BACKGROUND
in the post-genomic era, one major goal of functional genomics has been to identify and analyze molecular interactions in a cellular context to better understand the mechanisms according to which biological molecules interact and function.
a protein-protein interaction  is a specific type of molecular interaction that plays the central role in relaying signals, in building molecular machines, in engaging in enzyme reactions and in decision-making vis-à-vis multiple biological processes.
advancements in ppi-detection technology have unquestionably led to the rapid accumulation of ppi data  <cit> .
to accurately conceptualize a ppi by determining its precise description is to immediately allow for the utilization of the various tools currently accessible in network science  <cit> .
a ppi network, for instance, has been found to have a scale-free structure; i.e., the link count  of a protein  follows a broad-tailed distribution that is approximated as a power-law,p~k-γ, where k is the link count and γ is the degree exponent  <cit> .
a network diameter, defined as the average minimal path between two nodes, is reportedly small  in a ppi network  <cit> .
the contribution made by research on network motifs, where a network motif is the specific topology of a combination of nodes that occurs repeatedly at different positions in that network, is evidenced in the results obtained from the initial search for cause of the topological properties.
as the first step, one of the properties of a ppi network, the scale-free feature, was thoroughly examined  <cit> .
at issue was whether the selection force is the cause of one of the scale-free network features: a random mutation does not harm a network, as a whole, but can cause it to collapse, but only with a deliberate attack on the hubs   <cit> .
it was, therefore, reasonably inferred and later clearly observed that hubs are more likely to evolve at a slower rate than non-hub nodes  <cit> .
however, different conclusions have been drawn regarding the mutation rate of a hub  <cit> .
in addition to this, recent research into gene regulatory networks in yeast has uncovered both a power-law distribution for the number of regulated genes per regulating protein  <cit>  and, at the same time, has yielded invaluable information concerning the presence of typical patterns of motifs.
feed forward motifs, single-input motifs and dense overlapping regulons  <cit>  reportedly occur in the gene regulatory network  of saccharomyces cerevisiae and escherichia coli with greater frequency than they would based on chance alone.
network motifs have also been analyzed in the ppi network of saccharomyces cerevisiae, and from this, it has been concluded that motif topology is correlated with the conservation of motif proteins; besides this, it has been inferred that motifs probably represent the evolutionary-conserved topological units of cellular networks  <cit> .
true that the representation of a gene regulatory network where the transcriptional regulator is considered the master and the regulated gene the slave  <cit>  is appropriate, but such a dichotomous  representation cannot be used for a ppi since proteins have multiple functions.
in this study, we labeled the protein nodes on the basis of their functional attributes of gene ontology   <cit> .
we then pursued any recurring patterns of the functional attributes of protein interactions.
with this new representation of a ppi network and by categorizing the repertoire of network motifs of the same topology into "motif modes," with each motif mode featuring a special topological combination of molecular functions, we have been able to move one step ahead of what was accomplished by barabási's group  <cit> .
this, in turn, led us to the finding that the evolutionary constraints on the motifs of the same topology are certainly not the same when considering their functional attributes; on the contrary, they vary a great deal.
RESULTS
motif topology
the ppi data for saccharomyces cerevisiae contain a total of  <dig>  physical interactions formed by  <dig>  proteins .
we analyzed the occurrence of eight types of three-node and four-node motifs, referred to hereafter as the "motif topology" .
the motif counts  of eight motif topologies varies, from  <dig>  thousand  to an overwhelming  <dig>  million  .
motif mode
since we focused on the recurring patterns of the functional attributes of protein interactions, we used the molecular function ontology.
on these grounds, we used the molecular function ontology  to annotate each node of a ppi network .
we developed a new algorithm  to categorize network motifs into "motif modes" on the basis of the topology of the go terms annotated for motif nodes .
here a "motif mode" is defined as a special combination of go terms in a motif.
in fact, a motif mode illustrates a grouping of network motifs that contain the same topological combination of functional attributes of proteins .
when we employed the go terms at depths five and six, we found a total of nearly  <dig>  and  <dig>  million motif modes, respectively .
in general, the higher motif count a particular motif topology has, the more motif modes there are in that motif topology .
however, #4– <dig> has the largest counts per motif .
noteworthy too is that the motif count for each motif mode can vary considerably among a million motif modes.
we calculated the distribution of the motif count for each motif mode based on the logarithmic binning.
when we employed the go terms at depths five and six, nearly 49% and 58% of the motif modes respectively occur less than  <dig> times in a ppi network .
it is particularly interesting that, for all motif modes, there is a power-law distribution of the motif counts, p~m-φ, where m is the motif count and φ is the degree exponent ~ <dig>   .
in fact, quite a few motif modes contain more than one hundred motif counts .
in that motif modes allow for an analysis that extends beyond motif topology, we were able to look at the properties of motifs of the same topology at a higher resolution than had ever been done before  <cit> .
annotation transfer within a protein interaction network
since we were interested in finding the evolutionary trend of the proteins contained in a motif mode, we built an orthology gene list among the genes of the six organisms .
when the orthology gene list was used to compute the evolutionary constraint of motifs of different motif topology and motif modes, it was assumed that orthologous proteins also interact with each other.
it has been shown that the reliability of the annotation of protein interactions from one organism to another depends on the level of sequence identity for the two pairs of interacting proteins  <cit> .
the joint e-value  smaller than <10- <dig> was used as the threshold to evaluate whether such a transfer of the annotation of interactions is reliable  <cit> .
in order to investigate the validity of the orthology gene list by which the interaction annotations were transferred between organisms, we conducted a sequence comparison between orthologs of yeast and five other species.
we found 61% of the orthologous protein pairs have an e-value lower than 10- <dig> .
about 40% of the annotation transfers are less reliable; just the same, we have to emphasize that the orthology approach still remains important in terms of decoding many important biological phenomena  <cit> .
different evolutionary constraints on the motifs of the same topology
to discover the evolutionary trend of the proteins contained in a motif mode, we computed the "conservation fraction" for each motif topology.
the "conservation fraction" is the counts of the evolutionary fully conserved motif divided by total motif counts.
motifs #3– <dig>  #4– <dig>  and #4– <dig> have higher conservation fractions  than do the others .
important to note, these values are very similar to those reported earlier   <cit> .
we also calculated the distribution of the conservation fractions of each motif mode using  <dig>  as the bin.
when we employed the go terms at depths five and six, the conservation fraction of nearly 93% and 94% of all motif modes respectively was less than  <dig>  .
this is due to the fact that the majority of motif counts occur for #4– <dig> and #4– <dig> , with the average conservation fraction of ~ <dig>  .
however, we also noted that the conservation fraction for  <dig> % and  <dig> % of motif modes, when we employed the go terms at depths five and six respectively, reaches  <dig> .
the general trend stated above still holds if the distribution is shown on the basis of each motif topology .
we defined the "conservation ratio", a degree of evolutionary constraint, as the value of the conservation fraction stated above divided by the same value but computed after the random assignment of the orthology data to the proteins .
it is apparent that the more connected to each other the motif nodes are, the higher is the conservation ratio  .
this observation has been previously reported  <cit> .
to determine if the conservation ratio is the same for motif modes of the same topology, we calculated the conservation ratio for one million motif modes.
we calculated the distribution of the conservation ratio for each motif mode based on the logarithmic binning.
what we found is that when we employed the go terms at depths five and six, the conservation ratio for more than 93% and 94% of the motif modes is respectively lower than  <dig>  surprisingly, we also noted that the conservation ratio for  <dig>   and  <dig>   motif modes exceeds  <dig>  which is approximately the magnitude of the highest ratio observed for motif #4– <dig> .
support for the notion that the evolutionary constraints on motifs of the same topology are not the same gains considerable ground, and this suggests the presence of differential evolutionary constraints upon motif modes of the same motif topology.
we can fit the distribution of the conservation ratio for all motif modes on a logarithmic scale by employing a quadratic function if the value of the first bin  is not taken into account .
the above observations still hold if the distribution is shown on the basis of each motif topology .
a motif mode by chance alone?
as a unique combination of molecular function descriptions of go, a motif mode could possibly be the result of a special classification that occurs by chance.
we randomized the go annotations  on the nodes and re-calculated three features of each motif mode: the motif counts, the conservation fraction and the conservation ratio.
we found a significant difference in the motif counts and the conservation ratio of the motif modes with and without the randomization of the go annotations .
therefore, the motif modes categorized by the current go annotations and the properties derived from the motif modes  do indeed bear a greater significance than would normally be expected by chance alone.
discussion
we used nearly  <dig> and  <dig> go molecular function descriptions at different depths to annotate nearly  <dig>  protein nodes in the saccharomyces cerevisiae ppi network.
we employed a motif mode to represent any probable combination of go annotations with a three-node and four-node topology.
to this effect, we collected all of the existing million motif modes and examined the level of evolutionary constraints on their motif constituents .
we found two interesting distributions of the properties of the motif modes.
the first is the distribution of motif counts a motif mode consists of, p~m-φ, where m is the motif count and φ is the degree exponent ~ <dig>  .
this observation may be related to a recent finding that, in a complex network, the large-scale topological organization  and the variable counts of the different motif topologies can define each other  <cit> .
whether there is a direct correlation between the large-scale topological organization and the motif mode-motif count dependence has yet to be determined.
the second is the distribution that characterizes the dependence of the number of motif modes on the conservation ratio of that motif mode .
reportedly, the more interconnected the nodes of a motif are with each other, the more conserved the protein constituents of the motif are  <cit> .
if a motif, rather than a single protein , represents evolutionary-conserved topological units in the tapestry of a ppi network  <cit> , our study further shows that motifs belonging to different motif modes of the same topology are not under the same level of evolutionary constraints.
fewer motif modes are under higher evolutionary constraints, and the level of differences spans the order of three.
differences between this and previous studies
the use of go annotations has provided us with increased insight into protein interactions through the coloring of protein nodes in the interaction map  <cit> .
in this study, we categorized motifs on the basis of the topological combinations of go terms , and this has resulted in our discovery of motif modes.
it should not be overlooked that motifs in biological networks have previously been analyzed  <cit> .
the alon group, for example, developed mfinder to calculate the motif counts in gene-regulatory networks  <cit> .
our algorithm is capable not only of conducting motif counts but also of managing the grouping of motif modes based on go terms; as mentioned earlier, this analysis, in fact, reaches a higher resolution than any other reported before.
we recorded the protein identities and go terms of each motif using our algorithm for the computation of the conservation ratio.
we recorded all motif instances  of the motif modes , and they can be used in future analyses though this requires large computer memory.
for this very reason, we focused on the motif modes of three nodes and four nodes in this study.
until now, the evolutionary constraints have only been reported on the level of motif topology, and this by computing the evolutionary constraints of all motifs of the same motif topology  <cit> .
in this study, for the first time, we have been able to distinguish the evolutionary constraints of different motifs of the same topology.
a motif topology contains many motif modes which are under different levels of evolutionary constraints.
in proposing that motif modes may represent the evolutionary-conserved topological units of a protein interaction network, we have clearly progressed one step farther beyond what has been accomplished before.
future direction
it is possible to re-examine the motifs and motif modes of ppis of model organisms without relying on the orthology information.
one can take several real ppi networks of different organisms and, for each network, look independently for the motif they contain and use the go annotations to define motif modes, then compare if the same motif modes are used in these different organisms.
apart from this, it would be most enlightening to investigate the temporal patterns of various motif modes when gene expression data are used.
this would be just like a ppi network visualized within the context of cell-cycles  <cit> , hubs categorized as "party hubs," or "date hubs,"  <cit>  and topological changes in transcription regulatory networks observed under environmental or physiological conditions  <cit> .
furthermore, it would be most worthwhile enhancing the precision of module-detection methods  <cit>  and developing specialized tools designed to search for motifs with similar functional annotations.
this would greatly assist biologists interested in mining protein interaction networks.
pathblast  <cit> , topnet  <cit> , mavisto  <cit> , and fanmod  <cit>  are examples of work in these areas.
CONCLUSIONS
we have reported on using the molecular function vocabulary of go to annotate a yeast protein interaction network.
the motif mode, i.e., the special topological combination of the molecular functions of interacting proteins, was extracted from the yeast protein interaction network and employed in the analysis of the protein interaction network at a higher resolution than ever before.
the distribution of the motif counts for all the motif modes follows a scale-free like fashion.
the differential evolutionary constraints on the million motif modes are an indication that motif modes may very well represent the evolutionary-conserved topological units of the protein interaction network.

 in the post-genomic era, one major goal of functional genomics has been to identify and analyze molecular interactions in a cellular context to better understand the mechanisms according to which biological molecules interact and function. a protein-protein interaction is a specific type of molecular interaction that plays the central role in relaying signals, in building molecular machines, in engaging in enzyme reactions and in decision-making vis-à-vis multiple biological processes. advancements in ppi-detection technology have unquestionably led to the rapid accumulation of ppi data. to accurately conceptualize a ppi by determining its precise description is to immediately allow for the utilization of the various tools currently accessible in network science. a ppi network, for instance, has been found to have a scale-free structure; i.e., the link count of a protein follows a broad-tailed distribution that is approximated as a power-law,p~k-γ, where k is the link count and γ is the degree exponent. a network diameter, defined as the average minimal path between two nodes, is reportedly small in a ppi network. the contribution made by research on network motifs, where a network motif is the specific topology of a combination of nodes that occurs repeatedly at different positions in that network, is evidenced in the results obtained from the initial search for cause of the topological properties. as the first step, one of the properties of a ppi network, the scale-free feature, was thoroughly examined. at issue was whether the selection force is the cause of one of the scale-free network features: a random mutation does not harm a network, as a whole, but can cause it to collapse, but only with a deliberate attack on the hubs. it was, therefore, reasonably inferred and later clearly observed that hubs are more likely to evolve at a slower rate than non-hub nodes. however, different conclusions have been drawn regarding the mutation rate of a hub. in addition to this, recent research into gene regulatory networks in yeast has uncovered both a power-law distribution for the number of regulated genes per regulating protein and, at the same time, has yielded invaluable information concerning the presence of typical patterns of motifs. feed forward motifs, single-input motifs and dense overlapping regulons reportedly occur in the gene regulatory network of saccharomyces cerevisiae and escherichia coli with greater frequency than they would based on chance alone. network motifs have also been analyzed in the ppi network of saccharomyces cerevisiae, and from this, it has been concluded that motif topology is correlated with the conservation of motif proteins; besides this, it has been inferred that motifs probably represent the evolutionary-conserved topological units of cellular networks. true that the representation of a gene regulatory network where the transcriptional regulator is considered the master and the regulated gene the slave is appropriate, but such a dichotomous representation cannot be used for a ppi since proteins have multiple functions. in this study, we labeled the protein nodes on the basis of their functional attributes of gene ontology. we then pursued any recurring patterns of the functional attributes of protein interactions. with this new representation of a ppi network and by categorizing the repertoire of network motifs of the same topology into "motif modes," with each motif mode featuring a special topological combination of molecular functions, we have been able to move one step ahead of what was accomplished by barabási's group. this, in turn, led us to the finding that the evolutionary constraints on the motifs of the same topology are certainly not the same when considering their functional attributes; on the contrary, they vary a great deal.  motif topology the ppi data for saccharomyces cerevisiae contain a total of physical interactions formed by proteins. we analyzed the occurrence of eight types of three-node and four-node motifs, referred to hereafter as the "motif topology". the motif counts of eight motif topologies varies, from thousand to an overwhelming million. motif mode since we focused on the recurring patterns of the functional attributes of protein interactions, we used the molecular function ontology. on these grounds, we used the molecular function ontology to annotate each node of a ppi network. we developed a new algorithm to categorize network motifs into "motif modes" on the basis of the topology of the go terms annotated for motif nodes. here a "motif mode" is defined as a special combination of go terms in a motif. in fact, a motif mode illustrates a grouping of network motifs that contain the same topological combination of functional attributes of proteins. when we employed the go terms at depths five and six, we found a total of nearly and million motif modes, respectively. in general, the higher motif count a particular motif topology has, the more motif modes there are in that motif topology. however, #4– has the largest counts per motif. noteworthy too is that the motif count for each motif mode can vary considerably among a million motif modes. we calculated the distribution of the motif count for each motif mode based on the logarithmic binning. when we employed the go terms at depths five and six, nearly 49% and 58% of the motif modes respectively occur less than times in a ppi network. it is particularly interesting that, for all motif modes, there is a power-law distribution of the motif counts, p~m-φ, where m is the motif count and φ is the degree exponent ~. in fact, quite a few motif modes contain more than one hundred motif counts. in that motif modes allow for an analysis that extends beyond motif topology, we were able to look at the properties of motifs of the same topology at a higher resolution than had ever been done before. annotation transfer within a protein interaction network since we were interested in finding the evolutionary trend of the proteins contained in a motif mode, we built an orthology gene list among the genes of the six organisms. when the orthology gene list was used to compute the evolutionary constraint of motifs of different motif topology and motif modes, it was assumed that orthologous proteins also interact with each other. it has been shown that the reliability of the annotation of protein interactions from one organism to another depends on the level of sequence identity for the two pairs of interacting proteins. the joint e-value smaller than <10- was used as the threshold to evaluate whether such a transfer of the annotation of interactions is reliable. in order to investigate the validity of the orthology gene list by which the interaction annotations were transferred between organisms, we conducted a sequence comparison between orthologs of yeast and five other species. we found 61% of the orthologous protein pairs have an e-value lower than 10-. about 40% of the annotation transfers are less reliable; just the same, we have to emphasize that the orthology approach still remains important in terms of decoding many important biological phenomena. different evolutionary constraints on the motifs of the same topology to discover the evolutionary trend of the proteins contained in a motif mode, we computed the "conservation fraction" for each motif topology. the "conservation fraction" is the counts of the evolutionary fully conserved motif divided by total motif counts. motifs #3– #4– and #4– have higher conservation fractions than do the others. important to note, these values are very similar to those reported earlier. we also calculated the distribution of the conservation fractions of each motif mode using as the bin. when we employed the go terms at depths five and six, the conservation fraction of nearly 93% and 94% of all motif modes respectively was less than. this is due to the fact that the majority of motif counts occur for #4– and #4–, with the average conservation fraction of ~. however, we also noted that the conservation fraction for % and % of motif modes, when we employed the go terms at depths five and six respectively, reaches. the general trend stated above still holds if the distribution is shown on the basis of each motif topology. we defined the "conservation ratio", a degree of evolutionary constraint, as the value of the conservation fraction stated above divided by the same value but computed after the random assignment of the orthology data to the proteins. it is apparent that the more connected to each other the motif nodes are, the higher is the conservation ratio. this observation has been previously reported. to determine if the conservation ratio is the same for motif modes of the same topology, we calculated the conservation ratio for one million motif modes. we calculated the distribution of the conservation ratio for each motif mode based on the logarithmic binning. what we found is that when we employed the go terms at depths five and six, the conservation ratio for more than 93% and 94% of the motif modes is respectively lower than surprisingly, we also noted that the conservation ratio for and motif modes exceeds which is approximately the magnitude of the highest ratio observed for motif #4–. support for the notion that the evolutionary constraints on motifs of the same topology are not the same gains considerable ground, and this suggests the presence of differential evolutionary constraints upon motif modes of the same motif topology. we can fit the distribution of the conservation ratio for all motif modes on a logarithmic scale by employing a quadratic function if the value of the first bin is not taken into account. the above observations still hold if the distribution is shown on the basis of each motif topology. a motif mode by chance alone? as a unique combination of molecular function descriptions of go, a motif mode could possibly be the result of a special classification that occurs by chance. we randomized the go annotations on the nodes and re-calculated three features of each motif mode: the motif counts, the conservation fraction and the conservation ratio. we found a significant difference in the motif counts and the conservation ratio of the motif modes with and without the randomization of the go annotations. therefore, the motif modes categorized by the current go annotations and the properties derived from the motif modes do indeed bear a greater significance than would normally be expected by chance alone. discussion we used nearly and go molecular function descriptions at different depths to annotate nearly protein nodes in the saccharomyces cerevisiae ppi network. we employed a motif mode to represent any probable combination of go annotations with a three-node and four-node topology. to this effect, we collected all of the existing million motif modes and examined the level of evolutionary constraints on their motif constituents. we found two interesting distributions of the properties of the motif modes. the first is the distribution of motif counts a motif mode consists of, p~m-φ, where m is the motif count and φ is the degree exponent ~. this observation may be related to a recent finding that, in a complex network, the large-scale topological organization and the variable counts of the different motif topologies can define each other. whether there is a direct correlation between the large-scale topological organization and the motif mode-motif count dependence has yet to be determined. the second is the distribution that characterizes the dependence of the number of motif modes on the conservation ratio of that motif mode. reportedly, the more interconnected the nodes of a motif are with each other, the more conserved the protein constituents of the motif are. if a motif, rather than a single protein, represents evolutionary-conserved topological units in the tapestry of a ppi network, our study further shows that motifs belonging to different motif modes of the same topology are not under the same level of evolutionary constraints. fewer motif modes are under higher evolutionary constraints, and the level of differences spans the order of three. differences between this and previous studies the use of go annotations has provided us with increased insight into protein interactions through the coloring of protein nodes in the interaction map. in this study, we categorized motifs on the basis of the topological combinations of go terms, and this has resulted in our discovery of motif modes. it should not be overlooked that motifs in biological networks have previously been analyzed. the alon group, for example, developed mfinder to calculate the motif counts in gene-regulatory networks. our algorithm is capable not only of conducting motif counts but also of managing the grouping of motif modes based on go terms; as mentioned earlier, this analysis, in fact, reaches a higher resolution than any other reported before. we recorded the protein identities and go terms of each motif using our algorithm for the computation of the conservation ratio. we recorded all motif instances of the motif modes, and they can be used in future analyses though this requires large computer memory. for this very reason, we focused on the motif modes of three nodes and four nodes in this study. until now, the evolutionary constraints have only been reported on the level of motif topology, and this by computing the evolutionary constraints of all motifs of the same motif topology. in this study, for the first time, we have been able to distinguish the evolutionary constraints of different motifs of the same topology. a motif topology contains many motif modes which are under different levels of evolutionary constraints. in proposing that motif modes may represent the evolutionary-conserved topological units of a protein interaction network, we have clearly progressed one step farther beyond what has been accomplished before. future direction it is possible to re-examine the motifs and motif modes of ppis of model organisms without relying on the orthology information. one can take several real ppi networks of different organisms and, for each network, look independently for the motif they contain and use the go annotations to define motif modes, then compare if the same motif modes are used in these different organisms. apart from this, it would be most enlightening to investigate the temporal patterns of various motif modes when gene expression data are used. this would be just like a ppi network visualized within the context of cell-cycles, hubs categorized as "party hubs," or "date hubs," and topological changes in transcription regulatory networks observed under environmental or physiological conditions. furthermore, it would be most worthwhile enhancing the precision of module-detection methods and developing specialized tools designed to search for motifs with similar functional annotations. this would greatly assist biologists interested in mining protein interaction networks. pathblast, topnet, mavisto, and fanmod are examples of work in these areas.  we have reported on using the molecular function vocabulary of go to annotate a yeast protein interaction network. the motif mode, i.e., the special topological combination of the molecular functions of interacting proteins, was extracted from the yeast protein interaction network and employed in the analysis of the protein interaction network at a higher resolution than ever before. the distribution of the motif counts for all the motif modes follows a scale-free like fashion. the differential evolutionary constraints on the million motif modes are an indication that motif modes may very well represent the evolutionary-conserved topological units of the protein interaction network. 
the importance of a network motif lies in its position in the hierarchy between the protein molecule and the module in a protein-protein interaction network. while they have focused on the analysis in the resolution of a motif topology, they have not been able to distinguish particular motifs of the same topology in a protein-protein interaction network. we postulate that motif modes may very well represent the evolutionary-conserved topological units of a protein interaction network. for the first time, the motifs of a protein interaction network have been investigated beyond the scope of motif topology. the motif modes determined in this study have not only enabled us to differentiate among different evolutionary constraints on motifs of the same topology but have also opened up new avenues through which protein interaction networks can be analyzed. to our surprise, the conservation ratio, i.e., the extent of the evolutionary constraints upon the motif modes of the same motif topology, varies significantly, clearly indicative of distinct differences in the evolutionary constraints upon motifs of the same motif topology. for various motif topologies, we have developed an algorithm, enabling us to unveil one million "motif modes", each of which features a unique topological combination of molecular functions. equally important, for all motif modes, we have found a power-law distribution of the motif counts on each motif mode. we have been able to assign the molecular function annotations of gene ontology to each protein in the protein-protein interactions of saccharomyces cerevisiae.
 the importance of a network motif lies in its position in the hierarchy between the protein molecule and the module in a protein-protein interaction network. until now, however, the methods available have greatly restricted the scope of research. while they have focused on the analysis in the resolution of a motif topology, they have not been able to distinguish particular motifs of the same topology in a protein-protein interaction network.  we have been able to assign the molecular function annotations of gene ontology to each protein in the protein-protein interactions of saccharomyces cerevisiae. for various motif topologies, we have developed an algorithm, enabling us to unveil one million "motif modes", each of which features a unique topological combination of molecular functions. to our surprise, the conservation ratio, i.e., the extent of the evolutionary constraints upon the motif modes of the same motif topology, varies significantly, clearly indicative of distinct differences in the evolutionary constraints upon motifs of the same motif topology. equally important, for all motif modes, we have found a power-law distribution of the motif counts on each motif mode. we postulate that motif modes may very well represent the evolutionary-conserved topological units of a protein interaction network.  for the first time, the motifs of a protein interaction network have been investigated beyond the scope of motif topology. the motif modes determined in this study have not only enabled us to differentiate among different evolutionary constraints on motifs of the same topology but have also opened up new avenues through which protein interaction networks can be analyzed. 