Bioinformatics Advance Access originally published online on November 15, 2005
Bioinformatics 2006 22(2):209-214; doi:10.1093/bioinformatics/bti780
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Elucidation of directionality for co-expressed genes: predicting intra-operon termination sites
1Academic Services and Emerging Technologies, The Pennsylvania State University University Park, PA, USA
2Department of Chemical Engineering, The Pennsylvania State University University Park, PA, USA
3Department of Physics, The Pennsylvania State University University Park, PA, USA
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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Motivation: In this paper, we present a novel framework for inferring regulatory and sequence-level information from gene co-expression networks. The key idea of our methodology is the systematic integration of network inference and network topological analysis approaches for uncovering biological insights.
Results: We determine the gene co-expression network of Bacillus subtilis using Affymetrix GeneChip® time-series data and show how the inferred network topology can be linked to sequence-level information hard-wired in the organism's genome. We propose a systematic way for determining the correlation threshold at which two genes are assessed to be co-expressed using the clustering coefficient and we expand the scope of the gene co-expression network by proposing the slope ratio metric as a means for incorporating directionality on the edges. We show through specific examples for B. subtilis that by incorporating expression level information in addition to the temporal expression patterns, we can uncover sequence-level biological insights. In particular, we are able to identify a number of cases where (1) the co-expressed genes are part of a single transcriptional unit or operon and (2) the inferred directionality arises due to the presence of intra-operon transcription termination sites.
Availability: The software will be provided on request.
Contact: ralbert{at}phys.psu.edu
Supplementary information: http://www.phys.psu.edu/~ralbert/pdf/gma_bioinf_supp.pdf
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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Gene expression information captured in microarray data for a variety of environmental and genetic perturbations, in conjunction with other sources such as protein–protein/protein–DNA interaction and operon organization data, promises to yield unprecedented insights into the organization and functioning of biological systems (Brazhnik et al., 2002; Ge et al, 2003). It has now become clear that only by simultaneously accounting for all the multiple layers of regulation that exist in biological systems can one hope to uncover the biological knowledge embedded in the experimental data. In this paper, we take a first step by proposing an integrated approach that combines network inference and analysis with a detailed biological study of the uncovered regulatory patterns. Specifically, we study the gene co-expression network of Bacillus subtilis derived from Affymetrix GeneChip® time-series data and show how the observed expression patterns can be traced back to the sequence-level organization of the various genes. We construct a gene co-expression network, where nodes correspond to genes and an undirected edge exists between two genes if the similarity of their expression profiles exceeds a threshold value. We introduce a novel systematic way for determining the similarity threshold by applying ideas from network analysis. In addition, we expand the scope of the gene co-expression network representation by proposing a way to impose directionality on the edges. We show that this enables us to uncover additional biologically relevant insights that are not obvious at the level of the gene co-expression network.
Several methods aim to cluster genes on the basis of their expression profiles for identifying groups of genes that are co-expressed/co-regulated under particular experimental conditions (Eisen et al, 1998; Wen et al, 1998; Herwig et al, 1999; Tamayo et al, 1999; Dougherty et al, 2002; Xu et al, 2002; Schmitt et al, 2004). The graph-based method that we use is closely related to the widely used hierarchical clustering approach (Eisen et al, 1998; Spellman et al, 1998). In hierarchical clustering, one starts with all genes belonging to separate clusters. Subsequently, the two genes that are closest to each other with respect to a chosen similarity measure are assigned to a single cluster. A similarity measure between gene clusters is then used to determine the most similar pair of clusters, which are then merged. This procedure is repeated until all the genes belong to a single cluster and the clustering results are displayed as a dendrogram. Specific clusters are obtained by ‘slicing’ the dendrogram at a threshold of the similarity measure. In the same spirit, in our proposed approach all genes belong to a single cluster when the similarity threshold is set to zero while they constitute individual single-gene clusters when the similarity threshold is set at the other extreme of one. A common question to be answered for both hierarchical clustering and our graph-based approach is where to set the similarity threshold. In this work, we propose an objective and systematic method of determining the most informative similarity threshold by employing ideas from network analysis. Another key advantage of our method over hierarchical clustering is that we do not need to define a similarity measure between clusters and can rely solely on the similarity measure between individual genes for obtaining the clusters.
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2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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2.1 Gene co-expression network
The starting point of our analysis is time-series expression information for 746 B. subtilis genes in a cradle-to-grave experiment (Gupta et al., 2005). B. subtilis is one of the best characterized Gram positive bacteria and it is used extensively for industrial-scale protein production. The expression data were collected during feed-batch protease production and the majority of the genes included were involved in the central metabolism of B. subtilis. A total of 20 time points were sampled every 2 h over the course of the fermentation. Since the data were obtained using Affymetrix arrays, the expression levels were time-resolved absolute transcript signals as opposed to the relative expression changes typically measured with cDNA arrays.
In this work, we use the R2 metric (or equivalently the Pearson correlation coefficient) as a measure of similarity between the expression profiles of two genes. This metric, which ranges between 0 and 1, quantifies the ‘goodness-of-fit’ of a linear relationship between two variables. Suppose that the system is described by two variables X and Y, where Y is linearly dependent on X i.e. Y = aYX + bYXX. Given observed data (Yi,Xi), the parameters aYX and bYX are determined by solving the following quadratic least-squares minimization problem (Rencher, 1995).
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The optimal regression slope, which is determined by setting the first derivatives 
SSEYX/aYX and SSEYX/bYX to zero and by solving the resulting 2 x 2 system of linear equations, is given by
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is given by
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Next, the co-expression network is defined such that each gene corresponds to a node and an undirected edge is included between two nodes if the R2 value between the two genes is greater than a threshold value R*. Thus, the connectivity matrix aij, which encodes whether a particular gene/node i is connected to another gene/node j, is given by
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is the R2 value between the time-courses of genes i and j. Traditionally the similarity threshold R* has been chosen either by assuming a normal R2 distribution (which may or may not be valid) or by significance analysis using the R2 null distribution generated by permutation of the original data (Magwene and Kim, 2004). Though valid from the perspective of trying to minimize the number of false-positive edges, both these methods fail to take into consideration the linearity assumptions that underlie the R2 metric and do not provide any information regarding the sensitivity of the resulting network topology to the chosen cut-off value. In this work we determine the similarity threshold by employing a commonly used graph-theoretic transitivity measure, the clustering coefficient.
2.2 Clustering coefficient
The clustering coefficient Ci of a node (Watts and Strogatz, 1998; Albert and Barabasi, 2002) is defined as
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Figure 1 shows how the similarity threshold impacts the average clustering coefficient of an example network. If the similarity threshold is set at its minimum value of zero, a fully connected network with an average clustering coefficient (ACC) of one will be obtained. As the cut-off is increased, edges will get eliminated leading to a lowering of the ACC. However, at a reasonably high similarity threshold, one can expect the ACC to start increasing once again due to the emergence of highly ‘cliquish’ disconnected subnetworks or modules, a manifestation of the transitive property of linear functions at the network representation level. This predictable variation of the ACC with the similarity threshold suggests that in the general case, the similarity threshold should be chosen such that (1) it is low enough so that a sufficient number of relationships (edges) are retained in the first place, (2) it is consistent with the transitive property of linear relationships which is what it eventually captures and finally (3) it is high enough so that the probability of the implied linear relationships (edges) occurring by chance is low. Thus, by parametrically varying the similarity threshold and calculating the resulting ACC, the ‘critical’ threshold should be set at the highest similarity value above/below which a sharp increase/decrease in the ACC is observed.
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2.3 Edge directionality
A high similarity between gene expression profiles could mask important differences in the regulation of the gene expression levels. To highlight this point, consider two representative gene pairs shown in Figure 2. Even though the R2 values are comparable for the two gene pairs, it is clear from their expression profiles that there is a qualitative difference between the two pairs. Specifically, for genes A and B, not only is the overall shape of the expression profile similar, but also the magnitudes of the expression levels are almost identical at each of the time points. However, the level of peak expression of gene D is much higher than that of gene C. In view of this, we considered the regression slopes for the two gene pairs bAB = 1.004, bBA = 0.976, bCD = 0.198, bDC = 4.957.
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To quantify how different these slopes are we define the slope ratio metric SR as
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This metric allows for distinguishing between the two pairs since SRCD = 0.04 is significantly different than SRAB = 0.97. We incorporate the slope ratio information at the network representation level by assigning directionality to only those edges that have SR 
0 according to the following rules.
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D) is that a small change in the ‘source’ gene (C) is associated with a large change in the ‘sink’ gene (D). Consequently, using the slope ratio metric in tandem with the R2 metric, we can identify differentially (in terms of absolute level) co-expressed (in terms of temporal pattern) gene pairs such as C and D. In addition to the similarity threshold, we will now need to determine a SR threshold such that directed edges having SR value less than the threshold are considered significant. We use the distribution of SR values for the un-directed edges surviving the similarity threshold for determining the SR threshold. Specifically, in keeping with the spirit of how the similarity threshold is determined, the SR threshold is chosen as the critical value around which a sharp transition is observed in the SR distribution. By doing so we are able to focus on gene pairs that ‘stand out’ from the background of all co-expressed gene pairs.
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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Figure 3 highlights the dependence of the average clustering coefficient (ACC) of the co-expression network on the R2 threshold. Note that we excluded both the isolated nodes (node degree 0) and the leaf nodes (node degree 1) from the calculation of the ACC. As expected, when the threshold was set at 0, resulting in a fully connected network (since the R2 is greater than 0 for all gene pairs), an ACC of 1 was obtained. A small increase in the cut-off from 0 resulted in a sharp decline in the ACC as a result of edge deletion from the fully connected network. The ACC leveled off around 0.65 for a broad range of cut-off values (0.12–0.88). From a network topology perspective, this implied that the average cohesiveness of the neighborhood of the non-isolated nodes was largely constant even though the number of edges was continuously decreasing over this range. On subsequent increase of the threshold (0.9 and above) a sharp increase in the ACC was observed. This was, as expected, due to the emergence of highly self-connected subnetworks or modules. Given this plot, we chose the similarity threshold as 0.90 since we observe a sharp transition in the ACC around this value.
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The resulting co-expression network is shown in Figure S1 of the Supplementary Data. There were 47 separate clusters (subnetworks) in the network with the largest connected component consisting of 79 nodes and 260 edges (see Table S1 in Supplementary Data). Figure 4 shows the characteristic expression signatures of the top six clusters. These clusters were mainly composed of genes involved in t-RNA synthesis, amino acid metabolism (in particular tryptophan), biotin synthesis and pentose and glucuronate interconversion pathway (see Supplementary Data).
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Next, based on the distribution of slope ratios found in our network (Figure S2 in Supplementary Data), we chose the slope ratio threshold of 0.15 and imposed directionality on the edges that had slope ratio less than 0.15. The resulting directed network is shown in Figure S3 and described in the Supplementary Data. While differential regulation of co-expressed genes belonging to the same pathway could be implemented in several ways, a remarkably consistent picture emerged when we looked at how this was operationally achieved at the sequence level in an organism. In bacterial and other prokaryotic systems, genes that encode for proteins necessary to perform coordinated functions in a particular pathway are typically clustered into a single transcriptional unit or operon that is transcribed into a single polycistronic mRNA coding for multiple proteins (De Hoon et al., 2004). Indeed, we found a large number of instances of genes constituting an operon belonging to the same co-expressed cluster. For example, in cluster 2, genes could be grouped as argC-argB-argD, carA-carB, argH-argG and rocF-rocD according to their operon organization (Makarova et al., 2001), the tryptophan metabolism genes of cluster 3 constitute the trpEDCFB operon (Du et al., 2000), while the biotin biosynthesis genes of cluster 4 form the bioWAFDBI operon (Bower et al., 1996; Perkins et al., 1996). Overall, the fraction of operons preserved in our co-expression network (meaning that all genes of an operon belong to the same cluster) is found to be 82.6% with 38 of the 46 operons being preserved.1 Moreover, we were able to uncover the sequence-level basis for the differential regulation of genes in the same operon, namely the existence of alternative transcription termination sites as described next.
The network topology of one of the inferred sub-networks containing genes involved in biotin biosynthesis (Fig. 5) implied that (1) the expression levels of all six genes were highly correlated across time and (2) small changes in the expression level of bioI were translated into large changes in the expression of the remaining five genes (Fig. 5B). The underlying biological reasons for these observations were found at the sequence level since the six genes are organized into an operon (Bower et al., 1996; Perkins et al., 1996) with two putative rho-independent transcription termination sites t1 and t2 (Fig. 5C). This type of transcription termination occurs when the transcribing RNA polymerase encounters a GC-rich region with dyad symmetry (inverted repeats). Once transcribed, the inverted repeats self-hybridize (anneal) to form a stem–loop structure which causes the RNA polymerase to pause. This allows the DNA strand to re-anneal and results in the release of the RNA polymerase along with the newly synthesized mRNA transcript. Consequently, the presence of the two termination sites suggested the existence of two transcripts of different lengths as shown in Figure 5C. This was indeed the case as previous experimental work (Perkins et al., 1996) on the bio operon had uncovered a 7.2 kb RNA that corresponded to the entire 7-gene operon along with a 5.1 kb transcript that corresponded to only the first five genes. In addition to the difference in lengths, the relative amounts of the two transcripts were also determined to be very different. Specifically, the amount of the 5-gene transcript was found to be eight times greater than that of the 7-gene transcript (Perkins et al., 1996). This difference in relative abundance would translate into lower expression level of bioI (and orf2) as compared to the other five genes, in accordance with both our experimental measurements and the relationships implied by our network representation. From a biological control perspective, our results support previous suggestions (Perkins et al., 1996) that the reaction catalyzed by the bioI protein product, which is the very first reaction in the linear biotin synthesis pathway, is the rate limiting step in this pathway.
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Motivated by the results for the bio operon, we explored whether our approach could be used to validate/invalidate computational predictions of putative terminator sites. Typically, possible stem–loop structures between genes transcribed in the same direction are predicted by calculating the free-energy of base pairings in the stem region (de Hoon et al., 2005). If the calculated free energy is negative and is below a specified threshold value, the sequence region is inferred to code for a putative transcription termination site. One such computationally predicted stem–loop site embedded within the yjm operon of B. subtilis is shown in Figure 6C (Rivolta et al., 1998), along with the network inferred for some of the genes constituting this operon (Fig. 6A) and their expression profiles in the cradle-to-grave dataset (Fig. 6B).
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The directed arcs from yjmD and yjmE are included as dashed lines in Figure 6A because they barely miss the SR threshold of 0.15 with SR values of 0.214 (yjmD
yjmA) and 0.153 (yjmE yjmA). In light of the results for the bio operon, the large difference in the expression level of yjmA as compared with the other genes suggests that the putative stem–loop structure is indeed a site for transcription termination. Other previously known instances of read-through terminators embedded within operons that we were able to identify included terminators in the valS-folC operon (read-through terminator after valS) and the gap-pgk-tpi-pgm-eno operon (read-through terminator after gap). We are also able to predict the presence of truly novel putative intra-operon transcription termination sites as in the case of the opp operon shown in Figure 7. The genes oppA and oppC and oppD were found to comprise a 3-gene cluster with the directionality between them as shown in Figure 7A. These genes, along with oppB, oppD and oppF, constitute the oppABCDF operon encoding proteins involved in the oligopeptide transport system responsible for importing/exporting peptides of 3–5 amino acids across the cell membrane (Solomon et al., 2003). The expression data for these genes (Fig. 7B), in combination with their sequence map (Fig. 7C), strongly suggest the presence of an intra-operon termination site between oppA and oppB since the expression level of oppA was much larger than all the other genes. Previously, using free-energy calculations, it had been hypothesized that the secondary structure of the RNA corresponding to the oppA-oppB intergenic region may enhance the stability of the mRNA molecule or function as a read-through terminator (de Hoon et al., 2005). Our results support the read-through terminator hypothesis since there is large difference in the expression profiles of oppA and oppCD. This would not be expected if the sequence region was contributing to mRNA stability.
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Next, we explore whether given the fact that we find good correspondence between our directed networks and the presence of intra-operon terminator sites, our analysis can be taken a step further to infer the relative strengths of known terminator stem–loop structures. Typically, two (or more) terminator sites are compared based on their free-energy values. The more negative the free-energy, the more stable the stem–loop, implying greater chance of termination at that site. Thus, a large difference in relative strengths of two terminators gets translated into significant difference in the amounts of the two possible transcripts, which corresponds to strong directionality (indicated by a small slope ratio) in our analysis. One such operon of B. subtilis for which the free-energy values were available was the glv operon (Fig. 8), where
G = –30.1 Kcal/mol for the terminator after glvA and G = –18.6 Kcal/mol for the terminator after glvC (Yamamoto et al., 2001). We find that the slope ratio of the glvA-glvC pair is 0.0678, suggesting that the terminator after glvA is much stronger than the one after glvC, in good agreement with the free energy results.
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In contrast to the glv operon, consider the pyrimidine biosynthesis genes (Fig. 9). For this operon, previous studies predicted that the two terminator sites were approximately identical with respect to their transcription termination potential (Turner et al., 1994; Lu et al., 1995; Lu and Switzer, 1996). In particular, the free-energy values for the pyrR-pyrP and pyrP-pyrB terminator sites were reported to be
G = –15.3 Kcal/mol and G = –21.6 Kcal/mol, respectively (Turner et al., 1994). As for the glv operon, our experimental data supported this claim since the relative distance between the expression profiles of pyrR and pyrP was approximately identical to that between pyrP and pyrB/pyrC and the slope ratio was found to be 0.9837 for the pyrR–pyrP pair and 0.8792 for the pyrP–pyrB pair.
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4 DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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This paper presents a systematic framework for integrating network inference and topological analysis for uncovering biological knowledge from large-scale gene expression data. Our starting point was the gene co-expression network for B. subtilis as inferred from Affymetrix GeneChip® time-series data. We constructed the gene co-expression network of B. subtilis where each gene corresponds to a node and an un-directed edge exists between two nodes if the similarity (R2 value) between their expression profiles is above a threshold. One of the key contributions of our work is the formal estimation of this threshold value by applying ideas from network analysis. Specifically, we demonstrated how the clustering coefficient, which is a measure of local connectedness or cliquishness in a network, is the appropriate graph-theoretic metric that must be used for determining the cut-off value. This reliance on the clustering coefficient, as opposed to other topological measures such as degree distributions, path lengths, etc., was shown to be a natural consequence of the manifestation of the transitive property of linear functions at the network representation level. We expanded the scope of the gene co-expression network by proposing a novel measure, the slope ratio, as a means for imposing directionality on the edges. By doing so, we were able to account for both the temporal similarity of gene expression profiles as well as the similarity/dissimilarity in the absolute levels of gene expression. Both these attributes of the expression profiles are important as the similarity in temporal pattern is indicative of co-regulation of genes by an endogenous/exogenous signal while the difference in absolute levels provides information about the relative turnovers of the specific reactions in a biological pathway.
We found that the B. subtilis gene co-expression network was highly modular, consisting of one large connected subnetwork and a large number of relatively smaller subnetworks. We observed no redundancy in our clustering results as there was no overlap between the expression signatures of the top six clusters. We verified that genes participating in the same biological pathway were co-expressed and consequently belonged to the same cluster and we identified a number of cases where some/all genes belonging to the same cluster constituted a single transcriptional unit or operon. Further probing of the operon structures of a number of gene clusters revealed that edge directionality, which was designed to capture the difference in expression levels, corresponded to the presence of intra-operon termination sites. We were able to (1) re-confirm previously experimentally determined termination sites as in the case of the bio operon, (2) provide validation for computationally derived termination sites as in the case of the yjm operon and (3) quantify their relative strengths to complement free-energy-based assessments. Given these results, we conclude that indeed there were important biological insights that were masked at the level of the un-directed co-expression network and that these were brought to light by considering the directed network. In the future, we plan to conduct a large-scale systematic study to see how well terminator free-energy data, which is now available on a genome-wide scale for B. subtilis (de Hoon et al., 2005), correlate with our slope ratio metric. Such a study would help identify instances where the two approaches (one based on sequence-level information and one based on expression level information) support as well as complement each other.
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Acknowledgments |
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The authors would like to thank Dr Jeffrey D. Varner from Genencor International for providing us with the microarray data used in this work and István Albert for helpful discussions. This work was partially supported by a Sloan Research Fellowship to R.A. Financial support by NSF award BES0120277 to C.D.M. is gratefully acknowledged.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: John Quackenbush
1An important point to note is that operons and clusters are not equivalent, in the sense that if the genes are known to be part of an operon then they can be expected to belong to the same cluster; however, all genes in a cluster do not constitute an operon. 
Received on June 29, 2005; revised on October 6, 2005; accepted on November 11, 2005
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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