Bioinformatics Advance Access originally published online on December 4, 2008
Bioinformatics 2009 25(3):387-393; doi:10.1093/bioinformatics/btn626
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Identification of microRNA regulatory modules in Arabidopsis via a probabilistic graphical model
1Boyce Thompson Institute for Plant Research, Cornell University and 2USDA Robert W. Holley Center for Agriculture and Health, Ithaca, NY 14853, USA
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS4 CONCLUSION AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Motivation: MicroRNAs miRNAs play important roles in gene regulation and are regarded as key components in gene regulatory pathways. Systematically understanding functional roles of miRNAs is essential to define core transcriptional units regulating key biological processes. Here, we propose a method based on the probabilistic graphical model to identify the regulatory modules of miRNAs and the core regulatory motifs involved in their ability to regulate gene expression.
Results: We applied our method to datasets of different sources from Arabidopsis consisting of miRNA-target pair information, upstream sequences of miRNAs, transcriptional regulatory motifs and gene expression profiles. The graphical model used in this study can efficiently capture the relationship between miRNAs and diverse conditions such as various developmental processes, thus allowing us to detect functionally correlated miRNA regulatory modules involved in specific biological processes. Furthermore, this approach can reveal core transcriptional elements associated with their miRNAs. The proposed method found clusters of miRNAs, as well as putative regulators controlling the expression of miRNAs, which were highly related to diverse developmental processes of Arabidopsis. Consequently, our method can provide hypothetical miRNA regulatory circuits for functional testing that represent transcriptional events of miRNAs and transcriptional factors involved in gene regulatory pathways.
Contact: zf25{at}cornell.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 CONCLUSION AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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MicroRNAs miRNAs are small, endogenous RNAs found in bacteria, plants and animals (Bartel, 2004) They cause transcriptional cleavage or translational repression through binding their target mRNAs. As miRNAs regulate the expression of their target genes, they play critical roles in a variety of cellular processes, such as development, cell proliferation, apoptosis and stress response (Hwang and Mendell, 2006; Jovanovic and Hengartner, 2006; Sunkar and Zhu, 2004). miRNAs are regarded as key components in complex networks of gene regulatory pathways. The combined complexity of miRNAs and transcription factors (TFs) may be relevant for creating cellular complexity in a developing organism (Hobert, 2004).
During the last several years, significant progress has been made toward elucidating the regulatory mechanisms of miRNAs. However, several fundamental questions regarding the role of miRNA still remain largely unanswered, including: (i) Which miRNAs are expressed under a specific condition? (ii) Which cell processes are regulated by specific miRNAs? (iii) Which genes regulate the expression of miRNAs? To answer these questions, it is important to identify functional miRNA regulatory modules (miRMs) which are involved in specific biological processes. Yoon and De Micheli (2005) developed an algorithm to predict miRMs, which are groups of miRNAs and their targets involved in similar biological process. Their method is based on miRNA-target gene binding information at the sequence level, and does not consider their expression profiles. An improved method, which considers the additional information of miRNA and mRNA expression profiles, may detect actual miRMs (Joung et al., 2007). However, this method encounters a problem in identifying miRMs over specific conditions since it is based on the expression correlation over all available conditions instead of a subset of conditions. Moreover, the method requires the expression profiles of both miRNAs and their targets under a set of common conditions, which are not available in most cases, thus limiting its applications.
Upstream regulatory sequences of miRNAs in several plant species were recently reported (Xie et al., 2005; Zhou et al., 2007a). From these sequences, it is possible to define over-represented regulatory elements in miRNA promoter regions (Megraw et al., 2006). Additional studies presented statistically significant motifs from upstream regions of human intergenic miRNAs through genomic sequence analysis (Lee et al., 2007; Saini et al., 2007; Zhou et al., 2007a). These motifs may provide crucial insights in miRNA regulation and allow us to grasp the relationship between miRNAs involved in the regulation of target genes in specific biological processes as well as their regulators.
In this article, we present a probabilistic graphical model-based method for inferring regulatory modules of miRNAs involved in various cellular processes. Here, the miRMs are defined as functional clusters of a set of miRNAs with their target mRNAs involved in the same biological processes. Additionally, the regulatory modules can contain the regulators of miRNAs. To identify regulatory modules, our method integrates datasets from diverse sources including: (i) large-scale gene expression dataset; (ii) miRNAs and their target genes; (iii) known transcription factor binding elements; and (iv) promoter sequences of miRNAs.
The model underlying our method is an author-topic model that is a family of probabilistic graphical models which have been used for information discovery from large text collections (Steyvers et al., 2004). Probabilistic graphical models have been successfully applied in identifying gene regulatory modules (Qi and Ge, 2006; Segal et al., 2003). Our method can summarize dominant patterns from several different data sources that are not likely to be handled by conventional co-clustering techniques such as biclustering.
We applied our method to an Arabidopsis gene expression dataset consisting of 79 samples related to different developmental series (Schmid et al., 2005). Regulatory modules of miRNAs were inferred by integrating information of miRNA-target pairs, gene expression profiles and promoter binding motifs. miRNAs that were allocated to each module were then classified as associated with the specific developmental processes. Furthermore, over-represented regulatory elements were identified from miRNA promoter regions for each miRM. Finally, their modularity was validated by the literature and functional analysis of the corresponding miRNA target genes. Our analysis revealed 10 miRMs including miRNAs assigned to novel functional roles that are highly correlated to five representative development processes, and with core promoter elements of miRNAs related to their modules.
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2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 CONCLUSION AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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2.1 Probabilistic graphical model for identifying miRMs
The method tries to find which miRNAs are involved in miRMs and which biological processes are associated with these miRMs. Figure 1 illustrates a schematic view of our model for identifying functionally correlated miRMs, based on a graphical probabilistic model.
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lEach gene has events of its expression in a specific condition that is likely to be associated with miRNAs. Thus, it can be represented as a vector of counts corresponding to the expression event for variables e={e
, e
,...,e
, e
. Here, (e
, e
) indicates an experimental condition representing over- and under-expression of a gene in this condition, respectively. We define e
as a condition type. Each variable contains the integer value representing the degree that a gene is expressed in i-th or (i+1)-th condition type. To get these integer values, we take a rounding operation for each normalized expression value including a constant c: |
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As illustrated in Figure 1, for each non-zero expression event of the i-th condition type of a gene g, eig, a hierarchical generation process is hypothesized. The process is characterized by the involvement of two kinds of hidden variables, xig and zig. The variable xig is a multinomial variable that indicates which miRNA is associated with the expression activity in eig. The variable zig is regarded as a miRM, a functional module related to the i-th condition type of a gene, g.
Each miRNA, m, is associated with a multinomial distribution over z, which is parameterized by 
. Each miRM, zk, assumes a multinomial distribution over the gene expression condition, where the parameter 
k characterizes the distribution. Furthermore, for and in the framework of Bayesian modeling, symmetric Dirichlet priors are assumed with parameters 
and β, respectively. Our model is closely related to the author-topic model for authors and text documents (Rosen-Zvi et al., 2004), and a miRNA in our problem setting corresponds to an author in the author-topic model.
The exact inference of the model is intractable, so an approximate inference method, specifically a collapsed Gibbs sampling which is a simple method for estimating parameters with Dirichlet priors (Rosen-Zvi et al., 2004), was used. The collapsed Gibbs sampling proceeds by the successive joint sampling for latent variables x and z, marginalizing out and in each state sampling. For the i-th condition type of a gene g, the sampling for xig and zig is done on the basis of the conditional probability of
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is the number of times miRNA l is assigned to the k-th miRM excluding the current instance. W
is the number of times expression type n is assigned to the k-th miRM excluding the current instance. T is the number of hidden variables for miRMs and Q is the total number of condition types.
After sufficient sampling iterations for miRNAs (x) and miRMs (z), we estimate and from a single sample (x, z) by
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and are calculated from the assignment results for all data points, unlike those in the above sampling process.
2.2 Expression dataset
Affymetrix CEL files of the gene expression dataset as described in Schmid et al. (2005) were obtained from the Nottingham Arabidopsis Stock Centre (NASC; Craigon et al., 2004). This microarray dataset contains 79 different samples derived from several tissue/organ developmental series in Arabidopsis, including root, shoot, leaf, seed and flower development. The CEL files were processed and normalized at the probe level using the GC content-based robust multi-array algorithm (GCRMA; Wu et al., 2004). After normalization, the average of triplicate values was calculated for each sample. Then the log ratio between each expression level and the mean expression level across all the samples was calculated in order to grasp the relative expression level between samples.
2.3 Target genes of miRNAs
In Arabidopsis, a number of miRNA targets have been identified through genome-wide screens based on computational methods and experimental validations (Adai et al., 2005; Bonnet et al., 2004; Jones-Rhoades and Bartel, 2004; Jones-Rhoades et al., 2006; Rhoades et al., 2002; Wang et al., 2004; Zhang, 2005). In this study, we also performed target predictions using the most recent collection of Arabidopsis miRNAs in miRBase (Release 11.0; Griffiths-Jones et al., 2008) based on the algorithm described in Jones-Rhoades and Bartel (2004). We gathered a total of 637 miRNA-target pairs for 137 miRNAs and 382 genes from the above reports and our prediction.
2.4 Identifying core regulators of miRMs
Ninety-five promoter sequences which are 300–350-bp upstream of Arabidopsis miRNAs as described in Zhou et al. (2007a) were used to screen for known transcriptional binding sites. The search of binding sites against these miRNA promoters was performed with the MotifScanner program (Thijs et al., 2001), using the position weight matrices (PWMs) of 99 known binding motifs constructed by Megraw et al. (2006). The significantly over-represented motifs were identified based on the strategy described in van Helden et al. (1998). Unknown motifs were also identified from the promoters in the 10 miRMs that were most related to different developmental processes. Details of the method are given in Supplementary Material.
2.5 Functional analysis of target genes in each miRNA regulatory module
Gene Ontology (GO) terms of Arabidopsis genes were downloaded from TAIR website (http://www.arabidopsis.org). GO term enrichment analysis was performed using the perl module GO::TermFinder (Boyle et al., 2004). Significantly, over-represented GO terms were identified for target genes in each miRM with a corrected P-value (FDR) cutoff of 0.05.
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 CONCLUSION AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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3.1 Identification of miRMs associated with developmental processes
miRNAs can serve as master regulators in the gene regulatory networks, targeting genes encoding regulators, such as TF. In the present study, we developed a probabilistic graphical model-based method for inferring regulatory modules of miRNAs involved in various cellular processes. The model simultaneously clusters the miRNAs and the conditions at which the target genes of miRNAs are expressed (see Section 2). The roles of miRNAs are modeled with probability distributions over conditions, using miRNA-target binding information and the expression profiles of target genes. Here, each gene is represented as a vector of counts indicating over- and under-expression under specific conditions. The parameters of the model were estimated by Gibbs sampling.
We applied our method to an Arabidopsis gene expression dataset consisting of 79 samples derived from different development series (Schmid et al., 2005). The clustering patterns of miRNAs and the sample sets were inferred from the input dataset consisting of miRNA, gene and expression variables. The input dataset was generated in a format of a [137 x 382] matrix of binary variables for miRNA-gene pairs and a [382 x 158] matrix of integer variables for gene expression pairs. In the first matrix, one/zero represents binding/non-binding between a miRNA and a gene. Each row of second matrix consists of 158 expression variables representing up- and down-regulations of genes in the 79 samples. In our model the number of clusters was set to 10, a constant for converting the expression value, c was set to 10, the number of Gibbs sampling iteration was set to 500, and two hyperparameters and β were set to 0.16 and 0.01, respectively. The algorithm clusters variables from the above matrices simultaneously. Details for model parameter settings are described in Section 4.
Figure 2 shows the list of top 5% condition types (samples) with highest probabilities in each cluster. It presents the probability that a certain condition type belongs to a certain cluster. As expected, condition types from the same developmental series were usually in the same clusters. However, we observed that occasionally several different condition types were assigned to the same clusters, suggesting that common miRNAs might affect different developmental processes.
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The top 5% (seven) ranked miRNAs with highest probabilities in each cluster were also extracted. The association between miRNAs and specific biological processes was inferred based on the miRNAs and condition types assigned to the same clusters (Fig. 3). The detail information of each miRM including miRNAs, their targets and the associated developmental processes, as well as the core regulatory elements, is listed in Supplementary Table S1.
3.2 Functional validation of associations from literatures
In this study, we identified a significant number of associations between miRNAs and developmental processes of Arabidopsis. It is worth noting that same miRNA families could be involved in different development processes, e.g. miR407 in the development of all five organs (Fig. 3). This finding is consistent with previous reports (Jones-Rhoades et al., 2006). In addition, as shown in Figure 3, different targets of the same miRNA families could be up- and down-regulated in the same process, e.g. targets of miR407 in seed, shoot and root, indicating that targets of miRNAs from the same family could have antagonistic roles in certain plant developmental processes. The implications of several miRNAs playing a role in the specific developmental processes identified here are supported by previous reports in the literature. These known associations are listed in Table 1.
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Among the miRMs identified in this study, most associations between miRNAs and developmental processes are novel. Although currently there is no direct evidence to support these associations, the targets of several miRNAs have a reported functional role in the corresponding developmental processes (Supplementary Table S2).
In summary, using a probabilistic graphical model which can efficiently integrate datasets from several different sources, we are able to assign a role of a set of miRNAs in certain plant developmental processes. A number of associations between miRNAs and developmental processes identified here are supported by the literature, indicating the validity of the strategy we used in this study. It is worth noting that as expected, several previously reported associations are not recovered in the current study due to the complexity of miRNA regulatory networks and gene regulations beyond the transcriptional level, such as in plants it has been reported that some miRNAs regulate their target genes through translational inhibition, although the regulation by endonucleolytic cleavage is prevalent (Brodersen et al., 2008).
3.3 Over-represented regulatory motifs in the miRNA promoters
Currently, a number of regulatory motifs have been reported in Arabidopsis (Davuluri et al., 2003; Palaniswamy et al., 2006). We screened the promoter regions of miRNAs for the presence of certain regulatory motifs and identified over-represented motif patterns in each miRM. The significance of the enrichment is determined by the P-values based on the background frequencies of motifs obtained from the 95 miRNA promoters. Using a threshold of adjusted P-value (FDR) <0.05, we identified a total of 18 over-represented motif patterns in the promoter sequences of miRNAs in each of the 10 miRMs (Table 2). Most over-represented motifs and the associated TFs have reported functional roles in the corresponding developmental processes (detailed description of the functions is provided in Supplementary Material).
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All 10 miRMs that we identified were highly related to plant development processes and contained 29 distinct miRNAs. Out of these 29 miRNAs, 19 have available promoter sequences. We further identified new motifs enriched in the promoters of the 19 miRNAs. The top 10 enriched motifs and their sequence logos are provided in Supplementary Figure S1. The presence of putative motifs in the promoter regions of these miRNAs indicates the existence of novel TFs that regulate a group of miRNAs during various Arabidopsis developmental processes.
3.4 Functional validation of miRNA target genes
If miRNAs are tightly associated with specific biological processes, then their target genes should also be highly relevant to the same processes. We extracted GO terms for the target genes of miRNAs belonging to each miRM and further identified over-represented GO terms in each miRM. In fact, most miRNA target genes are transcriptional regulators, as reported previously (Rhoades et al., 2002). Despite this bias, a number of significantly enriched GO terms annotated as different developmental processes were identified in each of these miRMs and several of them are consistent with the development processes in the corresponding miRMs (Table 3). This further validated the approach we used in this study.
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3.5 Evaluation of associations between miRNAs and biological processes
Currently, a total of 18 known associations between miRNAs and biological processes have been reported in Arabidopsis. Our method was able to extract 11 of them (61.1%; Table 1). We first calculated the distribution of the coverage of known associations through 100 runs with randomly shuffled miRNAs, which we used as the negative controls. As described in Section 3.1, the input dataset of our model consists of a matrix of miRNA-gene pairs. For each run, miRNAs in this matrix were randomly shuffled and the coverage of known associations, indicating the degree of retrieving true associations, was calculated. The significance of the coverage was measured from the probability density function (pdf) of the coverage obtained from 100 runs. The pdf was generated by the curve fitting toolbox (cftool) in Matlab. The result indicated that the coverage of known associations (11/18, 61.1%) retrieved by our method had high significance (P=0.02886 for coverage
61.1%) and unlikely occurred by chance (Fig. 4).
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The associations obtained by our method were then compared with those obtained by the biclustering approach for extracting transcriptional modules. The biclustering algorithm, ISA (Iterative Signature Algorithm), implemented in Biclustering Analysis Toolbox (BicAT) (Barkow et al., 2006) detected transcriptional modules by grouping in both dimensions of genes and conditions simultaneously (Ihmels et al., 2002; 2004). Then the associations between miRNAs and conditions were extracted by making connections between over-represented miRNAs in genes and conditions belonging to biclusters (23 non-redundant set) obtained from ISA. Here, over-represented miRNAs were obtained by calculating hypergeometric P-values (FDR) <0.05. The results of biclustering are shown in Supplementary Figure S2.
Among 355 possible combinations between 71 miRNA families and five different biological processes, currently only a small amount of associations (18) between miRNAs and biological processes have been reported. As indicated above, our method retrieved 11 out of 18 known associations (61.11%) whereas biclustering method found only three (16.67%). Our method also retrieved more unknown associations (62) than the biclustering method (20). Although the biclustering approach finds transcriptional modules of highly correlated genes under specific conditions, these modules do not always contain enriched miRNAs in sets of genes. Thus, this method fails to find relevant associations whereas our method can find them efficiently by clustering miRNAs and conditions simultaneously via the expression of target genes.
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4 CONCLUSION AND DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 CONCLUSION AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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miRNAs are emerging as key components in gene regulatory circuits of diverse plant species. The functional roles of most miRNAs are still unknown in the context of gene regulatory networks. The regulatory networks containing miRNAs are likely to contain subunits, such as feed-back and feed-forward loops (Tsang et al., 2007). These subunits are favored via evolutionary selection to maintain a nimble biological system. In the present study, we demonstrate a novel strategy which integrates different sources of data to identify putative miRMs involved in various developmental processes in Arabidopsis. Each module contained miRNAs, miRNA targets and the information of the associated developmental processes. We also identified putative regulators of a group of miRNAs in each miRM. As our method presents a comprehensive analysis among miRNAs, their targets and regulators, the results may provide insight toward the basis of evolution of gene regulation by TFs and miRNAs (Chen and Rajewsky, 2007).
The functional roles of several miRNAs in specific biological processes have been identified and validated by various computational and experimental approaches. However, the functions of most miRNAs still remain unknown. Our method can be utilized to suggest candidate miRNAs highly associated with their biological functions, providing new functional insight to these otherwise poorly understood sequences.
Although several abundant regulatory motifs in the miRNA promoters of Arabidopsis have been reported (Megraw et al., 2006), identifying the regulatory motifs related to some specific biological processes would raise another interesting question. For example, it was reported that the light-related regulatory motifs are significantly abundant in the promoter regions of a set of UV-B stress responsive miRNAs (Zhou et al., 2007b). In this study, we focused on finding condition-specific regulatory elements rather than the globally over-represented elements from promoters of all the miRNAs as in Zhou et al. (2007b). These elements may play a crucial role in regulation of miRNAs under certain specific cellular processes.
Our dataset consists of three different kinds of matrixes, i.e. miRNA-target, gene-condition and motif-miRNA. Conventional co-clustering techniques including biclustering are inadequate for this case since they usually handle only one matrix representing co-occurrences, making it difficult to catch useful patterns involving the whole dataset. The method presented in this study can directly integrate the datasets with multiple sources of matrices. In this way we can efficiently capture the regulatory relationship that would be difficult to be extracted from individual levels of miRNAs. In addition, our method has much broader applications than the one proposed by Joung et al. (2007) since our method does not require the miRNA expression profiles, which currently are not readily available for most tissues in Arabidopsis and other organisms.
The model presented here requires setting of several parameters. The number of cluster was determined by prior knowledge based on the number of different tissues. It is based on the fact that the expression dataset contains five representative developmental processes and target genes of miRNAs could be over- or under-expressed in the respected samples. Two hyperparameters, and β were fixed as constant, following previous experimental settings (Steyvers et al., 2004). With these parameter settings, a good description of the model for miRMs was made from genome-wide datasets in Arabidopsis. In the present study, top 5% miRNAs with highest probability were regarded as the members of each module. However, the determination of optimal cutoff value raises still the possibility of further improvements of our method.
The present work provides a framework to efficiently hypothesize associations between miRNAs and different phenotypes influenced by them. It may be utilized to detect the role of miRNAs in various interesting biological processes and environmental stimuli. Furthermore, this application could be opened up in building comprehensive regulatory maps modeling the relationship between miRNAs and some important processes in human and animals, such as cancers in human and mouse. Consequently, this approach could contribute to elucidation of the gene regulatory program related to functional modules of miRNAs in many additional species for which genome sequences and comprehensive expression datasets are available.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 CONCLUSION AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The authors would like to thank Dr Jeong-Ho Chang for helpful discussion and Dr Jim Giovannoni for critical review of this article.
Funding: National Science Foundation (DBI-0501778 to Z.F.).
Conflict of interest: none declared.
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FOOTNOTES |
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Associate Editor: John Quackenbush
Received on August 26, 2008; revised on November 11, 2008; accepted on December 1, 2008
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