Global similarity and local divergence in human and mouse gene co-expression networks
© Tsaparas et al; licensee BioMed Central Ltd. 2006
Received: 22 April 2006
Accepted: 12 September 2006
Published: 12 September 2006
A genome-wide comparative analysis of human and mouse gene expression patterns was performed in order to evaluate the evolutionary divergence of mammalian gene expression. Tissue-specific expression profiles were analyzed for 9,105 human-mouse orthologous gene pairs across 28 tissues. Expression profiles were resolved into species-specific coexpression networks, and the topological properties of the networks were compared between species.
At the global level, the topological properties of the human and mouse gene coexpression networks are, essentially, identical. For instance, both networks have topologies with small-world and scale-free properties as well as closely similar average node degrees, clustering coefficients, and path lengths. However, the human and mouse coexpression networks are highly divergent at the local level: only a small fraction (<10%) of coexpressed gene pair relationships are conserved between the two species. A series of controls for experimental and biological variance show that most of this divergence does not result from experimental noise. We further show that, while the expression divergence between species is genuinely rapid, expression does not evolve free from selective (functional) constraint. Indeed, the coexpression networks analyzed here are demonstrably functionally coherent as indicated by the functional similarity of coexpressed gene pairs, and this pattern is most pronounced in the conserved human-mouse intersection network. Numerous dense network clusters show evidence of dedicated functions, such as spermatogenesis and immune response, that are clearly consistent with the coherence of the expression patterns of their constituent gene members.
The dissonance between global versus local network divergence suggests that the interspecies similarity of the global network properties is of limited biological significance, at best, and that the biologically relevant aspects of the architectures of gene coexpression are specific and particular, rather than universal. Nevertheless, there is substantial evolutionary conservation of the local network structure which is compatible with the notion that gene coexpression networks are subject to purifying selection.
The amplitude, timing, and pattern of gene expression have important phenotypic consequences, and the potential evolutionary significance of changes in the regulation and expression of genes has long been recognized [1–3]. In the last few years, high-throughput gene expression data sets from related species have accumulated, to the extent that it has become possible to study the divergence of expression in a systematic way at the genome-scale.
Initial efforts at the comparative study of gene expression divergence have yielded some interesting and unexpected results. For instance, it has been shown that the level and pattern of mammalian gene expression can evolve in a way that is both rapid and apparently unconnected to the level of functional constraint on gene sequences [4, 5]. This led to the counter-intuitive suggestion that gene expression may evolve completely free of selective constraint, in other words, purely neutrally. Subsequent studies have refined the neutral view on the evolution of gene expression by demonstrating that, although selection does, in fact, constrain expression divergence, much of the observed change in expression between species may nevertheless be effectively neutral [6, 7]. The potential adaptive significance of some gene expression changes has also been posited . Several other recent studies have shown how patterns of gene expression, and entire regulatory networks, can quickly respond to environmental cues and substantially reorganize themselves over the course of evolution. For instance, the architecture of yeast gene regulatory networks has been shown to change dramatically in response to environmental stimuli , and gene expression patterns were found to diverge rapidly after gene duplication in yeast  and humans . Prokaryotic genomes, too, show evidence of rapid, whole-sale reorganization of gene regulatory networks .
Given the phenotypic relevance of gene expression patterns, the apparent evolutionary lability of expression suggests that it might represent an ideal substrate on which natural selection could act to drive the functional divergence between evolutionary lineages. Indeed, comparative studies of gene expression have also uncovered intriguing connections between expression divergence and gene function. For instance, it has been shown that physically interacting proteins tend to be encoded by coexpressed genes [12, 13], and that the expression levels of interacting proteins show coordinated changes across species . From a broader perspective, it has been demonstrated that functionally related genes are preferentially linked in coexpression networks, and this was taken to justify the so-called 'guilt by association' heuristic whereby expression patterns are used to inform functional annotation of uncharacterized genes . In a very specific example of how expression changes can lead to phenotypic divergence, the expression changes in yeast that facilitated the emergence of anaerobic metabolism have been identified and shown to be due to the evolution of a specific cis-regulatory sequence motif .
For the study presented here, we performed a comparative analysis of human-mouse gene expression patterns to assess the extent of expression divergence between the two species and to explore the connections between the evolution of gene expression and function. We employed the Novartis mammalian gene expression atlas  to compare changes in the relative expression levels between 9,105 orthologous human-mouse gene pairs across a panel of 28 shared tissues. Gene expression patterns were resolved into species-specific coexpression networks and the topological properties of these networks were compared. The interrogation of coexpression networks allows for the use of a well-developed set of analytical and conceptual tools [18–20] and provides an opportunity for the simultaneous comparison of evolution at different levels of systemic organization, i.e., global vs. local network properties. The results of this comparison indicate that human and mouse co-expression networks are indistinguishable in terms of their global properties but show drastic divergence at the local level.
Results and Discussion
Mammalian coexpression networks
The use of the PCC to build coexpression networks is predicated on the choice of a threshold correlation coefficient (r) at, or above which, genes are considered to be coexpressed and are thus connected by an edge in the network. As previously reported , a series of increasing r-values (0.4–0.9) was evaluated for utility in building coexpression networks. When r-values << 0.7 are used, coexpression networks tend to congeal into graphs that are so densely connected as to preclude meaningful analysis of their topological properties. On the other hand, r-value thresholds ranging from 0.7–0.9 yield analytically tractable networks and qualitatively similar results. Results for coexpression networks based on an r-value threshold of 0.7 are reported here since this cutoff gives networks that are unlikely to contain many spurious edges but are sufficiently large and dense for robust topological analysis. For the 28-dimensional gene expression profiles evaluated here, an r-value of 0.7 corresponds to a highly statistically significant correlation (P = 3.4e-5). Furthermore, gene expression profiles with r ≥ 0.7 can be visually appreciated to be highly similar (Figure 1c).
Global characteristics of the coexpression networks
A more refined notion of network density is given by the average clustering coefficient (<C>). The clustering coefficient C of a node i is defined as the fraction of the pairs of neighbors of node i that are linked to each other: Ci = 2n i /ki(ki-1), where n i is the number of observed links connecting the k i neighbors of node i and k i (k i -1)/2 is the total number of possible links. The average clustering coefficient (<C>) is the mean of this value for all nodes with at least two neighbors, and for both the human and mouse networks <C>≈0.4 (Table 1). For networks of this size, these <C> values are considered to be quite high. By way of comparison, for randomly generated networks with the same number of edges and same degree (k) sequences, the expected <C> is estimated to be 0.0643 for human and 0.0529 for mouse. The high density of the coexpression networks is not necessarily surprising because, as one could reasonably expect, co-expression is, largely (but not entirely), transitive. In other words, if gene A is coexpressed with genes B and C, then genes B and C are likely to be coexpressed as well. However, the high observed values of <C> for the human and mouse networks do not appear to be due to the transitivity of the PCC similarity measure alone. This is demonstrated by the observation that networks built using the PCC measures between randomly permuted gene expression profiles, thus preserving some transitivity, also have values of <C> that are far lower than the observed values: human = 0.0933, mouse = 0.1229.
The average path length (<l>) is the average shortest path, or the smallest number of edges needed to connect two nodes, between any two reachable nodes in the network. Clearly, the co-expression networks exhibit "small world phenomena": on average, any two nodes are separated by only a few edges (Table 1).
Human-mouse intersection network
Local conservation of the human-mouse intersection network
% Human N3
% Mouse N3
Several other factors also point to the local level divergence of the human and mouse coexpression networks. When the degrees (k) of nodes present in both the human and mouse networks were arranged into species-specific degree sequence vectors, only relatively low, albeit statistically significant (given the large number of observations), correlation (r = 0.27, P = 9e-149) was seen between species. In other words, a highly connected node (hub) in the human coexpression network is not especially likely to be a hub in the mouse coexpression network and vice versa. In addition, the human and mouse coexpression r-values for shared edges are not correlated at all (r = 0.03). Finally, there is no correlation between the principal eigenvector values of the human and mouse networks (r = -0.03), indicating that the dense areas of the networks do not overlap. Thus, whereas the global topological properties of the species-specific networks are highly conserved, the local architectures that underlie these topologies, in terms of the identities of the coexpressed genes pairs, are highly divergent.
The low level of conservation seen for the local network structures was unexpected, particularly, in light of the close similarity of the global topological properties, and suggested substantial divergence of gene expression patterns between human and mouse orthologs. A series of controls were implemented to assess the meaning and robustness of these findings (see Additional file 1). These controls included comparison of networks constructed separately from experimental and biological replicate data sets, and analysis of network conservation for subsets of the data with different experimental variances. The results of these controls indicate that the majority of the local divergence between human and mouse coexpression networks does not result from experimental noise. In addition, lowering the PCC threshold used to define edges in the coexpression networks does not result in a substantial increase in the fraction of edges conserved between species (see Additional file 1; Supplementary Figure 9a).
The high divergence of coexpressed gene pairs between human and mouse detected here is consistent with previous studies that have shown substantial divergence of the expression profiles for human and mouse orthologs [5, 6, 21, 22]. Indeed, when the expression profiles were directly compared for the 9,105 human-mouse orthologous gene pairs studied here, the average PCC, while positive, was fairly low and not statistically significant (average PCC = 0.22, Student's t = 1.15, df = 26, P = 0.26).
Functional coherence of gene coexpression networks
Average GO similarity for mammalian gene coexpression networks versus average GO similarity for all gene pairs
0.2637 ± 9.1e-4
0.1989 ± 4.9e-5
0.2736 ± 8.9e-4
0.2150 ± 8.2e-5
Correlation (r) between pairwise GO similarity and pairwise gene expression profile r-values
Average GO similarity for species-specific mammalian gene coexpression networks versus average GO similarity for the conserved human-mouse intersection network
0.2556 ± 9.3e-4
0.2678 ± 9.2e-4
0.3299 ± 3.4e-3
Correlation (r) between pairwise GO similarity and pairwise gene expression profile r-values
Network clusters and biological function
Consistent with the apparent increased functional coherence of the intersection network, the correspondence between network clusters, GO term overrepresentation and expression patterns is significantly more pronounced for the conserved intersection network than for the human and mouse species-specific networks. Thus, 38% of clustered genes from the intersection network mapped to overrepresented GO terms compared to 13% of human-specific (χ2 = 85.1, P = 2.8e-20) and 18% of mouse-specific network genes (χ2 = 43.0, P = 5.5e-11).
General significance of coexpression network structure
The global topological properties of the human and mouse gene coexpression networks studied here are very similar but the specific architectures that underlie these properties are drastically different. In other words, the actual pairs of orthologous genes that are found to be coexpressed in the different species are highly divergent, although we did detect a substantial conserved component of the co-expression network. The discordance between evolutionary conservation at distinct levels of network organization has implications for understanding the general significance of the topological properties of networks that represent various complex systems.
The last few years have seen an explosion of studies on various kinds of biological and non-biological networks [29, 30]. A central theme for much of this work has been the striking unity of the topological properties of networks representing very different complex systems, from biological (e.g., metabolic and protein interaction) networks to non-biological ones, such as social interaction networks and the world-wide-web. Almost all these complex networks show evidence of both scale-free  and small world  properties. In other words, the network node-degree distributions fit power laws and the diameter of the networks, in terms of the average number of links between two nodes in the network, stays small despite increases in network size. These observations have led to the hope that the network perspective might 'revolutionize our view of biology' . This hope is based on the idea that similar network properties are a result of universal laws that govern evolution and architecture of complex systems. As such, the comprehension of these basic laws, or simple principles, has the potential to yield unprecedented insight into biological organization and evolution. Implicit in this stance is the emphasis on a systems-level view of biology, which considers ensembles of interacting parts (genes, proteins etc.) as opposed to individual actors alone.
While this optimistic perspective on the biological significance of network topologies generated considerable excitement in some quarters, it has not gone unchallenged. A more guarded view of these findings holds that the conserved global topological properties of biological networks might actually reveal little or nothing about the evolutionary mechanisms that gave rise to them or the particular nature of their organization [33–36]. Instead, the relevant architectural features of the individual networks could be quite specific and determined by the functional constraints on the particular system. This world-view stresses the anecdotal nature of biological sciences, placing the focus back on the nature of the individual genes, proteins and/or systems under consideration, and eschews the search for universal laws. Based on the results obtained here, it would seem that mammalian gene expression evolves more in accordance with the latter, more cautious view on the significance, or lack thereof, of conserved network properties. In the case of gene expression, the highly conserved global network properties belie highly divergent local structures that result from the rapid evolution of gene expression patterns. Thus, the architecture of the coexpression networks is highly species-specific and the conservation of the global network properties occurs despite, not because of, extensive evolutionary changes in gene expression.
Accordingly, at least in the case of gene expression divergence, the biological relevance of the global network topological properties appears questionable. Of course, this does not prevent network analysis from being a powerful approach, possibly, the most appropriate one for the quantitative study of complex systems made up of numerous interacting parts. It is also worth noting that coexpression networks built from randomly permuted expression vectors differ from the observed networks in not containing high-degree nodes (hubs) and thus cannot be claimed to possess scale-free properties with respect to their node degree distributions (data not shown). Thus, some biological features of expression patterns that yield the observed node-degree distributions in coexpression networks might exist; identifying such features could be important for understanding evolution of gene expression.
With regard to the more specific aspects of this work, the conservation of a small but substantial component of the coexpression network indicates that, the rapid evolution notwithstanding, the network evolves under the constraints of purifying selection. The biological significance of the rapid interspecies divergence of coexpression networks remains an open problem [4–6, 21, 37, 38]. It is yet unclear how much of this divergence is neutral, biologically irrelevant noise and how much is functional divergence driven by positive selection and defining, in part, salient differences in the biology of the respective organisms. Addressing these questions is an important goal for future network studies.
Orthologous gene expression
Gene expression data, based on Affymetrix microarray experiments, for human, and mouse are obtained from the mammalian gene expression atlas . These expression data were retrieved from the UCSC Genome Browser . Affymetrix probe identifiers (ids) were mapped to human and mouse genomic loci using UCSC Genome Browser and NCBI annotations as shown below:
Affymetrix probe id → GenBank accession → RefSeq accession → NCBI Locus id
Only affymetrix probes that map to unique genomic loci were considered for further analysis. When loci were found to be covered by multiple probes, the probe yielding the highest overall expression level was used in subsequent analyses.
In order to directly compare gene coexpression networks of different species, a set of orthologous genes expressed over a set of common tissue samples was analyzed. 9,105 orthologous human-mouse genes pairs were identified, using reciprocal best BLASTP hits , along with 28 common tissues with expression data for both human and mouse. For each gene, for each tissue, there were two replicate measurements. The average of these two values was taken to produce a 9105 × 28 matrix of real values. This matrix was further normalized as follows. For each gene, the median of the expression values of the gene across all tissues was computed and the entries of the corresponding matrix row were normalized with this value. These values were then log2 normalized resulting in a set of values with median zero.
Vectors of normalized tissue-specific expression levels were compared using a number of different measures: Euclidean distance, Manhattan distance, Jensen-Shannon entropy, dot-product, cosine similarity and Pearson correlation coefficient. Results reported in the body of the manuscript are for networks constructed using the Pearson correlation coefficient (PCC), and a discussion of results based on other measures is included in the Supplementary Information section (see Additional file 1).
All-against-all gene expression profile comparisons for the human and mouse matrices (9,105 × 28) were used to generate species-specific coexpression networks. Network nodes correspond to genes and gene pairs with PCC r≥0.7 were linked by and edge. Networks' topological properties were analyzed using MATLAB®. For each network the number of nodes and number of edges was simply counted. The average degree <k> was calculated as the average number of connections per node. The average clustering coefficient <C> was calculated as the average clustering coefficient of all nodes with at least two neighbors using the formula: Ci = 2n i /ki(ki-1), where n i is the number of observed links connecting the k i neighbors of node i and k i (k i -1)/2 is the total number of possible links. The average path length (<l>) was calculated as the average shortest path, or the smallest number of edges needed to connect two nodes, between any two reachable nodes in the network. Node degree distributions were plotted with the degree (k) on the x-axis and the number of nodes with this degree f(k) on the y-axis. Clustering coefficient against node degree C(k) distributions were plotted with the degree (k) on the x-axis and the average clustering coefficient <C> for all nodes with degree k on the y-axis. Species-specific networks were compared to derive a conserved intersection network containing only edges that connect the same orthologous genes (Figure 4a), and the network properties of the intersection network were calculated. Controls for experimental variance were performed by constructing two replicate-specific networks for human and mouse respectively and then computing the species-specific replicate intersection networks. A normalized intersection network was calculated by comparing the two species-specific replicate intersection networks. A control for experimental and biological variance was conducted by comparing mouse expression data from Novartis  with and independently obtained mouse expression data set .
Network visualization and functional analysis was done using Cytoscape . Networks were partitioned into tightly linked clusters of genes using MCODE . Genes in the networks were functionally categorized using their Gene Ontology (GO) biological process annotation terms . Overrepresented GO terms were identified with BINGO  by comparing the relative frequencies of GO terms in specific clusters with the frequencies of randomly selected GO-terms. The Hypergeometric test was used to do this with the Benjamini and Hochberg false discovery rate correction for multiple tests and a P-value threshold of 0.001. Pairwise similarities between gene GO terms were measured using the semantic similarity method, which computes the relative distance between any two terms along the GO-graph .
The authors would like to thank Yuri Wolf and Quaid Morris for important suggestions and members of the Koonin group and Madan Babu Mohan for helpful discussions. The authors would like to thank Heikki Mannila for his support in bringing PT to the NCBI. This study utilized the high-performance computational capabilities of the Biowulf PC/Linux cluster at the National Institutes of Health, Bethesda, MD. This research was supported in part by the Intramural Research Program of the NIH, NLM, NCBI.
- Britten RJ, Davidson EH: Gene regulation for higher cells: a theory. Science. 1969, 165 (891): 349-357.View ArticlePubMedGoogle Scholar
- Britten RJ, Davidson EH: Repetitive and non-repetitive DNA sequences and a speculation on the origins of evolutionary novelty. Q Rev Biol. 1971, 46 (2): 111-138. 10.1086/406830.View ArticlePubMedGoogle Scholar
- King MC, Wilson AC: Evolution at two levels in humans and chimpanzees. Science. 1975, 188 (4184): 107-116.View ArticlePubMedGoogle Scholar
- Khaitovich P, Weiss G, Lachmann M, Hellmann I, Enard W, Muetzel B, Wirkner U, Ansorge W, Paabo S: A neutral model of transcriptome evolution. PLoS Biol. 2004, 2 (5): E132-10.1371/journal.pbio.0020132.PubMed CentralView ArticlePubMedGoogle Scholar
- Yanai I, Graur D, Ophir R: Incongruent expression profiles between human and mouse orthologous genes suggest widespread neutral evolution of transcription control. Omics. 2004, 8 (1): 15-24. 10.1089/153623104773547462.View ArticlePubMedGoogle Scholar
- Jordan IK, Marino-Ramirez L, Koonin EV: Evolutionary significance of gene expression divergence. Gene. 2005, 345 (1): 119-126. 10.1016/j.gene.2004.11.034.PubMed CentralView ArticlePubMedGoogle Scholar
- Khaitovich P, Hellmann I, Enard W, Nowick K, Leinweber M, Franz H, Weiss G, Lachmann M, Paabo S: Parallel patterns of evolution in the genomes and transcriptomes of humans and chimpanzees. Science. 2005, 309 (5742): 1850-1854. 10.1126/science.1108296.View ArticlePubMedGoogle Scholar
- Luscombe NM, Babu MM, Yu H, Snyder M, Teichmann SA, Gerstein M: Genomic analysis of regulatory network dynamics reveals large topological changes. Nature. 2004, 431 (7006): 308-312. 10.1038/nature02782.View ArticlePubMedGoogle Scholar
- Gu Z, Nicolae D, Lu HH, Li WH: Rapid divergence in expression between duplicate genes inferred from microarray data. Trends Genet. 2002, 18 (12): 609-613. 10.1016/S0168-9525(02)02837-8.View ArticlePubMedGoogle Scholar
- Makova KD, Li WH: Divergence in the spatial pattern of gene expression between human duplicate genes. Genome Res. 2003, 13 (7): 1638-1645. 10.1101/gr.1133803.PubMed CentralView ArticlePubMedGoogle Scholar
- Madan Babu M, Teichmann SA, Aravind L: Evolutionary Dynamics of Prokaryotic Transcriptional Regulatory Networks. J Mol Biol. 2006, 358 (2): 614-33. 10.1016/j.jmb.2006.02.019.View ArticlePubMedGoogle Scholar
- Ge H, Liu Z, Church GM, Vidal M: Correlation between transcriptome and interactome mapping data from Saccharomyces cerevisiae. Nat Genet. 2001, 29 (4): 482-486. 10.1038/ng776.View ArticlePubMedGoogle Scholar
- Wuchty S, Barabasi AL, Ferdig MT: Stable evolutionary signal in a Yeast protein interaction network. BMC Evol Biol. 2006, 6: 8-10.1186/1471-2148-6-8.PubMed CentralView ArticlePubMedGoogle Scholar
- Fraser HB, Hirsh AE, Wall DP, Eisen MB: Coevolution of gene expression among interacting proteins. Proc Natl Acad Sci U S A. 2004, 101 (24): 9033-9038. 10.1073/pnas.0402591101.PubMed CentralView ArticlePubMedGoogle Scholar
- Wolfe CJ, Kohane IS, Butte AJ: Systematic survey reveals general applicability of "guilt-by-association" within gene coexpression networks. BMC Bioinformatics. 2005, 6: 227-10.1186/1471-2105-6-227.PubMed CentralView ArticlePubMedGoogle Scholar
- Ihmels J, Bergmann S, Gerami-Nejad M, Yanai I, McClellan M, Berman J, Barkai N: Rewiring of the yeast transcriptional network through the evolution of motif usage. Science. 2005, 309 (5736): 938-940. 10.1126/science.1113833.View ArticlePubMedGoogle Scholar
- Su AI, Wiltshire T, Batalov S, Lapp H, Ching KA, Block D, Zhang J, Soden R, Hayakawa M, Kreiman G, Cooke MP, Walker JR, Hogenesch JB: A gene atlas of the mouse and human protein-encoding transcriptomes. Proc Natl Acad Sci U S A. 2004, 101 (16): 6062-6067. 10.1073/pnas.0400782101.PubMed CentralView ArticlePubMedGoogle Scholar
- Barabasi AL, Oltvai ZN: Network biology: understanding the cell's functional organization. Nat Rev Genet. 2004, 5 (2): 101-113. 10.1038/nrg1272.View ArticlePubMedGoogle Scholar
- Dorogovtsev SN, Mendes JFF: Evolution of networks: from biological networks to the internet and WWW. 2003, Oxford , Oxford University PressView ArticleGoogle Scholar
- Koonin EV, Wolf YI, Karev GP: Power laws, scale-free networks and genome biology. 2006, New York , SpringerView ArticleGoogle Scholar
- Jordan IK, Marino-Ramirez L, Wolf YI, Koonin EV: Conservation and coevolution in the scale-free human gene coexpression network. Mol Biol Evol. 2004, 21 (11): 2058-2070. 10.1093/molbev/msh222.View ArticlePubMedGoogle Scholar
- Su AI, Cooke MP, Ching KA, Hakak Y, Walker JR, Wiltshire T, Orth AP, Vega RG, Sapinoso LM, Moqrich A, Patapoutian A, Hampton GM, Schultz PG, Hogenesch JB: Large-scale analysis of the human and mouse transcriptomes. Proc Natl Acad Sci U S A. 2002, 99 (7): 4465-4470. 10.1073/pnas.012025199.PubMed CentralView ArticlePubMedGoogle Scholar
- Lord PW, Stevens RD, Brass A, Goble CA: Investigating semantic similarity measures across the Gene Ontology: the relationship between sequence and annotation. Bioinformatics. 2003, 19 (10): 1275-1283. 10.1093/bioinformatics/btg153.View ArticlePubMedGoogle Scholar
- Fay JC, Wu CI: The neutral theory in the genomic era. Curr Opin Genet Dev. 2001, 11 (6): 642-646. 10.1016/S0959-437X(00)00247-1.View ArticlePubMedGoogle Scholar
- Yang Z, Bielawski JP: Statistical methods for detecting molecular adaptation. Trends Ecol Evol. 2000, 15 (12): 496-503. 10.1016/S0169-5347(00)01994-7.View ArticlePubMedGoogle Scholar
- Wyckoff GJ, Wang W, Wu CI: Rapid evolution of male reproductive genes in the descent of man. Nature. 2000, 403 (6767): 304-309. 10.1038/35002070.View ArticlePubMedGoogle Scholar
- Bergelson J, Kreitman M, Stahl EA, Tian D: Evolutionary dynamics of plant R-genes. Science. 2001, 292 (5525): 2281-2285. 10.1126/science.1061337.View ArticlePubMedGoogle Scholar
- Barabasi AL: Linked: how everything is connected to everything else and what it means. 2002, Cambridge , PerseusGoogle Scholar
- Watts DJ: Six degrees: the science of a connected age. 2003, New York , NortonGoogle Scholar
- Barabasi AL, Albert R: Emergence of scaling in random networks. Science. 1999, 286 (5439): 509-512. 10.1126/science.286.5439.509.View ArticlePubMedGoogle Scholar
- Watts DJ, Strogatz SH: Collective dynamics of 'small-world' networks. Nature. 1998, 393 (6684): 440-442. 10.1038/30918.View ArticlePubMedGoogle Scholar
- Gisiger T: Scale invariance in biology: coincidence or footprint of a universal mechanism?. Biol Rev Camb Philos Soc. 2001, 76 (2): 161-209. 10.1017/S1464793101005607.View ArticlePubMedGoogle Scholar
- Keller EF: Revisiting "scale-free" networks. Bioessays. 2005, 27 (10): 1060-1068. 10.1002/bies.20294.View ArticlePubMedGoogle Scholar
- Newman MEJ: Power laws, Pareto distributions and Zipf's law. Contemporary Physics. 2005, 46: 323-351.View ArticleGoogle Scholar
- Wolf YI, Karev G, Koonin EV: Scale-free networks in biology: new insights into the fundamentals of evolution?. Bioessays. 2002, 24 (2): 105-109. 10.1002/bies.10059.View ArticlePubMedGoogle Scholar
- Liao BY, Zhang J: Low Rates of Expression-Profile Divergence in Highly-Expressed Genes and Tissue-Specific Genes During Mammalian Evolution. Mol Biol Evol. 2006, 23 (6): 1119-28. 10.1093/molbev/msj119.View ArticlePubMedGoogle Scholar
- Liao BY, Zhang J: Evolutionary conservation of expression profiles between human and mouse orthologous genes. Mol Biol Evol. 2006, 23 (3): 530-540. 10.1093/molbev/msj054.View ArticlePubMedGoogle Scholar
- Karolchik D, Baertsch R, Diekhans M, Furey TS, Hinrichs A, Lu YT, Roskin KM, Schwartz M, Sugnet CW, Thomas DJ, Weber RJ, Haussler D, Kent WJ: The UCSC Genome Browser Database. Nucleic Acids Res. 2003, 31 (1): 51-54. 10.1093/nar/gkg129.PubMed CentralView ArticlePubMedGoogle Scholar
- Altschul SF, Madden TL, Schaffer AA, Zhang J, Zhang Z, Miller W, Lipman DJ: Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res. 1997, 25 (17): 3389-3402. 10.1093/nar/25.17.3389.PubMed CentralView ArticlePubMedGoogle Scholar
- Zhang W, Morris QD, Chang R, Shai O, Bakowski MA, Mitsakakis N, Mohammad N, Robinson MD, Zirngibl R, Somogyi E, Laurin N, Eftekharpour E, Sat E, Grigull J, Pan Q, Peng WT, Krogan N, Greenblatt J, Fehlings M, van der Kooy D, Aubin J, Bruneau BG, Rossant J, Blencowe BJ, Frey BJ, Hughes TR: The functional landscape of mouse gene expression. J Biol. 2004, 3 (5): 21-10.1186/jbiol16.PubMed CentralView ArticlePubMedGoogle Scholar
- Shannon P, Markiel A, Ozier O, Baliga NS, Wang JT, Ramage D, Amin N, Schwikowski B, Ideker T: Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Res. 2003, 13 (11): 2498-2504. 10.1101/gr.1239303.PubMed CentralView ArticlePubMedGoogle Scholar
- Bader GD, Hogue CW: An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics. 2003, 4: 2-10.1186/1471-2105-4-2.PubMed CentralView ArticlePubMedGoogle Scholar
- Ashburner M, Ball CA, Blake JA, Botstein D, Butler H, Cherry JM, Davis AP, Dolinski K, Dwight SS, Eppig JT, Harris MA, Hill DP, Issel-Tarver L, Kasarskis A, Lewis S, Matese JC, Richardson JE, Ringwald M, Rubin GM, Sherlock G: Gene ontology: tool for the unification of biology. The Gene Ontology Consortium. Nat Genet. 2000, 25 (1): 25-29. 10.1038/75556.PubMed CentralView ArticlePubMedGoogle Scholar
- Maere S, Heymans K, Kuiper M: BiNGO: a Cytoscape plugin to assess overrepresentation of gene ontology categories in biological networks. Bioinformatics. 2005, 21 (16): 3448-3449. 10.1093/bioinformatics/bti551.View ArticlePubMedGoogle Scholar
- Babu MM: Introduction to microarray data analysis. Computational Genomics: Theory and Application. Edited by: Grant RP. 2004, Norwich , Horizon PressGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.