BACKGROUND
cellular functions are carried out in a modular way, and functional modules are basic building blocks of cellular organization  <cit> .
from the perspective of molecular biology, a functional module is regarded as a group of spatially isolated or chemically specific biological components that work together for a discrete biological function.
various functional modules such as protein complexes  <cit> , signalling/metabolic pathways  <cit>  and transcriptional clusters  <cit>  have been detected from functional genomic techniques or bioinformatics analyses of genomic data.
recent studies suggest, to varying degrees, functional modules correlate with evolutionary modules  <cit> , the latter being defined as cohesive evolutionary blocks in cellular systems  <cit> .
it was found that genes within functional modules tend to evolve in a coordinated way  <cit> , while some fraction of evolutionary modules  agree well with known functional modules  <cit> .
on the other hand, purely topological analysis by graph-theoretic methods has revealed that molecular networks, such as protein interaction  <cit> , gene regulatory  <cit>  and metabolic networks  <cit> , consist of topological modules – densely connected sub-networks within which there is a high density of edges, and between which there is a lower density of edges  <cit> .
since graph-theoretic methods analyze networks from topological point of view using minimal prior knowledge about biological function or evolution, they have the potential to shed new light on biological systems based on the unbiased structural information  <cit> .
actually, numerous studies have demonstrated, to some extent, topological modules in molecular networks tend to be functionally modularized  <cit> .
furthermore, studying molecular evolution from the viewpoint of network architecture is becoming a subject of current interest.
some recent studies suggested that the node degrees of molecular networks may constrain the evolution of proteins  <cit> , and protein interaction hubs situated within modules are more evolutionarily constrained than those bridging different modules  <cit> .
however, little has been known about how network modularity affects protein evolution.
thus more studies are expected to reveal the possible correlation between topological modules and evolutionary modules in molecular networks.
in this study, we ask to which extent the identified topological modules of metabolic networks co-evolve.
we explore this question by analysing the metabolic network of h. sapiens  reconstructed from the kegg database  <cit> .
we first break up the metabolic network into modules by the simulated annealing algorithm proposed in  <cit>  and study the linkage pattern between modules.
then we investigate the evidence for co-evolution of modules by analysing the phylogenetic profiles, evolutionary ages and evolutionary rates of enzyme genes within modules.
to mine the inherent relations between structure, function and evolution of metabolic networks, the features from h. sapiens network were then compared with those of the properly randomized counterparts, here, topological null model and biological null model, respectively.
RESULTS
identifying topological modules and their functions
we reconstructed the metabolic network of h. sapiens from the kegg database  <cit>  and represented the network by a directed substrate graph in such a way that the nodes correspond to metabolites and arcs correspond to enzyme-catalyzed reactions between these metabolites  <cit> .
the metabolic network of h. sapiens consists of  <dig> metabolites and  <dig> enzymes, with the biggest connected cluster includes  <dig> metabolites and  <dig> enzymes.
the simulated annealing algorithm  <cit>  was utilized to decompose the metabolic network.
totally  <dig> topologically compact modules were obtained.
in figure  <dig> we display the decomposition result as a network of modules, in which each node corresponds to a module and is represented by the functional cartography  <cit> .
further investigation revealed that most periphery modules correspond to a well-defined single pathway and perform relatively independent function.
on the contrary, the core modules are mixtures of several conventional biochemical pathways, thus are difficult to be assigned a simple function.
table  <dig> shows that the periphery modules carry out two categories of functions: catabolism of essential human nutrients taken from the diet , biosynthesis and metabolism for complex molecules , whereas the core modules generally perform basic metabolisms of sugars, amino acids, lipids and nucleotides.
since the h. sapiens metabolic network does not include biosynthetic pathways for essential human nutrients, the pathways for processing these substrates may have functioned in characterizing the species during evolutionary diversification.
on the other hand, owing to the function of hormones and glycans in mediating cell recognition, communication, and signal transduction, the ability to produce and utilize these complex molecules may have led the species to develop an advanced neural system for physiological regulation along the evolutionary process  <cit> .
thus the functions performed by periphery modules could be regarded as some high-level metabolisms specialized for h. sapiens, whereas the core modules are integrated to accomplish housekeeping processes of life.
especially, the three central pathways – embden-meyerhof-parnas , tricarboxylic acid  and pentose phosphate pathway  are broken up into several core modules, mainly in module  <dig>   <dig> and  <dig>  one possible explanation is that the metabolites in these central pathways are used as common precursors for biosynthesis of universal building blocks  <cit>  and are thus placed in different modules.
in addition, these metabolites have two or more functional classifications and that they may get assigned to different modules based on features other than the central pathway they belong to.
this result agrees with earlier observations concerning the high diversity of the tca and emp pathway  <cit> , as well as the clustering results for escherichia coli  metabolic network obtained by other algorithms  <cit> .
* represents that the corresponding module includes several pathways thus is difficult to assign it a simplex function.
the similarity between the phylogenetic profiles of enzymes within modules
the phylogenetic profiles of any pair of enzymes can be compared to determine whether these two enzymes exhibit significant co-occurrence, so as to result in similar phylogenetic profiles.
we adopted the jaccard coefficient  to measure the similarity between the phylogenetic profiles of enzyme pairs.
figure  <dig> shows the distribution of jc for all pairwise enzymes in the h. sapiens metabolic network.
it can be seen that most enzyme pairs exhibit low extent of similarity on their phylogenetic profiles.
the average jc of the global network is  <dig> .
the significant level p  of the distribution is  <dig> , i.e., the probability of enzyme pairs with jc bigger than  <dig>  is only  <dig> .
thus we set jc of  <dig>  as a threshold of similarity between phylogenetic profiles and regard enzyme pairs whose jc are bigger than  <dig>  as having similar phylogenetic profiles.
figure  <dig> illustrates the relationship between the average jc for enzyme pairs within modules and the inter-module degree of module , suggesting a statistically negative correlation tendency between these two variables.
since modules with high inter-module degrees are core modules, and those with low inter-module degrees are periphery modules, this result means that enzymes within periphery modules have higher extent of similar phylogenetic profiles than those within core modules.
we compare the similarity of phylogenetic profiles for enzyme pairs within each module with that within the global network.
figure  <dig> shows that enzyme pairs within most modules have higher average jc than those within the global network, and figure  <dig> demonstrates that most modules include high percentage of enzymes with similar phylogenetic profiles.
we used hypergeometric cumulative distribution  <cit>  to quantitatively measure whether a module is more enriched with enzymes of similar phylogenetic profiles  than that by chance.
given significance level α =  <dig> , a p-value smaller than α demonstrates low probability that the enzymes of similar phylogenetic profiles appear in the same module by chance.
integrating these three measures, we regard a module as an evolutionary module enriched with enzymes of similar phylogenetic profiles, if it satisfies all of the following three criteria:
average jc of the module is bigger than that of the global network.
the fraction of enzyme pairs with jc ≥  <dig>   in the module is significantly bigger than  <dig> , i.e., the fraction of that in the global network.
we set the cutoff to  <dig> .
the p-value is smaller than α =  <dig> .
as shown in figure  <dig>  all modules except module  <dig> satisfy the criteria , in which  <dig> modules  also satisfy the criteria .
of the  <dig> modules, only the p-value of module  <dig>  which equals to  <dig> , is bigger than  <dig> .
that is to say, although the average jc of enzyme pairs in module  <dig> is big enough, and this module also includes a high fraction of enzymes with similar phylogenetic profiles, this case has a high probability to occur by chance.
thus module  <dig> could not be regarded as an evolutionary module by our criteria.
in summary, a total of  <dig> modules out of  <dig>  were found to be evolutionary modules, most of which are periphery modules.
the inter-modules degree of eight modules are less than  <dig>  suggesting that periphery modules behave more cohesively in evolution than core modules.
that is to say, enzyme genes within periphery modules have higher tendency to be gained/lost together than those within core modules.
the evolutionary ages of modules
we classified enzyme genes in the h. sapiens network into seven evolutionary ages: prokaryota, protists, fungi, nematodes, arthropods, mammalian and human.
hypergeometric cumulative distribution  <cit>  was used to measure whether a module is more enriched with enzymes from a particular evolutionary age than would be expected by chance.
given significance level α =  <dig> , a p-value smaller than α demonstrates low probability that the enzyme genes of a particular evolution age have appeared by chance.
we defined the evolutionary age of a module as the biggest value of the evolutionary age of enzymes included in this module, which satisfies all of the two criteria:
more than 1/ <dig> enzymes of this module belong to the evolutionary age;
the corresponding p-value is smaller than α =  <dig> .
according to this definition, a total of  <dig> modules appear to belong to one specific evolutionary age.
see table  <dig> for the evolutionary age, percentage of enzymes in the specific age, p-value and inter-module degree for each module.
as can be seen in table  <dig>  all of the age- <dig> modules except for module  <dig> are core modules, while the modules with later evolutionary ages are periphery modules.
figure  <dig> shows the statistically significant negative correlation between evolutionary age of modules and average inter-module degrees.
the spearman's rank correlation between evolutionary age and inter-module degree is r = - <dig>  .
evolutionary age is defined as:  <dig>  prokaryota;  <dig>  protists;  <dig>  fungi;  <dig>  nematodes;  <dig>  arthropods;  <dig>  mammalian;  <dig>  human.
see method part for the detailed definition.
the distribution feature of core and periphery modules in different evolutionary ages provides some evidence for the evolutionary history of metabolic networks.
matching the evolutionary ages of modules with their functions suggests how ancient cellular functions may have evolved to gain new phenotypes with improved adaptation: the core modules appeared earlier in evolution and communicate frequently to perform the basic functions, while the periphery modules "sprout" from the compactly inter-connected core modules later via sparse linkages to carry out some novel, specialized functions.
in this way, the housekeeping functions are conserved in core modules while functional specialization is achieved by extending periphery modules.
evolutionary rates of constituent enzyme genes of modules
we adopted the evolutionary rate to estimate the evolutionary constraints on metabolic enzymes.
a small value of evolutionary rate suggests a smaller fraction of accepted amino acid substitutions , hence a higher evolutionary constraint on the enzyme.
we extracted the evolutionary rate of each enzyme gene included in the h. sapiens metabolic network from the homologene database  <cit> , computed by the approaches in  <cit> .
then the evolutionary rates were averaged over all enzyme genes within the same module.
the relationship between average evolutionary rate of enzyme genes within modules and inter-module degrees is shown in figure  <dig>  figure  <dig> indicates a statistically significant negative correlation between the average evolutionary rate of module and inter-module degree .
the histogram of average evolutionary rate of modules versus binned inter-module degree is displayed in figure  <dig>  indicating that enzymes in core modules evolve more slowly than those in periphery modules.
that is to say, core modules have higher evolutionary constraints, thus are more evolutionarily conserved than periphery modules.
this observation is in agreement with the housekeeping functions of core modules.
comparison of the h. sapiens network with its randomised counterparts
in order to investigate whether the topological, functional and evolutionary features of modularity we presented above are intrinsic for metabolic networks, we constructed two versions of randomised counterparts for the h. sapiens metabolic network and compared them with the real network.
the first version of randomized network, called topological null model, was constructed by rewiring the links between nodes while preserving some low-level topological properties of the h. sapiens metabolic network.
when shuffling the links, considering that the distribution of bi-directed arcs is an inherent topological feature of metabolic networks  <cit> , we kept not only the degree of each node  <cit> , but also the total number of directed and bi-directed arcs of the metabolic network .
totally  <dig> random networks were generated and then decomposed by simulated annealing, resulting in mean modularity metric  <dig>  and the standard deviation  <dig> .
the modularity metric of the h. sapiens metabolic network is  <dig> ,  <dig> multiples of standard deviation above that of the randomized counterparts, suggesting that the higher modularity of h. sapiens network is unlikely to arise by chance.
moreover, as shown in figure  <dig> and table a <dig> of additional file , the modules of the random network are so densely connected that their linkage pattern does not show a clear-cut core-periphery dichotomy.
these comparisons indicate that the highly modular core-periphery organization of h. sapiens network could be an intrinsic topological character of metabolic networks, rather than a random phenomenon.
we generated the second version of randomized network, called biological null model, through shuffling the enzymes that catalyze the reactions while preserving the network topology.
at each step of randomization, we randomly chose two reactions that are catalyzed by different enzymes and then exchanged the enzymes catalyzing them.
for one randomized network, we performed the same analysis about the functional distributions, phylogenic profiles, evolutionary ages, and evolutionary rates of its topological modules as we did for the h. sapiens network.
although the randomized network has the same topology as the h. sapiens network, its topological modules are high heterogeneity of reactions from different pathways , thus could not be functional specific modules.
from evolutionary view, enzymes within the same modules do not exhibit similar phylogenic profiles ; neither the modules have specific evolutionary ages.
in addition, the correlation between the average evolutionary rates of modules and the inter-module degrees is not statistically significant .
these results demonstrate that the topological modules of the biological null model show absence of evolutionary modularity.
therefore, the functional and evolutionary modularity of topological modules could be inherent for metabolic networks.
CONCLUSIONS
in this study we have conducted a system-level survey about how evolution of enzyme genes is related to the structure and function of metabolic networks.
from topological point of view, metabolic networks exhibit highly modular core-periphery organization pattern.
furthermore, the core modules are more evolutionarily conserved and perform some housekeeping metabolism functions, while the periphery modules appear later in evolution history and accomplish relatively specific functions.
our results suggest that the core-periphery modularity organization reflects the functional and evolutionary requirements of metabolic systems.
the denser inter-connections between core modules may offer effectual protections to the basic metabolic process and keep the robustness of the metabolic system.
on the other hand, the looser inter-linkages of periphery modules could function in favour of the flexibility and evolutionary ability of the system, so that the mutation or evolution of these parts may generate new phenotypes with improved adaptation while not significantly affecting other modules or even causing malfunction of the whole system.
our observation may shed light on a more global understanding of the topology, function and evolution for metabolic networks.

 cellular functions are carried out in a modular way, and functional modules are basic building blocks of cellular organization. from the perspective of molecular biology, a functional module is regarded as a group of spatially isolated or chemically specific biological components that work together for a discrete biological function. various functional modules such as protein complexes, signalling/metabolic pathways and transcriptional clusters have been detected from functional genomic techniques or bioinformatics analyses of genomic data. recent studies suggest, to varying degrees, functional modules correlate with evolutionary modules, the latter being defined as cohesive evolutionary blocks in cellular systems. it was found that genes within functional modules tend to evolve in a coordinated way, while some fraction of evolutionary modules agree well with known functional modules. on the other hand, purely topological analysis by graph-theoretic methods has revealed that molecular networks, such as protein interaction, gene regulatory and metabolic networks, consist of topological modules – densely connected sub-networks within which there is a high density of edges, and between which there is a lower density of edges. since graph-theoretic methods analyze networks from topological point of view using minimal prior knowledge about biological function or evolution, they have the potential to shed new light on biological systems based on the unbiased structural information. actually, numerous studies have demonstrated, to some extent, topological modules in molecular networks tend to be functionally modularized. furthermore, studying molecular evolution from the viewpoint of network architecture is becoming a subject of current interest. some recent studies suggested that the node degrees of molecular networks may constrain the evolution of proteins, and protein interaction hubs situated within modules are more evolutionarily constrained than those bridging different modules. however, little has been known about how network modularity affects protein evolution. thus more studies are expected to reveal the possible correlation between topological modules and evolutionary modules in molecular networks. in this study, we ask to which extent the identified topological modules of metabolic networks co-evolve. we explore this question by analysing the metabolic network of h. sapiens reconstructed from the kegg database. we first break up the metabolic network into modules by the simulated annealing algorithm proposed in and study the linkage pattern between modules. then we investigate the evidence for co-evolution of modules by analysing the phylogenetic profiles, evolutionary ages and evolutionary rates of enzyme genes within modules. to mine the inherent relations between structure, function and evolution of metabolic networks, the features from h. sapiens network were then compared with those of the properly randomized counterparts, here, topological null model and biological null model, respectively.  identifying topological modules and their functions we reconstructed the metabolic network of h. sapiens from the kegg database and represented the network by a directed substrate graph in such a way that the nodes correspond to metabolites and arcs correspond to enzyme-catalyzed reactions between these metabolites. the metabolic network of h. sapiens consists of metabolites and enzymes, with the biggest connected cluster includes metabolites and enzymes. the simulated annealing algorithm was utilized to decompose the metabolic network. totally topologically compact modules were obtained. in figure we display the decomposition result as a network of modules, in which each node corresponds to a module and is represented by the functional cartography. further investigation revealed that most periphery modules correspond to a well-defined single pathway and perform relatively independent function. on the contrary, the core modules are mixtures of several conventional biochemical pathways, thus are difficult to be assigned a simple function. table shows that the periphery modules carry out two categories of functions: catabolism of essential human nutrients taken from the diet, biosynthesis and metabolism for complex molecules, whereas the core modules generally perform basic metabolisms of sugars, amino acids, lipids and nucleotides. since the h. sapiens metabolic network does not include biosynthetic pathways for essential human nutrients, the pathways for processing these substrates may have functioned in characterizing the species during evolutionary diversification. on the other hand, owing to the function of hormones and glycans in mediating cell recognition, communication, and signal transduction, the ability to produce and utilize these complex molecules may have led the species to develop an advanced neural system for physiological regulation along the evolutionary process. thus the functions performed by periphery modules could be regarded as some high-level metabolisms specialized for h. sapiens, whereas the core modules are integrated to accomplish housekeeping processes of life. especially, the three central pathways – embden-meyerhof-parnas, tricarboxylic acid and pentose phosphate pathway are broken up into several core modules, mainly in module and one possible explanation is that the metabolites in these central pathways are used as common precursors for biosynthesis of universal building blocks and are thus placed in different modules. in addition, these metabolites have two or more functional classifications and that they may get assigned to different modules based on features other than the central pathway they belong to. this result agrees with earlier observations concerning the high diversity of the tca and emp pathway, as well as the clustering results for escherichia coli metabolic network obtained by other algorithms. * represents that the corresponding module includes several pathways thus is difficult to assign it a simplex function. the similarity between the phylogenetic profiles of enzymes within modules the phylogenetic profiles of any pair of enzymes can be compared to determine whether these two enzymes exhibit significant co-occurrence, so as to result in similar phylogenetic profiles. we adopted the jaccard coefficient to measure the similarity between the phylogenetic profiles of enzyme pairs. figure shows the distribution of jc for all pairwise enzymes in the h. sapiens metabolic network. it can be seen that most enzyme pairs exhibit low extent of similarity on their phylogenetic profiles. the average jc of the global network is. the significant level p of the distribution is, i.e., the probability of enzyme pairs with jc bigger than is only. thus we set jc of as a threshold of similarity between phylogenetic profiles and regard enzyme pairs whose jc are bigger than as having similar phylogenetic profiles. figure illustrates the relationship between the average jc for enzyme pairs within modules and the inter-module degree of module, suggesting a statistically negative correlation tendency between these two variables. since modules with high inter-module degrees are core modules, and those with low inter-module degrees are periphery modules, this result means that enzymes within periphery modules have higher extent of similar phylogenetic profiles than those within core modules. we compare the similarity of phylogenetic profiles for enzyme pairs within each module with that within the global network. figure shows that enzyme pairs within most modules have higher average jc than those within the global network, and figure demonstrates that most modules include high percentage of enzymes with similar phylogenetic profiles. we used hypergeometric cumulative distribution to quantitatively measure whether a module is more enriched with enzymes of similar phylogenetic profiles than that by chance. given significance level α =, a p-value smaller than α demonstrates low probability that the enzymes of similar phylogenetic profiles appear in the same module by chance. integrating these three measures, we regard a module as an evolutionary module enriched with enzymes of similar phylogenetic profiles, if it satisfies all of the following three criteria: average jc of the module is bigger than that of the global network. the fraction of enzyme pairs with jc ≥ in the module is significantly bigger than, i.e., the fraction of that in the global network. we set the cutoff to. the p-value is smaller than α =. as shown in figure all modules except module satisfy the criteria, in which modules also satisfy the criteria. of the modules, only the p-value of module which equals to, is bigger than. that is to say, although the average jc of enzyme pairs in module is big enough, and this module also includes a high fraction of enzymes with similar phylogenetic profiles, this case has a high probability to occur by chance. thus module could not be regarded as an evolutionary module by our criteria. in summary, a total of modules out of were found to be evolutionary modules, most of which are periphery modules. the inter-modules degree of eight modules are less than suggesting that periphery modules behave more cohesively in evolution than core modules. that is to say, enzyme genes within periphery modules have higher tendency to be gained/lost together than those within core modules. the evolutionary ages of modules we classified enzyme genes in the h. sapiens network into seven evolutionary ages: prokaryota, protists, fungi, nematodes, arthropods, mammalian and human. hypergeometric cumulative distribution was used to measure whether a module is more enriched with enzymes from a particular evolutionary age than would be expected by chance. given significance level α =, a p-value smaller than α demonstrates low probability that the enzyme genes of a particular evolution age have appeared by chance. we defined the evolutionary age of a module as the biggest value of the evolutionary age of enzymes included in this module, which satisfies all of the two criteria: more than 1/ enzymes of this module belong to the evolutionary age; the corresponding p-value is smaller than α =. according to this definition, a total of modules appear to belong to one specific evolutionary age. see table for the evolutionary age, percentage of enzymes in the specific age, p-value and inter-module degree for each module. as can be seen in table all of the age- modules except for module are core modules, while the modules with later evolutionary ages are periphery modules. figure shows the statistically significant negative correlation between evolutionary age of modules and average inter-module degrees. the spearman's rank correlation between evolutionary age and inter-module degree is r = -. evolutionary age is defined as: prokaryota; protists; fungi; nematodes; arthropods; mammalian; human. see method part for the detailed definition. the distribution feature of core and periphery modules in different evolutionary ages provides some evidence for the evolutionary history of metabolic networks. matching the evolutionary ages of modules with their functions suggests how ancient cellular functions may have evolved to gain new phenotypes with improved adaptation: the core modules appeared earlier in evolution and communicate frequently to perform the basic functions, while the periphery modules "sprout" from the compactly inter-connected core modules later via sparse linkages to carry out some novel, specialized functions. in this way, the housekeeping functions are conserved in core modules while functional specialization is achieved by extending periphery modules. evolutionary rates of constituent enzyme genes of modules we adopted the evolutionary rate to estimate the evolutionary constraints on metabolic enzymes. a small value of evolutionary rate suggests a smaller fraction of accepted amino acid substitutions, hence a higher evolutionary constraint on the enzyme. we extracted the evolutionary rate of each enzyme gene included in the h. sapiens metabolic network from the homologene database, computed by the approaches in. then the evolutionary rates were averaged over all enzyme genes within the same module. the relationship between average evolutionary rate of enzyme genes within modules and inter-module degrees is shown in figure figure indicates a statistically significant negative correlation between the average evolutionary rate of module and inter-module degree. the histogram of average evolutionary rate of modules versus binned inter-module degree is displayed in figure indicating that enzymes in core modules evolve more slowly than those in periphery modules. that is to say, core modules have higher evolutionary constraints, thus are more evolutionarily conserved than periphery modules. this observation is in agreement with the housekeeping functions of core modules. comparison of the h. sapiens network with its randomised counterparts in order to investigate whether the topological, functional and evolutionary features of modularity we presented above are intrinsic for metabolic networks, we constructed two versions of randomised counterparts for the h. sapiens metabolic network and compared them with the real network. the first version of randomized network, called topological null model, was constructed by rewiring the links between nodes while preserving some low-level topological properties of the h. sapiens metabolic network. when shuffling the links, considering that the distribution of bi-directed arcs is an inherent topological feature of metabolic networks, we kept not only the degree of each node, but also the total number of directed and bi-directed arcs of the metabolic network. totally random networks were generated and then decomposed by simulated annealing, resulting in mean modularity metric and the standard deviation. the modularity metric of the h. sapiens metabolic network is, multiples of standard deviation above that of the randomized counterparts, suggesting that the higher modularity of h. sapiens network is unlikely to arise by chance. moreover, as shown in figure and table a of additional file, the modules of the random network are so densely connected that their linkage pattern does not show a clear-cut core-periphery dichotomy. these comparisons indicate that the highly modular core-periphery organization of h. sapiens network could be an intrinsic topological character of metabolic networks, rather than a random phenomenon. we generated the second version of randomized network, called biological null model, through shuffling the enzymes that catalyze the reactions while preserving the network topology. at each step of randomization, we randomly chose two reactions that are catalyzed by different enzymes and then exchanged the enzymes catalyzing them. for one randomized network, we performed the same analysis about the functional distributions, phylogenic profiles, evolutionary ages, and evolutionary rates of its topological modules as we did for the h. sapiens network. although the randomized network has the same topology as the h. sapiens network, its topological modules are high heterogeneity of reactions from different pathways, thus could not be functional specific modules. from evolutionary view, enzymes within the same modules do not exhibit similar phylogenic profiles; neither the modules have specific evolutionary ages. in addition, the correlation between the average evolutionary rates of modules and the inter-module degrees is not statistically significant. these results demonstrate that the topological modules of the biological null model show absence of evolutionary modularity. therefore, the functional and evolutionary modularity of topological modules could be inherent for metabolic networks.  in this study we have conducted a system-level survey about how evolution of enzyme genes is related to the structure and function of metabolic networks. from topological point of view, metabolic networks exhibit highly modular core-periphery organization pattern. furthermore, the core modules are more evolutionarily conserved and perform some housekeeping metabolism functions, while the periphery modules appear later in evolution history and accomplish relatively specific functions. our results suggest that the core-periphery modularity organization reflects the functional and evolutionary requirements of metabolic systems. the denser inter-connections between core modules may offer effectual protections to the basic metabolic process and keep the robustness of the metabolic system. on the other hand, the looser inter-linkages of periphery modules could function in favour of the flexibility and evolutionary ability of the system, so that the mutation or evolution of these parts may generate new phenotypes with improved adaptation while not significantly affecting other modules or even causing malfunction of the whole system. our observation may shed light on a more global understanding of the topology, function and evolution for metabolic networks. 
such systems level analysis could demonstrate how the evolution of genes may be placed in a genome-scale network context, giving a novel perspective on molecular evolution. in this work, the functional and evolutionary modularity of homo sapiens metabolic network were investigated from a topological point of view. network decomposition shows that the metabolic network is organized in a highly modular core-periphery way, in which the core modules are tightly linked together and perform basic metabolism functions, whereas the periphery modules only interact with few modules and accomplish relatively independent and specialized functions. peripheral modules tend to evolve more cohesively and faster than core modules do. the architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. the correlation between functional, evolutionary and topological modularity suggests that the evolutionary history and functional requirements of metabolic systems have been imprinted in the architecture of metabolic networks. moreover, over half of the modules exhibit co-evolutionary feature and belong to specific evolutionary ages.
 the architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. however, how the modular topology of the molecular network affects the evolution of its member proteins remains unclear.  in this work, the functional and evolutionary modularity of homo sapiens metabolic network were investigated from a topological point of view. network decomposition shows that the metabolic network is organized in a highly modular core-periphery way, in which the core modules are tightly linked together and perform basic metabolism functions, whereas the periphery modules only interact with few modules and accomplish relatively independent and specialized functions. moreover, over half of the modules exhibit co-evolutionary feature and belong to specific evolutionary ages. peripheral modules tend to evolve more cohesively and faster than core modules do.  the correlation between functional, evolutionary and topological modularity suggests that the evolutionary history and functional requirements of metabolic systems have been imprinted in the architecture of metabolic networks. such systems level analysis could demonstrate how the evolution of genes may be placed in a genome-scale network context, giving a novel perspective on molecular evolution. 