (HS), hydrogen peroxide (H₂O₂), menadione (MD), dithiothreitol (DTT), diamide (DI), sorbitol (SORB), amino-acid starvation (AA starv), nitrogen starvation (N starv), and progression into stationary phase (STAT). Steady-state gene expression was also measured for cells growing on alternative carbon sources (C sources), indicated by the purple rectangle. See text for references.

Comparison of k-means and fuzzy k-means clustering. Genes are represented as points in space, where genes that are similarly expressed are close together. (a) An overview of standard k-means clustering. (1)The process is initiated by randomly partitioning the genes (small circles) into three groups, indicated by the three colors. (2) The average expression profile of each group of genes is calculated as the centroid (large circles), and the genes are reassigned to the centroid to which they are closest. (4-6) Steps 2 and 3 are iterated until the centroids are stable, at which point the genes are assigned to the cluster to which they are most similar. (b) An overview of fuzzy k-means clustering. (1) The process is initiated by seeding each centroid with an eigen vector identified by PCA, as shown here for one centroid (large circle). (2) For a given centroid, the membership of each gene is calculated from the distance (or similarity) between each gene-expression pattern and the centroid. (3) A new centroid is calculated as the weighted average of all of the gene-expression patterns in the dataset, where each gene's weight is proportionate to its membership in the cluster. Genes that are closer to the centroid will contribute more to the cluster mean; therefore the centroid position migrates toward those genes. (4-6) The process is iterated until convergence, and the membership of each gene in each cluster is calculated (as shown here for one cluster).

Overview of the FuzzyK method. Genes are represented as points in space, where genes that are similarly expressed are close together. (a) In the first fuzzy-clustering cycle, k/3 centroids are defined as the most informative k/3 eigen vectors identified by PCA of the input dataset (large colored circles). (b) The centroids are refined by iteratively calculating the gene-cluster memberships and updating the centroid positions until convergence (see Figure 2b). (c,d) Genes that are correlated >0.7 to the identified centroids are removed from the dataset, gene and array weights are recalculated, and the entire fuzzy k-means clustering process is repeated on the data subset for an additional k/3 clusters (see Materials and methods for details). (e,f) Steps c and d are repeated for a third round of fuzzy clustering. (g) The output of the algorithm is a list of unique centroids and a table of gene-cluster memberships.

Fuzzy clustering of yeast genomic expression data. (a) Each row in this diagram represents one of the 91 centroids identified by fuzzy k-means clustering. The data representation is the same as described in Figure 1. (b) Genes were assigned to each of the centroids shown in (a) using a membership cutoff of 0.08, as described in the text. Each cluster of selected genes is separated by a horizontal gray line. Examples of functionally related clusters of genes are indicated by numbers to the right of (b): cluster 2, amino-acid biosynthesis genes; cluster 7, genes induced as part of the environmental stress response; cluster 14, mitochondrial protein synthesis genes; cluster 39, genes involved in nitrogen utilization; cluster 45, oxidative phosphorylation and respiration components; cluster 53, specific amino-acid transporters; cluster 67, glycolysis genes; cluster 68, proteasome components; cluster 72, secretion, protein synthesis, and membrane synthesis genes; cluster 73, genes repressed as part of the environmental stress response; cluster 80, aminoacid biosynthesis genes; cluster 82, G2/M cyclins; cluster 86, histone genes. The complete clustering results can be viewed at [14].

Gene-cluster assignments based on sliding membership cutoffs. Genes that have membership in clusters 61, 2, 58, and 11 greater than the empirically derived membership cutoffs of 0.1 (left), 0.06 (middle), or 0.035 (right) are shown. The data representation is the same as that described in Figure 1. The genes selected in each cluster were hierarchically clustered for display in this figure.

Fuzzy clusters are enriched for genes that contain known transcription factor promoter elements. The enrichment of each cluster for genes that contain known transcription factor binding sites in their promoters was measured on the basis of the hypergeometric distribution, as described in Materials and methods. (a) Gene-expression data (as described in Figure 1) for genes that were assigned to cluster 2 (amino-acid biosynthesis genes), cluster 45 (respiration genes), cluster 73 (genes repressed as part of the environmental stress response (ESR)), cluster 7 (genes induced as part of the ESR), cluster 4 (oxidative stress defense genes), and cluster 8 (genes conditionally regulated by Yap1p or Msn2/Msn4p). The genes were assigned to each cluster with a membership cutoff of 0.08, with the exception of cluster 2 for which a cutoff of 0.06 was used. The hypergeometric distribution was used to measure the statistical enrichment of promoters containing the binding sites of Cbf1p (TGACGTG), the ESR motif GATGAG, the binding site of Hap2/3/4p (CCAAT), Met31/32p (AAACTGTG), Msn2/Msn4p (CCCCT), a C-rich element identified in cluster 7 (CCCCCV where V is any nucleotide but T), Rap1p (ACACCCAYACAY where Y is C or T), the ESR motif AAAAWTTTT (where W is A or T), and Yap1p (TTAGTMA where M is C or A). (b) For each gene displayed in (a), the copy number of the denoted transcription factor binding sites in the gene's promoter is indicated by a colored box. The copy number is indicated with a blue box only if the cluster to which the gene belonged was statistically enriched (P <2 × 10^-4) for the indicated binding site, whereas the copy number is indicated with a dark-gray box if the cluster to which the gene belonged was not statistically enriched for the site. The complete results are available at [14].

Motifs conserved in the promoters of the cell-wall genes. Two motifs were identified in the promoters of the cell-wall genes selected in cluster 61, using MEME [56]. The position weight matrices are represented by colored boxes, where each box indicates the frequency of the denoted nucleotide at that position in the matrix, according to the color key shown. The position weight matrices and consensus sites are shown for (a) the SBF-like sequence and the known SBF consensus site, and (b) the novel sequence identified in these promoters.

Differential hierarchical clustering of the conditions based on different fuzzy gene clusters. (a) The dendrogram generated by hierarchically clustering the experimental conditions based on all of the genes in the dataset is shown. (b-e) Portions of the dendrograms generated by hierarchically clustering the experiments based on (b) protein-folding chaperones and other genes assigned to cluster 11 (top 10 genes), (c) oxidative stress genes assigned to cluster 4 (top 24 genes), (d) UPR genes assigned to cluster 58 (top 33 genes), and (e) genes involved in respiration and carbon metabolism assigned to cluster 36 (top 96 genes). (f) A summary of the clustering results (discussed in detail in the text), where each arrow indicates the induced expression of the respective gene set in response to the conditions indicated. The known regulators of genes represented in each cluster are shown. The complete results are available at [14].

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 and (b) different environmental stresses. Each circle in the Venn diagram represents a cluster of genes that is enriched for the known binding site of the indicated transcription factor or is known to be regulated by the indicated factor in response to the denoted conditions.