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the nodes of the graph correspond to metabolic genes , and edges correspond to connections established by metabolic reactions .
metabolic genes x and y are considered connected if and only if there exists a metabolite that is present among the list of either reactants or products of reactions catalyzed by enzymes encoded by both x and y. the metabolic connectivity graph is used to calculate network distance ( or metabolic separation ) between genes .
we define a pair of directly connected metabolic genes as being separated by distance 1 . in general , we define network distance between the genes x and y as the length of the shortest path from x to y on the metabolic connectivity graph . a hand - curated metabolic network model of s. cerevisiae ( forster et al , 2003 )
was used to construct a comprehensive metabolic connectivity graph . while any metabolite can be used to deduce gene connectivity , the relationships established by the common cofactors , such as atp , are not likely to connect genes with similar metabolic functions . in compiling a global metabolic connectivity graph
, we consider a subset of metabolites , which excludes most highly connected metabolic species .
an exclusion threshold was determined based on the connectivity of the resulting gene dependency graph ( supplementary figure 1 ) .
a total of 14 most highly connected metabolites ( atp , adp , amp , co2 , coa , glutamate , h , nad , nadh , nadp , nadph , nh3 , orthophosphate , pyrophosphate ) and their mitochondrial and external analogs were excluded .
the general trends described in the paper are not sensitive to the precise choice of the metabolite set ; however , the actual values change when more or less metabolites are considered . for detailed analysis ,
genes encoding enzymes that are part of known complexes , according to mips complex database ( http://mips.gsf.de ) and sgd ( http://www.yeastgenome.org/ ) , were masked as unassigned enzymes , so that their expression profiles would not be included in any of the analysis ( 36 enzyme - encoding genes in total ) .
the rosetta 's  compendium ' data set ( hughes et al , 2000 ) measures expression profiles of over 6200 s. cerevisiae open reading frames ( orfs ) across 287 deletion strains and 13 chemical conditions .
in addition , the data set contains 63 negative control measurements comparing two independent cultures of the same strain . these were used to establish individual error models for each orf , providing not only the raw intensity and ratio measurement values for each experimental data point , but also a p - value gauging the significance of change in expression level .
we also used a data set from brown 's group , containing 173 environmental perturbations ( gasch et al , 2000 ) , and a data set from young 's group with 34 conditions describing seven environmental perturbation time courses ( causton et al , 2001 ) .
log 10 intensity ratios of each data set were normalized to have a mean of 0 and a variance of 1 .
separate time courses contained in these data sets were first normalized individually and then combined .
supplementary table 8 shows the relative variability of metabolic enzyme - encoding genes in each data set .
the expression distance measure between orfs x and y is then taken to be 1s(px , py) , where px and py are expression profile vectors of x and y , and s corresponds to spearman rank correlation coefficient , calculated according to press et al ( 2002 ) .
combined expression profile vectors are formed by concatenation of log 10 ratio values from three data sets .
conditions missing experimental value for at least one of the genes were omitted in calculating the expression distance of a given gene pair .
genes that were missing expression values for more than 25% of conditions were not considered in the analysis .
information on transcription factor binding to the metabolic gene promoter sites was taken from lee et al ( 2002 ) . a p - value threshold of 0.001
was used to select transcription factor binding occurrences . to assess genome context association based on the physical clustering of genes on the chromosome , we relied on gene order statistics .
chromosome clustering association score between genes x and y was calculated as s(xy)=ggp(dg(x , y ) ) , where g is a set of genomes and p(dg(x , y ) ) is the probability of observing gene order distance dg(x , y ) between genes x and y in a genome g , calculated based on the chromosome sizes of organism under the null hypothesis that genes are randomly ordered across the chromosomes .
orthology mapping was established using best bidirectional hits from kegg ssdb ( itoh et al , 2004 ) .
phylogenetic profile cooccurrence association ( pellegrini et al , 1999 ) was assessed using hypergeometric probability , as described by bowers et al ( 2004 ) .
the orthology data set was constructed based on best bidirectional blastp hits against ncbi nr protein data set .
the calculation was limited to organisms containing orthologs for at least 1% of s. cerevisiae genes .
the elementary topological motifs of the metabolite graph were classified in terms of the expression properties of the genes involved .
the elementary node structures were enumerated , and sets of genes that were connected in the appropriate topology were extracted for each structure .
it is possible for one gene to be included in multiple occurrences of the same motif ; in other words , we counted any substructure with the correct topology as an occurrence .
motif instances formed around top 14 most connected metabolites , as well as their mitochondrial and external forms , were not included in the analysis .
mean expression distances of different types of gene pairs were compared using the wilcoxon rank test ( wilcoxon , 1945 ) . in generating homolog - filtered data ,
a pair of metabolic genes was excluded from the analysis if the blast score comparing the two nucleotide sequences was below an e - value of 10 .
the nodes of the graph correspond to metabolic genes , and edges correspond to connections established by metabolic reactions .
metabolic genes x and y are considered connected if and only if there exists a metabolite that is present among the list of either reactants or products of reactions catalyzed by enzymes encoded by both x and y. the metabolic connectivity graph is used to calculate network distance ( or metabolic separation ) between genes .
we define a pair of directly connected metabolic genes as being separated by distance 1 . in general , we define network distance between the genes x and y as the length of the shortest path from x to y on the metabolic connectivity graph . a hand - curated metabolic network model of s. cerevisiae ( forster et al , 2003 )
was used to construct a comprehensive metabolic connectivity graph . while any metabolite can be used to deduce gene connectivity , the relationships established by the common cofactors , such as atp , are not likely to connect genes with similar metabolic functions . in compiling a global metabolic connectivity graph
, we consider a subset of metabolites , which excludes most highly connected metabolic species .
an exclusion threshold was determined based on the connectivity of the resulting gene dependency graph ( supplementary figure 1 ) .
a total of 14 most highly connected metabolites ( atp , adp , amp , co2 , coa , glutamate , h , nad , nadh , nadp , nadph , nh3 , orthophosphate , pyrophosphate ) and their mitochondrial and external analogs were excluded .
the general trends described in the paper are not sensitive to the precise choice of the metabolite set ; however , the actual values change when more or less metabolites are considered . for detailed analysis ,
genes encoding enzymes that are part of known complexes , according to mips complex database ( http://mips.gsf.de ) and sgd ( http://www.yeastgenome.org/ ) , were masked as unassigned enzymes , so that their expression profiles would not be included in any of the analysis ( 36 enzyme - encoding genes in total ) .
we used three data sets as sources of gene expression information . the rosetta 's  compendium ' data set ( hughes et al , 2000 ) measures expression profiles of over 6200 s. cerevisiae open reading frames ( orfs ) across 287 deletion strains and 13 chemical conditions .
in addition , the data set contains 63 negative control measurements comparing two independent cultures of the same strain . these were used to establish individual error models for each orf , providing not only the raw intensity and ratio measurement values for each experimental data point , but also a p - value gauging the significance of change in expression level .
we also used a data set from brown 's group , containing 173 environmental perturbations ( gasch et al , 2000 ) , and a data set from young 's group with 34 conditions describing seven environmental perturbation time courses ( causton et al , 2001 ) .
log 10 intensity ratios of each data set were normalized to have a mean of 0 and a variance of 1 .
separate time courses contained in these data sets were first normalized individually and then combined .
supplementary table 8 shows the relative variability of metabolic enzyme - encoding genes in each data set .
the expression distance measure between orfs x and y is then taken to be 1s(px , py) , where px and py are expression profile vectors of x and y , and s corresponds to spearman rank correlation coefficient , calculated according to press et al ( 2002 ) .
combined expression profile vectors are formed by concatenation of log 10 ratio values from three data sets .
conditions missing experimental value for at least one of the genes were omitted in calculating the expression distance of a given gene pair .
genes that were missing expression values for more than 25% of conditions were not considered in the analysis .
information on transcription factor binding to the metabolic gene promoter sites was taken from lee et al ( 2002 ) . a p - value threshold of 0.001
to assess genome context association based on the physical clustering of genes on the chromosome , we relied on gene order statistics .
chromosome clustering association score between genes x and y was calculated as s(xy)=ggp(dg(x , y ) ) , where g is a set of genomes and p(dg(x , y ) ) is the probability of observing gene order distance dg(x , y ) between genes x and y in a genome g , calculated based on the chromosome sizes of organism under the null hypothesis that genes are randomly ordered across the chromosomes .
orthology mapping was established using best bidirectional hits from kegg ssdb ( itoh et al , 2004 ) .
phylogenetic profile cooccurrence association ( pellegrini et al , 1999 ) was assessed using hypergeometric probability , as described by bowers et al ( 2004 ) .
the orthology data set was constructed based on best bidirectional blastp hits against ncbi nr protein data set .
the calculation was limited to organisms containing orthologs for at least 1% of s. cerevisiae genes .
the elementary topological motifs of the metabolite graph were classified in terms of the expression properties of the genes involved .
the elementary node structures were enumerated , and sets of genes that were connected in the appropriate topology were extracted for each structure .
it is possible for one gene to be included in multiple occurrences of the same motif ; in other words , we counted any substructure with the correct topology as an occurrence .
motif instances formed around top 14 most connected metabolites , as well as their mitochondrial and external forms , were not included in the analysis .
mean expression distances of different types of gene pairs were compared using the wilcoxon rank test ( wilcoxon , 1945 ) . in generating homolog - filtered data ,
a pair of metabolic genes was excluded from the analysis if the blast score comparing the two nucleotide sequences was below an e - value of 10 .
mean expression distance is plotted as a function of the metabolic network distance separating the metabolic gene pairs for ( a ) all metabolic gene pairs ; ( b ) positively coexpressed pairs and ( c ) negatively coexpressed pairs .
( d ) fraction of metabolic gene pairs that share at least one transcription factor binding site in their promoter region as a function of metabolic network distance .
( a ) all irreversible metabolite graph motifs consisting of two genes ( x and y ) are analyzed using only positively coexpressed gene pairs .
the motifs are ordered according to the mean expression distance of gene pairs belonging to each motif .
the pair types are ordered ( from left to right ) in the order of increasing mean expression distance .
toward the goal of understanding system properties of biological networks , we investigate the global and local regulation of gene expression in the saccharomyces cerevisiae metabolic network . 
 our results demonstrate predominance of local gene regulation in metabolism . 
 metabolic genes display significant coexpression on distances smaller than the average network distance , a behavior supported by the distribution of transcription factor binding sites in the metabolic network and genome context associations . 
 positive gene coexpression decreases monotonically with distance in the network , while negative coexpression is strongest at intermediate network distances . 
 we show that basic topological motifs of the metabolic network exhibit statistically significant differences in coexpression behavior .