Bioinformatics Advance Access originally published online on September 16, 2004
Bioinformatics 2005 21(4):509-516; doi:10.1093/bioinformatics/bti026
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Bioinformatics vol. 21 issue 4 © Oxford University Press 2005; all rights reserved.
Identifying time-lagged gene clusters using gene expression data
Department of Computer Science, National University of Singapore 3 Science Drive 2, Singapore 117543, Singapore
*To whom correspondence should be addressed.
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Abstract |
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 TOP Abstract INTRODUCTIONRELATED WORKAN ALGORITHM TO IDENTIFY...EXPERIMENTAL RESULTSCONCLUSIONREFERENCES |
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Motivation: Analysis of gene expression data can provide insights into the time-lagged co-regulation of genes/gene clusters. However, existing methods such as the Event Method and the Edge Detection Method are inefficient as they compare only two genes at a time. More importantly, they neglect some important information due to their scoring criterian. In this paper, we propose an efficient algorithm to identify time-lagged co-regulated gene clusters. The algorithm facilitates localized comparison and processes several genes simultaneously to generate detailed and complete time-lagged information for genes/gene clusters.
Results: We experimented with the time-series Yeast gene dataset and compared our algorithm with the Event Method. Our results show that our algorithm is not only efficient, but also delivers more reliable and detailed information on time-lagged co-regulation between genes/gene clusters.
Availability: The software is available upon request.
Contact: jiliping{at}comp.nus.edu.sg
Supplementary information: Supplementary tables and figures for this paper can be found at http://www.comp.nus.edu.sg/~jiliping/p2.htm.
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INTRODUCTION |
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TOPAbstractINTRODUCTIONRELATED WORKAN ALGORITHM TO IDENTIFY...EXPERIMENTAL RESULTSCONCLUSIONREFERENCES |
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DNA microarray technologies, with which the expression levels of thousands of genes can be measured simultaneously during biological processes, have facilitated the study of genetic regulatory networks. In particular, analysis of gene expression data can identify regulatory relationships between genes. While clustering techniques have been applied to identify co-expressed genes, and association rule mining has been used to detect gene regulation across numerous pathways, these methods usually consider gene expression levels under the same conditions or at the same time points, and they do not take any time-lagged relationships into consideration. In fact, from time-series gene expression data it is apparent that most genes do not regulate each other simultaneously but after a certain time lag. That is, the products that a gene produces during the expression process may affect other genes' expression later. Such regulation can be divided into two types: activation and inhibition. In the activation process, an increase in certain genes' expression levels will increase some other genes' expression levels after a time lag. During the inhibition process, an increase in some genes' expression levels will result in a decrease in other genes' expression levels.
Existing work on time-lagged analysis largely analyzes two genes at a time over all conditions and ranks the gene pairs based on the score generated using a certain criterion, such as the Cross-Correlation Function (Kato et al., 2001) and the Needleman–Wunsch alignment algorithm (Kwon et al., 2003). The gene pairs with higher scores are regarded as the interesting and promising pairs. Such an approach is clearly computationally inefficient: given n genes, we would need 
comparisons. More importantly, these techniques may overlook some interesting time-lagged patterns. Since the score is generated based on the analysis of the whole sequence, it is not sensitive to cases in which a small but interesting part of the genes is co-regulated while there is no distinct relationship between the remaining parts. As a result, some interesting gene pairs may not always be ranked higher than uninteresting ones. A higher scoring threshold will miss some interesting patterns while a lower one will generate a tremendous number of redundant pairs. In addition, there is a lack of detailed information on co-regulated gene pairs, such as the exact lag time, the starting and ending time points and the number of co-regulated patterns between two genes. Moreover, standard techniques mostly reveal co-regulation between genes rather than relationships between gene clusters.
Our work aims to address these limitations and to identify localized time-lagged co-regulations between genes and/or gene clusters efficiently. Our approach is to extract clusters, which we refer to as q-clusters, of (time-lagged) co-regulated genes over a subset of q consecutive conditions. Each such cluster essentially contains information on genes that have a similar expression pattern over q consecutive conditions (the q conditions may be different for different genes). This information includes the (geneID, st) pairs that indicate that the gene with identifier geneID has the corresponding pattern of the q-cluster starting from time point st. In our work, the pattern of a q-cluster is represented as a string of length (q – 1) to describe the changing tendency, which reflects how the expression value changes from condition i to condition i + 1 for the q conditions. We have discretized the changing tendency into three distinct classes. Thus, there are in total 3 q–1 q-clusters, and each q-cluster can be easily mapped to a unique value, or q-value, based on the q conditions, where 0 
q-value 3 q–1.
We can determine the following types of co-regulation from each q-cluster: (1) all genes with the same starting time point may be co-regulated; (2) all genes with starting time point st 1 may activate those genes with starting time point st 2, where st 1 < st 2. Moreover, we can determine the following co-regulations/inhibitions across q-clusters: (1) all genes with starting point st 1 from q-cluster Q 1 may inhibit the genes with starting point st 2 from q-cluster Q 2 if the expression pattern of Q 1 is complementary to that of Q 2 (i.e. if the changing tendency of the q conditions in Q 1 is opposite to that for Q 2); (2) all genes with starting point st 1 from q-cluster Q 1 may co-regulate the genes with starting point st 2 from q-cluster Q 2 if the expression pattern of the q conditions of Q 1 is {similar to} (but not exactly the same as) that of Q 2. Moreover, since we keep track of the starting time points, we can easily generate detailed information on the interacting portions, for example, how far one gene lags behind another.
We have implemented the proposed algorithm and experimented with the time series Yeast gene dataset. We also compared our scheme with the Event Method (Kwon et al., 2003). Our results show that our algorithm is more efficient and can deliver more detailed, complete and concise information.
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RELATED WORK |
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TOPAbstractINTRODUCTIONRELATED WORKAN ALGORITHM TO IDENTIFY...EXPERIMENTAL RESULTSCONCLUSIONREFERENCES |
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There are a number of previous approaches for identifying time-lagged gene co-regulations. One is the Cross-Correlation Method (Kato et al., 2001). Unlike the traditional Pearson Correlation Coefficient Method, this method takes into account the time-lag issue. However, it is only useful in determining whether two variables have strong global (i.e. similarity is measured over all conditions) but not local time-lagged similarity (i.e. similarity is measured for a subset of conditions). A second method is the Edge Detection Method (Chen et al., 1999). This method sums the number of edges of two gene expression curves where the edges have the same direction within a reasonable time lag to generate a score. Edges that are further apart are assigned a lower score than those that are closer together. As a result, the gene pairs with higher scores are regarded as the pairs that show promise of an activation relationship. Although this method considers more localized similarities, its current form can only determine potential activation relationships. In these two methods, the direction of regulation of gene pairs is not considered. Besides these two methods, Bayesian Networks (Barash and Friedman, 2001) have also been applied; however, the high computational cost renders this approach impractical.
Recently, Kwon et al. (2003) proposed the Event Method to deal with some of the above-mentioned limitations. The algorithm marks the directional changes as an event [Rising (R), Constant (C) or Falling (F)] by calculating the slope of the expression value at each time interval, resulting in a string of events. Then a global sequence alignment algorithm, the Needleman–Wunsch algorithm, is employed to match the corresponding events of two genes, based on which a numerical score is generated as an indicator of the likelihood of a regulatory relationship existing between those two genes. The alignment is run in both directions to decide the regulator and the target gene. As for the inhibition relationship, the event string is first re-encoded by changing each R to an F, and vice versa, while C remains unchanged. Then the alignment process is performed as above. This manner of processing can be characterized as ‘two genes, one relationship per alignment’, which means that each alignment can decide only one relationship (activation/inhibition) between two genes. Although this method delivers more information and is relatively efficient, its scoring system to identify promising time-lagged gene pairs is still questionable, for the following reasons: first, it cannot tell whether a relatively low score is due to a ‘mismatch’ or a ‘match with a large time lag’; second, the score does not determine whether two sequences have frequent ‘short matches’ or infrequent ‘long sequential matches’; third, it is not sensitive to genes whose event sequences are similar for only a small part of the time period but different from each other as a whole. Hence, some interesting time-lagged patterns are not always scored highly and may be missed out. In terms of its result, the Event Method generates only gene pairs, without detailed information such as the exact lag time and the starting and ending time of the co-regulation. Moreover, it tests all combinations of two genes, which is in some ways not very efficient, and finally, it provides only results between two genes, not co-regulated relationships between gene clusters.
Yet another approach is the Dominant Spectral Component Method (Yeung et al., 2004). Based on the autoregressive modeling technique, this method decomposes time-series expression sequences into spectral components, and the correlation between two sequences is formulated as a sum of scaled sub-correlations. Although this method looks into the temporal aspect of time-series microarray data, it measures only gene-to-gene relationships rather than relationships among multiple gene clusters.
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AN ALGORITHM TO IDENTIFY TIME-LAGGED GENE CLUSTERS |
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TOPAbstractINTRODUCTIONRELATED WORKAN ALGORITHM TO IDENTIFY...EXPERIMENTAL RESULTSCONCLUSIONREFERENCES |
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To overcome the limitations of existing methods, we propose to identify localized time-lagged gene clusters. We have developed an algorithm that can quickly determine a set of genes that co-regulate either simultaneously or after some time lag, as well as genes that may inhibit others. Our basic idea is to group genes with similar patterns over a subset of consecutive time points (conditions) together. Because these genes share similar (or opposite) patterns (over a subset of conditions), those with an earlier start time may have activated (inhibited) those with a later start time. The scheme comprises three phases. In the first phase, the original gene expression matrix is transformed into a ‘slope’ matrix to reflect the genes' changing tendency over time. In phase two, we generate q-clusters that contain information about genes with a similar pattern over (any) q consecutive conditions. Finally, in phase three, the time-lagged information is extracted from each q-cluster and between q-clusters.
Phase 1: matrix transformation
Let T = {T 1, T 2, ..., T m } be the set of time points, and G = {G 1, G 2, G 3, ..., G n } be the set of genes. The time-series gene expression data can be represented as an O = n x m matrix, where an entry O i,j in this matrix corresponds to the expression value of gene G i at time point T j . In the first phase, matrix O is transformed into an O' = n x (m – 1) matrix to reflect the changing tendency of each gene expression value over time. Each entry O' i,j in matrix O' reflects the directional change from the expression value O i,j to the expression value O i,j+1. Essentially, there are three possible changing tendencies: an expression value may increase from time point T j to T j+1; it may decrease; or it may remain unchanged. As we shall see shortly, we discretize these three changing tendencies into three classes, and denote them by 1, –1 and 0, respectively.
The matrix O' is obtained in two steps. In the first step, O is transformed into an O'' = n x (m – 1) matrix such that
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O'' essentially indicates how much a gene's expression value changes from one time point to the next (a positive value implies an increase, a negative value a decrease, and 0 means no change). Once matrix O' is generated, in step 2 we can obtain O' by binning the values of the transformed matrix. Binning the values is a good way to handle noise that may be introduced by experimental errors. Moreover, it allows us to focus on the more general increasing or decreasing tendency of gene values. We set a Normalization Threshold t(t > 0) to bin the new matrix as follows:
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As an example, let us take two genes from the Yeast dataset: YGL207W (G2163) and YDR224C (G1223). The original matrix O of their expression values at the first 10 time points is shown in Table 1, and the resultant binned slope matrix O' with a Normalization Threshold t = 1.0 is shown in Table 2.
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Phase 2: generation of q-clusters
We note that each sequence of values –1, 0 and 1 in matrix O' provides us with an indication of the changing pattern of a gene expression over time. Thus, two genes that share the same subsequence may be co-regulated. In this phase, we generate a set of q-clusters. Each q-cluster has the following property: all genes in the cluster have the same expression pattern over some q consecutive time points (conditions). This turns out to be nothing other than finding genes that share similar subsequences of length q – 1. We note that q is a user-defined parameter. Since the entries in O' have only three possible distinct values, there are at most 3 q–1 q-clusters. Each q-cluster has a unique identifier, called its q-clusterID, which is generated as follows. Let P = {p[1], p[2], ..., p[q–1]} be a pattern. Note that p[i] = –1, 0 or 1
i 
[1,q – 1]. Let
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Then, the q-clusterID of P is determined as follows:
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Clearly, 0 q-clusterID 3 q–1. We note that a small value of q will result in a small number of q-clusters but that there are also likely to be more genes with the same (sub)patterns. On the other hand, a large value for q implies a larger number of q-clusters, with fewer genes with the same patterns.
We are now ready to describe how q-clusters are generated. For each row (gene) of matrix O', we apply a sliding window of length (q – 1). As each (q – 1) substring is examined, its q-clusterID is determined and the (geneID, st) pairs are inserted into the corresponding q-cluster. Here, geneID is the identifier of the gene and st is the position of the starting time point of the (q – 1) substring. For example, suppose we set q = 7. Consider gene YGL207W (G2163) again, which has the sequence ‘01100(–1)00(–1)’. By applying a sliding window of length 6(= 7 – 1), we have the subsequence ‘01100(–1)’ in the first window. Now, the q-clusterID of ‘01100(–1) = 110’. Thus, we have (2163, 1) inserted into q-cluster 110. Similarly, examining the second pattern, ‘1100(–1) 0’, results in (2163, 2) being inserted into q-cluster 326. Table 3 shows the q-clusters generated by the two genes YGL207W (G2163) and YDR224C (G1223).
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From the set of q-clusters, we can extract three aspects of gene co-regulation. First, each q-cluster corresponds to an interesting pattern under which genes with similar expression pattern are grouped together. In fact, we can determine two relationships here. Those genes with the same starting time point may be co-regulated simultaneously. Such a set of genes and conditions actually forms a bicluster (Cheng and Church, 2000); examples will be given when we look at the next phase. For those genes with different pattern starting positions, those with smaller starting positions may be activators of those with larger starting positions. For example, q-cluster 110 in Table 3 gathers together Gene2163 and Gene1223, whose pattern starting positions are different by 1. This implies that Gene2163 may have activated Gene1223 after 1 time point. Second, to handle noise, it may be necessary to look for patterns with approximate match (rather than exact match as in the above case). For example, if ‘100(–1)00’ (third window of Gene2163) is considered similar to ‘100(–1)0(–1)’ (fourth window of Gene1223), we can determine relationships between genes in q-clusters 261 and 263. Third, we can also determine inhibition relationships between genes by comparing q-clusters with opposite patterns (where ‘1’ is the opposite of ‘–1’). For example, ‘100(–1)0(–1)’ is the opposite of ‘(–1)00101’.
Besides capturing all relationships between genes/gene clusters, our approach also allows several genes to be compared simultaneously, unlike in the existing ‘two genes, one relationship’ approaches. Moreover, our q-clusters can deliver more detailed but concise information. This explains why our scheme works more efficiently and effectively than previous methods.
Phase 3: generate time-lagged co-regulated relationships between genes/genes clusters
At the end of phase 2, we have a set of q-clusters. In phase 3, four main processing tasks are carried out on the q-clusters to extract (time-lagged) co-regulated relationships between genes/genes clusters. For efficiency, each q-cluster is first sorted on starting position, so that all (GeneID,st) pairs with the same starting position st are grouped together.
The first task is the mining of biclusters. According to the characteristics of a q-cluster, all genes with the same starting position share the same pattern under the same q conditions. Hence, the subset of genes and conditions essentially forms a bicluster. Like Cheng and Church (2000), we can introduce a mean-squared residue metric to determine the quality of a bicluster, so that those with mean-squared residue smaller than a user-specified value are retained as a high-quality bicluster, while the rest can be discarded. Let us take q-cluster 551, for example. As shown in Table 4, Gene906, Gene1518, Gene1811, Gene2704, Gene5535 and Gene5758, with the same pattern starting position, 17, form a bicluster; as shown in Figure 1, these genes have similar changing tendency from T 17 to T 23. Similarly, we can find a bicluster for the set of genes that share time point 15 as starting position (Fig. 2). To draw additional relationships among biclusters, we can carry out the second task (to identify the promising activation co-regulations) and the third task (to identify the inhibition regulations).
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Task two deals with gene relationships within a q-cluster by comparing the starting positions of biclusters obtained from the q-cluster. Since biclusters (within a q-cluster) with different starting positions share the same pattern, there is a promising time-lagged activation co-regulation relationship between these biclusters. In particular, given two biclusters, the one with the smaller starting position is a potential activator of the bicluster with the larger starting position. The time lag between the two activations is given by the difference in the starting positions. We note that there are two possible relationships that need further biological study: (1) it may be the case that only a certain gene in one bicluster individually activates another gene in the other bicluster; (2) it may be the case that all or most of the genes in a bicluster collectively activate some (or all) genes in the other bicluster. As an example, within q-cluster 551 in Table 4, Gene580, Gene836, Gene1681 and Gene4516, with starting position 15, form a bicluster (Fig. 2) that is a promising activator (either an individual gene or a combination of the genes) of the bicluster (Fig. 1) with starting position 17, at a time lag of 2.
Task three attempts to find inhibition regulations. This task is quite straightforward. Essentially, we need first to find a pair of q-clusters with opposite patterns. Such a pair of q-clusters is a promising inhibition pair. Two patterns are opposite to one another if corresponding elements between the two patterns are either both ‘0’ or else ‘1’ and ‘–1’, respectively. Genes/biclusters of one q-cluster with a smaller start position may inhibit genes/biclusters of the other q-cluster with a larger start position. For example, the pattern ‘(–1)0(–1)10(–1)’ (q-cluster 551) is the opposite of ‘101(–1)01’ (q-cluster 289). Thus, the pair of q-clusters (551, 289) is a promising inhibition pair. Genes/biclusters within q-cluster 289 are promising time-lagged inhibition regulator of those within q-cluster 551. Gene3962, Gene4210, Gene4378, Gene5415 and Gene6118, with starting position 14 in Table 5, form a bicluster (Fig. 3) which is a promising inhibitor of the bicluster (Gene906, Gene1518, Gene1811, Gene2704, Gene5535, Gene5758) with starting position 17 (Table 4; Figure 1) at a time lag of 3.
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Finally, task four handles approximate matching. Similar/opposite patterns with only one or two exceptional elements may still be regarded as interesting by some users. Our scheme is able to deal with this approximation as follows. For each q-cluster, we allow changes to be made to certain positions of the pattern. The corresponding q-cluster with the changed pattern is a potential candidate for co-regulation. For inhibition regulation, we need only to find the q-cluster that has an opposite pattern from the changed pattern.
Before leaving this section, we would like to make one final observation. Since ‘0’ indicates no obvious increasing or decreasing changing tendency, patterns with too many ‘0's are not interesting enough to be investigated. As such, in our algorithm, we have introduced another user-specified parameter, Maximum Zero, to control the maximum number of ‘0's allowed in interesting patterns. This implies that the number of ‘useful’ q-clusters is less than 3 q–1.
Compared with previous methods, our algorithm is more efficient at identifying both activation and inhibition relationships between co-regulated genes. And it also simplifies the identification of approximating patterns. As for the results, our algorithm provides a clear time-lagged relationship structure between genes and gene biclusters. And the results contain all user-needed information in a concise format. From the results, users can know exactly the starting point and ending point of the co-regulation period. And they can even know how many times two genes co-regulate with each other by counting how many q-clusters contain both of them within the user-permitted time lag (as illustrated in the next section). Depending on the information delivered by our results, deeper exploration can be made focusing on interesting genes/biclusters according to users' needs.
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EXPERIMENTAL RESULTS |
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TOPAbstractINTRODUCTIONRELATED WORKAN ALGORITHM TO IDENTIFY...EXPERIMENTAL RESULTSCONCLUSIONREFERENCES |
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We implemented our algorithm in C and studied the time-lagged gene clusters obtained. As a benchmark, we compare our results with the results generated by the Event Method (Kwon et al., 2003). All the calculations on a Pentium 4 PC with 256 MB RAM.
Experimental setup
For our experiments, we employ Spellman's dataset (downloaded from http://genome-www.stanford.edu/cellcycle/data/rawdata/). The dataset contains all the data for the alpha factor, cdc15, and elutriation time courses. Further, it includes the data for the Clb2 and Cln3 induction experiments, and the analysis of the data by Cho et al. (1998). We used only the alpha-factor and CDC28 datasets for our experiments, as did the Event Method. The dataset we used contains 6178 genes at 35 time points, forming a (6178 x 35) matrix (http://www.comp.nus.edu.sg/jiliping/p2/dataset.txt).
For the proposed algorithm, the matrix is transformed into a (6178 x 34) slope matrix and then binned with Normalization Threshold = 1.0. We generated q-clusters for q = 7. We also set the maximum number of ‘0's allowed in the pattern, Maximum Zero, to 3.
For the Event Method (Kwon et al. 2003) we first convert ‘–1, 0, 1’ to ‘F, C, R’ (representing ‘Falling, Constant, Rising’ status) and then apply the Needleman–Wunsch algorithm (downloaded from http://neobio.sourceforge.net) to align all gene pairs. The Needleman–Wunsch alignment algorithm uses our scoring system to sort the gene pairs. Gene pairs with relatively high scores are regarded as promising pairs. We set up the scoring matrix based on the Event Method. As shown in Table 6, the matrix is a form of similarity matrix used to evaluate how well two gene expression profiles match. Insertion penalties are specified by the last row while deletion penalties are located in the last column. The latter are equivalent to the time-delay penalty. The time-delay penalty is taken into account because if there is too long a gap between two genes' regulation, it is unlikely that they have a regulatory relationship. According to the original paper, the top 10 000 ranking pairs form the interesting results. In our study, we take the top 12 744 ranking pairs since the last 4529 pairs have the same score.
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Comparative study
We ran our algorithm and the Event Model on the data set. From the results, we made several interesting observations. First, our method can identify the relationships between gene pairs detected by the Event Method. Among the top 12 744 ranking pairs generated by the Event Method, 98.9% are detected within the same q-cluster in our results. In addition, our approach can provide more detailed information. Consider, for example, the co-regulated gene pairs YGL207W (Gene 2163) and YDR224C (Gene 1223). The Event Method gives only the score of the alignment, as shown in Table 7. Our method not only identifies their relationship, but also shows that there are two basic regulated periods between YGL207W and YDR224C. As shown in Table 8, the first time lag is 1 with the pattern ‘01100(–1)’ while the second time lag is 7 with the pattern ‘0(–1)0(–1)01’. The whole sequences of the two genes are presented in Figure 4, which clearly shows the time-lagged relationship between the patterns of the two sequences.
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Second, the Event Method may not always provide the correct ranking order among gene pairs. In other words, it is possible for a truly time-lagged co-regulated gene pair to be ranked lower than a gene pair that has no co-regulation relationship. Given the large number of results (10 000), it is likely that some of the truly co-regulated pairs are missed out. For example, genes YHR200W and YJL115W are known to be co-regulated gene pairs while gene YHR200W does not have any co-regulation with gene YGR282C. However, the Event Method ranks the latter pair higher than the former one, as shown in Table 9. Moreover, there is actually one more similar pattern (with one element approximation) in the former pair than the latter one, as shown in Table 10. Our method can detect this information with ease.
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Third, our results are complete, containing more information in a more concise format in 3 q–1 q-clusters. When the number of genes increases, the number of gene pairs will increase significantly, which greatly enlarges the complete result of the Event Method. As a result, the Event Method has to ignore a large number of lowly ranked gene pairs. This inevitably misses some interesting pairs since the Event Method cannot always rank them high. In our method, users can also decrease the number of q-clusters by ignoring patterns with relatively more ‘0's. Moreover, our results are ready for detailed exploration of co-regulation relationships between genes according to users' special needs.
Time-lagged co-regulated genes/gene clusters
We shall examine the results produced by our algorithm for time-lag co-regulated genes and gene clusters. In total, there are 640 non-empty q-clusters (patterns). Table 11 shows one representative q-cluster, with pattern ‘0(–1)0(–1)01’ and q-clustersID 181. The first number in each line indicates the starting position of the pattern in the genes, while the following numbers are the genes' identifiers. For example, the penultimate line means that Gene 951, Gene 2524, Gene 6059 and Gene 6086 have the changing pattern ‘0(–1)0(–1)01’ starting from the 27th time point. Time-lagged relationships between not only genes but also gene clusters are shown clearly in our results. Although these relationships may not all be true, existing time-lagged co-regulations, they help researchers to reduce the search space and focus their efforts on the promising relationships. Our results do deliver known co-regulated genes already established by biologists. For example, YGL207W and YDR224C are genes with activation co-regulation, and YHR200W and YGR282C are also such a gene pair (Cho et al., 1998). Moreover, our method is not limited to the ‘A 
B’ relationship. It can also infer the ‘A B C D’ regulation pattern. As shown in Table 11, the earlier Cluster8 (548 715 1061 1087 1576 5375) may activate the later Cluster10 (384 567 928 1213 1329 2541 4157 4386 4442) after two time lags, and Cluster10 may go on to activate an even later Cluster16 (2658 3452 3470 3489 3809 5944) after six time lags. We are unable to verify the validity of such gene regulations as this information is not available from publicly available databases. However, these co-regulated patterns may help the future discovery of such regulatory pathways.
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CONCLUSION |
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TOPAbstractINTRODUCTIONRELATED WORKAN ALGORITHM TO IDENTIFY...EXPERIMENTAL RESULTSCONCLUSIONREFERENCES |
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In this paper, we revisit the problem of analyzing gene expression data for time-lagged gene co-regulation relationships. We have presented a localized algorithm to identify the time-lagged gene clusters based on the concept of q-clusters. Genes with a similar pattern over a subset of q consecutive time points (conditions) are grouped into the same q-cluster. In this way, we can easily determine the co-regulations of genes within each q-cluster and between q-clusters. We have experimented on a real time-series gene expression dataset and compared our method and results with the Event Method. Our study shows that our approach is efficient at detecting both activation and inhibition time-lagged co-regulations, and our results can draw relationships between both genes and gene clusters and provide more detailed information. We believe that our approach delivers valuable information and provides an excellent tool that facilitates more detailed exploration for gene network research.
Received on January 24, 2004; revised on July 29, 2004; accepted on September 6, 2004
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Cho, R.J., Campbell, M.J., Winzeler, E.A., Steinmetz, L., Conway, A., Wodicka, L., Wolfsberg, T.G., Gabrielian, A.E., Landsman, D., Lockhart, D.J., Davis, R.W. (1998) A genome-wide transcriptional analysis of the mitotic cell cycle. Mol. Cell, 2, 65–73[CrossRef][Web of Science][Medline].
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