it represents a chemical 
 system generating all necessary chemical substances in living cells 
 through chemical reactions . it also represents a genetic system in 
 the sense that chemical reactions are catalyzed by genome - encoded 
 enzymes . the dual aspect of metabolism has been utilized for metabolic 
 reconstruction , where the repertoire of enzyme genes in the genome 
 is used to infer chemical capacity of an organism , such as biosynthetic 
 and biodegradation potentials and environmental adaptability . the 
 procedure for metabolic reconstruction generally involves finding 
 orthologous genes in the genome that match the network of enzymes 
 in known metabolic pathways . this type of analysis has revealed conserved functional 
 units in metabolic pathways ; for example , sets of enzyme genes adjacent 
 on the chromosome encoded in operon - like structures were linked to 
 functional units of successive reaction steps . in this paper our working hypothesis is that the functional units revealed by enzyme 
 clusters must also reflect chemical units of organic reactions . we 
 have thus developed a method to extract , what we call , reaction modules 
 without using the data on enzymes and enzyme genes . the metabolic 
 pathway reconstruction problem is a special case 
 of the pathway alignment problem , where the pathway similarity is 
 defined by the sequence similarity of orthologous enzyme genes . in another example of pathway alignment , tohsato 
 et al . used the ec number ( enzyme commission 
 number ) similarity to find similar reaction steps in the well - characterized 
 metabolic network . pinter et al . followed 
 tohsato s definition of ec number similarity , and developed 
 methods to detect conserved metabolic pathways among different organisms 
 and divergent pathways within an organism . followed pinter s definition of aligning 
 metabolic pathways and provided a faster algorithm . in yet another 
 example of pathway alignment , tohsato and nishimura used the similarity of substructure changes to detect similar 
 sequences of metabolites along known metabolic pathways . ay et al . developed a method that combined ec number similarity 
 and metabolite similarity , as well as the metabolic network topology 
 similarity to conduct the pathway alignment . . the assignment of orthologous enzyme genes 
 can only deal with the pathways that consist of the same reactions 
 catalyzed by the same enzymes . the use of ec number similarity allows 
 not only the same reactions but also somewhat different reactions 
 to be considered because of the ec number hierarchy . however , since 
 the ec numbers are manually given to experimentally characterized 
 enzymes with varying standards , the ec number similarity is not a 
 reliable measure for systematic analysis , for example , comparison 
 of genomic diversity of enzyme genes and chemical diversity of enzyme - catalyzed 
 reactions . furthermore , since the ec numbers are annotated to genes 
 in a genome according to sequence similarity , their use is not much 
 different from ortholog - based approaches in many types of analyses . here it is based on the similarity of chemical structure transformation 
 patterns along the metabolic pathways . this is a purely chemical similarity 
 measure without incorporating any protein sequence information or 
 the ec number information , enabling the analysis of reactions with 
 no ec numbers assigned or even with no enzymes identified . the new 
 measure applies to localized structural changes extracted from compound 
 pairs ( substrate  product pairs ) accommodating global structure 
 differences of individual compounds . our data set is derived from 
 the kegg database , more specifically 
 the kegg rpair ( reactant pair ) database and the kegg rclass ( reaction class ) database . kegg rpair contains 
 chemical structure transformation patterns in all known enzyme - catalyzed 
 reactions , and kegg rclass consists of reaction class ( rc ) entries 
 defined by the identity of chemical transformation patterns in the 
  main  reactant pairs that generally correspond to the 
 main substrate and product pairs shown on the kegg metabolic pathway 
 maps . the reaction modules , which are conserved sequences of similar 
 reactions , are systematically searched in the kegg metabolic pathways 
 using the similarity scoring scheme between reaction class entries . extracted reaction modules are then compared with the pathway modules 
 in the kegg module database , which are defined as sets of enzyme orthologs 
 represented by the kegg orthology ( ko ) entries . the present 
 analysis is 
 based on the kegg database ( http://www.kegg.jp/ ) release 
 62.0 + ( may 24 , 2012 ) . we used the metabolic pathways stored in the 
 metabolism section of the kegg pathway database , a collection of manually 
 drawn pathway maps representing knowledge on the molecular interaction 
 and reaction networks summarized from literature . generally , kegg 
 pathway maps are not organism specific and contain integrated information 
 from different organisms . the kegg  reference  pathway 
 maps are drawn in a generic form in terms of orthologs , so that they 
 can be expanded to organism - specific pathways by combining with the 
 gene information in individual genomes . a typical kegg metabolic pathway 
 map depicts how small molecules ( drawn as circles ) are converted by 
 reactions catalyzed by enzymes ( drawn as rectangles ) . the dual aspect 
 of metabolism is annotated in kegg by linking each rectangle in the 
 kegg reference metabolic pathway map to both the enzyme ortholog entry 
 ( identified by k number ) in the kegg orthology ( ko ) database and the 
 reaction entry ( identified by r number ) in the kegg reaction database . the kegg pathway maps in an xml format ( kgml files ) contain information 
 about the relationship of neighboring rectangles , which has been utilized 
 to extract consecutive reaction steps as sequences of r numbers . the kegg reaction database contains 
 all known enzymatic reactions taken from the enzyme nomenclature and also from the metabolic pathway section 
 of the kegg pathway database . the kegg release that we used contains 
 8990 reactions including 4321 enzyme nomenclature reactions . among 
 them , 6238 reactions including 2595 enzyme nomenclature reactions 
 appear on the kegg metabolic pathways . product pairs by considering 
 the flow of atoms ( other than hydrogen atoms ) in enzymatic reactions 
 as well as the six ec number classes . each reactant pair is associated with the chemical 
 transformation pattern in the rdm notation consisting of the kegg 
 atom type changes at the reaction center ( r ) , the difference substructure 
 ( d ) , and the matching substructure ( m ) atoms ( see the supporting information for more details ) . the 
 rdm notation for the pair of reactants a and b is as follows : for 
 example , a typical acyltransferase reaction 
 on primary amine is described as the kegg atom type generally 
 consists 
 of three characters , such as n1a for primary amine nitrogen and c5a 
 for ketone carbon . the first ( upper case letter ) indicates the atomic 
 species , the second ( numeral ) represents the predefined class of atomic 
 bonding for each atomic species , and the third ( lower case letter ) 
 represents the predefined class of topological information , e.g. , 
 the number of substituted groups . the total of 68 atom types have 
 been defined to distinguish important functional groups in biological 
 small molecules . in the above notation , * corresponds to a hydrogen 
 atom ( not defined in the kegg atom types ) for substitution reaction . 
 note that * sometimes means that there is no atom in the d - substructure . note also that the rdm notation generally represents a single chemical 
 bond that changes during a reaction ; in the case where a reaction 
 generates or degrades more than one chemical bond , then more than 
 one rdm notation is required . the kegg rclass database has been developed 
 to classify chemical structure transformation patterns associated 
 with all the reactions that appear in the kegg metabolic pathway maps . the database is a collection of reaction class entries ( identified 
 by rc numbers ) , each representing a unique rdm chemical structure 
 transformation pattern for a group of  main  reactant 
 pairs in the kegg rpair database . in other words , product pairs that appear 
 on the kegg metabolic pathway maps and whose chemical transformation 
 patterns are identical . the rclass entry is computationally generated 
 from the kegg rpair database and manually annotated with a diagram 
 of chemical transformation pattern and other information . because the rdm 
 chemical transformation patterns and the resulting rclass entries 
 are too finely classified , we first introduced a similarity scoring 
 scheme for rclass entries in order to detect similar ( in addition 
 to identical ) chemical transformation patterns . this is based on the 
 fingerprint representation of kegg atom types using twelve keys . the 
 keys indicate the presence or absence of a carbon atom , a carbon atom 
 having a  bond , a carbon atom in a carbonyl group , an oxygen 
 atom , an oxygen atom with unpaired electron , a nitrogen atom , a phosphorus 
 atom , a sulfur atom , a halogen atom , other atoms , an atom in aromatic 
 ring , and an atom in any ring ( see the supporting 
 information for more details ) . figure 1 illustrates how the rdm notation is converted into the 72-bit fingerprint 
 notation . for example , methyl ( c1a ) , methylene ( c1b ) , and other sp3 
 carbon atoms ( c1c and c1d ) are given different kegg atom types , but 
 they are the same in the fingerprint representation . fingerprint representation 
 of the rdm pattern . two reaction class 
 entries rc00106 and rc01192 are shown for the reactant pairs of pyruvate 
 and acetolactate ( upper ) and oxobutanoate and 2-aceto-2-hydroxybutanoate 
 ( lower ) . the rdm notation for these reaction class entries is converted 
 to the fingerprint representation , which reveals that they are the 
 same in the fingerprint representation despite the difference in the 
 m atom ( circled ) in the rdm notation . the similarity score s between two rclass 
 entries , 
 each consisting of a single rdm pattern , is defined aswhere the fingerprint v is 
 compared separately for the r , d , and m atoms , and the average jaccard s 
 coefficient ja is weighted depending on , for example , 
 whether the d atom is missing ( see the supporting 
 information for more details ) . in the present analysis , we 
 use the similarity threshold score of 1.0 ; namely , we simply use the 
 criterion of the same fingerprint to group rclass entries into a similarity 
 group . as a result , 2481 rclass entries were grouped into 376 similarity 
 groups with more than one member and the remaining 1190 singletons . on 
 the basis of the similarity measure among rclass entries as defined 
 above , we extracted  reaction modules  , which in our 
 definition are consecutive reaction steps ( reaction sequences ) with 
 conserved rclass sequence patterns that are observed in different 
 metabolic pathways . we used the following procedure to extract such 
 conserved patterns ( see the supporting information for more details ) . known metabolic pathways in the kegg pathway 
 database are split into all possible subsequences of 28 consecutive 
 reactions . the direction of the reaction pathway 
 is taken into consideration when generating consecutive reaction sequences 
 that contain irreversible reactions . when the pathway forms a cycle , 
 all possible reaction sequences that do not include the same metabolite 
 more than once are generated . for a given length between 2 and 
 8 , the reaction ( r number ) sequences thus generated were first converted 
 to the rclass ( rc number ) sequences . two rclass sequences are considered 
 to be identical when the corresponding rc numbers are the same , and 
 to be similar when they belong to the same similarity group in the 
 fingerprint representation . for each given length , conserved rclass 
 sequence patterns consisting of such similarity groups were extracted 
 from the entire collection of kegg metabolic pathways . the result 
 is shown in table 1 indicating roughly one - half 
 of the pathways correspond to conserved reaction sequence patterns . after computationally removing shorter patterns embedded in longer 
 patterns , we manually examined the results to identify reaction modules . the ratio to 5805 reactions , the 
 total number of reactions with rc assignment in the kegg pathways . the list 
 of manually refined reaction modules is partially shown in table 2 and fully shown at http://www.kegg.jp/kegg/reaction/rmodule.html . first , 
 reaction modules are repeatedly used in different pathways to generate 
 different chemical substances . second , reaction modules are used in 
 combination as if they are building blocks of the metabolic network . third , and most importantly , reaction modules ( also called rc modules ) 
 derived from chemical properties of substrate  product structure 
 transformation patterns tend to correspond to kegg pathway modules 
 ( also called ko modules ) defined as sets of enzyme orthologs in the 
 genome , especially gene clusters in operon - like structures coding 
 for the enzymes . the total of 26 corresponding ko modules were found 
 for 16 out 21 rc modules shown in table 2 , 
 and all the ko modules except one contained operon - like gene clusters 
 in some genomes ( for an updated list , see http://www.kegg.jp/brite/ko00003 ) . thus , we confirmed our working hypothesis mentioned in the introduction ; the functional units revealed by enzyme 
 clusters reflect chemical units of organic reactions . here we report 
 detailed analysis of the reaction modules for 2-oxocarboxylic acid 
 chain extension and modification , fatty acid synthesis and beta - oxidation , 
 and aromatic ring cleavage . one of the most 
 characteristic reaction modules was rm001 for the chain extension 
 of 2-oxocarboxylic acids , an important class of precursor metabolites . this module corresponds to the well - known sequence of reactions involving 
 citrate and other tricarboxylic acids in the tca cycle ( map00020 in 
 kegg ) , where an acetyl - coa derived carbon is used to extend the 2-oxocarboxylic 
 acid chain from oxaloacetate ( 2-oxobutanedioate ) to 2-oxoglutarate , 
 namely , from a four - carbon ( c4 ) compound to a five - carbon ( c5 ) compound . this is in fact the only part in the tca cycle that involves tricarboxylic 
 acids . one is a further extension from 2-oxoglutarate 
 ( c5 ) to 2-oxoadipate ( c6 ) in lysine biosynthesis pathway ( map00300 ) . another is found in valine , leucine , and isoleucine biosynthesis pathway 
 ( map00290 ) where pyruvate ( 2-oxopropanoate ) is extended to 2-oxobutanoate , 
 and 2-oxoisovalerate is extended to 2-oxoisocaproate . furthermore , in the biosynthesis pathway of glucosinolates 
 ( map00966 ) , which are plant secondary metabolites , a six tandem repeat 
 of rm001 is found from 2-oxo-4-methylthiobutanoate to 2-oxo-10-methylthiodecanoate 
 ( see supporting information figure s1 ) . these additional examples were found by considering not only the 
 similarity grouping of reaction class entries , but also the matching 
 of multistep reactions to an overall reaction . in the kegg pathway 
 map for the citrate cycle ( map00020 ) , the conversion from oxaloacetate 
 to 2-oxoglutarate ( rm001 ) is shown as follows : oxaloacetate and acetyl - coa 
 generating citrate ( rc00067 ) , converting to cis - aconitate ( rc00498 ) , 
 converting to isocitrate ( rc00618 ) , and converting to 2-oxoglutarate 
 in two reaction steps ( rc00084+rc00626 ) or in one step ( rc00114 ) . the variation of the last conversion originates from the definition 
 of ec numbers : ec 1.1.1.42 defined as two step reactions and ec 1.1.1.41 
 defined as one overall reaction ( rc00114 ) . furthermore , the second 
 and third reactions ( rc00498+rc00618 ) are catalyzed by the same enzyme 
 ec 4.2.1.3 , although the overall one - step reaction from citrate to 
 isocitrate ( rc00497 ) is not included in the kegg map . as shown in 
 table 3 , the reaction module rm001 apparently 
 consists of different rclass sequences , but they are actually the 
 same with these considerations . the reaction 
 module rm001 for 2-oxocarboxylic acid chain extension by tricarboxylic 
 acid pathway was found to be used in combination with three modification 
 modules , rm002 ( including rm032 ) , rm033 , and rm030 , together with 
 a reductive amination step ( rc00006 or rc00036 ) . in figure 2 , rm002 is for conversion of carboxyl group to amino 
 group in the biosynthesis of basic amino acids ( ornithine and lysine ) , 
 and rm033 is for addition of branched chains in the biosynthesis of 
 branched - chain amino acids ( valine , leucine , and isoleucine ) . rm030 
 in glucosinolate biosynthesis pathway is for conversion to oxime followed 
 by addition of thio - glucose moiety ( see supporting 
 information figure s2 ) . architecture of reaction modules consisting 
 of 2-oxocarboxylic 
 acid chain extension and modification , generating ( a ) basic amino 
 acids and ( b ) branched - chain amino acids . horizontal arrows indicate the modification 
 modules rm002 , rm032 , and rm033 together with the reductive amination 
 step ( rc00006 and rc00036 ) . for the chemical modification module rm002 in table 3 and figure 2 , the reaction 
 sequence 
 contains addition and removal of n - acetyl group as 
 a protective group in the first and last steps ( rc00064 ) . we found 
 the same overall reaction sequence without the protective group ( rm032 ) 
 in the conversion from aspartate to 4-diaminobutanoate in ectoine 
 biosynthesis pathway ( map00260 ) ( see figure 2 and table 3 ) . this seems to suggest an interesting 
 variation , possibly an evolution , of reaction modules . while rm032 
 ( rc00043 rc00684 rc00062 ) is used for shorter carboxylic acid chains , 
 rm002 ( rc00064 rc00043 rc00684 rc00062 rc00064 ) , containing n - acetylation and n - deacetylation steps 
 surrounding the core sequence of rm032 , is used for longer chains . furthermore , in the lysine biosynthesis pathway from 2-aminoadipate 
 to lysine , the surrounding steps are proteinaceous n - terminal modifications . thus , basically 
 the same overall reaction is achieved with varying degrees of complexity , 
 namely the involvement of a small modified group and a modified group 
 attached to a carrier protein , which may indicate a chemical evolution 
 of the metabolic network to cope with longer chains ( see supporting information figure s3 ) . the 
 kegg pathway modules ( ko modules ) in the kegg module database are 
 represented by manually defined sets of enzyme orthologs , which often 
 correspond to operon - like gene clusters in prokaryotic genomes . we 
 examined relationships between the reaction modules ( rc modules ) extracted 
 in the present analysis and the previously defined ko modules , especially 
 the gene clusters that constitute the ko modules , to exclude the ambiguity 
 of manual definition . we found , for example , that the rc module rm001 
 coincided well with the ko modules m00010 , m00432 , and m00535 . as 
 shown in table 4 , in the genome of pyrococcus furiosus , two gene clusters correspond to the reaction module rm001 : the gene 
 cluster ( pf0203 pf0201 pf0202 ) for the rclass sequence ( rc00067 rc00498+rc00618 
 rc00084+rc00626 ) in citrate cycle and the gene cluster ( pf0937 pf0938+pf0939 
 pf0940 ) for the rclass sequence ( rc00470 rc01041+rc01046 rc00084+rc00577 ) 
 in leucine biosynthesis . it is interesting to note that although the 
 first enzymes ( citrate synthase pf0203 and 2-isopropylmalate synthase 
 pf0937 ) do not share any sequence similarity , the second hydratases 
 ( pf0201 and pf0938+pf0939 ) and the third dehydrogenases ( pf0202 and 
 pf0940 ) form paralogous gene groups with sequence identity of around 
 35% , suggesting a link between genomic diversity and chemical diversity . 
 table 4 shows only a few examples of enzyme 
 gene clusters for rm001 and rm002 . many more examples can be found 
 in the kegg database from the ortholog table view of the kegg module 
 entries ( each entry is accessible at http://www.kegg.jp/module/m00010 , etc . ) . kegg organism codes are shown in 
 parentheses : pfu ( t00075 ) , pyrococcus furiosus dsm 3638 ; bth ( t00122 ) , bacteroides thetaiotaomicrometer vpi-5482 ; bsu ( t00010 ) , bacillus subtilis 168 ; ttr ( t01134 ) , thermobaculum terrenum atcc baa-798 . it is well - known that fatty acid 
 synthesis is a repetition of the four - step reaction sequence consisting 
 of ketoacyl synthase ( ks ) , ketoreductase ( kr ) , dehydratase ( dh ) , and 
 enoylreductase ( er ) reactions and each sequence increasing the acyl 
 chain length by two . the four enzymes may come from four separate 
 genes , two genes containing ks + kr and dh + er domains or a single 
 gene containing all domains . thus , there seems to be an evolution 
 of the genetic aspect of fatty acid synthesis . it is less known that 
 there is a minor pathway for fatty acid biosynthesis . in contrast 
 to the major pathway ( map00061 ) that involves acyl carrier protein 
 and uses malonyl - coa as a carbon source , the minor pathway ( map00062 ) 
 in mitochondria does not involve acyl carrier protein and uses acetyl - coa 
 as a carbon source . the minor pathway is essentially the reversal 
 of beta - oxidation ( rm018 ) in fatty acid degradation ( see below ) . the 
 reaction modules rm021 and rm020 , for the major and minor pathways 
 respectively , consist of the following rclass sequences ( see also supporting information figure s4).except for the first ks reaction 
 step distinguishing 
 malonyl-[acp ] and acetyl - coa , the two modules rm021 and rm020 are 
 essentially the same . we consider that the involvement of the acyl 
 carrier protein is an evolution of the chemical aspect of fatty acid 
 synthesis , possibly increasing the specificity and efficiency of reactions . the beta oxidation module rm018 ( the reversal of rm020 ) consists 
 of the following rclass sequences : in addition 
 to the fatty acid degradation 
 pathway ( map00071 ) , rm018 is found in caprolactum degradation ( map00930 ) 
 from adipyl - coa to succinyl - coa and isoleucine degradation ( map00280 ) 
 from 2-methylbutanoyl - coa to propanoyol - coa ( see supporting information figure s5 ) . a variation of rm018 , with 
 a somewhat different cleavage reaction , was found in the anaerobic 
 benzoate degradation pathway ( map00362 ) from pimeloyl - coa to glutaryl - coa 
 and in primary bile acid synthesis ( map00120 ) leading to chenodeoxycholoyl - coa 
 and choloyl - coa . more interestingly a distantly related module , 
 rm016 ( rc02034 rc00154 
 rc01429 ) , is found in the anaerobic benzoate degradation pathway ( map00362 ) 
 and the limonene and pinene degradation pathway ( map00903 ) . rm016 
 is for the aromatic ring cleavage ( hydrolysis ) rather than the acyl 
 chain cleavage ( thiolysis ) , but the strategy to add oxygen preceding 
 the cleavage reaction is similar . the rc similarity score was 0.8 
 for rc02034 and rc01095 ( or rc00831 ) and 0.7 for rc00154 and rc00029 
 ( or rc00117 ) . furthermore , the genes for rc00154 in the anaerobic 
 benzoate degradation pathway and for rc00029 in the fatty acid biosynthesis 
 pathway share sequence similarity . microorganisms are known to be capable of degrading diverse chemical 
 substances including nonbiological chemicals in the environment that 
 are mostly aromatic compounds . figure 3 illustrates 
 a representative set of reaction modules for biodegradation of aromatic 
 compounds consisting of ring dihydroxylation modules ( rm004rm006 ) , 
 cleavage modules ( rm008 and rm009 ) , and a preprocessing module ( rm003 ) 
 for oxyfunctionalization , i.e. , converting methyl group to carboxyl 
 group on the aromatic ring . rm003 consists of a monooxygenase reaction 
 ( ec 1.14.13 ) and two steps of dehydrogenase reactions ( ec 1.1.1 and 
 1.2.1 ) and is followed by a dihydroxylation module , as shown in figure 3 for toluene to benzoate and p - cymene 
 to p - cumate conversions . the first 
 step is an occasional preprocessing step ( rm003 ) converting a methyl 
 group into a carboxylic group on the aromatic ring . the second step 
 is the main step of dihydroxylation , which is classified into three 
 types ( rm006 , rm004 , and rm005 ) depending on how two hydroxyl groups 
 are added on the aromatic ring . the third step is either ortho - cleavage 
 ( rm008 ) or meta - cleavage ( rm009 ) followed by characteristic reaction 
 patterns leading to tca cycle intermediates . on the basis of the similarity grouping of rclass entries , 
 we categorized 
 dihydroxylation reaction steps into three main modules ( rm004 , rm005 , 
 and rm006 in figure 3 ) and several minor variant 
 modules ( not shown ) . the three main modules are most abundant and 
 are different in the steps for generating two hydroxyl groups . rm004 
 ( type 1 ) and rm005 ( type 1a ) use a dioxygenase reaction ( ec 1.14.12 ) 
 followed by a dehydrogenase reaction ( ec 1.3.1 ) , while rm006 ( type 
 2 ) uses two steps of monooxygenase reactions ( ec 1.14.13 ) . in rm005 , 
 which often results from the preprocessing module rm003 , one of the 
 hydroxyl groups is attached together with the carboxyl group ; thus , 
 the dehydrogenase reaction is decarboxylating . each dihydroxylation 
 module is followed by a ring - cleavage dioxygenase reaction ( ec 1.13.11 ) 
 either at the meta- or ortho - position of the two hydroxyl groups . rm008 and rm009 are the ortho- and meta - cleavage modules , respectively , 
 for catechol and related compounds , containing the cleavage reaction 
 and the subsequent reactions that generate tca cycle intermediates . 
 in the ortho - cleavage pathway , also known as beta - ketoadipate pathway , catechol is converted to succinyl - coa and acetyl - coa , 
 while catechol is converted to pyruvate and acetyl - coa in the meta - cleavage 
 pathway . it appears that the meta - cleavage is a more general processing 
 strategy because it is a partial processing applicable to larger molecules . we defined the reaction module rm010 ( figure 3 ) consisting of the dihydroxylation module rm004 and a portion of 
 the catechol meta - cleavage module rm009 . a variety of chemicals including trans - cinnamate , p - cumate , ethylbenzene , 
 styrene , and dioxin are degraded by this module resulting in 2-oxopent-4-enoate , 
 which is further processed by rm009 , and the remaining part , which 
 may be processed differently . for example , two - ring containing biphenyl 
 is partially processed to generate benzoate , which may further be 
 degraded by other degradation modules . the beta oxidation - like 
 module rm016 mentioned above is an anaerobic 
 version of the aromatic ring cleavage module . we have also identified 
 an anaerobic version of the preprocessing 
 methyl oxidation module rm015 involving coa ( see supporting information figure s6 for a comparison of the aerobic 
 module rm003 and the anaerobic module rm015 for toluene degradation ) . the biodegradation capacity of xenobiotic 
 compounds , such as benzene , 
 toluene , ethylbenzene , and xylene ( btex compounds ) , is limited to 
 specific organisms with appropriate sets of genes that are often carried 
 by plasmids . it is therefore expected that the reaction modules identified 
 here correspond to operon - like gene clusters in the genome . table 5 shows the correspondence 
 of the reaction modules ( rc modules ) and the kegg modules ( ko modules ) 
 for microbial biodegradation pathways , where the majority of ko modules 
 are encoded in operon - like gene clusters ( examine the ortholog table 
 link from each kegg module entry , such as http://www.kegg.jp/module/m00548 ) . for example , pseudoxanthomonas spadix bd - a59 ( kegg organism code : psd , t01643 ) 
 has preprocessing modules m00538 and m00537 for toluene and xylene , 
 respectively , both dioxygenase and monooxygenase - catalyzed dihydroxylation 
 modules m00551 and m00548 , meta - cleave module m00569 , and dioxin degradation 
 modules m00543 and m00544 , confirming its btex degradation potentials . our analysis has shown that the metabolic network 
 contains chemical 
 modules of conserved reaction patterns and that these chemical reaction 
 modules ( rc modules ) tend to correspond to traditional pathway modules 
 ( ko modules ) and gene clusters in prokaryotic genomes . the modularity 
 of the metabolic network has been mentioned in previous works , but we believe that this is the first report on the modularity of 
 the dual aspect of the metabolic network suggesting a coevolution 
 of the chemical unit and the genetic unit . in contrast to the previous 
 models of metabolic pathway evolution , such as the retrograde model , the patchwork model , and pathway duplication , the chemical 
 and genetic units are clearly defined in our approach allowing more 
 detailed analysis . for example , as mentioned for the ko modules of 
 m00010 and m00432 that correspond to the rc module of rm001 ( table 4 ) , only the second and the third enzymes in p. furiosus are paralogs , while the reactions are 
 similar in all the three steps . the collection 
 of ko modules and rc modules will continue to be updated in the kegg 
 database . here some other reaction modules that we did not include 
 in the results section are briefly discussed . we identified the reaction module rm025 for generating biogenic 
 amines and other important metabolites from amino acids ( see supporting information figure s7 ) . we already 
 mentioned the presence and absence of a protective group in the reaction 
 modules rm002 and rm032 , respectively , where the key reaction sequence 
 ( rc00684 rc00062 ) is for converting a carboxyl group to an amino group 
 following a phosphorylation step ( rc00043 ) . in contrast , rm025 contains 
 the reverse reaction sequence ( rc00062 rc00080 ) , in which rc00080 
 is identical to rc00684 in the fingerprint representation , for converting 
 an amino group to a carboxyl group following a decarboxylation step 
 ( rc00299 ) . the overall reaction of rm025 effectively removes the main 
 chain part of an amino acid leaving only the side chain part with 
 a newly introduced carboxylic group . from these examples , it appears 
 that the reaction modules contain design principles of a series of 
 organic reactions including , for example , how to introduce a protective 
 group , how to achieve an activated transition state , and how to increase 
 specificity for macromolecules . the rclass entries that contain 
 the largest numbers of reactant 
 pairs were related to phosphorylation and glycosylation . although 
 our approach focusing on localized structure patterns was successful 
 to characterize possible evolution of chemical reactions with varying 
 structural complexity , it may be necessary to consider overall structural 
 classes , in addition to localized reaction classes , to better characterize 
 reaction modules containing phosphorylation or glycosylation . there 
 are cases , however , in which a special class of overall structures 
 can be effectively extracted from the pattern of phosphorylation sequences . nucleotide sugars are activated forms of monosaccharides used for 
 biosynthesis of glycans and glycosylated substances . ( rc00017 rc00408 rc00002 ) 
 and rm023 ( rc00078 rc00002 ) , where the first module includes an isomerization 
 step , and the phosphate group on carbon 6 is linked to a nucleotide 
 ( see supporting information figure s8 ) . the metabolic network may be viewed as consisting of the conserved 
 core ( primary metabolism ) for maintaining life and the variable surface 
 ( secondary metabolism ) for interaction with the environment . microbial 
 biodegradation modules ( rm003 to rm016 ) represent convergent pathways 
 of secondary metabolism , feeding xenobiotic compounds with varying 
 structures to a limited number of compounds in primary metabolism . in contrast , biosynthetic pathways of secondary metabolites , especially 
 in plants , are divergent pathways for generating a large number of 
 structures from a limited number of compounds . we analyzed such plant 
 biosynthetic pathways but could not identify modules as significant 
 as the microbial degradation modules that often correspond to gene 
 clusters in chromosomes or plasmids . more importantly , the strategy to generate divergent compounds appears 
 to be different and involves a combination of short characteristic 
 reaction steps . the reaction module rm027 ( table 2 ) , a hydroxylation and methylation motif , is a well - known 
 reaction sequence involving cytochrome p450 monooxygenase . the phenylpropanoid 
 biosynthesis pathway as represented in kegg ( map00940 ) is a mesh - like 
 architecture of reactions consisting of the repeat of rm027 in the 
 horizontal direction and the coa involved acid aldehyde  alcohol 
 conversion in the vertical direction ( see supporting 
 information figure s9 ) . the ec ( enzyme commission ) number 
 system is a classification of 
 enzymatic reactions , where the first three numbers in the four number 
 system classify reactions in a hierarchical manner , namely , into class , 
 subclass , and subsubclass . there were 4321 fully 
 assigned ec numbers in our study , compared to 8990 reactions in kegg . the coverage of the ec system is much more limited because the ec 
 numbers are given only to those reactions with published records of 
 biochemically verified enzymes . in contrast the kegg database contains 
 additional reactions that are supported by pathways of less characterized 
 enzymes , in many cases the presence of genes in the genomes . we compared 
 the ec subsubclass , which is the most detailed reaction classification 
 in the ec system , and kegg rclass ( rc ) that is a grouping of reactions 
 accommodating overall structural differences of substrates . there 
 are 249 ec subsubclasses and 2481 rc entries , and on average 13 rc 
 entries are found for those ec subsubclasses that appear on the kegg 
 pathways . obviously , the rc system presents a much finer classification 
 of reactions than the ec system . this is shown in the list of ec subsubclasses 
 that contain the largest numbers of rc entries ( table 6 ) , where the most notable example is monooxygenases . in the 
 ec system , monooxygenases ( 1.14 ) are further classified based on the 
 cofactors ( 1.14.13 , 1.14.14 , 1.14.15 , etc . ) , but the distinction is 
 not made for reaction mechanisms . for example , cyp monooxygenases 
 may further be classified into hydroxylases , epoxidases ( epoxygenases ) , 
 baeyer  villiger monooxygenases , and so on ( see supporting information figure s10 ) . it is interesting 
 to note that the full ec number 1.14.14.1 ( single reaction with the 
 same substrate specificity in the ec system ) corresponds to 75 rc 
 entries ( different reactions in the rc system ) . knowledge of genes and proteins can be used to make predictions about 
 chemical compounds and reactions and , conversely , knowledge of chemical 
 compounds and reactions can be used to make predictions about genes 
 and proteins . the present analysis has already resulted in the improvement 
 of the kegg pathway maps for chlorocyclohexane and chlorobenzene degradation 
 ( map00361 ) , benzoate degradation ( map00362 ) , toluene degradation ( map00623 ) , 
 and xylene degradation ( map00622 ) in terms of both identifying additional 
 reactions and improving genome annotations . in the kegg database , the repertoire of genes in all available complete genomes are categorized 
 by the kegg orthology ( ko ) system , an attempt to understand the genomic 
 space of life . here the rc system has been introduced to categorize 
 all known reactions , an attempt to understand the chemical space of 
 life and the surrounding environment . we are trying to establish empirical 
 relationships between the ko system and the rc system , especially 
 in terms of the modular structures of the metabolic network represented 
 by the ko modules and the rc modules . the logic of chemical reactions 
 is so straightforward , compared to , for example , protein protein 
 interactions or protein  dna interactions , that these empirical 
 relationships can be safely extended to make predictions about metabolism 
 resulting either from new genes or from new reactions . this type of 
 predictive annotation is already implemented in the kegg database 
 toward better understanding of metabolic features encoded in the genome .
the 
 metabolic network is both a network of chemical reactions and 
 a network of enzymes that catalyze reactions . toward better understanding 
 of this duality in the evolution of the metabolic network 
 , we developed 
 a method to extract conserved sequences of reactions called reaction 
 modules from the analysis of chemical compound structure transformation 
 patterns in all known metabolic pathways stored in the kegg pathway 
 database . 
 the extracted reaction modules are repeatedly used as if 
 they are building blocks of the metabolic network and contain chemical 
 logic of organic reactions . 
 furthermore , the reaction modules often 
 correspond to traditional pathway modules defined as sets of enzymes 
 in the kegg module database and sometimes to operon - like gene clusters 
 in prokaryotic genomes . 
 we identified well - conserved , possibly ancient , 
 reaction modules involving 2-oxocarboxylic acids . 
 the chain extension 
 module that appears as the tricarboxylic acid ( tca ) reaction sequence 
 in the tca cycle is now shown to be used in other pathways together 
 with different types of modification modules . 
 we also identified reaction 
 modules and their connection patterns for aromatic ring cleavages 
 in microbial biodegradation pathways , which are most characteristic 
 in terms of both distinct reaction sequences and distinct gene clusters . 
 the modular architecture of biodegradation modules will have a potential 
 for predicting degradation pathways of xenobiotic compounds . 
 the collection 
 of these and many other reaction modules is made available as part 
 of the kegg database .